Calibration Report for the Imagers of the Descent Imager/Spectral Radiometer Instrument aboard the Huygens Probe of the Cassini Mission 1 Janurary 2006 L. R. Doose, B. Rizk, E. Karkoschka, and E. McFarlane Table of Contents 1.0 Introduction 1.1 Overview of Optical Systems 2.0 DISR Image Distortion and Geometry Calibrations 2.1 Introduction 2.2 Summary of Results 2.3 Distortion Calibration 2.4 Geometry Calibration 2.5. Error Analysis 2.6. Sample Mosaics 3.0. Deconvolution of DISR Images 3.1. Abstract 3.2.Introduction 3.3.Distortion 3.4.Smear due to Rotation of the Probe 4.0. Image Photometric Calibration 4.1. Relative Spectral Response 4.1.1. A Model for the relative spectral response of the imagers 4.1.1.1. Motivation for a Model 4.1.1.2. General Description of RSR data 4.1.1.3. Suspected Correlation: AR and RSR 4.1.1.4. Absolute Responsivity Measurements 4.1.1.5. Absolute Responsivity bins 4.1.1.6. Limitation of the AR-RSR Method 4.1.2. The Hump Ratio Model for determination of RSR 4.1.2.1. Development of the model at 239K 4.1.2.2. Development of the model at all Temperatures 4.1.2.3. Use of the model (or how to get the RSR for any pixel) 4.1.2.4. Sample Calculation 4.1.2.5. Location of Data and Supporting Programs 4.1.2.6. Model Performance 4.1.3. Conclusion 4.2. Image Absolute Responsivity Reductions 4.2.1. Method and Verification of Absolute Responsivity Reductions 4.2.2. Results 5.0. Flight and Ground Software Processing 5.1. Measurement scheduling 5.2. Bad Pixel Maps 5.3. Square-root processing 5.4. Flat-fielding 5.4.1. Flat Field Table 5.4.2. Flat Field Lookup Table 5.4.3. Flat Field Correction Operation 5.4.4. Method of Determining the Flat Field Table 5.4.5. Flat Field Performance at Other Temperatures 5.5. Compression 5.5.1. DCS automatic bad pixel replacement 5.6. Imaging system performance 5.6.1. Compression in the presence of increased dark current Contrast Temperature Version 3.30 RMS Version 3.40 RMS Change 5.7. Auto-exposure calculation 5.8. Ground software processing 5.9. Photometric Reduction Summary 6.0. Improved Processing of Compressed DISR Images 6.1. Abstract 6.2. The Discrete Cosine Transform 6.3. Estimation of the Threshold 6.4. Unbiased Estimation of Coefficients 6.5 Smoothing 16x16 Pixel Block Boundaries 6.6 Rounding 6.7 Bad Rows at Top/Bottom 6.8 Figures 6.8. Equations and the Fortran Code 6.8.2. Decrease of Small Amplitudes 6.8.3. Determination of Standard Smoothing Amplitude 6.8.4. Decrease of amplitudes in 32x32 pixel blocks 6.8.5. Interpolation between neighboring 32x32 pixel blocks 7.0. Test for Suitable Selection of Compression Ratios for DISR Imagers 7.1. Scientific Background 7.1.1. Introduction 7.2. Resolution 7.3. Noise 7.4. Evaluation 7.5. Variation of CR 7.6. Additional Considerations 7.7. The Test 8.0. Area Coverage and Image Statistics for a Simulated Descent Table of Figures Figure 1.1-1 Drawing of the front end of the optics of the imagers showing window, filter, lenses, etc Figure 1.1-2 Diagram of the fiber optic image conduits, which carry the image to the CCD Figure 1.1-3 The imager objective lenses are attached to an optical bench, which holds the fiber optic conduit Figure 2.2-1 Outline of DISR 2 Field of View Figure 2.2-2 Outline of DISR 3 Field of View Figure 2.3-1 DISR 2 MRI Target Grid (sharpened) Figure 2.3-2 Location of Observed Vertices for DISR 2 MRI Figure 2.3-3 Location of Desired Vertices for DISR 2 MRI Figure 2.3-4 DISR 2 SLI Target Grid (sharpened) Figure 2.3-5 Location of Observed Vertices for DISR 2 SLI Figure 2.3-6 Location of Desired Vertices for DISR#2 SLI Figure 2.3-7 DISR 2 HRI Target Grid (sharpened) Figure 2.3-8 Location of Observed Vertices for DISR 2 HRI Figure 2.3-9 Location of Desired Vertices for DISR 2 HRI Figure 2.3-10 DISR 3 MRI Target Grid (sharpened) Figure 2.3-11 Location of Observed Vertices for DISR 3 MRI Figure 2.3-12 Location of Desired Vertices for DISR 3 MRI Figure 2.3-13 DISR 3 SLI Target Grid (sharpened) Figure 2.3-14 Location of Observed Vertices for DISR 3 SLI Figure 2.3-15 Location of Desired Vertices for DISR 3 SLI Figure 2.3-16 DISR#3 HRI Target Grid (sharpened) Figure 2.3-17 Location of Observed Vertices for DISR 3 HRI Figure 2.3-18 Location of Desired Vertices for DISR 3 HRI Figure 2.4-1 DISR#2 MRI Geometry Calibration Bright Point Composite Image Figure 2.4-2 DISR 2 SLI Geometry Calibration Bright Point Composite Image Figure 2.4-3 DISR 2 HRI Geometry Calibration Bright Point Composite Image Figure 2.4-4 DISR 3 MRI Geometry Calibration Bright Point Composite Image Figure 2.4-5 DISR 3 SLI Geometry Calibration Bright Point Composite Image Figure 2.4-6 DISR 3 HRI Geometry Calibration Bright Point Composite Image Figure 2.6-1 Detail from LPL Rooftop Manual Rotating Test, 18 July 1998, SE corner of LPL Rooftop Figure 2.6-2 Detail from LPL Rooftop Manual Rotating Test, 18 July 1998, SE corner of LPL Rooftop Figure 2.6-3 LPL Rooftop Manual Rotating Test, 18 July 1998, SE corner of LPL Rooftop Figure 2.6-4 Mt. Bigelow Fire Observation Tower Test, 9 June 1999, Mt. Bigelow, Arizona Figure 2.6-5 Imaging Cool-Down Test, 18 September 1996, LPL Auditorium Figure 2.6-6 Imaging Cool-Down Test, 18 September 1996, LPL Auditorium Figure 3.0-1 Location of the Measured Quarter-Pixel PSFs Figure 3.0-2 Observed Point Spread Functions x 5 Figure 3.0-3 Smeared Point Spread Functions x 5 Figure 3.0-4 Fitted Point Spread Functions x 5 Figures 3.0-5 to 3.0-32 Fractional Enclosed Energy (%) by Pixels for each of the 28 PSFs locations for measured, smeared, standard synthetic, and alternative synthetic PSFs Figure 3.0-6 Figure 3.0-7 Figure 3.0-8 Figure 3.0-9 Figure 3.0-10 Figure 3.0-11 Figure 3.0-12 Figure 3.0-13 Figure 3.0-14 Figure 3.0-15 Figure 3.0-16 Figure 3.0-17 Figure 3.0-18 Figure 3.0-19 Figure 3.0-20 Figure 3.0-21 Figure 3.0-22 Figure 3.0-23 Figure 3.0-24 Figure 3.0-25 Figure 3.0-26 Figure 3.0-27 Figure 3.0-28 Figure 3.0-29 Figure 3.0-30 Figure 3.0-31 Figure 3.0-32 Figures 3.0-33 to 3.0-35 Fractional Enclosed Energy (%) by Pixels for the PSFs after deconvolution Figure 3.0-34 Figure 3.0-35 Figure 3.0-36 Location of Aperture Obstruction Figure 3.0-37 Synthetic PSFs for Basic Aberrations Figure 3.0-38 Synthetic PSFs for Each Camera Figure 3.0-39 Hypothetical PSFs for the MRI Figures 3.0-40 Figure 3.0-41 Figure 3.0-42 Figure 3.0-43 Figure 3.0-44 Figure 3.0-45 Figure 3.0-46 Figure 3.0-47 Figure 3.0-48 Figure 3.0-49 Figure 3.0-50 Figure 3.0-51 Figure 3.0-52 Figure 3.0-53 Figure 3.0-54 Figure 3.0-55 Images of the observed PSFs, the fitted PSFs, and their difference, from left to right in each case Figure 4.1.1.5-1 The HRI RSR at 820 nm vs. AR bin number Figure 4.1.1.5-2 Resultant Root Mean Square (RMS) difference values between the measured and model RSR values for each of the pixels in the HRI imager when using the AR-RSR model for computing RSR Figure 4.1.1.5-3 A probability plot for the HRI comparing the over all Root Mean Square (RMS) differences for the AR-RSR model versus a simple model using only the average within each bin Figure 4.1.2.1-1 The average within a bin normalized to the average of all the good pixels at 239K plotted versus wavelength for 171K, 185K, 201K and 225K. Figure 4.1.2.1-2 The average within a bin normalized to the average of all the good pixels at 239K plotted versus wavelength for 171K, 185K, 201K and 225K. Figure 4.1.2.2-1 Normalized average RSR versus Temperature for all 10 bins with polynomial fits. Figure 4.1.2.2-2 Normalized average RSR versus temperature for all bins with weighted fit. Figure 4.1.2.6-1 A probability plot of the RMS residuals for the HRI for every pixel at the 7 measured temperatures. Also included are the RMS residuals from the AR-RSR and Ave models for a temperature of 239K. Figure 4.1.2.6-2 A probability plot of the RMS for the MRI for every pixel at the 7 measured temperatures. Figure 4.1.2.6-3 A probability plot of the RMS for the SLI for every pixel at the 7 measured temperatures. Figure 4.2.1-1 Measured and model relative spectral responses for the HRI pixel. Figure 4.2.1-2 Measured and model relative spectral responses for the MRI pixel. Figure 4.2.1-3 Silicon monitor detector readings with the shutter closed during DISR image taking. Figure 4.2.2-1 Temperature model of the absolute responsivity for all good HRI pixels. Dots are the measurements, and the curve is a fourth-order polynomial fit. Figure 4.2.2-2 Temperature model of the absolute responsivity for all good MRI pixels. Dots are the measurements, and the curve is a fourth-order polynomial fit. Figure 4.2.2-3 Temperature model of the absolute responsivity for all good SLI pixels. Dots are the measurements, and the curve is a fourth-order polynomial fit. Figure 4.2.2-4 The distribution of absolute responsivity residuals expressed in percent as (measured - model) for the temperature dependence of the HRI. Figure 4.2.2-5 The distribution of absolute responsivity residuals expressed in percent as (measured - model) for the temperature dependence of the MRI. Figure 4.2.2-6 The distribution of absolute responsivity residuals expressed in percent as (measured - model) for the temperature dependence of the SLI. Figure 4.2.2-7 Spatial Distribution of Pixels that Fit the Temperature Model Poorly for the HRI Figure 4.2.2-8 Spatial Distribution of Pixels which Fit the Temperature Model Poorly for the MRI Figure 4.2.2-9 Spatial Distribution of Pixels which Fit the Temperature Model Poorly for the SLI Fig. 5.4-1 Images of the 20-inch integrating sphere wall taken with the DISR flight model imagers Figure 5.4.2-1 The relationship between correction factor and the flat field table entry for tabular values 1. Figure 5.4-1 Bad pixel replacement and flat-field processing for the High Resolution Imager Figure 5.4-2 Bad pixel replacement and flat-field processing for the Medium Resolution Imager Figure 5.4-3 Bad pixel replacement and flat-field processing for the Side- Looking Imager Figure 5.4.5-1 HRI original image, flat field processing, and ff+bpm at 176K Figure 5.4.5-2 Same as figure 5.4.5-1 except at 208K Figure 5.4.5-3 Same as figure 5.4.5-1 except at 223K Figure 5.4.5-4 Same as figure 5.4.5-1 except at 245K Figure 5.4.5-5 Same as figure 5.4.5-1 except at 260K Figure 5.4.5-6 Same as figure 5.4.5-1 except at 281K Figure 5.4.5-7 MRI original image, flat field processing, and ff+bpm at 176K Figure 5.4.5-8 Same as figure 5.4.5-7 except at 208K Figure 5.4.5-9 Same as figure 5.4.5-7 except at 223K Figure 5.4.5-10 Same as figure 5.4.5-7 except at 245K Figure 5.4.5-11 Same as figure 5.4.5-7 except at 260K Figure 5.4.5-12 Same as figure 5.4.5-7 except at 281K Figure 5.4.5-13 SLI original image, flat field processing, and ff+bpm at 176K Figure 5.4.5-14 Same as figure 5.4.5-13 except at 208K Figure 5.4.5-15 Same as figure 5.4.5-13 except at 223K Figure 5.4.5-16 Same as figure 5.4.5-13 except at 245K Figure 5.4.5-17 Same as figure 5.4.5-13 except at 260K Figure 5.4.5-18 Same as figure 5.4.5-13 except at 281K Figure 5.5.1-1 4 8x48 pixel sub-samples of an image before and after compression. The single bright pixel in the center causes the "checkerboard" pattern in its block Figure 5.6-1a The original scene on the CCD (left), the image produced by the flight and GSE software (center), and the image produced by the simulator (right) for the highest contrast scene and compression ratio 8 Figure 5.6-1b Same as figure 5.6-1a, except for a very low contrast scene Figure 5.6-2a Histograms of the high contrast image at various stages of processing. Figure 5.6-2b Histograms of the low contrast image at various stages of processing. Figure 5.6-3 The horizontal lines show the location of row 106 in the low contrast image. Figure 5.6-4a The data number in row 106 vs. column number in the HRI for four images (top to bottom): high contrast with 2X compression, high contrast with 8X compression, low contrast with 2X compression, and low contrast with 8X compression. Figure 5.6-4b Errors introduced by flight/GSE software for two scene contrasts and two compression ratios for HRI row 106. Figure 5.6.1-1 Cumulative histograms giving the probability than a pixel has dark current less than the abscissa value. The Descent curve is computed by extrapolating the best linear fit through the F3, F5, and F7 data downward at each abscissa value. Figure 5.6.1-2 Errors (RMS and maximum) in data number caused by compression for a low signal, low contrast scene for three different compression ratios and three different temperatures. Figure 5.6.1-3 Errors (RMS and maximum) in data number caused by compression for a low signal, high contrast scene for three different compression ratios and three different temperatures. Figure 5.6.1-4 Errors (RMS and maximum) in data number caused by compression for a high signal, low contrast scene for three different compression ratios and three different temperatures. Figure 1a Original Mt. Bigelow scene. Figure 1b Compression ratio of 4 with original decompression scheme. Figure 1c Compression ratio of 8 with original decompression scheme. Figure 1d Compression ratio of 8 with new decompression scheme and no smoothing. Figure 1e Compression ratio of 8 with new decompression scheme and smoothing factor of 0.5. Figure 1f Compression ratio of 8 with new decompression scheme and nominal smoothing. Figure 1g Compression ratio of 8 with new decompression scheme and smoothing factor of 1.5. Figure 2a Original Ganymede scene. Figure 2b Compression ratio of 4 with original decompression scheme. Figure 2c Compression ratio of 8 with original decompression scheme. Figure 2d Compression ratio of 8 with new decompression scheme and no smoothing. Figure 2e Compression ratio of 8 with new decompression scheme and smoothing factor of 0.5. Figure 2f Compression ratio of 8 with new decompression scheme and nominal smoothing. Figure 2g Compression ratio of 8 with new decompression scheme and smoothing factor of 1.5. Figure 3a Original LANDSAT scene. Figure 3b Compression ratio of 4 with original decompression scheme. Figure 3c Compression ratio of 8 with original decompression scheme. Figure 3d Compression ratio of 8 with new decompression scheme and no smoothing. Figure 3e Compression ratio of 8 with new decompression scheme and smoothing factor of 0.5. Figure 3f Compression ratio of 8 with new decompression scheme and nominal smoothing. Figure 3g Compression ratio of 8 with new decompression scheme and smoothing factor of 1.5. Figure 7.1.1-1a An original test image with low signal and high contrast. Figure 7.1.1-1b The scene in figure 1a with a compression ratio of 16. Figure 7.7-1a Original Ganymede image smoothed with no noise Figure 7.7-1b Low noise with CR 2 Figure 7.7-1c Low noise with CR 3 Figure 7.7-1d Low noise with CR 4 Figure 7.7-1e Low noise with CR 6 Figure 7.7-1f Low noise with CR 8 Figure 7.7-1g Low noise with CR 12 Figure 7.7-1h Low noise with CR 16 Figure 7.7-2a Moderate noise with CR 2 Figure 7.7-2b Moderate noise with CR 3 Figure 7.7-2c Moderate noise with CR 4 Figure 7.7-2d Moderate noise with CR 6 Figure 7.7-2e Moderate noise with CR 8 Figure 7.7-2f Moderate noise with CR 12 Figure 7.7-2g Moderate noise with CR 16 Figure 7.7-3a Original "lakes" image smoothed with no noise Figure 7.7-3b High noise with CR 2 Figure 7.7-3c High noise with CR 3 Figure 7.7-3d High noise with CR 4 Figure 7.7-3e High noise with CR 6 Figure 7.7-3f High noise with CR 8 Figure 7.7-3g High noise with CR 12 Figure 7.7-3h High noise with CR 16 Figure 8.0-3 Histogram of image compression ratios for original compression scheme. Figure 8.0-4 Distribution of image acquisition times for original compression scheme. Figure 8.0-5 Distribution of image acquisition altitudes for original compression scheme. Figure 8.0-6 Distribution of image sub-probe longitudes for original compression scheme. Figure 8.0-7 HRI footprint outlines for all HRI images for original compression scheme. Figure 8.0-8 HRI footprint outlines for all HRI images (magnified view) for original compression scheme Figure 8.0-9 HRI footprint outlines for mid to low altitude panoramas for original compression scheme. Figure 8.0-10 HRI footprint outlines for low panoramas for original compression scheme. Figure 8.0-11 HRI footprint outlines for lowest panoramas and non-panoramic images for original compression scheme. Figure 8.0-12 Distribution of image acquisition times for new compression scheme. Figure 8.0-13 Distribution of image compression ratio (with raw image data sets included) for new compression scheme. Figure 8.0-14 Distribution of image acquisition times for new compression scheme. Figure 8.0-15 Distribution of image acquisition altitudes for new compression scheme. Figure 8.0-16 Distribution of image sub-probe longitudes for new compression scheme. Figure 8.0-17 HRI footprint outlines for all HRI images for new compression scheme. Figure 8.0-18 HRI footprint outlines for all HRI images (magnified view) for new compression scheme. Figure 8.0-19 HRI footprint outlines for mid to low altitude panoramas for new compression scheme. Figure 8.0-20 HRI footprint outlines for low panoramas for new compression scheme. Table of Tables Figure 2.2-1 Outline of DISR 2 Field of View; Corners, centers and halfway points are indicated by squares. Figure 2.2-2 Outline of DISR 3 Field of View; Corners, centers and halfway points are indicated by squares. Figure 8.0-3 Histogram of image compression ratios for original compression scheme. Figure 8.0-4 Distribution of image acquisition times for original compression scheme. Figure 8.0-5 Distribution of image acquisition altitudes for original compression scheme. Figure 8.0-6 Distribution of image sub-probe longitudes for original compression scheme. Figure 8.0-7 HRI footprint outlines for all HRI images for original compression scheme. Figure 8.0-8 HRI footprint outlines for all HRI images (magnified view) for original compression scheme. Figure 8.0-9 HRI footprint outlines for mid to low altitude panoramas for original compression scheme. Figure 8.0-10 HRI footprint outlines for low panoramas for original compression scheme. Figure 8.0-11 HRI footprint outlines for lowest panoramas and non-panoramic images for original compression scheme. Figure 8.0-20 HRI footprint outlines for low panoramas for new compression scheme. 1.0 Introduction The DISR includes three imaging cameras, named the High Resolution Imager (HRI), Medium Resolution Imager (MRI), and Side-Looking Imager (SLI). The three cameras have adjacent fields of view in nadir angle. All three are centered at the same instrumental azimuth, namely out the front of the sensor head. The three imagers may be exposed simultaneously, yielding a field of view extended from nearly the nadir to above the horizon with an extent in azimuth of about 30. Twelve sets of exposures equidistant in azimuth cover nearly all the visible downward hemisphere, and these sets of 36 images are called panoramas. During its descent, DISR should acquire approximately 12 panoramas. The imaging cameras are wide field, as opposed to telephoto, in order to cover the hemisphere. Nominally the pixels subtend angular sizes of 0.06 milliradians (mr) (HRI), 0.12 mr (MRI), and 0.20 mr (SLI). The optical point spread function covers roughly 2 pixels to satisfy the sampling theorem, so the actual resolution is somewhat less. High spatial resolution on the ground is achieved by being close to it. The last image above the ground is taken from about 200m with the HRI, providing a resolution of approximately 24 cm per line pair. All three imagers have very nearly the same spectral bandpass, which extends from about 640 to 1050 nm. This near-infrared bandpass was chosen to improve visibility through the haze in Titan's atmosphere. The optical thickness of the atmospheric aerosols decreases markedly toward the infrared. The varying optical depth with altitude of methane in several bands complicates the effective bandpass of the instrument-atmosphere combination. In the sections below we discuss the imager optics and detector. Image display, including the construction of panoramic display from individual images, is discussed. A section covering image sharpening by taking advantage of knowledge of the image system point spread function follows. Photometry using the imagers is covered in sections on the relative spectral responsivity, absolute responsivity, and the on-board processing of the images. The final sections cover an improved method of decompressing DISR images and a tradeoff study of image compression ratios. 1.1 Overview of Optical Systems The imagers are unconventional, because the light is carried from the objective lens to the focal plane via a fiber optic conduit. The optical path is shown very schematically in figure 1. The objective lenses are compound lenses, normally used as eyepieces. They are also shown in figure 1.1-1. Figure 1.1-1 Drawing of the front end of the optics of the imagers showing window, filter, lenses, etc. The high resolution imager objective is a modified Cooke-triplet design. The medium resolution imager is a conventional Pl”ssl eyepiece design. The side- looking imager objective is a conventional Erfle eyepiece design. Figure 1.1-2 Diagram of the fiber optic image conduits, which carry the image to the CCD. Figure 1.1-3 The imager objective lenses are attached to an optical bench, which holds the fiber optic conduit. Figure 1.1-2 shows the fiber optic conduits, which carry the images from the objective focal planes to the CCD. Figure 1.1-3 shows the objective lenses in their housings as well as the optical bench, which supports the conduits. The conduits actually end about 20 m from the surface of the CCD. A looping fiber is shown entering the MRI. This is a fiber, which carries light from an internal calibration system, shown near the top of figure 3. The fiber actually enters the lens housing through the oval holes shown. Light from the fiber reflects off a very small mirror in the center of each outer window. In reality separate fibers run to each of three imager objective housings. This calibration light provides a nearly constant optical stimulus, which can be used to check to stability and health of the imagers. The CCD is an image transfer type. Anti-blooming gates inhibit the spread of excess charge over the chip when overexposure occurs. The pixels are 23 m squares. The CCD contains 512512 pixels, but one half of the surface is covered by an aluminum mask, which is opaque. The images are formed in three subsections of the CCD, and it is then rapidly shifted under the opaque mask. Each row of the image is deposited into a serial register, and a 12-bit analog- to-digital converter digitizes the amount of charge in each pixel in that register. The result is stored in computer memory. Subsequent processing of the image data is discussed below. The HRI uses an area of 160 columns by 254 rows on the CCD. 256 rows are not used, because the first and last rows contain corrupted pixels. This is true for all three imagers. The MRI uses an area of 176 columns by 254 rows. The SLI uses an area of 128 columns by 254 rows. In the sections below we discuss calibration of the DISR imagers in detail, including image distortion and geometry calibrations, relative spectral response calibrations, absolute response calibrations, on-board image processing, image compression ratio optimization, compression defect removal, image sharpening, and finally considerations of using DISR imager data for photometry. 2.0 DISR Image Distortion and Geometry Calibrations Bashar Rizk 2.1 Introduction In this document the calibration results characterizing the optical distortion of the DISR 2 and 3 near-IR imagers and their geometrical mapping to the upper and lower hemispheres of object space are presented and discussed. This calibration has recently (July-September 2001) been completely re-performed in order to take advantage of the improvement in resolution created by E. Karkoschka's image sharpening algorithm (see image sharpening section of the image calibration document.) The main results of this effort are the absolute assignment of each pixel contained within each of the 6 imagers to a direction in object space, which is conveniently represented as a sphere at infinity. We will call this sphere the object sphere. Its center is near the DISR sensor head front housing, e.g. the entrance pupils of each of the imagers or some other instrument-related point. In practice, because anticipated object distances are so much larger than image- related distances, the exact choice of center is assumed not to matter. This approximation is slightly violated in many of the laboratory and field images acquired by the HRI and MRI. In those cases, the center is assumed to be the entrance pupil of the imager in question and the resulting parallax observed in the imaging results. The direction on the object sphere associated with a specific pixel is absolutely located, just as in any standard spherical coordinate system, by two angles, usually zenith angle q (co-latitude) and counterclockwise azimuth f. Often, and especially in this work, nadir angle N is used instead of zenith angle, and clockwise azimuth f (positive to the right as seen from the point of view of the imager) is used instead of azimuths that are positive to the left. With respect to each imager, pixels can also located by the dihedral angels a and b, which resemble x and y Cartesian coordinates within each field of view and run parallel to columns and rows, respectively. The absolute assignments are presented in abbreviated form below and the paths to the complete transformations are provided. These assignments are accomplished for each imager by two separate polynomial transformations, one which largely removes the effects of optical distortion and one which absolutely assigns each pixel to an absolute object location. The matrix elements for each of these transformations are presented. The methods by which these maps were derived are subsequently described, first the distortion transformation, then the absolute transformation. Details concerning the actual procedures, relevant details and other data important for those required to re-perform the calibration are given in the appendices. 2.2 Summary of Results DISR's three near-IR imagers are designed to image the instrument's lower hemisphere as efficiently as possible within the spacecraft mission's constraints on data rate, power, mass and size. Their fields of view and relative arrangement enable them to image a 90o-high continuous vertical slice of the lower hemisphere, one at least 23.5o wide, from 6o above the horizon to 6o above the nadir. They represent a more or less successful compromise between the contradictory Huygens Probe goals of maximizing field of view and maximizing resolution. The nominal fields of view of each imager were designed and specified as 9.6 15.2o for the HRI, 21.1 30.5o for the MRI and 25.6 51.8o for the SLI. The nominal centers of each field were intended to be 166o for the HRI, 148.5o for the MRI and 109.4o for the SLI. These correspond to nadir angles of 14o, 31.5o and 70.6o, respectively. The actual fields of view are displayed in Figs. 1 and 2 for each imager, mapped to an object sphere coordinate system spanned by nadir angle N and clockwise azimuth f. As built, the dihedral fields of view of the imagers are rectangular for the MRI and HRI and slightly trapezoidal in the case of the SLI, and correspond to 9.8 15.4o for the HRI, 21.5 30.4o for the MRI and 25.9 50.4o for the SLI, where the dihedral angles quoted are averages of the top and bottom sides for the width and the left and right sides for the height. The dimensions given are those of DISR 3, the flight unit. Table 2.2-1 gives the locations for the corner and edge pixels, those indicated by squares in Figs. 2.2-1 and 2.2-2. The centers of each field of view are also included. The SLI, in both DISR models, can be seen to be some 4o longer on the left side than the right. As built, the system of three imagers can roughly image the lower object sphere below a nadir angle of 58o in one 12-around cycle, but need 2 12-around cycles to fully image nadir angles between 58 and 96o. The region covering nadir angles from 16-23o also needs more than just one 12-around cycle (the top of the HRI) and there is a small 1-3o nadir angle region at 45o nadir angle (the top of the MRI, just below the SLI) which also needs more than just one 12- around cycle. The actual matrix elements enabling the transformation from a raw, distorted image to an undistorted one are displayed in Table 2.2-1 for DISR#2 and #3. Those facilitating the mapping of the undistorted images onto object sphere azimuth and nadir angles are given in Tables 2.3-2. As presented the transformations assume the input images have been sharpened using the DISR#2 and #3 imager-sharpening algorithm developed by Erich Karkoschka. Figure 2.2-1 Outline of DISR 2 Field of View; Corners, centers and halfway points are indicated by squares. Figure 2.2-2 Outline of DISR 3 Field of View; Corners, centers and halfway points are indicated by squares. Table 2.2-1 Azimuth and nadir coordinates for the corners of the DISR#2 and DISR#3 fields of view DISR 2 DISR 2 Nadir DISR 3 DISR 3 Nadir LOCATION Spherical Angle N Spherical Angle N Azimuth f Azimuth f MRI bottom left corner -32.78 19.39 -32.58 19.04 MRI bottom right corner 32.62 19.52 34.79 19.23 MRI top left corner -14.19 47.42 -13.81 47.19 MRI top right corner 14.10 47.47 14.18 47.52 MRI bottom center 0.38 16.62 1.20 15.98 MRI top center 0.17 46.02 0.58 46.21 MRI center 0.05 31.27 0.63 31.29 SLI bottom left corner -16.58 46.47 -16.75 45.87 SLI bottom right corner 16.28 48.02 15.73 47.82 SLI top left corner -11.97 96.54 -11.88 96.45 SLI top right corner 11.72 95.31 11.74 95.51 SLI bottom center -0.23 45.61 -0.21 45.70 SLI top center -0.20 95.95 -0.13 96.12 SLI center 0.24 70.74 0.26 70.85 HRI bottom left corner -35.77 8.54 -35.37 8.24 HRI bottom right corner 34.94 8.27 36.91 8.42 HRI top left corner -12.92 22.56 -12.74 22.57 HRI top right corner 12.52 22.41 12.36 22.69 HRI bottom center -0.90 6.78 0.72 6.71 HRI top center -0.10 22.06 0.45 22.29 HRI center -0.42 14.53 0.40 14.50 Table 2.2-2 Matrix elements to transform raw DISR frames to undistorted ones DISR 2 MRI KX DISR 3 MRI KX 0.716 -0.0435 8.487E-05 2.789E-10 -1.892 -0.0284 7.194E-05 -1.418E-09 0.9907 2.748E-04 -5.754E-07 2.395E-11 1.00602 4.048E-05 -2.585E-08 -1.557E-12 -9.099E-06 4.246E-08 2.808E-10 -2.360E-13 -8.047E-05 1.729E-06 -3.487E-09 -5.479E-15 3.697E-08 -4.488E-10 1.116E-13 4.828E-16 1.317E-07 -3.432E-09 6.895E-12 -3.558E-17 DISR 2 MRI KY DISR 3 MRI KY -0.766 0.9895 8.728E-05 -1.157E-07 0.955 0.988 1.026E-04 -1.377E-07 -0.03018 5.430E-05 2.715E-07 -2.259E-10 -0.04804 7.644E-05 3.634E-07 -4.294E-10 8.629E-05 -8.044E-08 -1.262E-09 1.306E-12 1.243E-04 -3.394E-07 -9.257E-10 1.191E-12 2.255E-09 -5.540E-11 2.798E-13 -3.784E-16 -4.978E-09 4.945E-11 -6.037E-14 -7.363E-18 DISR 2 SLI KX DISR 3 SLI KX 11.674 -0.0974 1.956E-04 8.849E-10 6.462 -0.0940 2.034E-04 -6.373E-09 0.90449 6.741E-04 -1.382E-06 4.272E-11 0.91545 7.480E-04 -1.421E-06 2.418E-12 -6.961E-05 1.577E-06 -2.112E-09 -7.209E-13 5.187E-05 8.090E-07 -1.250E-09 3.980E-14 4.184E-07 -5.167E-09 7.237E-12 1.740E-15 -3.253E-08 -2.167E-09 3.509E-12 -7.781E-16 DISR 2 SLI KY DISR 3 SLI KY 13.499 0.8957 3.552E-04 -4.588E-07 9.973 0.909 3.403E-04 -4.589E-07 -0.07393 4.646E-05 1.283E-06 -1.598E-09 -0.08724 1.159E-04 1.021E-06 -1.288E-09 2.873E-04 -2.669E-07 -5.015E-09 6.491E-12 3.557E-04 -6.453E-07 -4.005E-09 5.502E-12 8.447E-08 -6.095E-10 1.607E-12 -1.886E-15 4.106E-08 -1.843E-10 2.295E-13 -2.961E-16 DISR 2 HRI KX DISR 3 HRI KX 0.680 -0.011 1.045E-06 -1.148E-09 -1.002 2.272E-03 7.734E-06 3.441E-10 1.02755 -6.880E-05 1.105E-07 2.903E-12 1.01017 3.693E-05 -7.635E-08 -4.397E-13 -1.431E-04 6.256E-07 -1.009E-09 8.920E-15 -7.332E-05 -1.220E-07 2.402E-10 1.507E-15 3.093E-07 -1.365E-09 2.178E-12 -5.801E-17 1.625E-07 2.051E-10 -3.396E-13 3.262E-18 DISR 2 HRI KY DISR 3 HRI KY -4.551 1.034 -9.468E-05 1.106E-07 0.4571 1.015 -6.036E-05 7.205E-08 0.01621 -1.025E-04 4.632E-07 -5.586E-10 -6.768E-03 -9.192E-06 1.047E-07 -1.809E-10 -1.265E-05 2.911E-07 -1.367E-09 1.641E-12 4.226E-06 2.271E-08 -2.899E-10 4.667E-13 3.908E-09 -2.149E-11 4.899E-14 -3.021E-17 -8.969E-10 -1.596E-12 4.994E-15 -7.583E-18 Table 2.2-3 Matrix elements to transform undistorted images onto object sphere azimuth and nadir angles DISR 2 MRI KX DISR 3 MRI KX -1.585 0.0893 -1.456E-03 3.595E-06 -3.394 0.1928 -4.522E-03 3.573E-05 -0.4715 -5.453E-02 1.754E-03 -1.799E-05 -0.65334 -3.526E-02 1.046E-03 -9.695E-06 -7.078E-04 2.269E-04 -1.247E-05 1.785E-07 -1.812E-03 2.787E-04 -1.177E-05 1.459E-07 -1.472E-03 1.520E-04 -4.999E-06 5.214E-08 -8.786E-04 8.232E-05 -2.375E-06 2.100E-08 DISR 2 MRI KY DISR 3 MRI KY 0.425 0.9402 1.836E-03 -1.811E-05 0.218 0.943 2.059E-03 -2.106E-05 -0.01852 2.377E-03 -8.371E-05 8.860E-07 0.02725 -2.339E-03 8.040E-05 -9.245E-07 -3.479E-03 3.870E-04 -1.339E-05 1.495E-07 -2.379E-04 6.081E-05 -2.687E-06 3.619E-08 5.390E-05 -5.835E-06 2.004E-07 -2.142E-09 -7.452E-05 8.233E-06 -2.933E-07 3.386E-09 DISR 2 SLI KX DISR 3 SLI KX 2.860 -0.0822 4.429E-04 1.258E-06 3.135 -0.0977 7.072E-04 -2.136E-07 -0.58137 -1.765E-02 2.439E-04 -1.107E-06 -0.65301 -1.547E-02 2.288E-04 -1.118E-06 2.697E-02 -1.169E-03 1.614E-05 -7.237E-08 3.166E-02 -1.252E-03 1.597E-05 -6.678E-08 -1.579E-03 5.971E-05 -7.780E-07 3.343E-09 -1.803E-04 1.265E-05 -3.218E-07 2.233E-09 DISR 2 SLI KY DISR 3 SLI KY 1.128 0.9832 3.948E-05 1.383E-07 -0.174 1.048 -9.235E-04 4.785E-06 -0.26821 1.266E-02 -1.737E-04 6.885E-07 -0.48880 2.299E-02 -3.269E-04 1.423E-06 -3.156E-02 1.446E-03 -2.132E-05 1.016E-07 -5.545E-03 2.380E-04 -3.160E-06 1.321E-08 5.188E-03 -2.076E-04 2.743E-06 -1.199E-08 4.709E-03 -1.982E-04 2.736E-06 -1.236E-08 DISR 2 HRI KX DISR 3 HRI KX 0.846 0.022 -6.510E-03 1.760E-04 -1.950 2.572E-01 -1.437E-02 2.587E-04 -0.62246 -7.017E-02 4.981E-03 -1.170E-04 -0.68931 -5.616E-02 3.958E-03 -9.309E-05 2.591E-03 -6.725E-04 3.728E-05 -3.667E-07 1.807E-03 -3.334E-04 4.320E-06 5.092E-07 -7.608E-04 2.043E-04 -1.754E-05 4.558E-07 -6.707E-04 1.835E-04 -1.600E-05 4.199E-07 DISR 2 HRI KY DISR 3 HRI KY 0.404 1.029 -1.897E-03 3.715E-05 0.5265 0.996 4.609E-04 -1.661E-05 -0.00555 1.444E-03 -1.382E-04 4.079E-06 -8.277E-04 1.053E-03 -1.046E-04 3.119E-06 -1.053E-03 2.416E-04 -1.582E-05 2.837E-07 -1.015E-03 2.241E-04 -1.352E-05 2.042E-07 6.957E-05 -1.974E-05 1.791E-06 -5.052E-08 5.178E-05 -1.498E-05 1.389E-06 -3.960E-08 2.3 Distortion Calibration The purpose of the calibration of the optical distortion of the 6 near-IR imaging systems of DISR 2 and 3 was to determine the extent to which magnification changed for off-axis image points. The significant barrel distortion possessed especially by the SLI made this calibration an important one. The distortion calibration data for the DISR 3 imagers was acquired on August 19, 1996. For the DISR 2 imagers it was acquired on March 4, 1997. Square grid-like targets printed on drafting paper were mounted in front of the imagers on a rigid surface. These targets consisted of black bars separated by white space, oriented both in a horizontal and vertical configuration. An alignment laser mounted on the altitude-azimuth yoke, parallel to the imaging system, and a mirror mounted on the rigid target surface enabled the surface to be adjusted perpendicular to each imaging system. The distance to the imaging system was also measured. The distance of each target, the thickness and separation of the black bars for each target and the assumed angular pixel size in degrees are listed in Table 2.3-1. Table 2.3-1 Imager distortion measurement parameters MRI 2 SLI 2 HRI 2 MRI 3 SLI 3 HRI 3 Distance of distortion target (mm.) 1486 1168 4693 1486 1168 4685 Width of black bars (mm.) 31.60 40.21 54.51 31.60 40.21 54.51 Separation of black bars (mm.) 92.61 119.5 162.0 92.61 119.5 162.0 Size of sharpened pixel (o) 0.06 0.1 0.0308 0.06 0.1 0.0308 Nominal Zenith Angle of Central Pixel 148.5 109.4 166 148.5 109.4 166 (o) Number of Columns (sharpened) 353 257 321 353 257 321 Number of Rows (sharpened) 509 509 509 509 509 509 The target images used for the final analysis are shown in Figures 2.3-1 through 2.3-6 for the 6 imagers. For each image an accompanying dark, bias and flat-field was acquired and used to reduce the image. The transition boundaries between black and white were identified and traced by a procedure originally written by Mike Bushroe and the intersections of these boundaries determined. This data is listed in Tables 2.3-3 through 2.3-8, and consists of the pixel locations of the corners of the black boxes making up the target grid system. The actual locations of these objects were assumed to be determined by the distances from Table 2.3-2, centrally projected to the image axis, i.e., as they would have been seen from the distance of each image in an undistorted view. Figure 2.3-1 DISR 2 MRI Target Grid (sharpened) Figure 2.3-2 Location of Observed Vertices for DISR 2 MRI Figure 2.3-3 Location of Desired Vertices for DISR 2 MRI Table 2.3-2 Vertex Information for DISR 2 MRI Distortion Fit C = Column R=Row Point Observed C Observed R Desired Desired Computed C Computed R C R ID C R Residual Residual 0 12.60 8.34 12.50 9.16 12.74 7.95 0.14 -0.39 1 11.93 26.52 12.50 28.28 12.03 26.94 0.10 0.41 2 10.71 64.04 12.50 65.70 10.80 64.28 0.10 0.24 3 10.14 84.08 12.50 85.32 10.25 83.94 0.11 -0.14 4 9.24 122.39 12.50 123.60 9.34 122.41 0.10 0.02 5 8.85 142.77 12.50 143.59 8.95 142.56 0.11 -0.21 6 8.28 181.71 12.50 182.45 8.39 181.82 0.11 0.11 7 8.07 202.41 12.50 202.68 8.18 202.29 0.11 -0.12 8 7.87 241.89 12.50 241.85 7.97 241.96 0.11 0.06 9 7.85 262.67 12.50 262.15 7.95 262.53 0.10 -0.13 10 8.01 301.96 12.50 301.32 8.11 302.20 0.10 0.25 11 8.19 322.95 12.50 321.55 8.28 322.67 0.09 -0.27 12 8.71 361.69 12.50 360.41 8.79 361.95 0.08 0.26 13 9.08 382.19 12.50 380.41 9.15 382.11 0.07 -0.07 14 9.93 420.40 12.50 418.68 10.00 420.61 0.07 0.21 15 10.48 440.52 12.50 438.30 10.53 440.28 0.05 -0.24 16 11.64 477.71 12.50 475.73 11.70 477.65 0.06 -0.06 17 12.32 496.59 12.50 494.84 12.39 496.66 0.07 0.07 18 32.63 7.89 32.33 9.16 32.42 7.43 -0.20 -0.46 19 32.04 25.96 32.33 28.28 31.81 26.45 -0.23 0.49 20 30.97 63.57 32.33 65.70 30.75 63.84 -0.22 0.27 21 30.47 83.66 32.33 85.32 30.27 83.53 -0.20 -0.13 22 29.67 122.03 32.33 123.60 29.48 122.07 -0.19 0.04 23 29.33 142.48 32.33 143.59 29.14 142.26 -0.18 -0.22 24 28.82 181.47 32.33 182.45 28.65 181.61 -0.17 0.14 25 28.64 202.27 32.33 202.68 28.47 202.12 -0.17 -0.15 26 28.44 241.85 32.33 241.85 28.28 241.88 -0.16 0.03 27 28.43 262.64 32.33 262.15 28.26 262.51 -0.16 -0.14 28 28.55 302.04 32.33 301.32 28.38 302.28 -0.17 0.24 29 28.70 323.05 32.33 321.55 28.53 322.81 -0.18 -0.24 30 29.14 361.97 32.33 360.41 28.96 362.19 -0.18 0.21 31 29.45 382.47 32.33 380.41 29.26 382.41 -0.19 -0.06 32 30.19 420.79 32.33 418.68 29.99 421.01 -0.20 0.22 33 30.65 440.96 32.33 438.30 30.44 440.73 -0.21 -0.22 34 31.66 478.23 32.33 475.73 31.44 478.22 -0.21 -0.01 35 32.24 497.29 32.33 494.84 32.03 497.28 -0.21 -0.01 36 70.61 7.21 70.93 9.16 70.74 6.63 0.13 -0.58 37 70.21 25.11 70.93 28.28 70.31 25.68 0.10 0.57 38 69.46 62.85 70.93 65.70 69.58 63.16 0.11 0.31 39 69.12 83.02 70.93 85.32 69.24 82.90 0.13 -0.12 40 68.56 121.49 70.93 123.60 68.69 121.55 0.13 0.06 41 68.32 142.04 70.93 143.59 68.46 141.80 0.13 -0.24 42 67.98 181.11 70.93 182.45 68.11 181.27 0.13 0.16 43 67.85 202.05 70.93 202.68 67.98 201.85 0.13 -0.19 44 67.71 241.79 70.93 241.85 67.84 241.76 0.13 -0.03 45 67.70 262.61 70.93 262.15 67.82 262.46 0.12 -0.14 46 67.79 302.17 70.93 301.32 67.90 302.39 0.11 0.22 47 67.89 323.20 70.93 321.55 68.00 323.00 0.10 -0.19 48 68.20 362.40 70.93 360.41 68.28 362.55 0.09 0.15 49 68.41 382.89 70.93 380.41 68.49 382.86 0.07 -0.03 50 68.92 421.38 70.93 418.68 68.98 421.63 0.06 0.26 51 69.25 441.62 70.93 438.30 69.29 441.44 0.04 -0.18 52 69.94 479.01 70.93 475.73 69.97 479.09 0.03 0.08 53 70.35 498.35 70.93 494.84 70.37 498.24 0.02 -0.11 54 90.64 6.93 91.06 9.16 90.72 6.31 0.07 -0.61 55 90.38 24.78 91.06 28.28 90.39 25.38 0.01 0.60 56 89.88 62.57 91.06 65.70 89.82 62.89 -0.06 0.33 57 89.64 82.77 91.06 85.32 89.56 82.65 -0.08 -0.12 58 89.26 121.27 91.06 123.60 89.14 121.34 -0.12 0.07 59 89.09 141.87 91.06 143.59 88.96 141.62 -0.13 -0.25 60 88.83 180.96 91.06 182.45 88.68 181.14 -0.15 0.18 61 88.73 201.94 91.06 202.68 88.58 201.75 -0.14 -0.20 62 88.60 241.76 91.06 241.85 88.47 241.71 -0.13 -0.05 63 88.57 262.59 91.06 262.15 88.46 262.44 -0.11 -0.15 64 88.58 302.22 91.06 301.32 88.52 302.43 -0.06 0.22 65 88.62 323.25 91.06 321.55 88.59 323.08 -0.03 -0.17 66 88.76 362.56 91.06 360.41 88.81 362.69 0.04 0.12 67 88.87 383.05 91.06 380.41 88.96 383.03 0.09 -0.02 68 89.14 421.60 91.06 418.68 89.34 421.87 0.20 0.27 69 89.32 441.88 91.06 438.30 89.57 441.72 0.26 -0.16 70 89.70 479.32 91.06 475.73 90.10 479.44 0.39 0.12 71 89.93 498.77 91.06 494.84 90.40 498.62 0.47 -0.14 72 129.56 6.54 130.11 9.16 129.47 5.89 -0.08 -0.65 73 129.39 24.35 130.11 28.28 129.33 24.99 -0.06 0.64 74 129.07 62.22 130.11 65.70 129.09 62.55 0.01 0.34 75 128.93 82.46 130.11 85.32 128.97 82.34 0.05 -0.12 76 128.69 121.00 130.11 123.60 128.79 121.08 0.10 0.08 77 128.59 141.66 130.11 143.59 128.71 141.39 0.12 -0.27 78 128.44 180.78 130.11 182.45 128.59 180.97 0.15 0.19 79 128.39 201.78 130.11 202.68 128.55 201.61 0.16 -0.17 80 128.33 241.72 130.11 241.85 128.50 241.64 0.17 -0.09 81 128.33 262.58 130.11 262.15 128.49 262.41 0.16 -0.17 82 128.36 302.28 130.11 301.32 128.51 302.47 0.15 0.20 83 128.41 323.30 130.11 321.55 128.54 323.15 0.14 -0.14 84 128.53 362.76 130.11 360.41 128.63 362.84 0.10 0.08 85 128.62 383.24 130.11 380.41 128.70 383.23 0.08 0.00 86 128.84 421.89 130.11 418.68 128.86 422.16 0.02 0.27 87 128.98 442.20 130.11 438.30 128.96 442.06 -0.01 -0.14 88 129.27 479.72 130.11 475.73 129.19 479.88 -0.08 0.16 89 129.44 499.33 130.11 494.84 129.32 499.12 -0.12 -0.21 90 149.51 6.43 150.40 9.16 149.61 5.78 0.10 -0.65 91 149.47 24.25 150.40 28.28 149.56 24.89 0.09 0.63 92 149.41 62.13 150.40 65.70 149.48 62.47 0.07 0.34 93 149.39 82.39 150.40 85.32 149.44 82.26 0.06 -0.13 94 149.35 120.94 150.40 123.60 149.38 121.02 0.03 0.08 95 149.33 141.61 150.40 143.59 149.35 141.33 0.02 -0.27 96 149.32 180.74 150.40 182.45 149.31 180.93 -0.01 0.19 97 149.31 201.71 150.40 202.68 149.29 201.57 -0.02 -0.14 98 149.32 241.71 150.40 241.85 149.28 241.61 -0.05 -0.10 99 149.33 262.57 150.40 262.15 149.27 262.39 -0.06 -0.18 100 149.37 302.29 150.40 301.32 149.28 302.47 -0.09 0.19 101 149.39 323.29 150.40 321.55 149.29 323.16 -0.10 -0.13 102 149.45 362.80 150.40 360.41 149.32 362.87 -0.13 0.07 103 149.49 383.27 150.40 380.41 149.34 383.27 -0.14 0.00 104 149.57 421.96 150.40 418.68 149.40 422.23 -0.17 0.27 105 149.61 442.27 150.40 438.30 149.43 442.14 -0.18 -0.13 106 149.72 479.82 150.40 475.73 149.51 479.99 -0.21 0.17 107 149.77 499.47 150.40 494.84 149.55 499.25 -0.22 -0.22 108 188.53 6.37 189.60 9.16 188.55 5.76 0.01 -0.60 109 188.64 24.28 189.60 28.28 188.67 24.88 0.03 0.60 110 188.85 62.16 189.60 65.70 188.89 62.48 0.04 0.32 111 188.95 82.42 189.60 85.32 188.99 82.28 0.04 -0.15 112 189.10 120.96 189.60 123.60 189.15 121.04 0.05 0.08 113 189.17 141.63 189.60 143.59 189.22 141.35 0.05 -0.28 114 189.27 180.75 189.60 182.45 189.33 180.93 0.06 0.18 115 189.30 201.61 189.60 202.68 189.37 201.57 0.06 -0.04 116 189.34 241.71 189.60 241.85 189.41 241.60 0.07 -0.11 117 189.34 262.58 189.60 262.15 189.41 262.37 0.07 -0.21 118 189.32 302.27 189.60 301.32 189.39 302.43 0.08 0.16 119 189.29 323.24 189.60 321.55 189.36 323.12 0.08 -0.12 120 189.20 362.76 189.60 360.41 189.28 362.82 0.08 0.06 121 189.14 383.21 189.60 380.41 189.22 383.22 0.08 0.01 122 188.99 421.93 189.60 418.68 189.08 422.18 0.08 0.25 123 188.90 442.23 189.60 438.30 188.99 442.10 0.09 -0.12 124 188.70 479.80 189.60 475.73 188.79 479.98 0.08 0.18 125 188.59 499.47 189.60 494.84 188.67 499.25 0.08 -0.22 126 208.90 6.42 209.89 9.16 208.70 5.86 -0.20 -0.56 127 209.09 24.41 209.89 28.28 208.91 24.98 -0.17 0.57 128 209.45 62.28 209.89 65.70 209.28 62.58 -0.17 0.30 129 209.61 82.53 209.89 85.32 209.45 82.37 -0.16 -0.16 130 209.88 121.04 209.89 123.60 209.72 121.12 -0.16 0.08 131 210.00 141.70 209.89 143.59 209.84 141.42 -0.16 -0.28 132 210.17 180.80 209.89 182.45 210.02 180.98 -0.16 0.17 133 210.24 201.58 209.89 202.68 210.08 201.60 -0.16 0.03 134 210.32 241.71 209.89 241.85 210.15 241.60 -0.17 -0.11 135 210.33 262.58 209.89 262.15 210.16 262.35 -0.17 -0.23 136 210.30 302.24 209.89 301.32 210.12 302.39 -0.18 0.15 137 210.26 323.18 209.89 321.55 210.08 323.06 -0.19 -0.11 138 210.14 362.68 209.89 360.41 209.94 362.74 -0.20 0.06 139 210.05 383.11 209.89 380.41 209.84 383.13 -0.21 0.01 140 209.83 421.83 209.89 418.68 209.59 422.07 -0.23 0.24 141 209.69 442.11 209.89 438.30 209.44 441.98 -0.24 -0.12 142 209.38 479.68 209.89 475.73 209.10 479.85 -0.28 0.17 143 209.20 499.33 209.89 494.84 208.90 499.13 -0.29 -0.20 144 247.44 6.68 248.94 9.16 247.54 6.24 0.10 -0.44 145 247.80 24.89 248.94 28.28 247.90 25.36 0.11 0.48 146 248.45 62.69 248.94 65.70 248.54 62.94 0.08 0.25 147 248.76 82.91 248.94 85.32 248.82 82.71 0.07 -0.20 148 249.24 121.34 248.94 123.60 249.30 121.40 0.06 0.06 149 249.46 141.96 248.94 143.59 249.50 141.67 0.05 -0.28 150 249.76 181.00 248.94 182.45 249.80 181.15 0.04 0.15 151 249.88 201.55 248.94 202.68 249.91 201.73 0.04 0.19 152 250.00 241.74 248.94 241.85 250.03 241.64 0.03 -0.10 153 250.01 262.61 248.94 262.15 250.04 262.34 0.04 -0.27 154 249.93 302.15 248.94 301.32 249.98 302.28 0.04 0.13 155 249.84 323.01 248.94 321.55 249.89 322.90 0.05 -0.12 156 249.58 362.40 248.94 360.41 249.64 362.48 0.06 0.08 157 249.39 382.81 248.94 380.41 249.47 382.82 0.07 0.01 158 248.95 421.49 248.94 418.68 249.04 421.69 0.09 0.21 159 248.67 441.70 248.94 438.30 248.77 441.57 0.11 -0.13 160 248.06 479.25 248.94 475.73 248.18 479.39 0.13 0.14 161 247.69 498.79 248.94 494.84 247.83 498.64 0.14 -0.15 162 267.67 6.90 269.07 9.16 267.57 6.54 -0.10 -0.36 163 268.09 25.25 269.07 28.28 268.01 25.66 -0.08 0.41 164 268.85 63.00 269.07 65.70 268.77 63.22 -0.07 0.22 165 269.19 83.19 269.07 85.32 269.12 82.97 -0.08 -0.22 166 269.75 121.58 269.07 123.60 269.68 121.62 -0.07 0.05 167 269.99 142.15 269.07 143.59 269.93 141.87 -0.07 -0.29 168 270.34 181.15 269.07 182.45 270.28 181.29 -0.05 0.13 169 270.46 201.55 269.07 202.68 270.41 201.84 -0.05 0.29 170 270.59 241.76 269.07 241.85 270.55 241.67 -0.04 -0.09 171 270.59 262.62 269.07 262.15 270.57 262.33 -0.03 -0.29 172 270.49 302.08 269.07 301.32 270.48 302.20 -0.01 0.12 173 270.37 322.90 269.07 321.55 270.38 322.78 0.01 -0.12 174 270.04 362.20 269.07 360.41 270.07 362.30 0.03 0.10 175 269.81 382.60 269.07 380.41 269.86 382.60 0.04 0.01 176 269.27 421.23 269.07 418.68 269.34 421.41 0.06 0.18 177 268.93 441.40 269.07 438.30 269.01 441.26 0.08 -0.14 178 268.20 478.92 269.07 475.73 268.30 479.03 0.10 0.11 179 267.76 498.37 269.07 494.84 267.88 498.27 0.11 -0.11 180 305.83 7.47 307.67 9.16 306.03 7.32 0.20 -0.15 181 306.39 26.16 307.67 28.28 306.60 26.42 0.21 0.26 182 307.39 63.78 307.67 65.70 307.58 63.92 0.19 0.14 183 307.86 83.90 307.67 85.32 308.02 83.63 0.17 -0.26 184 308.59 122.16 307.67 123.60 308.75 122.18 0.16 0.02 185 308.91 142.63 307.67 143.59 309.06 142.35 0.14 -0.28 186 309.38 181.53 307.67 182.45 309.51 181.63 0.13 0.09 187 309.54 201.58 307.67 202.68 309.67 202.09 0.13 0.52 188 309.71 241.81 307.67 241.85 309.83 241.75 0.12 -0.06 189 309.73 262.66 307.67 262.15 309.84 262.33 0.12 -0.34 190 309.60 301.92 307.67 301.32 309.71 302.01 0.12 0.09 191 309.45 322.64 307.67 321.55 309.57 322.50 0.12 -0.14 192 309.03 361.70 307.67 360.41 309.16 361.84 0.13 0.14 193 308.73 382.06 307.67 380.41 308.87 382.06 0.14 -0.01 194 308.03 420.58 307.67 418.68 308.17 420.70 0.15 0.12 195 307.59 440.65 307.67 438.30 307.75 440.48 0.16 -0.17 196 306.63 478.10 307.67 475.73 306.80 478.12 0.17 0.03 197 306.07 497.31 307.67 494.84 306.24 497.31 0.17 0.00 198 325.96 7.86 327.50 9.16 325.81 7.82 -0.15 -0.04 199 326.56 26.75 327.50 28.28 326.44 26.91 -0.12 0.15 200 327.62 64.28 327.50 65.70 327.51 64.37 -0.10 0.09 201 328.10 84.35 327.50 85.32 328.00 84.05 -0.10 -0.30 202 328.88 122.53 327.50 123.60 328.80 122.53 -0.08 0.00 203 329.21 142.94 327.50 143.59 329.13 142.66 -0.08 -0.28 204 329.69 181.78 327.50 182.45 329.62 181.84 -0.08 0.06 205 329.86 201.61 327.50 202.68 329.79 202.26 -0.07 0.65 206 330.04 241.85 327.50 241.85 329.96 241.81 -0.08 -0.04 207 330.05 262.69 327.50 262.15 329.97 262.33 -0.08 -0.36 208 329.90 301.81 327.50 301.32 329.81 301.90 -0.09 0.08 209 329.74 322.48 327.50 321.55 329.65 322.32 -0.09 -0.16 210 329.28 361.38 327.50 360.41 329.17 361.55 -0.11 0.17 211 328.96 381.72 327.50 380.41 328.85 381.71 -0.12 -0.01 212 328.20 420.17 327.50 418.68 328.07 420.26 -0.14 0.09 213 327.73 440.17 327.50 438.30 327.59 439.98 -0.14 -0.19 214 326.70 477.56 327.50 475.73 326.52 477.54 -0.18 -0.02 215 326.11 496.61 327.50 494.84 325.91 496.69 -0.20 0.08 Figure 2.3-4 DISR 2 SLI Target Grid (sharpened) Figure 2.3-5 Location of Observed Vertices for DISR 2 SLI Figure 2.3-6 Location of Desired Vertices for DISR#2 SLI Table 2.3-3 Vertex Information for DISR#2 SLI Distortion Fit C = R=Row Column Point Observed Observed Desired C Desired R Computed Computed C R ID C R C R Residual Residual 0 15.94 33.70 6.91 23.14 15.87 33.92 -0.07 0.23 1 14.59 49.77 6.91 40.03 14.50 49.42 -0.08 -0.35 2 12.22 81.42 6.91 74.48 12.04 81.57 -0.18 0.15 3 11.09 98.74 6.91 92.50 10.93 98.63 -0.16 -0.11 4 9.20 133.31 6.91 128.98 9.06 133.62 -0.14 0.31 5 8.37 152.24 6.91 147.91 8.28 151.97 -0.09 -0.27 6 7.16 188.98 6.91 185.87 7.12 189.11 -0.04 0.13 7 6.74 208.57 6.91 205.38 6.73 208.31 -0.01 -0.25 8 6.37 246.30 6.91 244.14 6.39 246.62 0.02 0.32 9 6.40 266.35 6.91 263.86 6.42 266.14 0.02 -0.21 10 6.92 304.21 6.91 302.62 6.93 304.47 0.00 0.26 11 7.42 323.95 6.91 322.13 7.39 323.70 -0.03 -0.25 12 8.77 360.64 6.91 360.09 8.70 360.91 -0.07 0.28 13 9.68 379.54 6.91 379.02 9.56 379.32 -0.12 -0.23 14 11.73 414.35 6.91 415.50 11.59 414.44 -0.14 0.09 15 12.94 431.85 6.91 433.52 12.77 431.57 -0.16 -0.27 16 15.44 463.59 6.91 467.97 15.38 463.88 -0.06 0.29 17 16.85 479.59 6.91 484.86 16.82 479.47 -0.04 -0.12 18 50.31 31.53 44.87 23.14 50.74 31.74 0.43 0.20 19 49.39 47.74 44.87 40.03 49.79 47.30 0.39 -0.45 20 47.82 79.35 44.87 74.48 48.08 79.62 0.26 0.27 21 47.06 96.88 44.87 92.50 47.31 96.80 0.25 -0.08 22 45.79 131.78 44.87 128.98 46.01 132.09 0.22 0.31 23 45.24 150.86 44.87 147.91 45.47 150.61 0.24 -0.25 24 44.44 188.02 44.87 185.87 44.68 188.13 0.24 0.11 25 44.17 207.87 44.87 205.38 44.41 207.55 0.25 -0.31 26 43.94 246.05 44.87 244.14 44.19 246.30 0.25 0.24 27 43.98 266.28 44.87 263.86 44.22 266.05 0.24 -0.23 28 44.37 304.58 44.87 302.62 44.59 304.83 0.23 0.25 29 44.72 324.49 44.87 322.13 44.93 324.29 0.21 -0.20 30 45.67 361.62 44.87 360.09 45.87 361.92 0.19 0.30 31 46.31 380.71 44.87 379.02 46.48 380.52 0.17 -0.19 32 47.73 415.87 44.87 415.50 47.92 415.98 0.19 0.11 33 48.57 433.50 44.87 433.52 48.76 433.27 0.19 -0.23 34 50.31 465.54 44.87 467.97 50.61 465.81 0.30 0.27 35 51.29 481.62 44.87 484.86 51.63 481.50 0.34 -0.12 36 68.80 30.71 64.38 23.14 68.65 30.94 -0.14 0.23 37 68.10 46.97 64.38 40.03 67.94 46.51 -0.16 -0.46 38 66.89 78.55 64.38 74.48 66.65 78.89 -0.24 0.34 39 66.31 96.18 64.38 92.50 66.07 96.12 -0.24 -0.06 40 65.34 131.18 64.38 128.98 65.09 131.50 -0.25 0.32 41 64.91 150.31 64.38 147.91 64.69 150.09 -0.22 -0.22 42 64.31 187.63 64.38 185.87 64.10 187.75 -0.21 0.12 43 64.11 207.57 64.38 205.38 63.91 207.25 -0.19 -0.33 44 63.94 245.93 64.38 244.14 63.77 246.15 -0.18 0.22 45 63.98 266.23 64.38 263.86 63.81 265.98 -0.18 -0.24 46 64.29 304.69 64.38 302.62 64.11 304.93 -0.18 0.24 47 64.57 324.67 64.38 322.13 64.38 324.47 -0.19 -0.19 48 65.32 361.96 64.38 360.09 65.13 362.26 -0.20 0.30 49 65.82 381.12 64.38 379.02 65.61 380.93 -0.21 -0.19 50 66.93 416.41 64.38 415.50 66.73 416.52 -0.20 0.10 51 67.59 434.10 64.38 433.52 67.39 433.86 -0.20 -0.24 52 68.94 466.25 64.38 467.97 68.83 466.50 -0.11 0.25 53 69.70 482.37 64.38 484.86 69.62 482.22 -0.08 -0.15 54 104.22 29.79 103.14 23.14 104.32 30.00 0.09 0.22 55 103.97 46.10 103.14 40.03 104.07 45.59 0.10 -0.51 56 103.54 77.64 103.14 74.48 103.65 78.02 0.11 0.39 57 103.34 95.40 103.14 92.50 103.46 95.29 0.12 -0.11 58 103.01 130.46 103.14 128.98 103.16 130.78 0.15 0.32 59 102.87 149.64 103.14 147.91 103.04 149.43 0.17 -0.21 60 102.70 187.12 103.14 185.87 102.89 187.24 0.19 0.12 61 102.65 207.16 103.14 205.38 102.86 206.82 0.21 -0.34 62 102.65 245.71 103.14 244.14 102.87 245.91 0.22 0.20 63 102.70 266.09 103.14 263.86 102.93 265.84 0.22 -0.26 64 102.90 304.74 103.14 302.62 103.12 304.97 0.22 0.24 65 103.04 324.79 103.14 322.13 103.26 324.61 0.21 -0.18 66 103.41 362.28 103.14 360.09 103.61 362.57 0.20 0.29 67 103.64 381.49 103.14 379.02 103.83 381.33 0.18 -0.16 68 104.15 416.96 103.14 415.50 104.32 417.07 0.17 0.11 69 104.45 434.73 103.14 433.52 104.60 434.48 0.16 -0.25 70 105.05 466.99 103.14 467.97 105.21 467.23 0.16 0.24 71 105.38 483.13 103.14 484.86 105.54 482.99 0.16 -0.14 72 122.73 29.66 122.86 23.14 122.52 29.88 -0.22 0.22 73 122.73 45.97 122.86 40.03 122.52 45.46 -0.21 -0.51 74 122.74 77.48 122.86 74.48 122.53 77.88 -0.20 0.40 75 122.75 95.28 122.86 92.50 122.55 95.14 -0.20 -0.14 76 122.78 130.31 122.86 128.98 122.59 130.63 -0.19 0.32 77 122.81 149.49 122.86 147.91 122.62 149.29 -0.19 -0.20 78 122.88 186.98 122.86 185.87 122.69 187.11 -0.19 0.13 79 122.93 207.02 122.86 205.38 122.74 206.70 -0.19 -0.32 80 123.04 245.61 122.86 244.14 122.84 245.81 -0.19 0.20 81 123.10 266.00 122.86 263.86 122.90 265.74 -0.20 -0.26 82 123.25 304.67 122.86 302.62 123.04 304.91 -0.21 0.23 83 123.33 324.74 122.86 322.13 123.11 324.56 -0.22 -0.18 84 123.50 362.26 122.86 360.09 123.26 362.55 -0.24 0.29 85 123.60 381.47 122.86 379.02 123.35 381.32 -0.25 -0.15 86 123.80 416.96 122.86 415.50 123.52 417.08 -0.28 0.12 87 123.90 434.77 122.86 433.52 123.61 434.50 -0.29 -0.27 88 124.11 467.03 122.86 467.97 123.79 467.27 -0.31 0.24 89 124.22 483.17 122.86 484.86 123.89 483.05 -0.33 -0.13 90 158.42 30.07 161.62 23.14 158.49 30.32 0.07 0.25 91 158.88 46.33 161.62 40.03 158.95 45.85 0.08 -0.48 92 159.68 77.80 161.62 74.48 159.81 78.18 0.13 0.38 93 160.08 95.65 161.62 92.50 160.21 95.39 0.13 -0.26 94 160.77 130.47 161.62 128.98 160.91 130.78 0.14 0.31 95 161.08 149.59 161.62 147.91 161.21 149.39 0.13 -0.20 96 161.58 186.95 161.62 185.87 161.71 187.10 0.13 0.16 97 161.78 206.92 161.62 205.38 161.91 206.64 0.12 -0.28 98 162.05 245.43 161.62 244.14 162.17 245.65 0.12 0.22 99 162.12 265.80 161.62 263.86 162.24 265.54 0.13 -0.26 100 162.12 304.37 161.62 302.62 162.25 304.61 0.14 0.24 101 162.05 324.42 161.62 322.13 162.20 324.22 0.14 -0.20 102 161.81 361.87 161.62 360.09 161.96 362.13 0.16 0.27 103 161.62 380.99 161.62 379.02 161.79 380.87 0.16 -0.13 104 161.17 416.46 161.62 415.50 161.33 416.58 0.17 0.12 105 160.88 434.31 161.62 433.52 161.05 433.98 0.17 -0.33 106 160.28 466.45 161.62 467.97 160.41 466.71 0.13 0.26 107 159.94 482.57 161.62 484.86 160.05 482.47 0.11 -0.10 108 177.05 30.64 181.13 23.14 176.72 30.89 -0.33 0.25 109 177.72 46.85 181.13 40.03 177.40 46.39 -0.32 -0.46 110 178.89 78.28 181.13 74.48 178.66 78.63 -0.24 0.35 111 179.48 96.14 181.13 92.50 179.24 95.80 -0.25 -0.34 112 180.47 130.78 181.13 128.98 180.24 131.08 -0.23 0.30 113 180.92 149.84 181.13 147.91 180.68 149.63 -0.24 -0.21 114 181.62 187.06 181.13 185.87 181.37 187.23 -0.25 0.17 115 181.89 206.95 181.13 205.38 181.63 206.71 -0.26 -0.24 116 182.22 245.34 181.13 244.14 181.97 245.59 -0.25 0.25 117 182.29 265.68 181.13 263.86 182.04 265.42 -0.25 -0.26 118 182.21 304.13 181.13 302.62 181.99 304.37 -0.23 0.24 119 182.07 324.13 181.13 322.13 181.86 323.93 -0.21 -0.21 120 181.62 361.48 181.13 360.09 181.44 361.74 -0.19 0.26 121 181.30 380.53 181.13 379.02 181.13 380.43 -0.17 -0.10 122 180.53 415.92 181.13 415.50 180.37 416.05 -0.16 0.13 123 180.05 433.78 181.13 433.52 179.91 433.42 -0.14 -0.37 124 179.06 465.81 181.13 467.97 178.87 466.10 -0.19 0.29 125 178.50 481.90 181.13 484.86 178.28 481.84 -0.22 -0.06 126 211.84 32.35 219.09 23.14 212.49 32.71 0.65 0.36 127 212.95 48.41 219.09 40.03 213.56 48.10 0.61 -0.31 128 214.88 79.79 219.09 74.48 215.50 80.10 0.62 0.30 129 215.85 97.61 219.09 92.50 216.39 97.12 0.54 -0.49 130 217.44 131.78 219.09 128.98 217.92 132.10 0.48 0.32 131 218.17 150.68 219.09 147.91 218.58 150.48 0.41 -0.20 132 219.28 187.49 219.09 185.87 219.60 187.72 0.32 0.23 133 219.70 207.15 219.09 205.38 219.97 207.01 0.27 -0.14 134 220.18 245.21 219.09 244.14 220.40 245.52 0.22 0.31 135 220.26 265.41 219.09 263.86 220.47 265.16 0.21 -0.25 136 220.06 303.51 219.09 302.62 220.28 303.75 0.22 0.24 137 219.78 323.39 219.09 322.13 220.03 323.12 0.24 -0.26 138 218.95 360.41 219.09 360.09 219.23 360.61 0.29 0.21 139 218.36 379.26 219.09 379.02 218.69 379.15 0.33 -0.11 140 216.98 414.41 219.09 415.50 217.36 414.52 0.38 0.11 141 216.13 432.27 219.09 433.52 216.56 431.77 0.43 -0.50 142 214.39 463.98 219.09 467.97 214.79 464.26 0.39 0.28 143 213.40 479.98 219.09 484.86 213.79 479.93 0.39 -0.05 144 230.95 33.64 238.02 23.14 230.49 33.97 -0.47 0.32 145 232.13 49.59 238.02 40.03 231.72 49.29 -0.41 -0.30 146 234.20 80.92 238.02 74.48 233.95 81.12 -0.25 0.20 147 235.23 98.69 238.02 92.50 234.97 98.05 -0.26 -0.64 148 236.90 132.53 238.02 128.98 236.72 132.82 -0.18 0.29 149 237.67 151.31 238.02 147.91 237.47 151.09 -0.20 -0.22 150 238.81 187.84 238.02 185.87 238.62 188.09 -0.19 0.25 151 239.23 207.33 238.02 205.38 239.03 207.26 -0.20 -0.08 152 239.69 245.15 238.02 244.14 239.49 245.51 -0.20 0.36 153 239.74 265.26 238.02 263.86 239.54 265.02 -0.20 -0.24 154 239.45 303.10 238.02 302.62 239.27 303.36 -0.18 0.25 155 239.11 322.90 238.02 322.13 238.96 322.61 -0.16 -0.29 156 238.13 359.68 238.02 360.09 237.99 359.87 -0.14 0.19 157 237.45 378.39 238.02 379.02 237.33 378.31 -0.12 -0.08 158 235.87 413.37 238.02 415.50 235.73 413.49 -0.14 0.12 159 234.91 431.21 238.02 433.52 234.78 430.66 -0.13 -0.55 160 232.95 462.69 238.02 467.97 232.67 463.03 -0.29 0.34 161 231.84 478.62 238.02 484.86 231.49 478.64 -0.35 0.02 Figure 2.3-7 DISR 2 HRI Target Grid (sharpened) Figure 2.3-8 Location of Observed Vertices for DISR 2 HRI Figure 2.3-9 Location of Desired Vertices for DISR 2 HRI Table 2.3-4 Vertex Information for DISR#2 HRI Distortion Fit C = Column R=Row Point Observed C Observed R Desired Desired Computed C Computed R C R ID C R Residual Residual 0 15.53 37.52 15.01 40.67 15.60 37.55 0.07 0.03 1 15.28 59.45 15.01 61.97 15.35 59.37 0.07 -0.08 2 14.80 102.32 15.01 104.13 14.87 102.39 0.07 0.07 3 14.56 124.14 15.01 125.58 14.62 124.19 0.07 0.06 4 14.08 167.35 15.01 167.98 14.15 167.17 0.06 -0.17 5 13.85 188.85 15.01 189.53 13.91 188.96 0.06 0.12 6 13.38 231.76 15.01 232.09 13.44 231.92 0.06 0.16 7 13.14 254.10 15.01 253.70 13.20 253.70 0.06 -0.40 8 12.69 296.51 15.01 296.31 12.74 296.63 0.06 0.13 9 12.46 318.31 15.01 317.91 12.51 318.40 0.05 0.09 10 12.01 361.16 15.01 360.47 12.06 361.32 0.05 0.17 11 11.78 383.24 15.01 382.02 11.84 383.08 0.06 -0.16 12 11.34 425.81 15.01 424.42 11.39 425.99 0.05 0.18 13 11.12 448.07 15.01 445.87 11.17 447.75 0.06 -0.32 14 10.69 490.54 15.01 488.03 10.74 490.65 0.05 0.11 15 37.70 37.75 36.52 40.67 37.52 37.83 -0.18 0.08 16 37.42 59.75 36.52 61.97 37.26 59.62 -0.16 -0.12 17 36.89 102.52 36.52 104.13 36.74 102.61 -0.15 0.09 18 36.63 124.45 36.52 125.58 36.49 124.40 -0.14 -0.05 19 36.12 167.47 36.52 167.98 35.99 167.38 -0.12 -0.09 20 35.87 189.11 36.52 189.53 35.75 189.18 -0.12 0.07 21 35.38 231.97 36.52 232.09 35.27 232.15 -0.11 0.17 22 35.13 254.27 36.52 253.70 35.03 253.93 -0.10 -0.33 23 34.67 296.73 36.52 296.31 34.57 296.89 -0.10 0.16 24 34.44 318.63 36.52 317.91 34.34 318.66 -0.10 0.04 25 33.99 361.43 36.52 360.47 33.89 361.60 -0.10 0.17 26 33.77 383.59 36.52 382.02 33.67 383.36 -0.10 -0.23 27 33.35 426.09 36.52 424.42 33.24 426.27 -0.11 0.19 28 33.13 448.30 36.52 445.87 33.02 448.02 -0.11 -0.28 29 32.73 490.79 36.52 488.03 32.61 490.90 -0.12 0.11 30 80.39 38.20 79.02 40.67 80.60 38.36 0.21 0.16 31 80.14 60.30 79.02 61.97 80.33 60.11 0.19 -0.18 32 79.65 102.93 79.02 104.13 79.81 103.05 0.15 0.12 33 79.40 125.03 79.02 125.58 79.55 124.84 0.14 -0.19 34 78.93 167.76 79.02 167.98 79.04 167.81 0.12 0.05 35 78.68 189.63 79.02 189.53 78.79 189.61 0.11 -0.02 36 78.21 232.40 79.02 232.09 78.30 232.60 0.09 0.20 37 77.97 254.62 79.02 253.70 78.06 254.40 0.09 -0.23 38 77.51 297.17 79.02 296.31 77.60 297.38 0.09 0.21 39 77.27 319.21 79.02 317.91 77.37 319.17 0.10 -0.04 40 76.82 361.94 79.02 360.47 76.93 362.12 0.11 0.19 41 76.59 384.23 79.02 382.02 76.71 383.89 0.12 -0.34 42 76.14 426.59 79.02 424.42 76.28 426.79 0.14 0.20 43 75.92 448.76 79.02 445.87 76.08 448.53 0.16 -0.23 44 75.48 491.26 79.02 488.03 75.67 491.36 0.19 0.10 45 102.52 38.44 100.60 40.67 102.40 38.62 -0.13 0.18 46 102.25 60.57 100.60 61.97 102.13 60.37 -0.12 -0.21 47 101.72 103.16 100.60 104.13 101.61 103.28 -0.11 0.13 48 101.46 125.32 100.60 125.58 101.35 125.06 -0.11 -0.25 49 100.96 167.93 100.60 167.98 100.85 168.04 -0.11 0.11 50 100.71 189.90 100.60 189.53 100.60 189.83 -0.11 -0.06 51 100.23 232.62 100.60 232.09 100.12 232.83 -0.11 0.21 52 99.99 254.82 100.60 253.70 99.88 254.63 -0.11 -0.18 53 99.53 297.40 100.60 296.31 99.42 297.62 -0.12 0.22 54 99.30 319.49 100.60 317.91 99.19 319.42 -0.12 -0.08 55 98.87 362.19 100.60 360.47 98.74 362.38 -0.13 0.19 56 98.65 384.52 100.60 382.02 98.52 384.15 -0.13 -0.38 57 98.25 426.84 100.60 424.42 98.10 427.05 -0.15 0.21 58 98.04 449.00 100.60 445.87 97.89 448.78 -0.15 -0.22 59 97.65 491.50 100.60 488.03 97.48 491.59 -0.17 0.10 60 145.11 38.93 143.20 40.67 145.31 39.14 0.20 0.21 61 144.85 61.10 143.20 61.97 145.06 60.87 0.21 -0.23 62 144.36 103.61 143.20 104.13 144.57 103.76 0.21 0.15 63 144.11 125.85 143.20 125.58 144.33 125.53 0.22 -0.32 64 143.63 168.31 143.20 167.98 143.85 168.50 0.21 0.19 65 143.39 190.43 143.20 189.53 143.60 190.29 0.22 -0.14 66 142.92 233.06 143.20 232.09 143.14 233.29 0.22 0.23 67 142.68 255.22 143.20 253.70 142.90 255.10 0.22 -0.12 68 142.23 297.85 143.20 296.31 142.44 298.10 0.21 0.25 69 142.00 320.02 143.20 317.91 142.21 319.89 0.21 -0.12 70 141.56 362.65 143.20 360.47 141.76 362.86 0.21 0.21 71 141.33 385.04 143.20 382.02 141.54 384.63 0.21 -0.41 72 140.91 427.30 143.20 424.42 141.10 427.52 0.20 0.22 73 140.69 449.45 143.20 445.87 140.88 449.24 0.20 -0.21 74 140.28 491.93 143.20 488.03 140.46 492.03 0.18 0.10 75 167.31 39.19 164.80 40.67 167.06 39.40 -0.25 0.21 76 167.05 61.36 164.80 61.97 166.82 61.12 -0.23 -0.24 77 166.56 103.86 164.80 104.13 166.35 104.01 -0.21 0.15 78 166.31 126.11 164.80 125.58 166.11 125.78 -0.20 -0.34 79 165.83 168.53 164.80 167.98 165.64 168.74 -0.18 0.21 80 165.58 190.71 164.80 189.53 165.41 190.53 -0.17 -0.18 81 165.11 233.29 164.80 232.09 164.94 233.53 -0.17 0.24 82 164.87 255.45 164.80 253.70 164.71 255.34 -0.16 -0.11 83 164.42 298.09 164.80 296.31 164.25 298.33 -0.16 0.25 84 164.18 320.27 164.80 317.91 164.02 320.13 -0.16 -0.14 85 163.74 362.88 164.80 360.47 163.57 363.09 -0.17 0.21 86 163.51 385.28 164.80 382.02 163.35 384.86 -0.16 -0.42 87 163.08 427.52 164.80 424.42 162.90 427.75 -0.18 0.23 88 162.86 449.69 164.80 445.87 162.68 449.47 -0.18 -0.22 89 162.45 492.15 164.80 488.03 162.24 492.25 -0.21 0.10 90 209.83 39.71 207.40 40.67 209.97 39.91 0.14 0.20 91 209.62 61.85 207.40 61.97 209.75 61.63 0.13 -0.22 92 209.19 104.36 207.40 104.13 209.30 104.52 0.11 0.16 93 208.97 126.60 207.40 125.58 209.08 126.28 0.11 -0.32 94 208.53 169.00 207.40 167.98 208.63 169.23 0.10 0.23 95 208.30 191.26 207.40 189.53 208.40 191.02 0.10 -0.24 96 207.86 233.74 207.40 232.09 207.95 234.01 0.09 0.26 97 207.62 255.90 207.40 253.70 207.72 255.81 0.10 -0.10 98 207.16 298.55 207.40 296.31 207.26 298.79 0.10 0.24 99 206.92 320.74 207.40 317.91 207.03 320.58 0.11 -0.16 100 206.45 363.30 207.40 360.47 206.58 363.53 0.13 0.22 101 206.20 385.67 207.40 382.02 206.34 385.29 0.14 -0.39 102 205.72 427.93 207.40 424.42 205.88 428.17 0.16 0.24 103 205.47 450.14 207.40 445.87 205.65 449.89 0.18 -0.26 104 204.98 492.55 207.40 488.03 205.19 492.66 0.21 0.12 105 232.00 40.00 228.98 40.67 231.76 40.17 -0.23 0.17 106 231.76 62.10 228.98 61.97 231.54 61.90 -0.22 -0.20 107 231.31 104.62 228.98 104.13 231.10 104.78 -0.21 0.16 108 231.08 126.84 228.98 125.58 230.88 126.55 -0.20 -0.29 109 230.63 169.27 228.98 167.98 230.43 169.49 -0.19 0.22 110 230.39 191.55 228.98 189.53 230.21 191.28 -0.18 -0.27 111 229.94 233.98 228.98 232.09 229.76 234.25 -0.18 0.27 112 229.71 256.15 228.98 253.70 229.53 256.04 -0.18 -0.10 113 229.26 298.79 228.98 296.31 229.07 299.01 -0.19 0.23 114 229.02 320.97 228.98 317.91 228.84 320.80 -0.18 -0.17 115 228.57 363.51 228.98 360.47 228.38 363.74 -0.19 0.23 116 228.33 385.85 228.98 382.02 228.14 385.49 -0.19 -0.36 117 227.89 428.13 228.98 424.42 227.68 428.37 -0.21 0.24 118 227.65 450.38 228.98 445.87 227.44 450.09 -0.21 -0.30 119 227.20 492.75 228.98 488.03 226.97 492.87 -0.23 0.12 120 274.53 40.56 271.48 40.67 274.84 40.67 0.31 0.12 121 274.32 62.56 271.48 61.97 274.61 62.42 0.29 -0.14 122 273.90 105.16 271.48 104.13 274.15 105.32 0.25 0.16 123 273.68 127.27 271.48 125.58 273.92 127.09 0.24 -0.18 124 273.25 169.84 271.48 167.98 273.46 170.02 0.21 0.18 125 273.03 192.11 271.48 189.53 273.23 191.80 0.20 -0.32 126 272.59 234.44 271.48 232.09 272.77 234.74 0.17 0.30 127 272.36 256.65 271.48 253.70 272.53 256.52 0.17 -0.14 128 271.91 299.26 271.48 296.31 272.07 299.45 0.15 0.19 129 271.68 321.37 271.48 317.91 271.83 321.22 0.15 -0.15 130 271.22 363.88 271.48 360.47 271.36 364.13 0.14 0.24 131 270.97 386.13 271.48 382.02 271.12 385.88 0.15 -0.26 132 270.51 428.49 271.48 424.42 270.66 428.74 0.15 0.25 133 270.26 450.84 271.48 445.87 270.42 450.46 0.16 -0.38 134 269.78 493.11 271.48 488.03 269.95 493.26 0.17 0.15 135 296.93 40.86 292.99 40.67 296.76 40.93 -0.17 0.06 136 296.67 62.80 292.99 61.97 296.51 62.69 -0.15 -0.11 137 296.16 105.45 292.99 104.13 296.03 105.60 -0.13 0.15 138 295.90 127.49 292.99 125.58 295.78 127.37 -0.12 -0.12 139 295.40 170.16 292.99 167.98 295.30 170.30 -0.10 0.14 140 295.15 192.41 292.99 189.53 295.05 192.07 -0.09 -0.35 141 294.66 234.69 292.99 232.09 294.58 234.99 -0.09 0.30 142 294.41 256.93 292.99 253.70 294.34 256.76 -0.07 -0.17 143 293.93 299.51 292.99 296.31 293.86 299.67 -0.07 0.16 144 293.69 321.57 292.99 317.91 293.62 321.43 -0.06 -0.14 145 293.22 364.07 292.99 360.47 293.15 364.32 -0.07 0.25 146 292.98 386.25 292.99 382.02 292.92 386.06 -0.06 -0.19 147 292.52 428.66 292.99 424.42 292.45 428.92 -0.07 0.25 148 292.29 451.08 292.99 445.87 292.22 450.64 -0.07 -0.44 149 291.84 493.29 292.99 488.03 291.76 493.45 -0.08 0.16 Figure 2.3-10 DISR 3 MRI Target Grid (sharpened) Figure 2.3-11 Location of Observed Vertices for DISR 3 MRI Figure 2.3-12 Location of Desired Vertices for DISR 3 MRI Table 2.3-5 Vertex Information for DISR#3 MRI Distortion Fit C = Column R=Row Point Observed C Observed R Desired Desired Computed C Computed R C R ID C R Residual Residual 0 10.20 10.35 12.50 10.16 10.40 10.43 0.19 0.09 1 9.77 29.64 12.50 29.28 9.92 29.42 0.16 -0.21 2 9.06 66.72 12.50 66.70 9.14 66.79 0.08 0.08 3 8.75 86.38 12.50 86.32 8.81 86.47 0.06 0.09 4 8.31 125.02 12.50 124.60 8.32 125.02 0.02 0.00 5 8.15 145.35 12.50 144.59 8.15 145.22 0.00 -0.13 6 8.00 184.42 12.50 183.45 7.98 184.58 -0.02 0.16 7 8.00 205.08 12.50 203.68 7.97 205.10 -0.02 0.02 8 8.15 244.90 12.50 242.85 8.12 244.88 -0.03 -0.02 9 8.32 265.82 12.50 263.15 8.29 265.51 -0.03 -0.31 10 8.78 305.00 12.50 302.32 8.76 305.28 -0.02 0.28 11 9.11 325.94 12.50 322.55 9.09 325.80 -0.02 -0.14 12 9.88 365.05 12.50 361.41 9.89 365.14 0.01 0.09 13 10.36 385.32 12.50 381.41 10.38 385.32 0.02 0.01 14 11.41 423.75 12.50 419.68 11.47 423.83 0.06 0.09 15 12.03 443.61 12.50 439.30 12.11 443.50 0.08 -0.12 16 13.33 480.89 12.50 476.73 13.48 480.82 0.15 -0.07 17 14.05 499.71 12.50 495.84 14.25 499.78 0.20 0.07 18 30.64 9.46 32.33 10.16 30.30 9.60 -0.34 0.15 19 30.15 28.84 32.33 29.28 29.86 28.62 -0.29 -0.21 20 29.37 65.97 32.33 66.70 29.15 66.06 -0.22 0.09 21 29.04 85.74 32.33 86.32 28.86 85.78 -0.18 0.04 22 28.54 124.40 32.33 124.60 28.43 124.41 -0.11 0.01 23 28.36 144.78 32.33 144.59 28.28 144.66 -0.08 -0.11 24 28.18 183.96 32.33 183.45 28.15 184.13 -0.03 0.17 25 28.18 204.70 32.33 203.68 28.16 204.71 -0.01 0.01 26 28.33 244.62 32.33 242.85 28.34 244.60 0.01 -0.02 27 28.51 265.55 32.33 263.15 28.51 265.29 0.01 -0.26 28 29.00 304.92 32.33 302.32 29.00 305.18 0.00 0.26 29 29.36 325.87 32.33 322.55 29.34 325.76 -0.02 -0.11 30 30.18 365.14 32.33 361.41 30.13 365.22 -0.06 0.08 31 30.70 385.49 32.33 381.41 30.61 385.46 -0.09 -0.03 32 31.83 423.98 32.33 419.68 31.69 424.08 -0.15 0.10 33 32.50 443.92 32.33 439.30 32.31 443.79 -0.19 -0.14 34 33.90 481.23 32.33 476.73 33.65 481.20 -0.26 -0.03 35 34.69 500.16 32.33 495.84 34.40 500.20 -0.29 0.04 36 68.76 8.08 70.93 10.16 68.93 8.26 0.17 0.18 37 68.46 27.58 70.93 29.28 68.62 27.32 0.17 -0.26 38 68.00 64.77 70.93 66.70 68.14 64.85 0.15 0.08 39 67.81 84.68 70.93 86.32 67.95 84.63 0.14 -0.06 40 67.57 123.37 70.93 124.60 67.70 123.39 0.14 0.02 41 67.50 143.81 70.93 144.59 67.64 143.72 0.14 -0.09 42 67.50 183.15 70.93 183.45 67.63 183.34 0.13 0.19 43 67.57 204.02 70.93 203.68 67.69 204.00 0.13 -0.02 44 67.82 244.09 70.93 242.85 67.94 244.07 0.12 -0.01 45 68.02 265.04 70.93 263.15 68.13 264.86 0.11 -0.18 46 68.53 304.71 70.93 302.32 68.62 304.93 0.10 0.21 47 68.86 325.67 70.93 322.55 68.94 325.60 0.08 -0.07 48 69.62 365.17 70.93 361.41 69.68 365.23 0.07 0.06 49 70.07 385.65 70.93 381.41 70.12 385.56 0.05 -0.10 50 71.05 424.21 70.93 419.68 71.09 424.33 0.04 0.12 51 71.62 444.29 70.93 439.30 71.64 444.12 0.02 -0.17 52 72.80 481.63 70.93 476.73 72.82 481.67 0.02 0.05 53 73.46 500.72 70.93 495.84 73.47 500.74 0.02 0.01 54 88.96 7.49 91.06 10.16 89.02 7.70 0.06 0.21 55 88.76 27.04 91.06 29.28 88.81 26.77 0.04 -0.27 56 88.48 64.25 91.06 66.70 88.48 64.33 0.00 0.08 57 88.38 84.22 91.06 86.32 88.37 84.13 -0.01 -0.09 58 88.27 122.91 91.06 124.60 88.24 122.94 -0.03 0.03 59 88.26 143.37 91.06 144.59 88.22 143.29 -0.04 -0.08 60 88.34 182.77 91.06 183.45 88.30 182.97 -0.04 0.20 61 88.43 203.70 91.06 203.68 88.39 203.67 -0.04 -0.03 62 88.71 243.82 91.06 242.85 88.67 243.80 -0.04 -0.01 63 88.91 264.77 91.06 263.15 88.87 264.62 -0.04 -0.15 64 89.38 304.56 91.06 302.32 89.36 304.76 -0.02 0.19 65 89.68 325.52 91.06 322.55 89.67 325.46 -0.01 -0.06 66 90.35 365.11 91.06 361.41 90.36 365.16 0.01 0.05 67 90.74 385.65 91.06 381.41 90.77 385.52 0.03 -0.12 68 91.58 424.23 91.06 419.68 91.65 424.36 0.07 0.13 69 92.06 444.36 91.06 439.30 92.15 444.18 0.09 -0.18 70 93.05 481.70 91.06 476.73 93.20 481.78 0.15 0.08 71 93.60 500.87 91.06 495.84 93.78 500.87 0.18 0.00 72 127.89 6.66 130.11 10.16 127.92 6.90 0.03 0.24 73 127.88 26.26 130.11 29.28 127.91 25.97 0.03 -0.29 74 127.90 63.48 130.11 66.70 127.94 63.56 0.05 0.08 75 127.94 83.51 130.11 86.32 127.99 83.37 0.05 -0.14 76 128.06 122.17 130.11 124.60 128.13 122.23 0.07 0.06 77 128.16 142.67 130.11 144.59 128.23 142.61 0.07 -0.06 78 128.40 182.13 130.11 183.45 128.49 182.35 0.09 0.22 79 128.56 203.14 130.11 203.68 128.65 203.09 0.09 -0.05 80 128.92 243.31 130.11 242.85 129.01 243.29 0.09 -0.02 81 129.14 264.26 130.11 263.15 129.23 264.15 0.09 -0.11 82 129.61 304.21 130.11 302.32 129.70 304.37 0.09 0.16 83 129.89 325.15 130.11 322.55 129.97 325.11 0.09 -0.03 84 130.47 364.86 130.11 361.41 130.55 364.89 0.08 0.03 85 130.80 385.45 130.11 381.41 130.87 385.29 0.07 -0.16 86 131.48 424.05 130.11 419.68 131.54 424.20 0.06 0.15 87 131.86 444.25 130.11 439.30 131.91 444.05 0.05 -0.20 88 132.62 481.58 130.11 476.73 132.66 481.71 0.04 0.13 89 133.04 500.86 130.11 495.84 133.07 500.83 0.03 -0.03 90 148.19 6.37 150.40 10.16 148.09 6.62 -0.10 0.25 91 148.30 25.98 150.40 29.28 148.20 25.69 -0.10 -0.29 92 148.54 63.19 150.40 66.70 148.43 63.27 -0.10 0.08 93 148.68 83.24 150.40 86.32 148.57 83.09 -0.11 -0.15 94 148.97 121.87 150.40 124.60 148.87 121.94 -0.11 0.07 95 149.14 142.37 150.40 144.59 149.03 142.33 -0.11 -0.05 96 149.49 181.85 150.40 183.45 149.39 182.08 -0.11 0.23 97 149.69 202.88 150.40 203.68 149.58 202.81 -0.11 -0.06 98 150.11 243.05 150.40 242.85 149.99 243.03 -0.11 -0.02 99 150.33 263.99 150.40 263.15 150.22 263.90 -0.11 -0.10 100 150.80 303.98 150.40 302.32 150.68 304.13 -0.12 0.15 101 151.05 324.91 150.40 322.55 150.93 324.88 -0.12 -0.02 102 151.57 364.64 150.40 361.41 151.44 364.67 -0.13 0.03 103 151.85 385.26 150.40 381.41 151.71 385.08 -0.13 -0.17 104 152.40 423.84 150.40 419.68 152.26 424.01 -0.14 0.17 105 152.70 444.07 150.40 439.30 152.55 443.86 -0.15 -0.20 106 153.28 481.38 150.40 476.73 153.13 481.54 -0.15 0.15 107 153.59 500.70 150.40 495.84 153.44 500.66 -0.15 -0.04 108 187.12 6.11 189.60 10.16 187.04 6.36 -0.08 0.25 109 187.44 25.71 189.60 29.28 187.37 25.41 -0.07 -0.30 110 188.03 62.88 189.60 66.70 188.01 62.94 -0.02 0.07 111 188.34 82.91 189.60 86.32 188.33 82.74 -0.01 -0.17 112 188.90 121.45 189.60 124.60 188.92 121.55 0.02 0.10 113 189.19 141.95 189.60 144.59 189.22 141.92 0.03 -0.03 114 189.71 181.40 189.60 183.45 189.77 181.63 0.05 0.24 115 189.98 202.44 189.60 203.68 190.04 202.36 0.06 -0.09 116 190.46 242.57 189.60 242.85 190.53 242.54 0.07 -0.03 117 190.70 263.49 189.60 263.15 190.77 263.40 0.07 -0.10 118 191.13 303.48 189.60 302.32 191.21 303.60 0.08 0.13 119 191.33 324.36 189.60 322.55 191.42 324.34 0.08 -0.02 120 191.70 364.09 189.60 361.41 191.79 364.11 0.08 0.03 121 191.88 384.70 189.60 381.41 191.96 384.51 0.08 -0.18 122 192.19 423.24 189.60 419.68 192.26 423.42 0.07 0.18 123 192.34 443.47 189.60 439.30 192.40 443.27 0.06 -0.20 124 192.59 480.74 189.60 476.73 192.64 480.93 0.05 0.18 125 192.71 500.12 189.60 495.84 192.74 500.04 0.04 -0.08 126 207.08 6.12 209.89 10.16 207.18 6.37 0.10 0.25 127 207.58 25.70 209.89 29.28 207.63 25.40 0.05 -0.30 128 208.48 62.83 209.89 66.70 208.46 62.89 -0.02 0.06 129 208.93 82.83 209.89 86.32 208.87 82.67 -0.06 -0.16 130 209.73 121.32 209.89 124.60 209.62 121.44 -0.11 0.12 131 210.12 141.81 209.89 144.59 209.98 141.78 -0.14 -0.03 132 210.81 181.21 209.89 183.45 210.63 181.45 -0.18 0.24 133 211.14 202.25 209.89 203.68 210.94 202.15 -0.20 -0.10 134 211.69 242.33 209.89 242.85 211.47 242.30 -0.22 -0.03 135 211.95 263.23 209.89 263.15 211.72 263.13 -0.22 -0.10 136 212.36 303.17 209.89 302.32 212.14 303.30 -0.21 0.13 137 212.54 324.03 209.89 322.55 212.33 324.02 -0.21 -0.01 138 212.81 363.71 209.89 361.41 212.63 363.75 -0.18 0.04 139 212.91 384.31 209.89 381.41 212.76 384.13 -0.16 -0.17 140 213.04 422.81 209.89 419.68 212.94 423.01 -0.11 0.20 141 213.08 443.04 209.89 439.30 213.00 442.84 -0.08 -0.20 142 213.08 480.28 209.89 476.73 213.06 480.47 -0.02 0.19 143 213.05 499.67 209.89 495.84 213.06 499.57 0.02 -0.10 144 245.97 6.44 248.94 10.16 245.95 6.67 -0.02 0.23 145 246.61 25.94 248.94 29.28 246.60 25.64 -0.01 -0.30 146 247.74 62.96 248.94 66.70 247.79 63.02 0.04 0.05 147 248.30 82.87 248.94 86.32 248.36 82.73 0.05 -0.14 148 249.28 121.22 248.94 124.60 249.37 121.38 0.09 0.16 149 249.75 141.68 248.94 144.59 249.84 141.65 0.09 -0.02 150 250.55 180.96 248.94 183.45 250.67 181.20 0.11 0.24 151 250.93 201.95 248.94 203.68 251.04 201.83 0.11 -0.12 152 251.53 241.89 248.94 242.85 251.65 241.84 0.12 -0.04 153 251.80 262.75 248.94 263.15 251.92 262.61 0.12 -0.14 154 252.19 302.53 248.94 302.32 252.32 302.65 0.13 0.12 155 252.34 323.33 248.94 322.55 252.47 323.30 0.13 -0.03 156 252.53 362.87 248.94 361.41 252.65 362.91 0.13 0.04 157 252.57 383.40 248.94 381.41 252.69 383.24 0.12 -0.16 158 252.55 421.79 248.94 419.68 252.66 422.00 0.11 0.21 159 252.49 441.97 248.94 439.30 252.59 441.78 0.10 -0.19 160 252.28 479.12 248.94 476.73 252.35 479.32 0.07 0.20 161 252.13 498.51 248.94 495.84 252.18 498.38 0.05 -0.13 162 265.83 6.74 269.07 10.16 265.95 6.96 0.12 0.22 163 266.60 26.18 269.07 29.28 266.69 25.89 0.09 -0.29 164 267.94 63.15 269.07 66.70 268.02 63.19 0.08 0.04 165 268.60 82.98 269.07 86.32 268.66 82.87 0.07 -0.11 166 269.74 121.25 269.07 124.60 269.79 121.43 0.05 0.18 167 270.29 141.68 269.07 144.59 270.32 141.66 0.03 -0.02 168 271.21 180.88 269.07 183.45 271.22 181.11 0.01 0.23 169 271.63 201.83 269.07 203.68 271.62 201.70 -0.01 -0.14 170 272.29 241.67 269.07 242.85 272.27 241.62 -0.02 -0.05 171 272.57 262.50 269.07 263.15 272.54 262.33 -0.03 -0.17 172 272.97 302.16 269.07 302.32 272.93 302.28 -0.03 0.12 173 273.10 322.92 269.07 322.55 273.07 322.89 -0.03 -0.03 174 273.23 362.36 269.07 361.41 273.20 362.41 -0.03 0.06 175 273.23 382.83 269.07 381.41 273.21 382.69 -0.03 -0.14 176 273.11 421.15 269.07 419.68 273.08 421.38 -0.02 0.23 177 272.98 441.29 269.07 439.30 272.96 441.12 -0.02 -0.17 178 272.62 478.39 269.07 476.73 272.59 478.59 -0.02 0.20 179 272.37 497.76 269.07 495.84 272.34 497.61 -0.02 -0.14 180 304.55 7.62 307.67 10.16 304.33 7.78 -0.22 0.16 181 305.37 26.92 307.67 29.28 305.19 26.63 -0.18 -0.29 182 306.81 63.73 307.67 66.70 306.75 63.76 -0.06 0.03 183 307.51 83.37 307.67 86.32 307.49 83.33 -0.02 -0.05 184 308.73 121.46 307.67 124.60 308.78 121.69 0.05 0.23 185 309.31 141.83 307.67 144.59 309.38 141.81 0.08 -0.02 186 310.27 180.81 307.67 183.45 310.40 181.04 0.12 0.23 187 310.72 201.67 307.67 203.68 310.84 201.51 0.13 -0.16 188 311.41 241.27 307.67 242.85 311.55 241.20 0.15 -0.07 189 311.69 262.04 307.67 263.15 311.84 261.79 0.15 -0.25 190 312.08 301.39 307.67 302.32 312.23 301.51 0.15 0.12 191 312.21 322.07 307.67 322.55 312.35 322.01 0.14 -0.06 192 312.31 361.24 307.67 361.41 312.43 361.32 0.11 0.07 193 312.29 381.59 307.67 381.41 312.38 381.49 0.09 -0.10 194 312.11 419.73 307.67 419.68 312.15 419.98 0.03 0.25 195 311.95 439.77 307.67 439.30 311.95 439.63 0.00 -0.14 196 311.52 476.74 307.67 476.73 311.41 476.93 -0.10 0.19 197 311.22 496.04 307.67 495.84 311.07 495.87 -0.15 -0.17 198 323.95 8.20 327.50 10.16 324.07 8.34 0.12 0.14 199 324.90 27.41 327.50 29.28 324.97 27.14 0.07 -0.27 200 326.56 64.13 327.50 66.70 326.59 64.16 0.03 0.02 201 327.36 83.67 327.50 86.32 327.36 83.67 0.00 0.00 202 328.75 121.65 327.50 124.60 328.70 121.90 -0.04 0.25 203 329.40 141.97 327.50 144.59 329.33 141.96 -0.08 -0.01 204 330.48 180.83 327.50 183.45 330.38 181.05 -0.11 0.22 205 330.97 201.61 327.50 203.68 330.84 201.44 -0.13 -0.17 206 331.71 241.07 327.50 242.85 331.57 240.99 -0.14 -0.07 207 332.01 261.81 327.50 263.15 331.87 261.51 -0.14 -0.29 208 332.39 300.96 327.50 302.32 332.27 301.09 -0.13 0.13 209 332.50 321.59 327.50 322.55 332.39 321.51 -0.12 -0.07 210 332.53 360.59 327.50 361.41 332.45 360.68 -0.08 0.09 211 332.46 380.85 327.50 381.41 332.40 380.79 -0.06 -0.06 212 332.16 418.90 327.50 419.68 332.14 419.15 -0.02 0.26 213 331.91 438.87 327.50 439.30 331.92 438.74 0.02 -0.12 214 331.30 475.77 327.50 476.73 331.36 475.94 0.06 0.17 215 330.89 495.03 327.50 495.84 330.98 494.84 0.09 -0.19 Figure 2.3-13 DISR 3 SLI Target Grid (sharpened) Figure 2.3-14 Location of Observed Vertices for DISR 3 SLI Figure 2.3-15 Location of Desired Vertices for DISR 3 SLI Table 2.3-6 Vertex Information for DISR 3 SLI Distortion Fit C = Column R=Row Point Observed C Observed R Desired Desired Computed C Computed R C R ID C R Residual Residual 0 12.70 30.40 8.91 23.14 12.70 30.46 0.00 0.06 1 11.46 46.48 8.91 40.03 11.43 46.17 -0.03 -0.30 2 9.31 78.29 8.91 74.48 9.17 78.73 -0.13 0.44 3 8.26 96.31 8.91 92.50 8.17 96.00 -0.09 -0.31 4 6.61 130.98 8.91 128.98 6.52 131.37 -0.09 0.39 5 5.90 150.11 8.91 147.91 5.86 149.90 -0.04 -0.20 6 4.94 186.96 8.91 185.87 4.94 187.37 0.00 0.41 7 4.65 207.06 8.91 205.38 4.68 206.73 0.03 -0.33 8 4.53 245.17 8.91 244.14 4.58 245.31 0.05 0.14 9 4.71 265.40 8.91 263.86 4.74 264.95 0.04 -0.45 10 5.47 303.35 8.91 302.62 5.49 303.48 0.02 0.14 11 6.10 323.15 8.91 322.13 6.07 322.80 -0.03 -0.35 12 7.68 359.96 8.91 360.09 7.61 360.15 -0.06 0.20 13 8.67 378.40 8.91 379.02 8.58 378.61 -0.10 0.20 14 10.93 413.56 8.91 415.50 10.81 413.79 -0.12 0.23 15 12.25 431.16 8.91 433.52 12.09 430.95 -0.15 -0.21 16 14.94 463.12 8.91 467.97 14.87 463.26 -0.07 0.15 17 16.43 479.04 8.91 484.86 16.40 478.84 -0.03 -0.19 18 47.85 27.88 46.87 23.14 48.23 27.99 0.38 0.10 19 47.06 44.22 46.87 40.03 47.40 43.78 0.34 -0.44 20 45.72 76.13 46.87 74.48 45.95 76.55 0.23 0.42 21 45.08 94.20 46.87 92.50 45.32 93.95 0.24 -0.25 22 44.09 129.16 46.87 128.98 44.30 129.63 0.21 0.47 23 43.68 148.58 46.87 147.91 43.91 148.34 0.23 -0.25 24 43.17 185.98 46.87 185.87 43.42 186.18 0.24 0.21 25 43.05 206.20 46.87 205.38 43.31 205.75 0.26 -0.45 26 43.13 244.53 46.87 244.14 43.39 244.75 0.26 0.22 27 43.33 264.91 46.87 263.86 43.58 264.61 0.25 -0.30 28 44.00 303.39 46.87 302.62 44.25 303.58 0.25 0.20 29 44.51 323.45 46.87 322.13 44.73 323.12 0.22 -0.33 30 45.74 360.54 46.87 360.09 45.95 360.87 0.22 0.33 31 46.51 379.60 46.87 379.02 46.70 379.52 0.19 -0.08 32 48.18 414.78 46.87 415.50 48.39 415.05 0.21 0.27 33 49.16 432.61 46.87 433.52 49.35 432.36 0.20 -0.25 34 51.12 464.67 46.87 467.97 51.42 464.94 0.30 0.27 35 52.21 480.83 46.87 484.86 52.54 480.62 0.33 -0.21 36 66.88 26.93 66.38 23.14 66.55 27.10 -0.33 0.17 37 66.32 43.37 66.38 40.03 65.96 42.92 -0.36 -0.45 38 65.38 75.32 66.38 74.48 64.94 75.76 -0.43 0.44 39 64.93 93.39 66.38 92.50 64.51 93.20 -0.42 -0.19 40 64.26 128.46 66.38 128.98 63.84 128.98 -0.43 0.52 41 64.00 147.98 66.38 147.91 63.59 147.75 -0.40 -0.24 42 63.70 185.57 66.38 185.87 63.33 185.72 -0.38 0.15 43 63.66 205.85 66.38 205.38 63.30 205.36 -0.36 -0.48 44 63.81 244.25 66.38 244.14 63.48 244.51 -0.33 0.27 45 64.02 264.68 66.38 263.86 63.69 264.45 -0.33 -0.23 46 64.63 303.35 66.38 302.62 64.32 303.57 -0.31 0.22 47 65.07 323.51 66.38 322.13 64.75 323.19 -0.32 -0.33 48 66.09 360.71 66.38 360.09 65.81 361.09 -0.29 0.37 49 66.74 380.01 66.38 379.02 66.44 379.80 -0.30 -0.20 50 68.10 415.19 66.38 415.50 67.85 415.46 -0.25 0.26 51 68.89 433.11 66.38 433.52 68.64 432.83 -0.25 -0.28 52 70.47 465.21 66.38 467.97 70.33 465.50 -0.13 0.29 53 71.34 481.47 66.38 484.86 71.24 481.23 -0.10 -0.23 54 102.72 25.93 105.14 23.14 103.07 26.13 0.35 0.20 55 102.62 42.48 105.14 40.03 102.96 41.97 0.34 -0.52 56 102.50 74.46 105.14 74.48 102.83 74.85 0.33 0.39 57 102.47 92.49 105.14 92.50 102.80 92.33 0.33 -0.16 58 102.48 127.67 105.14 128.98 102.82 128.19 0.34 0.53 59 102.53 147.27 105.14 147.91 102.87 147.02 0.34 -0.25 60 102.72 185.04 105.14 185.87 103.07 185.12 0.35 0.08 61 102.88 205.39 105.14 205.38 103.22 204.83 0.34 -0.56 62 103.26 243.81 105.14 244.14 103.61 244.13 0.35 0.32 63 103.52 264.31 105.14 263.86 103.85 264.15 0.33 -0.16 64 104.10 303.17 105.14 302.62 104.41 303.43 0.32 0.26 65 104.45 323.44 105.14 322.13 104.74 323.13 0.29 -0.31 66 105.19 360.78 105.14 360.09 105.46 361.19 0.27 0.41 67 105.62 380.34 105.14 379.02 105.86 379.99 0.24 -0.35 68 106.48 415.53 105.14 415.50 106.70 415.79 0.22 0.26 69 106.96 433.51 105.14 433.52 107.16 433.23 0.19 -0.29 70 107.89 465.69 105.14 467.97 108.09 466.02 0.20 0.33 71 108.39 482.04 105.14 484.86 108.57 481.81 0.18 -0.23 72 122.01 25.81 124.86 23.14 121.70 26.04 -0.32 0.23 73 122.14 42.39 124.86 40.03 121.84 41.86 -0.30 -0.53 74 122.41 74.35 124.86 74.48 122.16 74.73 -0.25 0.37 75 122.58 92.35 124.86 92.50 122.34 92.20 -0.24 -0.15 76 122.92 127.52 124.86 128.98 122.72 128.05 -0.20 0.53 77 123.12 147.12 124.86 147.91 122.93 146.87 -0.19 -0.25 78 123.54 184.88 124.86 185.87 123.37 184.97 -0.17 0.09 79 123.78 205.27 124.86 205.38 123.61 204.68 -0.17 -0.59 80 124.25 243.64 124.86 244.14 124.10 243.98 -0.15 0.34 81 124.52 264.14 124.86 263.86 124.36 264.00 -0.16 -0.13 82 125.06 303.02 124.86 302.62 124.89 303.30 -0.17 0.28 83 125.35 323.30 124.86 322.13 125.16 323.00 -0.19 -0.30 84 125.92 360.67 124.86 360.09 125.71 361.08 -0.21 0.41 85 126.23 380.27 124.86 379.02 125.99 379.88 -0.24 -0.39 86 126.81 415.46 124.86 415.50 126.54 415.71 -0.27 0.25 87 127.12 433.43 124.86 433.52 126.82 433.16 -0.30 -0.27 88 127.69 465.65 124.86 467.97 127.35 465.98 -0.34 0.34 89 127.99 482.00 124.86 484.86 127.62 481.78 -0.37 -0.22 90 158.20 26.39 163.62 23.14 158.40 26.66 0.20 0.27 91 158.85 42.94 163.62 40.03 159.04 42.42 0.18 -0.51 92 160.03 74.85 163.62 74.48 160.24 75.17 0.22 0.31 93 160.63 92.73 163.62 92.50 160.83 92.57 0.20 -0.16 94 161.72 127.80 163.62 128.98 161.92 128.28 0.19 0.48 95 162.27 147.26 163.62 147.91 162.43 147.03 0.16 -0.23 96 163.19 184.81 163.62 185.87 163.34 184.98 0.15 0.17 97 163.63 205.25 163.62 205.38 163.75 204.62 0.12 -0.62 98 164.32 243.42 163.62 244.14 164.45 243.78 0.13 0.36 99 164.63 263.88 163.62 263.86 164.75 263.74 0.12 -0.14 100 165.07 302.60 163.62 302.62 165.21 302.91 0.13 0.31 101 165.24 322.84 163.62 322.13 165.37 322.56 0.14 -0.28 102 165.42 360.20 163.62 360.09 165.58 360.54 0.16 0.34 103 165.45 379.69 163.62 379.02 165.62 379.30 0.17 -0.39 104 165.40 414.86 163.62 415.50 165.59 415.06 0.19 0.20 105 165.33 432.72 163.62 433.52 165.52 432.49 0.19 -0.23 106 165.09 464.99 163.62 467.97 165.28 465.29 0.18 0.30 107 164.93 481.27 163.62 484.86 165.11 481.09 0.18 -0.18 108 177.16 27.11 183.13 23.14 176.92 27.38 -0.25 0.27 109 178.06 43.61 183.13 40.03 177.79 43.09 -0.26 -0.51 110 179.64 75.47 183.13 74.48 179.44 75.73 -0.20 0.26 111 180.45 93.26 183.13 92.50 180.23 93.07 -0.22 -0.19 112 181.88 128.23 183.13 128.98 181.67 128.66 -0.21 0.43 113 182.58 147.57 183.13 147.91 182.33 147.34 -0.25 -0.23 114 183.74 184.90 183.13 185.87 183.47 185.15 -0.26 0.25 115 184.27 205.35 183.13 205.38 183.97 204.71 -0.29 -0.63 116 185.05 243.37 183.13 244.14 184.77 243.73 -0.28 0.36 117 185.37 263.78 183.13 263.86 185.08 263.61 -0.29 -0.16 118 185.77 302.33 183.13 302.62 185.50 302.65 -0.27 0.32 119 185.87 322.50 183.13 322.13 185.62 322.24 -0.26 -0.26 120 185.87 359.81 183.13 360.09 185.65 360.10 -0.23 0.29 121 185.78 379.15 183.13 379.02 185.57 378.82 -0.21 -0.33 122 185.43 414.31 183.13 415.50 185.24 414.49 -0.19 0.19 123 185.17 432.06 183.13 433.52 184.99 431.89 -0.18 -0.17 124 184.56 464.36 183.13 467.97 184.36 464.63 -0.20 0.27 125 184.18 480.55 183.13 484.86 183.97 480.41 -0.22 -0.13 126 212.81 29.24 221.09 23.14 213.00 29.56 0.19 0.32 127 214.16 45.56 221.09 40.03 214.33 45.15 0.18 -0.42 128 216.54 77.30 221.09 74.48 216.81 77.49 0.27 0.19 129 217.74 94.89 221.09 92.50 217.98 94.66 0.24 -0.23 130 219.82 129.55 221.09 128.98 220.08 129.89 0.26 0.34 131 220.81 148.55 221.09 147.91 221.02 148.37 0.21 -0.18 132 222.41 185.30 221.09 185.87 222.60 185.78 0.20 0.47 133 223.11 205.75 221.09 205.38 223.26 205.13 0.15 -0.62 134 224.08 243.38 221.09 244.14 224.24 243.73 0.16 0.35 135 224.42 263.65 221.09 263.86 224.58 263.40 0.16 -0.25 136 224.72 301.71 221.09 302.62 224.91 302.03 0.20 0.32 137 224.69 321.67 221.09 322.13 224.92 321.42 0.23 -0.25 138 224.33 358.82 221.09 360.09 224.61 358.94 0.28 0.12 139 223.97 377.70 221.09 379.02 224.29 377.50 0.32 -0.20 140 223.03 412.82 221.09 415.50 223.39 412.90 0.36 0.09 141 222.42 430.28 221.09 433.52 222.80 430.18 0.38 -0.10 142 221.05 462.63 221.09 467.97 221.39 462.76 0.34 0.13 143 220.26 478.58 221.09 484.86 220.58 478.48 0.32 -0.10 144 231.18 30.73 240.02 23.14 231.00 31.03 -0.17 0.30 145 232.72 46.92 240.02 40.03 232.56 46.54 -0.16 -0.38 146 235.47 78.57 240.02 74.48 235.43 78.69 -0.03 0.12 147 236.84 96.05 240.02 92.50 236.78 95.76 -0.05 -0.28 148 239.21 130.50 240.02 128.98 239.19 130.75 -0.02 0.26 149 240.33 149.27 240.02 147.91 240.26 149.11 -0.07 -0.16 150 242.13 185.62 240.02 185.87 242.05 186.24 -0.08 0.62 151 242.93 206.06 240.02 205.38 242.79 205.45 -0.14 -0.61 152 243.99 243.44 240.02 244.14 243.85 243.77 -0.14 0.33 153 244.36 263.61 240.02 263.86 244.20 263.30 -0.16 -0.31 154 244.63 301.34 240.02 302.62 244.49 301.66 -0.15 0.32 155 244.57 321.15 240.02 322.13 244.43 320.92 -0.13 -0.23 156 244.07 358.18 240.02 360.09 243.95 358.20 -0.11 0.03 157 243.62 376.73 240.02 379.02 243.52 376.65 -0.10 -0.07 158 242.44 411.82 240.02 415.50 242.33 411.87 -0.12 0.06 159 241.70 429.09 240.02 433.52 241.57 429.08 -0.13 -0.02 160 240.02 461.45 240.02 467.97 239.78 461.53 -0.24 0.08 161 239.06 477.23 240.02 484.86 238.75 477.20 -0.31 -0.03 Figure 2.3-16 DISR#3 HRI Target Grid (sharpened) Figure 2.3-17 Location of Observed Vertices for DISR 3 HRI Figure 2.3-18 Location of Desired Vertices for DISR 3 HRI Table 2.3-7 Vertex Information for DISR#3 HRI Distortion Fit C = Column R=Row Point Observed C Observed R Desired Desired Computed C Computed R C R ID C R Residual Residual 0 12.97 39.86 13.78 39.28 13.02 40.15 0.05 0.28 1 13.04 62.05 13.78 60.61 13.10 61.69 0.06 -0.37 2 13.19 104.04 13.78 102.84 13.26 104.20 0.08 0.16 3 13.27 126.02 13.78 124.32 13.35 125.78 0.08 -0.24 4 13.46 168.11 13.78 166.80 13.55 168.36 0.09 0.25 5 13.57 190.23 13.78 188.39 13.67 189.96 0.09 -0.27 6 13.80 232.30 13.78 231.02 13.91 232.57 0.10 0.27 7 13.94 254.27 13.78 252.66 14.04 254.18 0.10 -0.08 8 14.21 296.62 13.78 295.34 14.31 296.80 0.10 0.18 9 14.37 318.58 13.78 316.98 14.47 318.41 0.10 -0.18 10 14.68 360.82 13.78 359.61 14.78 361.00 0.10 0.18 11 14.86 382.89 13.78 381.20 14.95 382.59 0.09 -0.30 12 15.22 424.78 13.78 423.68 15.31 425.13 0.09 0.35 13 15.42 447.07 13.78 445.16 15.50 446.68 0.08 -0.39 14 15.81 489.01 13.78 487.39 15.89 489.14 0.07 0.14 15 34.86 39.74 35.32 39.28 34.74 40.00 -0.12 0.27 16 34.96 61.90 35.32 60.61 34.82 61.54 -0.14 -0.35 17 35.16 103.88 35.32 102.84 35.00 104.06 -0.15 0.18 18 35.27 125.86 35.32 124.32 35.10 125.64 -0.16 -0.22 19 35.49 168.01 35.32 166.80 35.32 168.23 -0.18 0.22 20 35.62 190.07 35.32 188.39 35.43 189.83 -0.19 -0.23 21 35.87 232.19 35.32 231.02 35.68 232.45 -0.19 0.26 22 36.01 254.18 35.32 252.66 35.81 254.07 -0.20 -0.11 23 36.28 296.48 35.32 295.34 36.08 296.69 -0.20 0.21 24 36.43 318.48 35.32 316.98 36.23 318.30 -0.20 -0.18 25 36.73 360.72 35.32 359.61 36.53 360.89 -0.20 0.17 26 36.90 382.76 35.32 381.20 36.70 382.47 -0.20 -0.28 27 37.22 424.68 35.32 423.68 37.03 425.00 -0.19 0.33 28 37.40 446.91 35.32 445.16 37.21 446.55 -0.19 -0.36 29 37.75 488.86 35.32 487.39 37.57 488.98 -0.18 0.12 30 77.30 39.50 77.89 39.28 77.49 39.73 0.19 0.23 31 77.41 61.60 77.89 60.61 77.60 61.27 0.19 -0.33 32 77.61 103.59 77.89 102.84 77.81 103.79 0.20 0.20 33 77.73 125.57 77.89 124.32 77.92 125.38 0.20 -0.19 34 77.95 167.82 77.89 166.80 78.15 167.97 0.20 0.16 35 78.07 189.77 77.89 188.39 78.27 189.58 0.20 -0.19 36 78.31 231.97 77.89 231.02 78.52 232.22 0.21 0.25 37 78.44 254.01 77.89 252.66 78.65 253.84 0.21 -0.17 38 78.70 296.22 77.89 295.34 78.92 296.46 0.22 0.25 39 78.84 318.27 77.89 316.98 79.06 318.07 0.22 -0.20 40 79.11 360.50 77.89 359.61 79.35 360.66 0.23 0.16 41 79.26 382.50 77.89 381.20 79.50 382.24 0.23 -0.26 42 79.55 424.46 77.89 423.68 79.80 424.75 0.25 0.29 43 79.71 446.59 77.89 445.16 79.96 446.28 0.25 -0.31 44 80.01 488.58 77.89 487.39 80.28 488.67 0.26 0.10 45 99.33 39.38 99.51 39.28 99.15 39.59 -0.18 0.21 46 99.45 61.45 99.51 60.61 99.26 61.13 -0.19 -0.32 47 99.67 103.45 99.51 102.84 99.48 103.66 -0.19 0.21 48 99.79 125.42 99.51 124.32 99.60 125.25 -0.19 -0.18 49 100.03 167.71 99.51 166.80 99.84 167.85 -0.19 0.14 50 100.16 189.63 99.51 188.39 99.96 189.46 -0.20 -0.17 51 100.41 231.85 99.51 231.02 100.21 232.10 -0.20 0.25 52 100.54 253.91 99.51 252.66 100.35 253.72 -0.20 -0.19 53 100.81 296.08 99.51 295.34 100.61 296.35 -0.20 0.26 54 100.95 318.15 99.51 316.98 100.75 317.96 -0.20 -0.20 55 101.22 360.38 99.51 359.61 101.03 360.54 -0.19 0.16 56 101.37 382.36 99.51 381.20 101.17 382.12 -0.20 -0.24 57 101.65 424.34 99.51 423.68 101.46 424.62 -0.19 0.27 58 101.81 446.43 99.51 445.16 101.61 446.14 -0.19 -0.29 59 102.10 488.43 99.51 487.39 101.92 488.52 -0.19 0.09 60 141.60 39.16 142.18 39.28 141.83 39.34 0.23 0.19 61 141.71 61.18 142.18 60.61 141.95 60.88 0.24 -0.30 62 141.94 103.19 142.18 102.84 142.20 103.41 0.26 0.22 63 142.06 125.16 142.18 124.32 142.32 125.00 0.26 -0.16 64 142.30 167.49 142.18 166.80 142.57 167.60 0.27 0.11 65 142.43 189.37 142.18 188.39 142.70 189.22 0.27 -0.16 66 142.68 231.61 142.18 231.02 142.96 231.85 0.28 0.24 67 142.81 253.71 142.18 252.66 143.09 253.48 0.28 -0.23 68 143.07 295.83 142.18 295.34 143.35 296.11 0.28 0.27 69 143.21 317.91 142.18 316.98 143.48 317.71 0.27 -0.20 70 143.49 360.13 142.18 359.61 143.75 360.29 0.26 0.16 71 143.63 382.10 142.18 381.20 143.89 381.86 0.26 -0.23 72 143.92 424.10 142.18 423.68 144.16 424.35 0.25 0.25 73 144.07 446.12 142.18 445.16 144.30 445.86 0.23 -0.26 74 144.36 488.13 142.18 487.39 144.58 488.21 0.22 0.08 75 163.68 39.05 163.82 39.28 163.47 39.22 -0.22 0.18 76 163.82 61.04 163.82 60.61 163.59 60.76 -0.22 -0.29 77 164.07 103.06 163.82 102.84 163.85 103.29 -0.22 0.22 78 164.20 125.03 163.82 124.32 163.98 124.87 -0.22 -0.16 79 164.45 167.37 163.82 166.80 164.23 167.48 -0.22 0.11 80 164.58 189.25 163.82 188.39 164.36 189.09 -0.22 -0.16 81 164.84 231.48 163.82 231.02 164.62 231.73 -0.22 0.25 82 164.98 253.60 163.82 252.66 164.75 253.35 -0.22 -0.24 83 165.23 295.70 163.82 295.34 165.01 295.98 -0.22 0.28 84 165.37 317.78 163.82 316.98 165.15 317.59 -0.22 -0.19 85 165.63 359.99 163.82 359.61 165.41 360.16 -0.22 0.17 86 165.77 381.95 163.82 381.20 165.55 381.73 -0.22 -0.23 87 166.03 423.97 163.82 423.68 165.81 424.20 -0.22 0.24 88 166.17 445.96 163.82 445.16 165.95 445.71 -0.22 -0.24 89 166.43 487.97 163.82 487.39 166.21 488.05 -0.22 0.08 90 205.98 38.84 206.49 39.28 206.15 38.99 0.17 0.16 91 206.11 60.79 206.49 60.61 206.29 60.53 0.17 -0.26 92 206.37 102.84 206.49 102.84 206.56 103.05 0.18 0.22 93 206.51 124.79 206.49 124.32 206.69 124.64 0.18 -0.15 94 206.77 167.13 206.49 166.80 206.96 167.24 0.19 0.11 95 206.91 189.03 206.49 188.39 207.09 188.85 0.18 -0.17 96 207.18 231.23 206.49 231.02 207.36 231.49 0.18 0.26 97 207.32 253.37 206.49 252.66 207.49 253.10 0.17 -0.26 98 207.59 295.46 206.49 295.34 207.76 295.73 0.17 0.26 99 207.73 317.51 206.49 316.98 207.89 317.33 0.16 -0.18 100 208.01 359.71 206.49 359.61 208.15 359.89 0.14 0.18 101 208.15 381.68 206.49 381.20 208.28 381.45 0.13 -0.23 102 208.43 423.70 206.49 423.68 208.54 423.92 0.11 0.22 103 208.57 445.66 206.49 445.16 208.67 445.42 0.09 -0.24 104 208.85 487.66 206.49 487.39 208.92 487.74 0.07 0.07 105 228.05 38.73 228.11 39.28 227.81 38.88 -0.24 0.15 106 228.20 60.67 228.11 60.61 227.95 60.42 -0.25 -0.25 107 228.49 102.73 228.11 102.84 228.23 102.94 -0.26 0.21 108 228.64 124.68 228.11 124.32 228.37 124.53 -0.27 -0.15 109 228.92 167.00 228.11 166.80 228.64 167.12 -0.27 0.12 110 229.06 188.92 228.11 188.39 228.78 188.73 -0.28 -0.19 111 229.32 231.09 228.11 231.02 229.05 231.36 -0.27 0.28 112 229.46 253.24 228.11 252.66 229.19 252.98 -0.27 -0.26 113 229.71 295.34 228.11 295.34 229.45 295.59 -0.26 0.25 114 229.84 317.36 228.11 316.98 229.58 317.19 -0.25 -0.17 115 230.08 359.56 228.11 359.61 229.84 359.75 -0.23 0.19 116 230.20 381.53 228.11 381.20 229.97 381.31 -0.22 -0.23 117 230.42 423.55 228.11 423.68 230.23 423.77 -0.20 0.22 118 230.54 445.50 228.11 445.16 230.35 445.26 -0.18 -0.24 119 230.75 487.50 228.11 487.39 230.60 487.58 -0.15 0.08 120 270.34 38.54 270.68 39.28 270.57 38.68 0.23 0.14 121 270.50 60.44 270.68 60.61 270.72 60.21 0.23 -0.23 122 270.80 102.54 270.68 102.84 271.02 102.73 0.22 0.19 123 270.95 124.47 270.68 124.32 271.17 124.31 0.22 -0.16 124 271.24 166.74 270.68 166.80 271.46 166.89 0.22 0.15 125 271.39 188.73 270.68 188.39 271.60 188.50 0.21 -0.23 126 271.67 230.81 270.68 231.02 271.88 231.11 0.22 0.30 127 271.81 252.99 270.68 252.66 272.02 252.72 0.22 -0.27 128 272.07 295.11 270.68 295.34 272.30 295.32 0.22 0.21 129 272.21 317.06 270.68 316.98 272.43 316.91 0.22 -0.15 130 272.46 359.25 270.68 359.61 272.69 359.46 0.24 0.21 131 272.59 381.25 270.68 381.20 272.82 381.01 0.24 -0.24 132 272.83 423.25 270.68 423.68 273.08 423.46 0.25 0.21 133 272.95 445.21 270.68 445.16 273.20 444.95 0.25 -0.26 134 273.17 487.18 270.68 487.39 273.44 487.27 0.27 0.09 135 292.40 38.44 292.22 39.28 292.28 38.58 -0.11 0.14 136 292.56 60.33 292.22 60.61 292.44 60.11 -0.11 -0.21 137 292.86 102.45 292.22 102.84 292.76 102.63 -0.10 0.18 138 293.01 124.37 292.22 124.32 292.91 124.20 -0.10 -0.17 139 293.30 166.60 292.22 166.80 293.21 166.78 -0.09 0.18 140 293.46 188.64 292.22 188.39 293.36 188.38 -0.10 -0.27 141 293.74 230.66 292.22 231.02 293.65 230.98 -0.09 0.32 142 293.89 252.84 292.22 252.66 293.79 252.59 -0.10 -0.26 143 294.17 294.99 292.22 295.34 294.07 295.18 -0.10 0.19 144 294.31 316.89 292.22 316.98 294.20 316.76 -0.10 -0.13 145 294.58 359.08 292.22 359.61 294.47 359.30 -0.11 0.23 146 294.72 381.10 292.22 381.20 294.60 380.85 -0.12 -0.25 147 294.98 423.09 292.22 423.68 294.85 423.30 -0.13 0.21 148 295.11 445.06 292.22 445.16 294.98 444.79 -0.14 -0.27 149 295.37 487.01 292.22 487.39 295.22 487.11 -0.15 0.10 Having established a mapping between the set of points in Tables 2.3-2 through 2.3-7, the mapping was modeled to third order by two-dimensional polynomial transformations between the original MRI, SLI and HRI image coordinates in pixels to the new image coordinates. The coefficients of the fit (i.e., the multipliers of the xy-looking terms which store the column and row positions of the image signal) rest in two matrices, one which gives the new x (column) position and one which gives the new y (row) position. They are called Kx and Ky. The mapping is expressed mathematically as: TABLE_2.3-7_EQU_1.GIF and is computed by the IDL procedure polywarp. It is applied to an image by the IDL procedure poly_2d. The original coordinates are given by xo and yo and the measured resulting coordinates in xi and yi. A concrete example of the equations applied to the DISR2 MRI x coordinate is shown below, where the matrix of numbers is K^X. TABLE_2.3-7_EQU_2.GIF The description of the mapping in the notes of the IDL polywarp and poly_2d procedures is somewhat counter-intuitive in that the pixel coordinates for the desired geometry (xo and yo) are treated as the inputs and those for the observed geometry (xi and yi) are treated as the outputs, with the implication that the derived matrices will transform from an undistorted system to a distorted. In fact, the exact opposite happens, which is what is needed. Inputting the observed coordinates for the vertices of the raw MRI, SLI and HRI images into the xi and yi slots of the polywarp and poly_2d arguments and providing the desired (unwarped) coordinates for the vertices into the xo and yo slots produces an undistortion model, a transformation that converts a raw image where orthogonal lines are curved into barrel distortion into an undistorted image. The conceptual solution to this paradox lies in the fact that a warping is going on: the distorted pixel coordinates of the original raw image are being elevated to the status of the correct coordinates, and the resultant image being displayed in a way where this coordinate system has primacy, i.e., where it is completely orthogonal. This has the effect of unwarping or undistorting the image. 2.4 Geometry Calibration The purpose of the calibration of absolute geometry of the 6 near-IR imaging systems of DISR 2 and 3 was to assign each pixel in a sharpened and undistorted image to a single point on the object sphere. The data contributing to the geometry calibrations was acquired on May 6, 1996 for DISR 2 and August 9, 1996 for DISR 3. The essence of the calibration was to image point sources at infinity, sources that were precisely located on the object sphere. Their images were injected into the imagers' field of views by back-illuminated pinholes at the focus of the laboratory collimator system. The DISR Sensor Head was mounted on the altitude-azimuth mount and the window of the imager being calibrated was placed at the center of rotation. The camera was oriented into several dozen positions, enough to sample all regions of the relevant imager's field of view. The resulting composite for each imager is shown in Figs. 2.4-1 through 2.4-6. Tables 2.4-1 through 2.4-6 show the relevant data for each system. Columns 2 and 3 provide the laboratory altitude-azimuth mount azimuth and elevation as each point was imaged. The illumination pattern of a single "point" is generally smeared out over a group of more than two dozen pixels. Identifying the maximum and the nearest two dozen surrounding the maximum, the centroid of each point in pixels was computed. These are provide in Columns 4 and 5 as the column and row number of each point. The "observed" points are the laboratory azimuth and elevation from Columns 2 and 3 were converted to a spherical coordinate system of clockwise azimuth and nadir angle, where the azimuth coordinate was centered at the center of the image. The conversion between laboratory azimuth and elevation and the image-based spherical system is given by SECTION_2.4_EQU_1.GIF where e and a are laboratory elevation and azimuth. The results are given in Columns 6 and 7 as xi (clockwise azimuth) and yi (nadir angle). The xi and yi correspond to the IDL polywarp formalism explained in the previous section. The indexed counterclockwise azimuth and nadir angles are given in Columns 8 and 9 as xo and yo and are calculated by assuming the pixel sizes and zenith angles for image centers assumed in Table 2.3-1 and computing the counterclockwise azimuth and nadir angles, assuming the azimuth angles at image center are 0.0. The expressions for the conversion are given by SECTION_2.4_EQU_2.GIF where a and b are the dihedral angles associated with the pixel columns and rows and q0 is the central zenith angle. The angles a and b are given by SECTION_2.4_EQU_3.GIF where m is the pixel size from Table 2.3-1 and nc and nr are the number of columns and rows in each image (also from Table 2.3-1). The specific column and row c and r of each point are given in Columns 2 and 3. Just as for the distortion maps, the model derived to match the indexed azimuth and nadir angles (xo and yo) to the observed angles (xi and yi) are third-order two-dimensional polynomial transformations constructed by the IDL procedure polywarp and applied by the procedure poly_2d. The coefficients of the relevant matrices are given in Table 2.2-3. The observed points xn and yn computed by the model are given in Columns 10 and 11 and should be compared with xi and yi in Columns 6 and 7. The residuals between the observed points and resulting synthetic observed points are given in Columns 12 and 13. The root-mean-square residual for azimuth and nadir angle for each imager is listed in Table 2.5-1. Figure 2.4-1 DISR#2 MRI Geometry Calibration Bright Point Composite Image Table 2.4-1 Point Information for DISR 2 MRI Absolute Location Fit line cal_azcal_el col row x_i y_i x_o y_o x_n y_n xresid y_resid 0 0 -68 173.8732 99.0505 0 22 -0.4121 22.1736 0.1358 21.9756 0.1358 -0.0244 1 0 -69 173.8799 82.2321 0 21 -0.4284 21.1645 0.1192 20.9723 0.1192 -0.0277 2 0 -70 173.8828 65.7089 0 20 -0.4465 20.1731 0.1018 19.988 0.1018 -0.012 3 0 -71 173.9029 48.8376 0 19 -0.4638 19.1609 0.0796 18.9846 0.0796 -0.0154 4 0 -72 173.9391 31.9262 0 18 -0.48 18.1462 0.0526 17.9803 0.0526 -0.0197 5 0 -73 173.9408 15.0427 0 17 -0.5049 17.1332 0.0307 16.9795 0.0307 -0.0205 6 -3.73 -68.3 112.7295 94.6148 9.9995 22.003 -10.0234 22.2137 9.891 22.0048 -0.1085 0.0018 7 -3.57 -69.29 114.1555 78.0096 10.0052 21.0021 -10.2075 21.2172 10.0237 21.0121 0.0185 0.01 8 -3.4 -70.28 116.8015 61.6681 9.9858 19.9995 -10.1989 20.2243 9.9497 20.0239 -0.0361 0.0244 9 -3.24 -71.27 118.9501 44.9859 9.9981 18.9983 -10.2896 19.2161 9.9629 19.0214 -0.0352 0.0231 10 -3.08 -72.26 121.0005 28.203 10.0149 17.9969 -10.4144 18.2027 9.9966 18.0147 -0.0183 0.0177 11 3.73 -68.3 236.9379 94.0603 -9.9995 22.003 9.5206 22.1498 -9.9182 21.9917 0.0813 -0.0113 12 3.57 -69.29 235.5519 77.7609 -10.0052 21.0021 9.6835 21.1711 -10.0787 21.0182 -0.0735 0.0161 13 3.4 -70.28 232.9494 61.1265 -9.9858 19.9995 9.6669 20.1613 -10.0519 20.0129 -0.0661 0.0134 14 3.24 -71.27 230.4169 44.7402 -9.9981 18.9983 9.6579 19.1666 -10.0263 19.023 -0.0282 0.0247 15 3.08 -72.26 228.1572 27.9557 -10.0149 17.9969 9.7133 18.1508 -10.057 18.0124 -0.0421 0.0155 16 8.3 -46.63 315.3425 455.1982 -11.9936 44.0016 11.7435 44.1474 -11.9895 43.9992 0.0041 -0.0024 17 2.78 -46.07 222.8437 465.0479 -4.0037 44 3.8937 44.1991 -4.0932 44.0055 -0.0895 0.0055 18 -2.78 -46.07 128.2845 464.8581 4.0037 44 -4.0517 44.1932 3.919 44.0036 -0.0847 0.0036 19 8.3 -46.63 315.3658 455.288 -11.9936 44.0016 11.7441 44.1529 -11.9902 44.0047 0.0034 0.0031 20 9.1 -56.06 325.3377 298.6641 -16.0073 34.9971 15.6222 35.1586 -16.0014 34.9929 0.0059 -0.0042 21 3.44 -55.15 232.8657 313.7224 -6.0051 34.998 5.8634 35.1948 -5.9865 35.0015 0.0186 0.0035 22 -3.44 -55.15 118.3063 313.7001 6.0051 34.998 -6.0528 35.2028 5.9704 35.0074 -0.0347 0.0094 23 -9.1 -56.06 24.0925 298.2975 16.0073 34.9971 -15.9929 35.1857 16.011 34.9917 0.0037 -0.0054 24 8.93 -64.42 323.0425 158.8522 -19.9977 26.9945 19.4991 27.1099 -20.0017 26.9995 -0.004 0.005 25 3.17 -63.17 228.2193 180.0418 -6.9957 27.0028 6.7818 27.1957 -7.075 27.0073 -0.0793 0.0045 26 -3.17 -63.17 122.3837 180.0756 6.9957 27.0028 -7.0931 27.2132 7.0522 26.997 0.0565 -0.0058 27 -8.93 -64.42 26.2768 159.1668 19.9977 26.9945 -19.9462 27.1946 19.9963 27.0008 -0.0014 0.0063 28 8.31 -71.74 315.9376 35.7708 -24.9932 20.0032 24.4328 20.0456 -24.9497 19.9903 0.0435 -0.0129 29 3.07 -70.23 227.5781 61.8476 -9.0099 19.9975 8.7437 20.1566 -9.1253 20.004 -0.1154 0.0065 30 -3.07 -70.23 123.1584 62.1098 9.0099 19.9975 -9.1193 20.1916 8.8528 19.9921 -0.1571 -0.0054 31 -8.31 -71.74 33.7168 36.7339 24.9932 20.0032 -24.8948 20.1763 25.0384 19.9892 0.0452 -0.014 32 0 -44 173.8593 499.6712 0 46 -0.2123 46.2105 0.0033 46.0031 0.0033 0.0031 33 0 -45 173.8447 482.8487 0 45 -0.2181 45.2011 0.0291 44.9994 0.0291 -0.0006 34 0 -46 173.806 465.9901 0 44 -0.2262 44.1896 0.0556 43.9923 0.0556 -0.0077 35 0 -47 173.8183 449.2585 0 43 -0.2302 43.1858 0.076 42.9916 0.076 -0.0084 36 -8.3 -46.63 34.7301 454.727 11.9936 44.0016 -11.9948 44.1455 12.0029 44.0027 0.0093 0.0011 Figure 2.4-2 DISR 2 SLI Geometry Calibration Bright Point Composite Image Table 2.4-2 Point Information for DISR 2 SLI Absolute Location Fit line cal_az cal_el col row x_i y_i x_o y_o x_n y_n xresid y_resid 0 0 -41 128.8229 34.2458 0 49 0.0399 48.5746 0.0151 48.996 0.0151 -0.004 1 0 -42 129.0983 24.1056 0 48 0.0746 47.5606 0.0122 47.9947 0.0122 -0.0053 2 0 -43 129.3305 13.9742 0 47 0.1045 46.5475 0.0155 46.9943 0.0155 -0.0057 3 0 -44 129.9156 3.8477 0 46 0.1797 45.5349 -0.0243 45.995 -0.0243 -0.005 4 -7.53 -41.43 48.228 32.9523 9.9986 49.0046 -9.9007 48.8716 9.9719 48.9441 -0.0267 -0.0605 5 -7.41 -42.44 48.8919 22.8706 9.9946 47.996 -9.9019 47.8652 10.0049 47.9212 0.0103 -0.0747 6 -7.3 -43.44 49.7631 12.9818 10.0056 46.9982 -9.8769 46.8752 10.0115 46.9158 0.0059 -0.0824 7 7.53 -41.43 209.1895 26.0535 -9.9986 49.0046 10.0087 48.1923 -9.9717 48.9857 0.0269 -0.0189 8 7.41 -42.44 209.1602 16.0848 -9.9946 47.996 10.0895 47.2039 -10.0005 48.0252 -0.0059 0.0293 9 7.3 -43.44 209.1121 5.3533 -10.0056 46.9982 10.1774 46.1395 -10.0283 46.9914 -0.0227 -0.0068 10 8.18 -35.41 211.1155 88.1819 -10.0024 55.0034 9.7614 54.3648 -9.9804 55.0006 0.022 -0.0028 11 2.46 -35.04 153.2805 93.8822 -3.0037 54.997 2.9229 54.5735 -3.029 54.9805 -0.0253 -0.0165 12 -2.46 -35.04 102.2648 95.1597 3.0037 54.997 -3.0915 54.7053 2.9764 55.0022 -0.0273 0.0052 13 -8.18 -35.41 42.8315 93.0205 10.0024 55.0034 -10.0844 54.873 9.9964 55.006 -0.006 0.0026 14 9.05 -25.34 215.732 191.733 -9.9949 64.9973 9.605 64.6378 -10.0186 65.0016 -0.0237 0.0043 15 2.72 -25.03 153.0577 195.593 -3.0014 65.0001 2.7014 64.7339 -2.9805 65.0069 0.0209 0.0068 16 -2.72 -25.03 98.5828 196.1687 3.0014 65.0001 -3.2896 64.8033 3.0245 65.0149 0.0231 0.0148 17 -9.05 -25.34 35.2019 193.6412 9.9949 64.9973 -10.2581 64.8709 10.0095 65.0434 0.0146 0.0461 18 9.85 -10.15 225.0851 347.7345 -10.0035 80.0012 9.6798 80.064 -10.0075 80.0016 -0.004 0.0004 19 2.95 -10.01 156.0445 347.7962 -2.9955 80.0034 2.7605 79.9411 -3.0039 80.0072 -0.0084 0.0038 20 -2.95 -10.01 96.3257 346.8146 2.9955 80.0034 -3.2264 79.8473 2.9806 79.9977 -0.0149 -0.0057 21 -9.85 -10.15 26.8575 344.3359 10.0035 80.0012 -10.2069 79.7449 9.9943 79.9658 -0.0092 -0.0354 22 10 0 232.8836 451.7332 -10 90 9.8385 90.3186 -9.9784 90.0003 0.0216 0.0003 23 3 0 159.8093 449.0475 -3 90 2.9525 90.0547 -2.9967 89.9906 0.0033 -0.0094 24 -3 0 96.249 447.0421 3 90 -3.0451 89.8544 3.0073 89.9927 0.0073 -0.0073 25 -10 0 22.8708 444.8398 10 90 -9.9976 89.6395 10.003 90.014 0.003 0.014 26 9.96 5.08 237.7451 503.7632 -9.9985 95.0032 9.9736 95.4433 -10.0154 95.0155 -0.0169 0.0123 27 9.98 4.06 236.7078 493.1216 -10.0046 93.9985 9.9446 94.3954 -10.0058 93.9887 -0.0012 -0.0098 28 9.99 3.05 235.7304 482.8695 -10.0039 93.0037 9.9173 93.3857 -9.9976 92.9999 0.0063 -0.0038 29 -8 -44.2 41.7687 8.7342 11.0914 46.3398 -10.9111 46.5455 11.0968 46.4737 0.0054 0.1339 30 -4 -44.2 85.2708 3.9844 5.571 45.9356 -5.4798 45.6796 5.5769 46.0056 0.0059 0.07 31 0 5 129.8659 498.5912 0 95 0.1249 95.0091 -0.0024 95.0102 -0.0024 0.0102 Figure 2.4-3 DISR 2 HRI Geometry Calibration Bright Point Composite Image Table 2.4-3 Point Information for DISR 2 HRI Absolute Location Fit line cal_az cal_el col row x_i y_i x_o y_o x_n y_n xresid y_resid 0 3.4 -70.28 273.0043 423.2419 -9.9858 19.9995 10.3921 19.4934 -9.8893 19.9903 0.0965 -0.0092 1 1.2 -70.03 203.2394 430.9192 -3.5097 20.0046 3.9332 19.4761 -3.6764 20.0039 -0.1667 -0.0007 2 -1.2 -70.03 124.8073 431.051 3.5097 20.0046 -3.2854 19.4674 3.2838 19.9948 -0.2259 -0.0098 3 -3.4 -70.28 52.9553 423.9641 9.9858 19.9995 -9.9311 19.49 9.836 20.0013 -0.1498 0.0018 4 4.09 -74.52 293.2812 284.1229 -14.9979 15.9984 15.5255 15.4506 -14.9264 15.9838 0.0715 -0.0146 5 2.06 -74.13 230.5174 297.2361 -7.4934 15.9997 8.1112 15.4637 -7.4932 15.9959 0.0002 -0.0038 6 -2.06 -74.13 96.5422 297.7012 7.4934 15.9997 -7.4101 15.4536 7.3437 15.9991 -0.1497 -0.0006 7 -4.09 -74.52 30.752 284.932 14.9979 15.9984 -15.1626 15.4507 14.9959 15.9784 -0.002 -0.02 8 4.08 -78.7 292.4067 147.0639 -20.003 12.005 20.9185 11.4261 -19.9995 12.0045 0.0035 -0.0005 9 2.07 -78.18 230.7032 165.3409 -10.007 11.9974 10.9373 11.4567 -10.0065 12.0042 0.0005 0.0068 10 -2.07 -78.18 95.9148 165.9093 10.007 11.9974 -10.065 11.443 10.0141 12.0045 0.0071 0.0071 11 -4.08 -78.7 30.6029 148.1301 20.003 12.005 -20.5693 11.4354 20.008 12.0086 0.005 0.0036 12 3.99 -83.06 289.7889 6.2016 -29.9965 8.0004 31.9463 7.4744 -29.8615 8.004 0.135 0.0036 13 2.06 -82.27 230.1078 32.7666 -14.9717 7.9982 16.5826 7.4783 -14.7401 7.9999 0.2316 0.0017 14 -2.06 -82.27 95.3974 33.3132 14.9717 7.9982 -15.5281 7.4567 14.9306 7.9945 -0.0411 -0.0037 15 -3.99 -83.06 31.9652 7.1532 29.9965 8.0004 -31.6798 7.4874 30.0108 8.0009 0.0143 0.0005 16 0 -68 160.8631 497.3835 0 22 0.0303 21.4808 0.0282 22.0086 0.0282 0.0086 17 0 -69 160.8713 464.7743 0 21 0.0325 20.4765 0.0455 21.0055 0.0455 0.0055 18 0 -70 160.7636 431.946 0 20 0.0243 19.4653 0.0815 19.9963 0.0815 -0.0037 19 0 -71 160.6327 399.2119 0 19 0.0129 18.4571 0.128 18.9906 0.128 -0.0094 20 0 -72 160.4581 366.4062 0 18 -0.0043 17.4467 0.1864 17.9831 0.1864 -0.0169 21 -3.73 -68.3 42.0356 488.1948 9.9995 22.003 -9.9243 21.4906 10.0116 21.9904 0.0121 -0.0126 22 -3.57 -69.29 45.915 456.179 10.0052 21.0021 -10.0632 20.5014 10.0438 21.0059 0.0386 0.0038 23 -3.4 -70.28 51.0587 423.914 9.9858 19.9995 -10.1038 19.498 10.0097 20.0088 0.0239 0.0093 24 -3.24 -71.27 55.8668 391.4109 9.9981 18.9983 -10.1832 18.4887 10.0436 19.0067 0.0455 0.0084 25 -3.08 -72.26 60.4036 359.1645 10.0149 17.9969 -10.2932 17.4884 10.1321 18.0141 0.1172 0.0172 26 3.73 -68.3 283.9307 488.0068 -9.9995 22.003 10.3355 21.5098 -9.9443 21.9906 0.0552 -0.0124 27 3.57 -69.29 280.26 455.988 -10.0052 21.0021 10.512 20.5222 -10.0534 21.0089 -0.0482 0.0068 28 3.4 -70.28 274.9318 423.6396 -9.9858 19.9995 10.56 19.5156 -10.0526 20.011 -0.0668 0.0115 29 3.24 -71.27 269.489 391.1222 -9.9981 18.9983 10.6037 18.5029 -10.0554 19.0075 -0.0573 0.0092 30 3.08 -72.26 264.1176 358.9026 -10.0149 17.9969 10.6527 17.4992 -10.0678 18.0129 -0.0529 0.016 31 3.08 -83 263.3215 7.6696 -23.8225 7.6446 26.2056 7.1234 -24.0116 7.6399 -0.1891 -0.0047 32 3.08 -82 263.3635 39.9887 -21.1378 8.5688 23.1375 8.0316 -21.2206 8.564 -0.0828 -0.0048 33 3.08 -81 263.3439 72.5948 -18.9814 9.5083 20.6637 8.9656 -19.0763 9.5129 -0.0949 0.0046 Figure 2.4-4 DISR 3 MRI Geometry Calibration Bright Point Composite Image Table 2.4-4 Point Information for DISR 3 MRI Absolute Location Fit line cal_az cal_el col row x_i y_i x_o y_o x_n y_n xresid y_resid 0 0 -68 169.6838 100.165 0 22 -1.0664 22.2434 0.1447 21.9835 0.1447 -0.0165 1 0 -69 169.6859 83.5225 0 21 -1.1103 21.245 0.1393 20.9817 0.1393 -0.0183 2 0 -70 169.7386 66.8424 0 20 -1.1499 20.2443 0.1235 19.979 0.1235 -0.021 3 0 -71 169.7397 49.9966 0 19 -1.2033 19.2337 0.115 18.9679 0.115 -0.0321 4 0 -72 169.7503 33.3116 0 18 -1.2599 18.2328 0.1035 17.968 0.1035 -0.032 5 0 -73 169.8088 16.848 0 17 -1.3126 17.2452 0.0819 16.9831 0.0819 -0.0169 6 -3.73 -68.3 109.0635 95.4031 9.9995 22.003 -10.569 22.2962 9.9146 22.0101 -0.0849 0.0071 7 -3.57 -69.29 110.8201 79.021 10.0052 21.0021 -10.7159 21.3103 9.9965 21.0202 -0.0087 0.0181 8 -3.4 -70.28 113.1006 62.3875 9.9858 19.9995 -10.7981 20.3041 9.9988 20.0112 0.013 0.0117 9 -3.24 -71.27 115.6862 46.0976 9.9981 18.9983 -10.8281 19.3149 9.9365 19.0203 -0.0616 0.022 10 -3.08 -72.26 117.8077 29.8279 10.0149 17.9969 -10.949 18.3316 9.9553 18.0365 -0.0596 0.0396 11 3.73 -68.3 232.161 95.4768 -9.9995 22.003 8.7489 22.1922 -9.9163 21.9938 0.0832 -0.0092 12 3.57 -69.29 230.8061 79.1704 -10.0052 21.0021 8.8852 21.2125 -10.0747 21.0139 -0.0695 0.0118 13 3.4 -70.28 228.1991 62.7982 -9.9858 19.9995 8.8264 20.2183 -10.033 20.0194 -0.0472 0.0199 14 3.24 -71.27 225.9523 46.1906 -9.9981 18.9983 8.8344 19.213 -10.0582 19.0162 -0.0601 0.0179 15 3.08 -72.26 223.7919 29.7655 -10.0149 17.9969 8.8577 18.2191 -10.0971 18.0264 -0.0822 0.0295 16 8.3 -46.63 308.1146 453.2779 -11.9936 44.0016 11.1677 43.9738 -11.9348 43.9567 0.0588 -0.0449 17 2.78 -46.07 217.0392 463.1001 -4.0037 44 3.4153 44.0669 -4.0598 43.9932 -0.0561 -0.0068 18 -2.78 -46.07 123.152 462.8583 4.0037 44 -4.4939 44.0897 3.9038 44.0084 -0.0999 0.0084 19 8.3 -46.63 308.1397 453.8037 -11.9936 44.0016 11.1622 44.0048 -11.9288 43.9877 0.0648 -0.0139 20 9.1 -56.06 318.7089 298.2591 -16.0073 34.9971 14.9573 35.0485 -16.0085 34.9991 -0.0012 0.002 21 3.44 -55.15 226.7403 312.8784 -6.0051 34.998 5.2355 35.1153 -6.0096 34.9974 -0.0045 -0.0006 22 -3.44 -55.15 113.8696 312.6257 6.0051 34.998 -6.5225 35.1625 6.0013 34.9981 -0.0038 0.0001 23 -8.31 -71.74 31.0919 37.195 24.9932 20.0032 -25.2723 20.2635 25.0238 19.9953 0.0306 -0.0079 24 8.31 -71.74 310.3185 37.7519 -24.9932 20.0032 23.4252 20.0292 -24.9618 19.9965 0.0314 -0.0067 25 3.07 -70.23 222.8212 63.3504 -9.0099 19.9975 7.9076 20.2079 -9.0983 20.0013 -0.0884 0.0038 26 -3.07 -70.23 119.29 63.0547 9.0099 19.9975 -9.7457 20.2826 8.9161 19.9909 -0.0938 -0.0066 27 -8.3 -46.63 30.9491 452.1719 11.9936 44.0016 -12.3504 44.0304 11.9373 43.9664 -0.0563 -0.0352 28 9.1 -56.06 318.7068 298.2287 -16.0073 34.9971 14.9578 35.0467 -16.0091 34.9972 -0.0018 0.0001 29 3.44 -55.15 226.7207 312.8483 -6.0051 34.998 5.2337 35.1135 -6.0078 34.9956 -0.0027 -0.0024 30 -3.44 -55.15 113.8524 312.5976 6.0051 34.998 -6.5246 35.161 6.0035 34.9965 -0.0016 -0.0015 31 -3.44 -45 111.8394 480.0388 4.8591 45.1031 -5.3241 45.1562 4.7491 45.0821 -0.11 -0.021 32 -3.44 -46 112.0406 463.7608 4.9457 44.1068 -5.421 44.184 4.842 44.1045 -0.1037 -0.0023 33 9.1 -56.06 318.6888 298.2512 -16.0073 34.9971 14.9555 35.0477 -16.0067 34.9982 0.0006 0.0011 34 3.44 -55.15 226.7091 312.8742 -6.0051 34.998 5.2323 35.115 -6.0063 34.9971 -0.0012 -0.0009 35 -3.44 -55.15 113.8408 312.6193 6.0051 34.998 -6.5256 35.1623 6.0045 34.9979 -0.0006 -0.0001 36 -9.1 -56.06 20.7378 297.1546 16.0073 34.9971 -16.3605 35.1663 16.0335 34.9965 0.0262 -0.0006 37 8.93 -64.42 317.5248 160.0051 -19.9977 26.9945 18.7657 27.0783 -20.0066 26.9977 -0.0089 0.0032 38 3.17 -63.17 222.8054 180.6324 -6.9957 27.0028 6.0693 27.1987 -7.0454 27.0087 -0.0497 0.0059 39 -3.17 -63.17 118.6003 180.2169 6.9957 27.0028 -7.5825 27.2473 7.05 26.9992 0.0543 -0.0036 40 -8.93 -64.42 23.4903 159.3338 19.9977 26.9945 -20.2856 27.2556 19.9761 27.0013 -0.0216 0.0068 41 8.31 -71.74 310.3076 37.7295 -24.9932 20.0032 23.4249 20.0277 -24.9617 19.995 0.0315 -0.0082 42 3.07 -70.23 222.8626 63.3258 -9.0099 19.9975 7.9151 20.2067 -9.1059 20.0001 -0.096 0.0026 43 -3.07 -70.23 119.6747 63.0693 9.0099 19.9975 -9.6808 20.2799 8.8492 19.9883 -0.1607 -0.0092 44 -8.31 -71.74 31.0643 37.1627 24.9932 20.0032 -25.2787 20.2624 25.0305 19.9942 0.0373 -0.009 45 0 -44 168.0405 497.1564 0 46 -0.6823 46.0614 0.0684 45.9811 0.0684 -0.0189 46 0 -44.999 168.1268 480.714 0 45.001 -0.6898 45.0749 0.0725 44.9943 0.0725 -0.0067 47 0 -46 168.1987 464.0941 0 44 -0.6988 44.0778 0.0791 43.9953 0.0791 -0.0047 48 0 -47 168.2731 447.7045 0 43 -0.7078 43.0945 0.0864 43.0088 0.0864 0.0088 49 -8.3 -46.63 30.8747 452.243 11.9936 44.0016 -12.3555 44.0352 11.9427 43.9713 -0.0509 -0.0303 50 -7.18 -44.44 46.9716 489.1903 10.0062 45.999 -10.5001 46.065 10.0641 46.0157 0.0579 0.0167 51 -7.05 -45.44 49.6935 472.8254 9.996 44.9982 -10.4973 45.0831 10.0383 45.0245 0.0423 0.0263 52 -6.93 -46.439 51.921 456.1902 10.0027 43.9994 -10.5379 44.0883 10.0637 44.0199 0.061 0.0205 53 -6.8 -47.44 54.7907 439.8388 9.9985 42.9971 -10.5198 43.1046 10.0346 43.0258 0.0361 0.0287 54 7.18 -44.44 291.9113 490.7425 -10.0062 45.999 9.3471 46.0573 -10.0515 46.0199 -0.0453 0.0209 55 7.05 -45.44 289.1129 473.9658 -9.996 44.9982 9.3192 45.0486 -10.0306 45.0126 -0.0346 0.0144 56 6.93 -46.439 286.8018 457.2849 -10.0027 43.9994 9.3282 44.0482 -10.0494 44.0121 -0.0467 0.0127 57 6.8 -47.44 284.0685 440.9361 -9.9985 42.9971 9.296 43.0639 -10.028 43.0259 -0.0295 0.0288 Figure 2.4-5 DISR 3 SLI Geometry Calibration Bright Point Composite Image Table 2.4-5 Point Information for DISR 3 SLI Absolute Location Fit line cal_az cal_el col row x_i y_i x_o y_o x_n y_n xresid y_resid 0 0 -41 128.4253 33.2868 0 49 -0.0092 48.4787 0.0448 49.0108 0.0448 0.0108 1 0 -42 128.948 23.1042 0 48 0.0559 47.4604 0.0122 48.0013 0.0122 0.0013 2 0 -43 129.2843 12.9379 0 47 0.0987 46.4438 0.0032 46.9924 0.0032 -0.0076 3 0 -44 129.7982 2.9398 0 46 0.1649 45.4441 -0.028 45.9999 -0.028 -0.0001 4 -7.53 -41.43 48.851 31.8856 9.9986 49.0046 -9.833 48.7593 9.9408 48.9905 -0.0578 -0.0141 5 -7.41 -42.44 49.2074 21.9629 9.9946 47.996 -9.8704 47.7718 10.0125 48.0001 0.0179 0.0042 6 -7.3 -43.44 50.1846 11.9607 10.0056 46.9982 -9.833 46.7694 10.0089 46.999 0.0033 0.0008 7 -7.18 -44.44 50.9546 2.0601 10.0062 45.999 -9.8215 45.7789 10.0327 46.0083 0.0265 0.0093 8 7.53 -41.43 210.2068 25.3284 -9.9986 49.0046 10.1401 48.1315 -9.9879 49.0013 0.0107 -0.0033 9 7.41 -42.44 210.0955 14.9517 -9.9946 47.996 10.2155 47.102 -9.9936 47.9886 0.001 -0.0074 10 7.3 -43.44 210.2039 4.8866 -10.0056 46.9982 10.3183 46.1055 -10.0233 47.0102 -0.0177 0.012 11 8.18 -35.41 211.4398 86.8223 -10.0024 55.0034 9.8093 54.2333 -9.9739 54.9953 0.0285 -0.0081 12 2.46 -35.04 153.2278 92.641 -3.0037 54.997 2.9194 54.4493 -3.0373 54.9987 -0.0336 0.0017 13 -2.46 -35.04 102.1465 93.9611 3.0037 54.997 -3.1082 54.586 2.9778 54.9923 -0.0259 -0.0047 14 -8.18 -35.41 43.112 91.9885 10.0024 55.0034 -10.0591 54.7682 9.9975 54.9958 -0.0049 -0.0076 15 9.05 -25.34 215.6277 190.0814 -9.9949 64.9973 9.6036 64.474 -10.0204 65.0077 -0.0255 0.0104 16 2.72 -25.03 153.0704 194.0388 -3.0014 65.0001 2.7055 64.5787 -2.9927 64.991 0.0087 -0.0091 17 -2.72 -25.03 98.3623 195.0092 3.0014 65.0001 -3.3163 64.6881 3.0263 65.0079 0.0249 0.0078 18 -10 -25.03 25.945 195.7694 11.0123 65.3758 -11.2564 65.154 11.0338 65.3861 0.0215 0.0103 19 2.95 -10.01 155.5841 346.6533 -2.9955 80.0034 2.7162 79.8265 -2.9855 80.0057 0.01 0.0023 20 -2.95 -10.01 95.9194 345.867 2.9955 80.0034 -3.269 79.7531 2.9945 80.0104 -0.001 0.007 21 -9.85 -10.15 26.7265 343.6903 10.0035 80.0012 -10.2239 79.6819 9.9849 79.9941 -0.0186 -0.0071 22 10 0 232.1162 449.6865 -10 90 9.778 90.1169 -9.9805 89.9925 0.0195 -0.0075 23 3 0 159.34 447.7899 -3 90 2.9105 89.9291 -3.0228 90.002 -0.0228 0.002 24 -3 0 96.0063 445.8297 3 90 -3.0703 89.7334 2.9952 89.9884 -0.0048 -0.0116 25 -3 6 96.6319 505.8495 3.0165 95.9918 -2.9001 95.7277 3.0219 95.9967 0.0054 0.0049 26 -3 5 96.5803 495.8878 3.0114 94.9931 -2.9233 94.7327 3.0083 94.9982 -0.0031 0.0051 27 4 5 171.8739 498.27 -4.0152 94.9878 3.9669 94.9651 -3.985 94.9833 0.0302 -0.0045 28 8 5 215.6777 499.9947 -8.0302 94.9512 7.972 95.1 -8.056 94.9601 -0.0258 0.0089 29 0 5 129.0424 496.8497 0 95 0.0496 94.835 -0.0044 94.9958 -0.0044 -0.0042 30 -10 2 21.8467 463.9483 10.006 91.9696 -9.9788 91.5215 9.9998 91.9811 -0.0062 0.0115 31 -10.15 1.849 20.1234 462.2125 10.1552 91.8201 -10.1512 91.3498 10.1675 91.8108 0.0123 -0.0093 Figure 2.4-6 DISR 3 HRI Geometry Calibration Bright Point Composite Image Table 2.4-6 Point Information for DISR 3 HRI Absolute Location Fit line cal_az cal_el col row x_i y_i x_o y_o x_n y_n xresid y_resid 0 3.4 -70.28 265.6574 424.775 -9.9858 19.9995 9.7021 19.5028 -9.8753 19.9986 0.1105 -0.0009 1 1.2 -70.03 196.3839 431.9562 -3.5097 20.0046 3.2983 19.4955 -3.6734 19.9995 -0.1637 -0.0051 2 -1.2 -70.03 117.9797 432.0021 3.5097 20.0046 -3.9064 19.509 3.3211 19.9903 -0.1886 -0.0143 3 -3.4 -70.28 46.715 424.9585 9.9858 19.9995 -10.48 19.5521 9.8329 19.9936 -0.1529 -0.0059 4 4.09 -74.519 286.3105 285.3601 -14.997 15.9994 14.7091 15.4333 -14.9337 15.9859 0.0633 -0.0135 5 2.06 -74.13 223.5197 298.3319 -7.4934 15.9997 7.2936 15.4693 -7.4851 15.9951 0.0083 -0.0046 6 -2.06 -74.13 89.8796 298.6345 7.4934 15.9997 -8.158 15.5088 7.3708 15.9982 -0.1226 -0.0015 7 -4.09 -74.519 24.2804 285.9049 14.997 15.9994 -15.8544 15.5311 15.0102 15.9797 0.0132 -0.0197 8 4.08 -78.7 285.7664 148.2529 -20.003 12.005 19.8861 11.3906 -19.9968 12.0043 0.0062 -0.0007 9 2.07 -78.18 223.9659 166.5439 -10.007 11.9974 9.8775 11.4564 -10.0164 12.0033 -0.0094 0.0059 10 -2.07 -78.18 89.2131 166.7876 10.007 11.9974 -11.0604 11.5066 10.0109 12.0029 0.0039 0.0055 11 -4.08 -78.7 24.1916 149.069 20.003 12.005 -21.4456 11.5319 20.0008 12.0086 -0.0022 0.0036 12 3.99 -83.06 283.9912 6.9692 -29.9965 8.0004 30.683 7.4033 -29.8699 8.0071 0.1266 0.0067 13 2.06 -82.27 223.463 33.7841 -14.9717 7.9982 15.0125 7.4536 -14.7439 8.0056 0.2278 0.0074 14 -2.06 -82.27 89.2929 33.9789 14.9717 7.9982 -16.8612 7.5281 14.9306 7.994 -0.0411 -0.0042 15 -3.99 -83.06 25.9256 7.7053 29.9965 8.0004 -32.8033 7.5996 30.0119 8.0012 0.0154 0.0008 16 0 -68 154.2608 498.9758 0 22 -0.5191 21.5307 0.0231 22.0127 0.0231 0.0127 17 0 -69 154.2721 465.9307 0 21 -0.5439 20.5129 0.0444 21.0022 0.0444 0.0022 18 0 -70 154.2681 433.1337 0 20 -0.5723 19.5028 0.0738 19.9981 0.0738 -0.0019 19 0 -71 154.2288 400.2557 0 19 -0.6072 18.4902 0.1124 18.9904 0.1124 -0.0096 20 0 -71.999 154.0582 367.6858 0 18.001 -0.6591 17.4872 0.1682 17.9912 0.1682 -0.0098 21 -3.73 -68.3 35.2682 489.8702 9.9995 22.003 -10.4558 21.5755 10.0147 21.9922 0.0152 -0.0108 22 -3.57 -69.29 39.3587 457.6263 10.0052 21.0021 -10.605 20.579 10.0505 21.0074 0.0453 0.0053 23 -3.4 -70.28 44.8495 425.0905 9.9858 19.9995 -10.6462 19.566 10.0011 20.0063 0.0153 0.0068 24 -3.24 -71.27 49.7173 392.7951 9.9981 18.9983 -10.7451 18.5632 10.0309 19.014 0.0328 0.0157 25 -3.08 -72.26 54.3348 360.2796 10.0149 17.9969 -10.8831 17.5548 10.1143 18.0151 0.0994 0.0182 26 3.73 -68.3 277.0097 489.7414 -9.9995 22.003 9.7418 21.528 -9.948 21.9958 0.0515 -0.0072 27 3.57 -69.29 273.0652 457.0184 -10.0052 21.0021 9.8766 20.5168 -10.057 20.9983 -0.0518 -0.0038 28 3.4 -70.28 267.6936 424.7712 -9.9858 19.9995 9.8868 19.5127 -10.0551 20.0076 -0.0693 0.0081 29 3.24 -71.27 262.2548 392.3739 -9.9981 18.9983 9.8925 18.5033 -10.0536 19.0101 -0.0555 0.0118 30 3.08 -72.26 256.9058 360.0118 -10.0149 17.9969 9.9062 17.495 -10.0637 18.0121 -0.0488 0.0152 31 3.08 -83 257.0316 8.3546 -23.8225 7.6446 24.7275 7.0604 -24.0024 7.6342 -0.1799 -0.0104 32 3.08 -82 256.8348 40.9238 -21.1378 8.5688 21.7331 7.9827 -21.219 8.5642 -0.0812 -0.0046 33 3.08 -80.999 256.6499 73.6285 -18.9795 9.5093 19.3537 8.9261 -19.0683 9.5116 -0.0888 0.0023 2.5. Error Analysis Table 2.5-1 Propagated and Observed Errors in Degrees and Pixels DISR 2 DISR 3 MRI SLI HRI MRI SLI HRI Calibration Alt-Az Mount Azimuth Error (o) 0.055 0.014 0.025 0.031 0.019 0.023 Calibration Alt-Az Mount Elevation Error (o) 0.025 0.039 0.007 0.017 0.008 0.008 Propagated Observed Azimuth Error (o) 0.068 0.016 0.104 0.069 0.022 0.097 RMS Residual Error in Observed Azimuth (o) 0.068 0.016 0.104 0.070 0.022 0.097 Propagated Observed Nadir Angle Error (o) 0.013 0.038 0.009 0.017 0.008 0.009 RMS Residual Error in Observed Nadir Angle (o) 0.013 0.038 0.009 0.018 0.008 0.009 RMS Residual Error in Observed Azimuth (pixels) 0.252 0.087 0.440 0.294 0.130 0.411 RMS Residual Error in Observed Nadir Angle (pixels) 0.108 0.185 0.147 0.140 0.038 0.143 The propagated errors listed in Table 2.5-1 were computed based on the assumption that the major source of error for the rms residuals between the modeled and observed bright points in the imager geometry calibrations was inaccuracies in the pointing of the altitude-azimuth mount itself. These errors have often observed and estimated in the laboratory as ranging from 0.01 to 0.05o. The formulae for computing these errors are given as TABLE_2.5_EQU_1.GIF where a and e are the cal azimuth and elevation and sa and se are the cal azimuth and elevation errors (rows 1 and 2 in Table 2.5-1), respectively. The data in Table 2.5-1 are complete agreement with the a priori estimates of cal azimuth and elevation error, as can be seen by the agreement between Row 3 and Row 4 for observed clockwise azimuth and the agreement between Row 5 and Row 6 for observed nadir angle. The average cal azimuth error implied by the rms residuals in azimuth was 0.028o and the average cal elevation error implied by the rms residuals in nadir angle was 0.017o for the geometrical calibration of the 6 imagers, in total agreement with previously observed cal pointing error estimates of 0.03o for cal azimuth and 0.02o for cal elevation. The rms residuals in clockwise azimuth and nadir angle were converted to pixel errors, a non-trivial conversion because of the varying dimensions of the pixels of each imager over the range of its field of view. The average column dihedral pixel error implied for all 6 imagers was less than 0.3 pixels and the average row dihedral pixel error was less than 0.15 pixels. A more detailed breakdown, imager by imager, confirms that the average cal azimuth and elevation errors of 0.028 and 0.017o simply translate to similar dihedral pixel angle errors of 0.028 and 0.17o. The agreement observed between the pointing errors of the calibration test- bed and the measured discrepancies between the modeled and the observed locations of the images of the bright point sources confirm that the essential results of the calibration-the matrix coefficients of Table 2.3-1-are working as well as can be expected. In other words, no other significant sources of systematic error, e.g., mis-assignment of points, coding errors, spurious points throwing off the fit, seem to be present. The sources of the largest discrepancies still evident in some of the pictures are the degree of the polywarp used to actually tile the image panels into the final mosaic and the presence of parallax in the near-field, especially between panels. 2.6. Sample Mosaics Another confirmation of the validity of the absolute assignment information contained in the plots of Figures 2.2-1 and 2.2-2 and the matrix coefficients of Tables 2.2-2 and 2.2-3 is the construction of sample mosaics that demonstrate the alignment of the three imagers. Several are pictured in Figures 2.6-1 through 2.6-6. They show good alignment at the boundaries between SLI and MRI and between MRI and HRI. Some of the visible discrepancies can be explained by the parallax between the three imagers. The displacements between the three imager windows are given in Table 2.6-1, basically the same for both models of the instrument. A vertical displacement of 10 mm, such as occurs between the MRI and the HRI, leads to a nadir angle displacement of 0.03o at a range of 20 m, or half an HRI pixel. Between panels, the horizontal displacements were of the order of 50 mm horizontally, translating to angular displacements of about 0.13o in azimuth and somewhat less than that in nadir angle. Table 2.6-1 Displacements between imager windows (mm). In DISR coordinate system, X is vertical, Z is along direction in which Sensor Head points and Y is perpendicular to this direction. (mm) XSH YSH ZSH DX DY DZ MRI 17.6 49.2 208.3 -28.8 -3.6 -16.2 SLI 46.4 52.8 224.5 38.3 -3.4 37.4 HRI 8.1 56.2 187.1 -9.6 7.0 -21.2 Figure 2.6-1 Detail from LPL Rooftop Manual Rotating Test, 18 July 1998, SE corner of LPL Rooftop. DISR 2 in Single Measurement Mode. Images sharpened (wc=0.7, we=1.0). Azimuth = 90.0o. Figure 2.6-2 Detail from LPL Rooftop Manual Rotating Test, 18 July 1998, SE corner of LPL Rooftop. DISR 2 in Single Measurement Mode. Images sharpened (wc=0.7, we=1.0). Azimuth = 45.0o. Figure 2.6-3 LPL Rooftop Manual Rotating Test, 18 July 1998, SE corner of LPL Rooftop. DISR 2 in Single Measurement Mode. Images sharpened (wc=0.7, we=1.0). Figure 2.6-4 Mt. Bigelow Fire Observation Tower Test, 9 June 1999, Mt. Bigelow, Arizona. DISR 2 Sensor Head in Descent Mode, alternating 3-6 hardware compression ratios. Images sharpened (wc=0.7, we=1.0). Figure 2.6-5 Imaging Cool-Down Test, 18 September 1996, LPL Auditorium. DISR 3 Sensor Head on its side in Single Measurement Mode. Mercator Projection with HRI on the right and SLI on the left. Images sharpened (wc=0.7, we=1.0). Figure 2.6-6 Imaging Cool-Down Test, 18 September 1996, LPL Auditorium. DISR 3 Sensor Head on its side in Single Measurement Mode. Mercator Projection with HRI on the right and SLI on the left. Parallax evident in overlap of MRI with SLI; otherwise alignment good. Images sharpened (wc=0.7, we=1.0). 3.0. Deconvolution of DISR Images Erich KarkoschkaMay 2001 3.1. Abstract For the DISR #2/3 instruments, a total of 28 point spread functions (PSF) sampled at quarter-pixels are available. These data were fitted by optical aberrations in order to calculate PSFs for each location across the field of views. Software was written to generate PSFs and deconvolve images. 3.2. Introduction The information in an image can fully be evaluated only if the size and shape of the PSF is known for every location in the image. The size and shape of PSFs of DISR imagers varies across the field of views of each CCD. This is especially true for the MRIs. The best characterization of the PSFs comes from 28 laboratory measurements for the DISR #2 and #3 instruments, between two and six PSFs for each of the six cameras: HRI3, MRI3, SLI3 (the flight cameras on Cassini) and HRI2, MRI2, and SLI2. Due to the variations across the field of views, these data are not sufficient to characterize the PSF for every location without further knowledge of the spatial variations. Lyn Doose performed some ray tracing calculations with a commercial software package using the parameters of the optical design. These theoretical PSFs showed the expected variation of the PSFs. They were consistent with some of the observed features, but they were sufficiently different from the observed PSFs that they could not be used directly. However, I noticed that these theoretical PSFs look like examples of the primary optical aberrations. Indeed, I performed some calculations with the primary optical aberrations which approximated the calculations using the design quite well. The hope was that the measured PSFs would also be fitted well by primary optical aberrations with some parameters such as the focus location changed somewhat with respect to Lyn's calculations. This would then allow us to calculate PSFs for every location across the field of views. Table 3.0-1 lists equations for the four aberrations: defocus, spherical aberration, astigmatism, and coma. The equations describe the coordinates of a beam at the CCD as function of the coordinates of the beam at the aperture. The following quantity need to be specified: R, the distance of the center of light from the optical axis in the focal plane, which uniquely corresponds to the angle of the incoming beam. In order to build up an image for an aberration, one typically calculates some 1000 beams spread across the aperture. Coma is assumed to vary with a linear and cubic dependence on R. Astigmatism is assumed to vary with the square of R. The defocus term is a constant defocus combined with a term dependent on the square of R, called field curvature. Spherical aberration is assumed to have the same kind of dependence on R as the defocus term. When fitting theoretical PSFs to the measured ones, the parameters for the defocus term were allowed to be different for the #2 and #3 instruments. The other four optical aberrations were assumed to be identical for both instruments and changed only between HRI, MRI, and SLI. For a better fit, three pairs of parameters were added for each camera, the location of the interception of the image plane with the optical axis, the slope of the image plane (not necessarily perpendicular to the optical axis), and the decentering of the aperture obstruction. The size and shape of the obstruction was taken from the instrument design drawings. The smearing of the image by the fibers, the spacing between fibers and CCD, and the finite pixel size were modeled in the following way. The observed SLI3 and SLI2 PSFs in the center of the field of view had the sharpest PSFs. Their elongation in the vertical direction can be explained by sensitive pixel areas of 23x15 mm (DISR#3) and 23x14 mm (DISR#2), accurate to about 1 mm. The adopted area was 23x15. While an aperture with isotropic illumination causes an intensity distribution proportional to cos4a (a is the angle of the beam in the spacing between fibers and CCD with respect to the normal on the image plane), the wings of the measured PSFs indicate that the exponent is at least 5 and probably closer to 6 (a value somewhat above 4 is expected due to reflection at the end of the fibers). The adopted exponent was 6. The distance between fibers and CCD based on this dependence is then 1.02ń0.1 and 1.20ń0.1 pixels for DISR3 and DISR2, respectively, about 23 and 28 mm. I tested the data for a possible variation of the spacing with location or imager, but no significant variation was found. Note that the measured PSFs do not constrain the physical spacing. They only show that the smearing due to fibers and spacing is similar to that of a cos6a dependence and a 23 or 28 mm spacing. Table 3.0-2 lists the adopted parameters derived by least-square fitting of the PSFs. PSFs generated with the adopted parameter are very similar to the 28 observed ones. There are some small deviations unlikely to be noise. However, deviations are so different in different parts of the field of view that it seems close to impossible to achieve a better understanding of the true PSFs across the field of view. Even for especially accurate photometric measurements of small features where knowledge of PSFs are critical, the generated PSFs probably approximate the true PSFs sufficiently well. PSFs were generated for a grid every 9 pixels in both coordinates for each of the six investigated cameras. Each PSF was sampled in 0.6 pixel steps, the largest step size which essentially preserves all spatial information. All PSFs were centered according to their center of light. These PSFs were Fourier transformed for the deconvolution process using the Fourier or Wiener method. The specified PSFs in the deconvolution program have Fourier transforms of the form (1 - fx2/4 - fy2/4)e where fx and fy are the spatial frequencies in cycles/pixel and the exponent e can be chosen freely to control sharpness. In the program, e is a function of the distance from the center of the image. In principle, a specified PSF should not contain any spatial frequencies which are not contained in the PSF of the camera, since such a case causes a division by zero and an infinite boost factor for the amplitude of that frequency. In reality, such cases will happen, especially near the corners of the MRI where the PSF does not contain some moderately high frequencies. The software then modifies the specified PSF so that boost factors remain finite. A free parameter allows the choice between s small modification of the specified PSF with large boost factors and thus noisy deconvolved images versus a large modification of the specified PSF with more pleasing looking results. 3.3. Distortion Since the locations of the 28 measured PSFs are also known in the azimuth- elevation system of the mount, one can explore the approximate mapping between these coordinates and the pixel coordinates. For each of the six cameras, four parameters were determined: the azimuth and elevation for the center of the image, the scale (in the center), and the rotation angle with respect to the vertical. For both HRIs, this gives an almost perfect mapping. For the MRI, a standard radial distortion is obvious. Considering this distortion, the mapping is also almost perfect. The radial distortion is even more obvious for the SLI. Yet, the simple distortion gives a mapping only accurate to about 1 pixel. For purposes which don't require higher precision, a subroutine was written which converts the coordinates for all six cameras in both ways, pixels coordinates into azimuth/elevation and vise versa. 3.4. Smear due to Rotation of the Probe The finite integration times and the rotation of the probe cause a smear which is typically about 1.5 pixels. This smear can be deconvolved. A program was written which calculates smear lengths and smear orientations based on one input parameter, the angular rotation during the exposure, which is the product of the integration time and spin rate. It is assumed that the rotation occurs around the axis azimuth = 0ř and elevation = ń90ř. The program then smears the synthetic PSFs. For deconvolution of smeared images, the deconvolution program needs this file. Table 3.0-1 Aberrations Defocus r = d r cosf d = d0 + d2R2 + (dxx + dyy)/100 t = d r sinf Spherical r = s(3r2 - 2)r cosf s = s0 + s2R2 Aberration t = s(3r2 - 2)r sinf Astigmatism r = a r cosf a = a2R2 t = -a r sinf Coma r = c(r2cos2f + 2r2 - 1) c = c1R + c3R3 t = c(r2sin2f) Table 3.0-2 Adopted Parameters Parameter HRI3 HRI2 MRI3 MRI2 SLI3 SLI2 ____________________________________________________________ d0 -0.50 -0.31 -0.76 0.50 -0.03 -0.03 d2 -0.46 -0.23 1.54 2.30 -0.50 -0.50 dx -0.04 0.09 0.12 0 -0.05 0 dy -0.15 0.25 -0.03 0 -0.05 0 s0 0.73 0.73 -0.64 -0.64 -0.56 -0.56 s2 -0.87 -0.87 0.56 0.56 0 0 a2 -0.23 -0.23 2.71 2.71 0.65 0.65 c1 -1.26 -1.26 1.45 1.45 -0.93 -0.93 c3 0.68 0.68 -0.56 -0.56 1.15 1.15 ox 0.55 -0.35 0.38 0 0.20 0 oy 0.35 -0.20 -0.05 0 0.05 0 xa -10 54 -4 3 0 0 ya -5 38 0 1 0 0 Table 3.0-3 Explanation of Parameters x (pixels) x-coordinate in image, from center to right y (pixels) y-coordinate in image, from center up xa (pixels) x-coordinate of optical axis ya (pixels) y-coordinate of optical axis R 0 ... 1 normalized distance from optical axis R = 1 in image corner if xa = ya = 0 r 0 ... 1 normalized distance from center of aperture r = 1 at edge of aperture stop f 0 ... 2p azimuthal angle in aperture (radial=0ř) r (pixels) radial distance from center of light t (pixels) tangential distance from center of light c (pixels) 1/3-diameter of coma a (pixels) half-diameter of astigmatism d (pixels) half-diameter of defocused image s (pixels) half-diameter of spherical aberration ox, oy relative offset of aperture obstruction c1, c3, a2, d0, d2, dx, dy, s0, s2, ox, oy, xa, ya (pixels) constants for each camera (cf. Table 3.0-2) Figure 3.0-1 Location of the Measured Quarter-Pixel PSFs. Displayed are the 28 measured PSFs in the azimuth-elevation system of the mount. Positions are numbered within each camera from bottom (1-3) to top (7-9) and from left to right. The thin dotted lines are meridians separated by 30ř of probe rotation, corresponding to a panorama of 12 images. Figure 3.0-2 Observed Point Spread Functions x 5. Contour lines for the observed PSFs magnified five times are shown for 50%, 10%, and 1% of maximum intensity. Figure 3.0-3 Smeared Point Spread Functions x 5. Same as Fig. 2 except that the PSFs are smeared according to a probe rotation of 0.36ř. Figure 3.0-4 Fitted Point Spread Functions x 5. Same as Fig. 2 except that the synthetic PSFs are displayed. Figures 3.0-5 to 3.0-32 Fractional Enclosed Energy (%) by Pixels for each of the 28 PSFs locations for measured, smeared, standard synthetic, and alternative synthetic PSFs. The alternative synthetic PSFs are calculated with a spacing between the fibers and the CCD of half the actual spacing. The top panel shows the enclosed energy for the brightest pixel, the brightest two pixels, etc. After 20 pixels, only every fifth pixel is marked. The bottom panel shows contours of 0.5, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100% (central dot). The order is measured PSF (top left), smeared PSF (top right), fitted PSF (bottom left), and spacing/2 (bottom right). Figure 3.0-6 Figure 3.0-7 Figure 3.0-8 Figure 3.0-9 Figure 3.0-10 Figure 3.0-11 Figure 3.0-12 Figure 3.0-13 Figure 3.0-14 Figure 3.0-15 Figure 3.0-16 Figure 3.0-17 Figure 3.0-18 Figure 3.0-19 Figure 3.0-20 Figure 3.0-21 Figure 3.0-22 Figure 3.0-23 Figure 3.0-24 Figure 3.0-25 Figure 3.0-26 Figure 3.0-27 Figure 3.0-28 Figure 3.0-29 Figure 3.0-30 Figure 3.0-31 Figure 3.0-32 Figures 3.0-33 to 3.0-35 Fractional Enclosed Energy (%) by Pixels for the PSFs after deconvolution. The display is the same as in Figs. 5-32. SpePSF is the specified PSF in the deconvolution program for the widths 1, 1.5, 2, and 2.5. SLI3.c is the actual PSF after deconvolution in the center of the SLI3. It is slightly different because the SLI3 PSF does not contain all frequencies with the required amplitude for the deconvolution with limited amplitude boosts. MRI3.e is the actual PSF after deconvolution in the corner of the MRI3. It is quite different because the MRI3 PSF does not contain many frequencies with the required amplitude for the deconvolution with limited amplitude boosts. Figure 3.0-34 Figure 3.0-35 Figure 3.0-36 Location of Aperture Obstruction. For each of the 28 measured PSF locations, the location of the aperture obstruction is shown according to the design. The fitting of the observed PSFs suggested that the actual locations may be slightly different although other effects such as slight lens misalignments could cause similar deviations. Figure 3.0-37 Synthetic PSFs for Basic Aberrations. Displayed are spot diagrams without aperture obstructions. The central column is the focused image while the left and right columns show it defocused on either side. The top row is for a perfect system. The second, fourth, and sixth rows show spherical aberration, astigmatism, and coma, respectively. The rows in between show the mix of two aberrations. Figure 3.0-38 Synthetic PSFs for Each Camera. Spot diagrams are displayed for each camera and for five equally spaced positions from the optical axis to the corner of the field of view. No obstruction is included. The image plane is assumed to be perpendicular to the optical axis for this plot. The tick marks show the size of pixels. Figure 3.0-39 Hypothetical PSFs for the MRI. Spot diagrams as in Fig. 38 but for various designs of the MRI, from top to bottom: MRI3, MRI2, focus parameters half way between those of the MRI3 and MRI2, the same for the system stopped down to f/3.5, a design with two f/2.5 field stops (the additional stop is placed such that the central beam in the actual stop grazes the edge of the additional stop for the corner of the field, which causes vignetting and thus an average effective f/3), and a design with an Erfle eyepiece as for the SLI. Figures 3.0-40 to 3.0-54: Examples of original images (top) and deconvolved images (bottom) with the width set at 1.0 (center) and 1.5 (corner). The geometric pattern of SLI3 comes in four versions, smeared by 0, 2, 3, and 4 pixels, respectively, and the deconvolution included similar amount of smear. Figure 3.0-41 Figure 3.0-42 Figure 3.0-43 Figure 3.0-44 Figure 3.0-45 Figure 3.0-46 Figure 3.0-47 Figure 3.0-48 Figure 3.0-49 Figure 3.0-50 Figure 3.0-51 Figure 3.0-52 Figure 3.0-53 Figure 3.0-54 Figure 3.0-55 Images of the observed PSFs, the fitted PSFs, and their difference, from left to right in each case. The top panel is for DISR3, the bottom panel for DISR2. The left three columns are for the HRI, the middle three for the MRI, and the right three for the SLI. (the figure is oriented correctly if the big black rectangle shows up at bottom right) 4.0. Image Photometric Calibration 4.1. Relative Spectral Response The relative spectral response (RSR) defines the wavelength-dependent response of the entire imaging system, including all component transmissions and the CCD response. By definition it is normalized to 1 at the peak. The RSR of the DISR imagers was measured in the lab using the large integrating sphere. The interior of the sphere is illuminated through the monochromator with an incandescent light source, producing near-monochromatic illumination on the interior of the sphere. The brightness of the illuminated interior is measured with the monochromator standard detector, and the three imagers are exposed nearly simultaneously. This procedure is repeated at 10 nm intervals from 600 nm to 1050 nm. At each wavelength the relative spectral response of the standard detector, Rref, is known. The measured current from the standard detector is Iref. The data number per second from a pixel in the DISR imagers is r. The relative spectral response of the pixel at the current wavelength is given by SECTION_4.1_EQU_1.GIF Corrections must be applied for dark current by exposing a dark image, and the result for each pixel is normalized to 1 at the wavelength where the peak occurs. The values of Rref can be found on cassini in the file /local/cal.cal/si.std. Measurements using this procedure were taken for DISR#3 from July 26, 1996, until August 1, 1996, at 7 temperatures. The results of these measurements are stored on cassini in the directory /local/Imagers/Rel_Spectral_Resp/output/DISR#3 in DISRSOFT files with the naming convention imager_temperature, i.e., mri_185, e.g. Data returned by executing a d_read statement on these files returns an array of floating point numbers with dimensions number-of-columns number-of-rows (254) 50 wavelengths (600 nm - 1050 nm in increments of 10 nm). To make access to the RSR data more tractable, a parametric model has been developed to describe the RSR of each pixel at all wavelengths and temperatures. This model is discussed below. 4.1.1. A Model for the relative spectral response of the imagers 4.1.1.1. Motivation for a Model The relative spectral response (RSR) measurements for the imagers represent an enormous amount of data. There are three imagers (HRI, MRI and SLI) with 40,640, 44,704 and 32,512 pixels respectively for a total of 117,856 pixels. In addition, relative spectral response data (as the name implies) depends upon wavelength, and measurements were made from 600 nm to 1090 nm in increments of ten corresponding to 50 wavelengths. Finally, the relative response data is also a function of temperature, and measurements were made at 7 temperatures encompassing a range from 171 to 294 K. Thus, well over 41 million numbers [(40,640 + 44,704 + 32,512) 50 7] would be required to fully represent the relative spectral response data for each pixel of all three imagers. The sheer size of this data set was motivation for development of a parametric model for the RSR. The ultimate goal is to find a model that works not only for the majority of pixels but for all pixels in all imagers at all temperatures with small deviations from the measurements. 4.1.1.2. General Description of RSR data Displayed in Figure 4.1.1.1-1 is the average RSR for all pixels for the 7 measured Figure 4.1.1.1-1 RSR averaged over all the pixels for the HRI at measured temperatures versus wavelength for the HRI. The RSR bandpass has a characteristic shape, similar in appearance to a normal distribution skewed toward shorter wavelengths with 3 "humps", the middle of which is the highest. temperatures. Plots of RSR curves at different temperatures show a systematic shift in shape, its left and right humps increasing and decreasing with temperature. At shorter wavelengths, at the blue edge of the bandpass, lower temperatures show a higher RSR while the higher temperatures show a lower RSR. The opposite is true at longer wavelengths near the red end of the bandpass, where the higher temperatures show higher RSR. Figure 4.1.1.1-2 is a drawing of the front end of the optics for all three imagers, showing window, filter, lenses, etc. The general shape of the RSR curve is caused principally by the bandpass filter, which defines the blue edge, and by the decreasing detector responsivity with wavelength, which defines the red end. Variations in the shape of the RSR curve are caused by different affects. At short wavelengths, the bandpass filter changes transmission with temperature, while at long wavelengths, change with temperature of the detector responsivity is the dominant effect. On a pixel-by-pixel level at least two factors act to shift the RSR curve: 1) different amounts of silicon doping on the CCD itself, and 2) variations in the transmission of the fiber optic conduit. The fiber optic conduit has blemishes, and is yellowish in color and so absorbs in the blue. Figure 4.1.1.1-2 Drawing of the front end of the optics of the imagers showing window, filter, lenses, etc. 4.1.1.3. Suspected Correlation: AR and RSR Every pixel in an imager has a unique Absolute Responsivity (AR), but there is no variation with wavelength to consider, and the temperature dependence of the AR can be described by a simple polynomial. Thus, the number of values needed to fully represent the Absolute Responsivity measurements is roughly 100 times less (assuming 3 coefficients replace the 50 wavelengths 7 temperatures) than the over 41 million numbers required to fully represent the RSR data for each pixel of all three imagers. In our first attempt to develop a parametric model we hypothesized that pixels with a relatively lower AR may be fed by relatively more fibers with extramural absorption and have a different shaped RSR. It was speculated that pixels that have a low overall AR would tend to be more responsive in the red end of the spectrum and less responsive in the blue. If there was a correlation between the AR and RSR we sought to parameterize this relationship to enable determination of RSR values when AR values are known. Thus, we initially sought a quantifiable relationship between the AR and the RSR of the imager pixels. 4.1.1.4. Absolute Responsivity Measurements The frequency of AR values for the HRI is shown in a histogram plot in Figure 3. The Figure 4.1.1.4-1 Histogram showing numbers of pixels and AR values in units of (1e-6 DN/sec)/ Watts per m2 micro-m str. Pixel AR values show a somewhat normal distribution skewed toward higher values of AR, with a hump of more pixels evident towards the high end. The average AR value is 1.736 x106, or 1.759 x106 if the bad pixels are excluded (there are 511 bad pixels in the HRI). The AR curves for the MRI and SLI are similar. 4.1.1.5. Absolute Responsivity bins In the interest of seeking a correlation between AR and RSR, ten groupings of pixels were chosen to represent 10 bins based upon average AR levels. The average of the good pixels for the AR array was computed and all individual AR values were divided by this average. The resulting normalized AR ratios were sorted from large to small, grouping pixels into bins that are most responsive, slightly less responsive, less responsive still, etc., to see if different groupings of pixels based on AR may have a different RSR character. The RSR data were examined for the imager of interest using AR measurements at a temperature of 237.75 K and RSR measurements for a temperature of 239 K. Most of the variation in the RSR occurs in the left and right "humps". While initial samples of populations seemed to indicate a trend, when considering all the data trends become much less clear as there is a tremendous amount of scatter (Figure 4.1.1.5-1). There is Figure 4.1.1.5-1 The HRI RSR at 820 nm vs. AR bin number. This plot shows all the pixels in the HRI imager encompassing all possible bin values (1-10). considerable spread in the value of the RSR within each bin, and the correlation between AR and RSR is weak. However, there is some correlation and so we proceeded with the development of a RSR model based on AR. Coefficients were determined that describe how the RSR varies with wavelength within each of these ten AR bins by fitting a second order polynomial to the ratio of the average RSR within a bin to the average RSR for the entire imager versus wavelength: EQUATION_01.GIF, where i indicates the bin number (1) Polynomial fits for ai, bi, and ci as a function of ARi were then made. Because these fits were not adequate when a single polynomial was used, the fits were made in two pieces. Thus, a different set of coefficients is used depending upon whether or not the AR of the pixel of interest exceeded a threshold value. Thus, 3 groups (one per imager) of 6 (constant, linear and quadratic terms of both the low AR and high AR variety) sets of coefficients were determined, and basically, three equations were used to derive ai, bi, and ci. The RSR could then be determined from the AR of any pixel using equation (1). The root mean square (RMS) difference between the measured and modeled RSR was computed for each good pixel for each of the 7 temperatures at which the RSR measurements were made (171,185,201,225, 239, 269,294). Figure Figure 4.1.1.5-2 shows the computed RMS values plotted versus AR. The conclusion from figure Figure 4.1.1.5-2 is that the model is not very successful, because the RSR and AR of pixels are not very well correlated. Figure 4.1.1.5-2 Resultant Root Mean Square (RMS) difference values between the measured and model RSR values for each of the pixels in the HRI imager when using the AR-RSR model for computing RSR. Note the significant scatter. Figure 4.1.1.5-3 shows a probability plot of RMS difference values for both the AR-RSR model and a model called Ave that simply uses the average RSR within each bin for the RSR of each pixel in that bin. The simple average performs better for a majority of pixels, while the AR-RSR model does better for a small percentage of pixels. The cross over occurs just beyond 99.9 % of the pixels. The conclusion is that the AR-RSR model is not successful when compared to a much simpler model of using the average RSR within each bin for the RSR of the pixel of interest, although the AR-RSR model performs better for a subset of pixels. Figure 4.1.1.5-3 A probability plot for the HRI comparing the over all Root Mean Square (RMS) differences for the AR-RSR model versus a simple model using only the average within each bin. Generally the models are similar, with the AR-RSR model yielding better results (lower RMS deviations) for the vast majority of pixels. For a small subset of pixels toward the right of the graph, the Ave model gives a result preferable to using the AR-RSR model. 4.1.1.6. Limitation of the AR-RSR Method Thus, while there is some relationship between AR and the RSR, there is significant scatter in this relationship. For the majority of pixels, the AR- RSR model performs better than a simple average to represent the RSR of a pixel. However for the AR-RSR model and the Ave model the RMS deviation of some pixels approaches 5% and almost 7% respectively for the HRI at 239K. The implication is that the correlation between the AR and the RSR is not sufficiently strong for the development of a successful RSR model. Our goal was to develop a model for which the RMS deviations are lower than some threshold for all pixels within an imager. Such a model that does not employ the AR has now been developed and is explained below. 4.1.2. The Hump Ratio Model for determination of RSR 4.1.2.1. Development of the model at 239K As was mentioned previously, the RSR array is composed of a peak with two "humps" on either side of the peak. For the purposes of constructing a parametric model, the left hump is defined to be at a wavelength of 700 nm and the right hump is defined to exist at 820 nm. It was noticed that large variations in the RSR versus wavelength curve generally occurs in the close vicinity of these two humps. The RSR model is based on the ratio of the RSR at these two wavelengths (700 and 820 nm) at a temperature of 239K for each pixel. The hump ratio or "h ratio" is defined as the RSR of the left hump divided by the RSR of the right hump, and every pixel is assigned to one of 10 bins based upon this ratio (see Tables 4.1.2.1-1 through 4.1.2.1-3). Initially, 20 bins were arbitrarily chosen, but the choice of ten bins was ultimately made as fewer than ten bins increased root mean square (RMS) deviations, while more than ten bins did not offer improvement in the RMS. The h ratio limits for the bins are the same for all three imagers, and are given in table 4.1.2.1-1: Table 4.1.2.1-1 h ratio bin limit values bin h ratio h ratio lower upper limit limit 1 1.12 1.17 2 1.10 1.12 3 1.06 1.10 4 1.04 1.06 5 1.02 1.04 6 1.00 1.02 7 0.96 1.00 8 0.93 0.96 9 0.90 0.93 10 0.75 0.90 Bad pixels (as defined by the bad pixel map) are assigned a flag value of 255. Four plots at different temperatures (171K, 185K, 201K and 225K) comprise Figure 4.1.2.1-1. On each graph the average RSR within a bin, normalized to the RSR of all the good pixels at 239K, is plotted versus wavelength, for each of the ten bins. Figure 4.1.2.1-2 shows the equivalent graph for the three remaining temperatures at which RSR measurements were taken (239K, 269K and 294K). The left vertical line (at 700 nm) shows the position of the left hump and the right vertical line (at 820 nm) shows the position of the right hump. These seven graphs demonstrate that there are groups of pixels, assigned to one of ten bins that show different spectral responses from one another. Thus, the pixels within these ten bins behave distinctly from one another in terms of their average RSR within a bin. In addition, the bins are persistent over temperature. In other words, bin1 (the red line) is always highest left of the peak (or crossover point) in the lower wavelength portion of the spectrum, while bin 10 (the black line) is always lowest in this region. Likewise, bin 10 is always higher than bin 1 in the longer wavelength portion of the spectrum. There is a large spike at an approximate wavelength of 640 nm that appears to be a real feature. The RSR at this wavelength differs greatly with temperature, although the response at 640 nm is so low that this does not have a large effect on the overall RSR curve. Figure 4.1.2.1-1 The average within a bin normalized to the average of all the good pixels at 239K plotted versus wavelength for 171K, 185K, 201K and 225K. Figure 4.1.2.1-2 The average within a bin normalized to the average of all the good pixels at 239K plotted versus wavelength for 171K, 185K, 201K and 225K. Tables 1, 2 and 31 in appendix A show the bin assignments for each pixel in the HRI, MRI and SLI respectively. The bin values range from 1 to 10 for all three imagers, with the caveat that the MRI has 10 "out of family" pixels. Each of the ten "out of family" pixels for the MRI is assigned a value from 20-29. The model was developed at a base temperature of 239K. Thus, obtaining the representative RSR for a given pixel at 239K simply requires looking up the bin for that pixel, then using the RSR for that bin. 4.1.2.2. Development of the model at all Temperatures Although the RSR data was originally taken at seven temperatures (171K, 185K, 201K, 225K, 239K, 269K, 294K), the RSR of any temperature can be computed with the model. Temperature coefficients that enable the computation of the RSR at other temperatures are derived as follows: for each of the temperatures and for each bin (recall the bin of each pixel is defined by the RSR "h ratio" at 239K) we compute the mean RSR of the pixels within each bin. Figure 4.1.2.2-1 is a plot of the average RSR within a bin normalized to Figure 4.1.2.2-1 Normalized average RSR versus Temperature for all 10 bins with polynomial fits. the average RSR in the same bin at 239K for one wavelength (830 nm), all plotted versus temperature for all ten bins. Coefficients are determined by doing a second order polynomial fit of the above-mentioned normalized average RSR versus temperature. As can be seen in Figure 4.1.2.2-1, the temperature dependence of the RSR is well fit by a 2nd order polynomial. The result is three coefficients (multipliers in the constant, linear and quadratic terms) . Such coefficients are computed for each of the 10 bins at each wavelength. A weighted coefficient is then computed for each of the three terms based upon the numbers of pixels within each bin multiplied by its coefficients. Thus, the result is a weighted coefficient expressed as a 2nd order polynomial in temperature for each wavelength (see Table 4.1.2.4-2). Figure 4.1.2.2-2 shows the same graph as Figure 4.1.2.2-1, but with only the weighted fit shown. Clearly there is very little variation in temperature dependence among the bins. Figure 4.1.2.2-2 Normalized average RSR versus temperature for all bins with weighted fit. Coefficients at one wavelength (830 nm) are included below to enable a sense of the variations between the bins and the resultant weighted coefficient (see Table 4.1.2.2-1). Table 4.1.2.2-1 Coefficients for each of the 10 bins for the constant, linear and quadratic terms at 830 nm. The lowest line is the weighted coefficient used in this model as it appears in Table 4.1.2.4-2. bin a b c 1 0.771737 5.50036E-04 1.65102E-06 2 0.785720 4.29481E-04 1.90630E-06 3 0.769909 5.90394E-04 1.51800E-06 4 0.767452 6.08742E-04 1.48339E-06 5 0.769370 5.85084E-04 1.54880E-06 6 0.772336 5.48266E-04 1.65152E-06 7 0.767795 5.93230E-04 1.54627E-06 8 0.782577 4.98224E-04 1.70743E-06 9 0.823810 2.12714E-04 2.12991E-06 10 0.801691 6.16234E-04 8.73406E-07 830 0.769592 5.84289E-04 1.548489E-06 A second order polynomial is used to describe the temperature variation of the RSR. The temperature of interest and the weighted coefficients from Table 4.1.2.4-2 for the appropriate imager are used to compute the polynomial fit as shown in equation 2, where a, b, and c are given in Table 4.1.2.4-2. EQUATION_02.GIF (2) The RSR for any pixel at any temperature is obtained by multiplying this polynomial by the average RSR within the bin for that pixel, normalized by the average RSR at the base temperature of 239K (see Tables 6-82 for these normalized averages). While only bins 1-10 are possible for the HRI and SLI, the MRI has several anomalous pixels designated by bins 20-29 and there is a separate table for the normalized averages within a bin for these pixels (see Table 7b3). 4.1.2.3. Use of the model (or how to get the RSR for any pixel) There are three steps to obtaining the RSR for a temperature, imager and pixel of interest: 1) Find the bin of the pixel of interest (Appendix A, Tables 1-34) 2) Find the temperature coefficients for the imager of interest (Table 4.1.2.4- 2, or appropriate table from Appendix A) 3) Use equation 2 for the temperature of interest and the average within a bin for each wavelength (Tables 6-85) 4.1.2.4. Sample Calculation For example, assume we are interested in knowing the RSR for the pixel in column 14 and row 24 of the HRI at a temperature of 208K and a wavelength of 700 nm. Since we are interested in the HRI in columns 0-32 we go to Table 4.1.2.4-1a. The "h ratio" bin designator is a value of 7. Next, go to Table 4.1.2.4-2 and get the weighted coefficients for the HRI at 700 nm. These are the polynomial coefficients: 1.095146 -8.66387E-05 -1.270609E-06 Thus, the (a+b*T+c*T^2) portion is: a+b*T+c*T^2 = 1.095146 -8.66387E-05*(208.0) - 1.270609E-06*(208.0)^2 = 1.02215 Finally, go to Table 66 for the average within bin 7 at 700 nm (normalized to the average with a bin at 239K) for the HRI. 0.857343 Thus, the RSR for pixel HRI (14,24) at 700 nm and a temperature of 208K is: 0.876333 Tables giving the bin designators for each imager pixel are too large to fit on a single page. In figure 4.1.2.4-1a we reproduce such a table from Appendix A, in order to illustrate a calculation. Each imager has a distinct number of columns (HRI: 160; MRI: 176; SLI: 128) such that each table is divided up by column and designated by letter as follows: HRI (Table 1a-1e), MRI (Table 2a- 2f), and SLI (Table 3a-3d). The designated letter and associated columns in parentheses are: a (0-32), b (33-64), c (65-96), d (97-128), e (129-160) and f (129-159). All three tables are color coded in the identical manner for readability, but the top left cell of each page designates the imager. Note that columns and rows are numbered from zero. Table 4.1.2.4-1a Columns 0-32 of the H ratio bin designator for the HRI HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 0 3 4 4 4 3 4 4 4 4 5 5 4 4 4 6 4 5 4 4 5 4 4 4 4 4 4 4 4 4 5 5 4 1 5 5 5 5 6 5 6 6 5 6 6 5 5 5 6 5 6 6 6 5 6 6 6 5 5 6 6 5 6 6 6 6 2 6 6 5 5 6 6 6 6 5 6 6 6 5 5 5 5 6 6 5 6 6 6 6 5 6 6 6 6 6 7 6 6 3 5 5 5 6 6 5 6 6 6 6 5 5 6 5 5 6 6 6 5 7 5 6 6 7 7 6 6 6 6 6 6 6 4 5 6 6 5 5 6 6 5 6 5 5 5 6 5 5 5 6 6 6 5 6 6 6 5 5 6 6 7 6 5 6 6 5 5 5 5 5 6 6 5 5 6 5 5 5 5 6 6 5 5 6 7 6 6 6 5 5 6 6 6 6 6 6 7 6 6 6 6 6 5 5 6 6 6 6 6 5 6 6 6 7 6 7 6 6 6 7 6 6 6 5 6 6 7 6 6 6 6 7 6 6 6 6 6 6 5 5 6 5 6 6 6 5 6 6 6 6 6 6 6 7 5 6 6 6 6 6 7 6 6 6 8 5 6 6 6 5 5 6 5 6 6 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 5 6 5 6 6 5 9 6 5 5 6 6 6 5 6 6 5 5 4 6 5 6 7 6 7 6 6 6 5 6 6 6 7 6 6 7 6 6 6 10 5 6 6 5 5 5 4 5 5 5 6 5 6 6 5 6 7 6 6 7 7 6 5 6 6 6 5 6 6 6 6 6 11 5 6 5 5 6 5 5 5 6 5 5 6 5 6 5 6 6 7 6 6 6 5 6 6 7 6 5 6 6 6 6 6 12 5 6 6 5 5 5 5 5 5 5 5 6 5 5 6 6 6 6 6 6 6 6 6 6 7 6 6 6 7 7 6 6 13 5 6 5 5 6 6 6 6 5 6 6 6 6 5 5 6 6 6 6 6 6 7 6 6 6 5 6 6 6 6 6 6 14 5 6 6 6 6 5 6 5 5 6 5 5 6 6 5 5 6 6 6 6 6 6 6 6 6 6 6 7 7 6 6 5 15 6 5 5 6 5 6 6 5 5 6 5 5 6 6 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 7 6 16 5 5 5 5 5 6 6 6 6 5 6 7 6 6 5 5 6 5 6 5 6 6 5 5 6 5 7 6 6 6 5 6 17 5 6 6 6 6 6 5 6 6 5 5 6 6 5 6 7 5 5 6 7 6 6 6 6 6 7 6 6 7 6 6 6 18 6 6 5 6 6 5 5 6 5 6 5 5 5 6 5 5 6 6 6 7 6 7 6 6 6 6 6 6 6 6 7 6 19 5 6 6 6 6 5 6 6 5 6 6 5 6 6 5 6 6 6 7 6 6 6 6 6 6 6 7 6 6 5 7 7 20 6 6 7 6 6 6 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 6 6 6 21 6 6 6 6 6 6 5 5 6 6 6 5 6 6 6 6 6 6 7 6 6 6 6 6 6 6 6 6 6 6 6 6 22 5 5 5 6 5 5 6 5 5 5 5 5 6 6 6 6 6 6 6 6 7 5 6 6 6 6 6 6 6 6 6 6 23 5 5 5 6 6 5 5 6 6 6 6 5 6 5 6 6 6 6 6 7 6 6 7 6 6 6 6 7 5 6 6 6 24 5 6 6 6 7 6 6 5 6 5 6 5 5 5 7 6 6 6 6 6 6 6 5 6 6 6 6 7 6 7 6 6 25 6 5 6 5 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 6 7 6 5 7 6 6 7 26 4 6 5 5 6 6 6 5 7 5 6 6 6 6 6 5 6 6 6 6 7 6 6 5 6 6 7 6 6 7 7 6 27 4 6 6 6 5 6 6 6 6 5 5 6 7 6 6 5 6 6 6 6 7 6 6 6 6 6 6 6 7 6 7 6 28 5 5 5 6 6 5 6 6 6 6 6 5 5 6 6 6 6 6 6 7 6 6 6 7 6 5 6 6 6 5 7 6 29 5 6 6 6 6 6 6 6 6 6 5 6 6 6 6 6 6 6 7 6 6 6 7 6 6 6 6 6 6 7 6 6 HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 30 5 6 6 6 6 6 6 6 5 6 5 6 6 6 6 6 6 6 6 7 6 6 7 7 6 6 7 6 6 6 6 6 31 4 5 6 6 6 6 5 6 5 5 6 6 6 6 6 6 6 6 6 7 6 7 6 7 6 6 5 7 6 6 6 6 32 5 5 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 6 7 6 6 6 6 6 6 6 6 6 5 33 4 6 6 5 6 6 6 5 5 6 6 5 5 5 6 6 7 7 6 7 6 7 6 5 6 6 7 6 6 6 7 6 34 255 6 7 6 6 6 6 6 6 5 5 5 8 6 6 7 7 6 6 6 6 6 6 6 5 6 6 6 6 6 7 6 35 255 5 6 5 6 6 6 4 6 6 6 5 6 5 6 6 6 6 7 6 6 6 6 6 6 6 6 5 6 6 6 6 36 255 5 6 6 6 6 5 6 5 6 5 5 5 6 6 6 6 5 6 7 7 7 6 6 6 6 6 7 5 6 7 6 37 255 6 7 6 6 6 6 6 7 5 6 6 5 6 6 6 6 6 5 6 6 6 6 6 6 6 6 6 6 6 7 6 38 255 6 6 6 6 5 5 5 6 5 6 6 6 6 6 7 5 6 8 6 6 6 6 7 6 6 6 6 6 6 6 7 39 255 6 6 5 6 6 6 6 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 7 6 6 6 6 6 6 6 40 255 5 6 5 6 6 5 6 5 6 6 5 6 6 5 4 5 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 41 255 5 5 6 6 6 6 5 5 6 6 5 6 5 5 6 7 6 7 7 6 6 6 6 6 5 6 6 6 6 6 6 42 255 5 6 5 6 6 6 6 5 5 6 6 6 6 6 6 6 6 6 6 7 6 6 7 5 6 6 6 7 7 7 6 43 255 5 6 6 5 6 5 5 5 5 6 6 6 6 6 7 6 6 7 6 6 6 6 6 5 6 6 6 6 6 6 6 44 255 255 6 5 5 6 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 6 6 6 45 255 255 6 6 6 5 6 6 5 5 5 6 6 6 5 6 6 5 6 6 6 6 6 6 6 7 6 6 7 6 6 6 46 255 255 6 6 6 5 5 5 6 6 6 6 5 6 6 6 6 6 6 6 7 6 6 6 6 6 6 6 6 6 6 6 47 255 255 5 5 5 5 5 6 5 5 7 5 5 5 6 5 6 6 7 6 7 6 6 6 5 6 6 6 6 6 6 6 48 255 255 5 5 6 5 6 6 5 6 6 6 6 5 5 5 6 5 7 6 6 5 6 6 5 6 6 6 7 6 6 6 49 255 255 5 6 6 5 6 6 5 5 6 5 5 5 5 5 5 6 6 6 5 6 6 6 6 6 6 6 6 6 5 6 50 255 255 6 5 5 6 5 5 5 5 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 5 6 6 6 5 6 51 255 255 4 6 5 6 6 6 5 5 5 6 6 5 6 5 5 6 6 6 6 6 6 6 5 6 6 6 5 6 6 6 52 255 255 6 5 5 5 4 6 6 6 5 6 6 6 6 6 6 6 6 6 5 6 6 5 7 6 6 6 6 6 6 6 53 255 255 5 5 6 6 6 5 5 5 5 5 6 5 6 6 6 6 6 6 6 6 6 5 6 5 6 6 6 6 5 6 54 255 255 6 6 6 6 6 5 5 6 6 5 5 6 5 6 6 6 6 6 6 7 5 7 6 6 6 6 7 6 6 6 55 255 255 6 5 5 6 5 6 5 6 5 4 6 6 6 6 6 6 5 5 6 6 6 6 6 6 6 6 6 5 6 6 56 255 255 5 6 6 6 6 5 5 5 5 5 5 5 6 6 5 5 5 5 5 6 6 5 6 6 6 6 5 5 6 6 57 255 255 6 6 5 6 5 5 5 4 5 5 5 5 6 6 5 7 10 7 5 6 7 6 5 6 6 6 5 6 6 6 58 255 255 6 6 6 5 4 5 6 5 5 4 5 5 6 6 5 7 10 8 6 6 6 6 7 6 6 6 6 6 6 6 59 255 255 6 6 5 5 6 5 5 6 5 5 5 5 5 6 5 5 6 5 6 7 6 6 7 6 6 6 5 6 5 6 60 255 255 6 5 6 5 5 6 6 5 6 6 5 5 5 5 5 6 6 6 6 5 6 6 7 5 5 6 6 6 5 5 61 255 255 5 5 6 5 6 6 5 6 5 5 6 5 6 5 5 6 6 6 6 6 6 6 6 6 6 6 5 6 6 6 HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 62 255 255 6 6 4 5 5 5 5 6 5 5 6 5 5 4 5 6 5 6 5 6 6 6 6 6 5 7 6 6 6 6 63 255 255 5 5 5 5 5 5 5 6 6 4 5 5 5 5 5 5 6 6 6 6 6 6 5 5 6 5 7 5 6 6 64 255 255 5 5 5 5 5 5 5 5 4 5 5 5 5 6 5 5 6 6 6 6 5 6 6 5 5 6 6 6 7 7 65 255 255 5 6 5 5 5 5 4 5 5 5 5 5 6 5 6 6 5 6 5 5 5 6 5 6 5 6 6 6 6 6 66 255 255 6 6 5 5 5 5 6 5 5 5 4 6 5 6 6 6 6 6 6 6 6 5 6 6 6 5 5 6 5 6 67 255 255 5 5 5 6 5 5 4 5 5 5 5 5 5 5 5 6 6 5 6 5 6 6 6 6 7 5 6 6 6 6 68 255 255 5 5 6 5 6 5 5 6 6 5 6 6 6 6 5 6 5 5 6 6 5 6 7 6 6 6 6 5 6 5 69 255 255 6 5 6 4 5 5 6 6 6 5 5 5 5 5 6 5 6 6 6 5 5 6 6 6 5 6 6 6 6 5 70 255 255 6 5 5 5 6 5 6 6 5 5 5 5 5 5 6 5 6 5 6 5 6 5 6 6 6 6 6 6 6 6 71 255 255 5 6 6 5 6 5 6 5 5 6 6 6 6 5 5 5 6 5 5 6 5 5 5 6 6 6 6 5 6 5 72 255 255 5 5 6 5 5 5 5 5 5 6 5 5 6 4 6 5 5 6 5 6 6 5 5 6 6 6 6 6 6 6 73 255 255 4 5 6 5 5 5 5 5 6 5 6 6 5 5 5 5 6 6 6 6 6 6 6 5 6 6 5 6 5 6 74 255 255 5 6 4 5 5 5 5 5 5 5 5 5 5 6 6 6 5 5 6 6 5 6 6 5 5 6 6 5 6 6 75 255 3 5 4 5 6 5 5 5 5 6 5 5 5 5 6 5 6 6 5 5 5 6 4 6 6 6 6 5 6 5 6 76 255 4 6 5 5 6 6 5 6 5 6 5 6 6 5 6 6 6 5 5 5 6 6 6 8 5 6 5 6 6 6 5 77 255 5 5 5 6 5 5 6 6 6 6 6 5 5 6 5 6 6 6 6 6 6 5 5 6 5 6 6 5 6 6 5 78 255 5 6 5 5 6 5 6 5 6 5 5 6 5 5 5 5 6 7 7 6 5 6 5 6 6 6 5 6 5 7 6 79 4 6 5 5 5 5 5 6 5 5 5 5 5 5 5 5 6 5 6 6 6 6 6 6 6 6 6 5 6 6 6 6 80 4 6 6 5 5 5 5 5 6 5 5 5 5 5 5 5 5 5 7 6 5 5 6 6 6 5 6 6 6 5 6 6 81 5 6 6 6 6 5 6 5 5 4 5 5 4 5 5 6 5 6 6 5 6 5 6 6 6 6 6 6 5 6 5 5 82 4 5 5 5 5 5 5 5 5 5 6 4 5 4 5 7 5 6 6 6 6 6 5 5 6 6 6 6 6 6 6 6 83 4 5 6 6 6 4 5 5 4 5 5 5 5 5 5 7 6 5 6 6 5 6 5 6 6 5 6 6 6 6 5 6 84 4 5 6 5 6 5 4 5 5 5 5 5 6 5 5 5 5 6 6 6 6 6 6 6 5 5 5 5 6 5 5 6 85 4 5 5 5 4 5 5 5 5 5 5 6 5 6 6 5 5 6 6 5 6 5 6 5 6 5 6 6 5 5 6 6 86 4 5 5 5 5 4 5 5 5 6 5 5 5 5 6 5 5 6 5 5 5 5 5 5 6 5 5 5 5 5 5 5 87 4 5 5 5 5 5 5 5 5 4 5 6 5 5 5 5 5 6 6 6 5 5 5 5 6 6 5 5 6 5 6 5 88 4 5 6 5 4 5 4 5 5 5 5 5 5 5 5 6 5 6 5 6 6 6 6 5 5 6 6 5 6 5 6 6 89 4 5 6 6 5 4 6 4 5 5 5 5 5 5 5 6 5 6 6 6 6 6 6 6 5 6 6 6 6 6 5 5 90 3 6 6 5 5 5 6 5 5 5 5 5 5 4 5 5 5 6 6 6 5 5 5 6 5 5 6 5 6 6 5 5 91 4 6 6 5 5 6 5 4 5 5 5 5 6 5 6 5 6 6 6 6 6 6 6 6 5 5 6 4 6 6 5 6 92 5 5 5 5 5 5 5 6 4 4 5 5 5 4 5 6 6 5 6 6 6 6 6 6 6 5 5 5 6 5 6 6 93 3 5 5 5 5 5 6 4 5 5 5 5 5 6 6 5 5 5 6 5 5 5 5 5 4 6 5 5 5 5 5 5 HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 94 4 5 5 5 5 5 6 5 5 4 6 5 5 4 4 5 6 5 6 6 6 5 6 6 5 6 5 6 6 6 5 6 95 4 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 6 5 5 5 5 4 6 6 4 7 6 96 3 5 5 5 6 5 5 5 5 6 5 5 6 5 5 5 5 5 5 5 6 5 5 4 6 5 6 5 4 5 6 6 97 4 5 5 5 5 5 5 5 6 6 5 5 5 5 5 5 5 6 5 6 5 6 5 6 5 5 5 5 5 5 5 5 98 3 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 6 5 5 5 6 5 5 5 6 5 5 5 5 6 6 5 99 3 5 6 5 5 5 4 5 5 5 4 5 5 5 5 4 5 4 5 5 6 5 5 6 5 5 5 5 6 6 6 6 100 3 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 5 6 5 5 5 6 5 5 5 6 6 101 4 5 6 4 5 5 5 4 5 5 5 4 5 5 4 5 5 6 5 5 6 6 5 5 6 6 6 5 6 5 5 5 102 3 5 6 5 5 4 5 5 6 4 4 5 5 5 5 6 5 5 5 5 5 5 5 5 6 6 5 5 5 5 6 5 103 3 4 4 5 6 4 4 4 5 5 5 5 3 4 4 5 6 6 6 6 6 5 6 5 6 6 5 5 4 5 6 5 104 3 5 5 5 5 4 5 4 4 4 5 5 5 4 4 6 5 5 6 6 5 5 6 5 5 5 5 4 5 7 5 5 105 3 5 5 5 5 4 5 5 4 5 5 4 5 4 5 5 5 5 5 5 5 5 5 5 5 5 6 5 5 5 6 6 106 3 5 4 5 5 5 5 5 4 5 4 5 5 5 5 5 5 5 4 5 5 5 5 5 5 4 5 5 5 5 6 6 107 3 4 5 5 5 5 6 5 5 5 4 4 5 5 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 5 5 5 108 4 3 5 5 5 5 5 6 5 5 5 4 5 5 4 6 5 6 5 5 4 5 5 5 6 5 5 5 5 5 5 5 109 3 5 5 4 4 4 5 5 5 6 5 4 5 5 4 6 5 5 5 5 5 5 4 5 5 5 5 5 5 5 6 5 110 3 5 5 4 5 5 5 5 4 5 5 5 5 5 4 5 6 5 5 5 5 6 5 5 5 5 4 6 6 6 5 5 111 4 5 5 5 4 5 4 5 5 4 5 5 4 5 6 5 6 5 5 6 5 5 6 5 6 5 5 6 5 6 6 5 112 4 5 5 4 4 5 6 5 5 4 5 5 5 5 5 5 5 5 5 5 6 5 6 5 6 5 5 5 5 6 5 5 113 3 5 5 5 5 4 5 5 4 5 5 5 4 5 5 4 5 5 6 5 5 5 5 5 5 5 5 5 5 5 5 5 114 4 5 5 5 5 4 5 4 4 4 4 4 4 4 5 5 6 6 5 6 5 5 5 5 5 5 5 5 6 5 5 5 115 3 6 5 4 5 5 4 4 5 4 5 5 4 5 5 5 5 5 5 5 5 5 5 5 6 6 5 5 5 5 5 5 116 4 5 5 5 5 5 5 5 4 4 4 5 5 4 4 5 5 5 6 5 6 5 5 5 5 5 6 5 5 5 5 5 117 3 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 6 5 5 5 6 5 5 5 5 5 5 5 118 4 5 5 5 4 5 4 4 5 4 5 4 5 5 5 5 5 5 5 5 6 5 5 6 5 5 5 6 5 6 6 5 119 3 5 5 5 4 4 4 4 4 4 4 4 4 5 6 5 5 6 6 5 5 5 5 5 5 5 5 5 5 6 5 5 120 3 4 4 5 4 5 4 5 5 4 5 5 5 5 5 5 4 5 5 5 4 6 6 6 6 5 6 5 5 5 5 5 121 3 4 5 5 4 4 5 5 5 5 5 5 4 5 5 4 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 6 122 3 4 5 5 5 5 5 5 5 5 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 123 4 5 5 5 5 4 5 5 4 5 4 5 5 5 5 5 5 5 5 5 6 6 6 6 5 5 5 5 5 5 5 5 124 3 4 5 4 5 5 4 4 5 5 4 5 4 4 5 5 4 5 6 5 5 5 5 5 5 5 4 4 5 5 5 5 125 3 5 5 5 5 5 5 5 4 4 5 4 5 4 4 5 5 5 4 5 5 5 4 6 5 5 5 5 5 5 5 5 HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 126 3 5 5 4 5 5 4 5 5 5 4 4 8 4 7 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 127 3 5 4 5 6 6 5 5 5 4 5 5 5 4 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 4 128 3 5 5 5 5 4 4 4 5 5 6 5 4 5 5 4 5 5 5 5 6 5 5 5 5 5 5 5 6 6 5 5 129 3 4 5 5 5 4 5 5 5 5 5 5 5 5 5 5 4 6 5 5 5 5 5 5 5 5 6 5 5 5 5 5 130 3 5 5 4 6 4 5 4 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 6 5 5 5 5 5 5 5 131 255 4 4 4 4 5 4 4 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 5 4 5 132 255 7 4 5 5 4 5 4 4 4 4 5 5 5 5 5 5 5 5 6 5 5 4 5 4 5 5 5 5 5 5 5 133 255 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 4 5 4 4 5 5 4 4 4 5 5 5 5 6 5 134 255 4 5 5 4 4 4 5 5 5 4 5 5 5 5 4 4 5 5 5 5 5 5 4 4 4 4 5 5 6 6 6 135 255 4 5 5 4 5 5 5 5 5 5 4 4 4 5 4 4 5 5 5 5 5 5 4 5 10 7 4 4 5 5 4 136 255 5 5 4 5 4 4 5 5 5 6 4 4 5 4 6 5 5 5 5 5 4 5 5 4 8 5 4 5 5 6 5 137 255 4 5 5 5 5 4 5 5 4 5 5 4 4 5 6 4 4 5 5 5 5 4 5 4 4 4 5 5 5 5 5 138 255 4 5 5 5 5 5 5 6 4 5 5 5 5 6 4 5 5 6 5 6 5 5 7 6 5 5 5 7 4 5 5 139 255 5 5 4 4 5 5 4 4 5 5 5 5 4 5 5 5 5 5 5 5 5 5 4 4 5 5 4 4 5 5 5 140 255 5 5 5 5 4 4 5 5 4 6 5 5 4 4 5 5 6 5 5 6 6 5 5 5 4 4 4 5 4 5 5 141 255 4 5 5 4 5 4 5 5 5 5 5 5 4 4 5 5 5 5 5 5 6 5 4 5 4 4 4 5 5 4 5 142 255 4 5 4 5 4 4 5 5 5 5 5 6 5 5 5 4 5 4 5 5 5 5 5 4 5 5 5 5 5 5 5 143 255 4 5 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 4 5 6 5 5 4 5 5 5 5 5 5 5 4 144 255 6 5 5 5 5 5 4 5 5 5 5 5 5 5 5 6 4 5 5 5 5 4 5 5 6 5 6 5 6 5 6 145 255 4 4 5 5 6 5 5 5 5 5 5 5 5 5 5 5 4 5 4 5 5 5 5 5 4 6 4 4 5 5 4 146 255 4 5 5 5 5 5 5 5 5 5 4 4 5 5 5 5 5 5 6 4 5 5 5 4 5 5 5 4 6 5 5 147 255 4 5 5 5 5 6 4 5 4 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 4 5 5 5 5 5 5 148 255 4 4 5 5 5 5 5 6 4 4 5 5 6 5 4 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 149 255 4 4 4 5 5 6 4 5 4 5 4 5 5 4 4 5 5 5 5 5 5 5 6 6 5 6 5 5 5 5 6 150 255 5 4 5 5 5 4 5 4 4 4 4 5 4 5 5 5 5 6 5 5 5 5 5 6 5 5 5 5 5 5 5 151 255 5 5 5 5 5 5 4 5 5 4 4 4 5 5 4 5 5 5 5 5 5 6 5 5 5 5 5 5 5 4 5 152 255 4 4 4 5 5 5 4 5 4 5 5 5 5 5 5 5 5 4 5 5 4 5 5 5 5 4 5 5 5 5 5 153 255 4 4 5 5 4 4 5 4 5 4 4 4 4 5 5 4 5 5 5 5 5 4 5 5 5 5 4 5 5 5 5 154 255 4 5 4 4 4 5 5 5 5 4 5 5 5 4 4 3 8 7 4 5 5 5 4 5 5 4 5 5 5 6 5 155 255 5 5 5 4 5 4 5 5 5 4 5 4 5 4 4 4 5 5 6 5 6 5 4 5 6 4 4 4 6 4 5 156 255 4 5 4 5 5 5 4 4 5 4 4 4 5 5 4 5 4 5 5 5 5 5 4 5 4 5 5 6 4 6 5 157 255 4 4 4 5 5 4 4 4 4 5 5 5 5 5 5 5 5 5 4 4 5 5 5 4 5 5 5 4 5 5 5 HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 158 255 3 5 4 5 5 4 4 5 5 4 4 5 5 4 4 4 5 5 5 5 5 6 5 5 5 5 5 4 5 5 5 159 255 4 5 5 5 4 4 5 4 4 5 4 5 5 4 4 5 5 5 6 5 5 5 5 5 5 4 4 4 5 5 5 160 255 4 4 5 5 5 5 5 4 4 4 4 4 5 4 4 5 4 5 5 5 5 5 5 4 5 5 5 5 4 4 5 161 255 4 5 5 5 4 5 4 5 5 7 5 4 5 4 5 4 5 5 5 5 6 4 4 5 5 5 4 5 4 5 5 162 255 5 5 5 4 5 7 5 4 5 4 3 4 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 163 255 3 5 5 5 5 4 4 5 5 5 3 4 4 4 4 5 5 6 5 4 5 5 6 4 5 5 5 4 5 5 5 164 255 4 5 4 5 4 4 5 4 5 4 4 5 4 4 5 4 4 5 5 5 5 5 5 5 5 4 5 5 5 5 5 165 255 4 4 5 4 4 4 5 4 5 4 4 4 4 4 4 5 5 5 5 5 4 5 5 5 7 5 5 5 5 5 6 166 255 3 6 5 4 5 4 5 5 5 4 5 5 5 4 4 4 5 5 5 4 4 5 4 4 5 5 5 5 5 5 5 167 255 3 5 4 4 5 5 5 5 4 5 4 5 5 5 5 5 4 5 5 5 6 5 5 5 5 4 4 5 5 5 4 168 255 4 4 5 4 6 6 4 4 4 5 5 4 5 5 5 4 5 5 5 5 5 5 4 5 5 4 5 4 5 5 5 169 255 4 5 5 5 5 4 4 5 4 5 5 5 5 4 4 5 5 4 5 5 5 5 5 4 5 4 3 5 5 5 6 170 255 4 5 4 4 4 4 4 5 4 4 4 4 5 5 5 5 5 5 5 5 6 5 5 5 5 5 5 5 4 5 5 171 255 4 5 5 5 5 4 5 4 4 5 5 5 4 4 5 4 6 5 5 5 5 5 5 5 5 5 5 4 4 5 5 172 255 4 5 5 5 4 5 5 5 4 4 4 4 4 5 5 6 5 6 5 5 5 4 5 5 5 5 4 5 5 5 5 173 255 4 5 5 4 5 4 4 5 4 5 4 4 4 5 5 5 4 5 4 4 5 5 5 4 5 5 5 4 5 5 5 174 255 3 4 5 5 5 4 5 4 4 4 4 5 4 4 5 4 4 6 5 5 5 4 5 5 5 4 5 5 5 5 5 175 255 4 5 5 4 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 5 5 5 176 255 4 5 5 4 5 4 5 5 4 5 5 4 5 4 5 4 5 4 5 5 5 5 6 5 5 5 4 5 4 5 5 177 255 4 5 4 5 4 5 5 4 4 4 5 4 4 4 5 5 5 5 5 5 4 5 5 5 5 5 4 5 5 5 5 178 255 4 4 4 3 4 4 5 5 4 3 4 4 4 4 5 5 4 4 3 5 4 5 5 4 5 5 5 4 5 5 5 179 255 4 5 4 6 7 4 5 4 5 4 4 5 5 4 5 5 4 5 4 4 5 5 5 5 5 4 5 6 5 5 5 180 255 3 4 4 5 5 3 4 5 5 5 4 5 4 4 5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 4 5 181 255 3 5 4 4 3 5 5 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 4 5 5 182 255 3 5 4 4 4 5 4 5 4 5 5 5 4 5 4 4 4 4 4 4 4 5 5 5 5 4 5 4 5 5 4 183 255 3 5 5 4 4 4 3 4 4 5 4 4 4 5 4 5 4 5 5 6 5 5 6 4 5 5 5 5 5 5 5 184 255 4 4 4 4 4 4 7 3 4 4 4 5 4 4 5 4 5 5 5 5 4 5 5 5 5 5 4 5 5 5 5 185 255 3 4 5 4 4 5 7 4 4 4 4 5 5 4 4 5 4 5 5 5 4 4 5 5 4 5 4 5 5 4 4 186 255 4 5 5 5 4 3 4 3 4 4 4 3 4 5 5 4 4 5 5 5 5 5 5 4 5 5 5 5 4 5 5 187 255 3 5 5 4 4 4 4 4 5 5 4 4 5 5 5 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 7 188 255 3 4 5 4 4 4 4 4 5 4 5 5 5 5 4 5 5 4 5 5 5 4 4 4 4 5 4 5 5 5 5 189 255 3 5 5 4 4 5 4 4 4 4 4 5 4 5 4 4 4 5 5 5 6 5 5 4 4 4 5 4 5 5 5 HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 190 255 4 4 5 5 5 4 4 4 4 5 4 4 4 4 5 5 4 5 4 5 5 5 4 4 6 5 5 4 5 5 4 191 255 4 5 5 5 4 4 4 4 5 4 5 4 4 5 4 5 4 4 5 4 4 5 5 4 4 4 5 4 4 4 5 192 255 3 4 4 4 4 4 4 4 5 4 4 4 4 4 4 5 4 4 4 4 5 4 5 4 5 5 5 5 5 4 5 193 255 4 4 3 4 3 3 4 4 4 4 4 4 4 4 4 5 4 5 5 5 4 5 5 4 5 5 5 4 5 5 4 194 255 3 4 4 4 4 3 5 4 4 4 4 5 4 4 5 4 4 5 4 4 4 5 4 5 4 4 4 5 5 4 5 195 255 3 4 4 4 4 4 5 6 3 4 4 4 4 4 4 3 4 5 5 5 5 5 4 5 5 5 5 5 4 4 5 196 255 3 4 5 4 5 4 4 4 4 4 4 4 4 4 6 5 4 5 4 4 5 5 5 5 5 4 4 5 5 4 4 197 255 255 5 4 4 3 4 3 5 5 4 4 4 4 4 4 6 5 5 5 4 5 5 4 5 4 4 4 5 4 4 5 198 255 255 255 3 4 3 3 4 4 4 4 4 5 4 4 4 4 4 5 6 4 4 5 4 4 4 4 4 5 5 5 5 199 255 255 255 3 3 4 3 4 5 4 4 4 4 5 3 4 4 5 4 5 5 4 5 5 4 5 5 5 4 5 5 5 200 255 255 255 3 5 5 4 4 5 4 5 4 4 4 4 5 4 5 5 5 5 4 5 4 4 5 5 4 5 5 5 5 201 255 255 255 2 3 4 4 4 4 4 4 5 5 5 4 4 4 5 4 4 4 4 5 4 5 5 5 4 5 5 4 5 202 255 255 255 255 4 4 5 5 5 4 4 4 5 4 5 4 5 4 4 4 4 5 5 4 4 5 5 5 5 5 4 5 203 255 255 255 255 4 3 5 5 4 5 5 4 4 4 5 4 4 5 5 4 5 5 5 5 5 4 4 5 4 5 5 4 204 255 255 255 255 3 3 3 4 5 5 4 4 4 5 4 3 4 5 5 5 5 4 4 5 4 5 4 5 5 4 4 4 205 255 255 255 255 4 4 4 4 4 4 4 4 5 3 4 5 4 5 5 4 5 5 5 4 5 4 4 4 5 5 4 5 206 255 255 255 255 3 4 3 4 4 4 4 5 5 3 4 5 4 5 5 4 4 5 5 4 6 5 4 4 5 5 5 4 207 255 255 255 255 3 4 3 3 3 5 4 3 4 3 4 4 5 4 5 5 4 5 5 5 4 5 5 4 4 4 4 5 208 255 255 255 255 3 3 4 3 3 4 4 3 4 4 4 4 5 4 4 5 5 5 4 5 5 5 5 4 4 4 5 5 209 255 255 255 255 3 4 4 4 3 4 4 4 4 4 3 3 4 5 4 5 5 5 4 4 4 5 4 5 4 4 4 4 210 255 255 255 255 3 3 3 4 4 4 4 4 5 4 5 4 4 4 4 5 5 4 5 4 4 5 4 5 4 4 4 4 211 255 255 255 255 3 4 5 4 4 4 4 4 3 4 4 4 4 4 4 4 5 4 5 5 5 4 4 4 5 5 4 4 212 255 255 255 255 3 3 4 4 4 3 4 4 4 3 4 4 4 4 4 3 5 4 4 4 4 5 4 5 5 5 4 4 213 255 255 255 255 3 3 4 4 5 4 4 4 4 4 4 3 4 4 3 3 4 4 5 5 4 4 4 4 5 4 5 4 214 255 255 255 255 3 3 3 3 4 4 4 4 4 4 4 4 5 5 4 5 4 5 5 4 5 3 4 4 4 4 5 4 215 255 255 255 255 3 4 3 4 3 4 4 4 4 4 4 4 4 3 4 4 5 5 4 4 5 5 5 4 3 5 4 3 216 255 255 255 255 3 4 4 4 3 3 4 4 4 4 4 3 4 3 4 5 4 5 5 5 4 5 5 4 4 4 4 4 217 255 255 255 3 3 3 4 3 4 3 3 3 4 4 4 3 4 3 4 4 4 5 5 4 4 5 4 4 4 5 4 4 218 255 255 3 3 4 3 3 4 4 4 4 4 3 4 3 3 7 5 4 5 4 4 4 4 4 4 5 4 4 4 4 4 219 255 255 3 4 4 3 4 4 4 4 3 5 4 4 3 3 6 4 4 5 5 5 4 4 5 4 5 4 4 5 4 4 220 255 255 3 4 3 4 4 4 4 4 4 4 4 4 4 3 5 4 5 4 4 5 4 4 5 5 5 4 4 4 4 4 221 255 255 3 4 4 4 5 4 4 3 4 4 3 4 4 4 4 4 4 4 4 5 4 4 4 5 4 5 4 4 4 4 HRI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 222 255 255 3 4 4 4 4 4 4 3 4 4 4 4 4 4 3 4 5 5 4 4 5 5 5 5 5 4 4 4 5 4 223 255 255 3 4 4 4 3 4 4 4 4 3 4 4 5 4 4 4 4 4 4 6 4 4 5 5 5 4 4 5 4 4 224 255 255 4 4 4 4 4 4 5 4 4 4 4 4 4 4 5 4 4 5 4 4 4 5 4 5 4 4 5 4 5 4 225 255 255 3 5 4 3 5 5 4 4 4 4 3 4 4 4 4 4 4 5 4 5 4 4 4 7 4 4 5 5 5 4 226 255 255 3 4 4 3 3 3 3 4 4 4 3 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 5 4 4 5 227 255 255 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 5 4 5 4 228 255 255 3 5 3 4 3 4 5 4 4 4 4 3 5 4 4 4 3 4 4 4 4 4 5 4 4 4 4 4 4 3 229 255 255 4 4 3 4 4 4 4 4 3 4 4 4 4 3 3 4 4 4 5 4 4 4 5 5 4 4 4 4 4 4 230 255 255 3 4 4 4 3 3 4 3 3 4 3 3 4 3 5 4 4 4 4 4 4 4 4 4 5 4 4 3 3 4 231 255 255 4 4 3 4 3 3 3 3 3 4 3 4 4 4 4 4 4 5 4 4 4 4 4 5 4 4 4 4 4 4 232 255 255 3 4 3 3 3 3 4 5 3 4 3 3 3 4 4 3 4 4 5 5 5 4 4 4 4 3 4 4 4 4 233 255 255 3 4 3 4 3 3 4 3 3 4 3 4 4 3 4 4 4 4 4 4 4 4 4 4 4 5 4 4 4 4 234 255 255 3 3 3 4 4 3 3 3 3 4 4 4 4 3 3 4 4 4 5 4 3 4 5 4 4 4 4 4 3 4 235 255 255 4 4 3 3 3 3 3 3 3 4 3 4 3 4 3 3 4 3 4 4 4 4 4 4 4 3 4 5 4 4 236 255 255 3 3 4 3 4 4 3 4 4 3 3 4 3 3 4 4 4 4 5 3 4 3 3 4 4 3 4 4 4 4 237 255 255 3 4 3 3 5 3 3 3 3 3 3 4 3 3 4 4 5 7 5 4 4 4 3 4 4 5 4 4 4 4 238 255 255 3 3 3 3 4 3 3 3 3 4 3 4 4 5 4 3 3 5 4 4 4 3 5 4 4 4 4 3 3 3 239 255 255 3 3 3 4 3 3 3 3 3 3 4 3 3 3 4 3 3 3 3 4 4 3 4 3 4 4 4 4 4 4 240 255 255 3 4 3 3 3 3 3 3 3 3 4 3 3 4 3 4 3 3 4 4 5 4 4 3 4 4 4 4 4 4 241 255 255 3 3 3 4 3 4 3 3 3 3 3 3 3 4 3 4 5 4 5 4 3 4 4 3 4 3 3 4 4 4 242 255 255 3 3 3 3 3 3 3 3 3 3 3 3 4 3 4 4 6 3 3 4 4 4 4 4 4 4 4 3 3 4 243 255 255 3 3 3 3 3 3 3 3 3 4 3 3 3 4 3 3 4 4 4 3 4 3 4 4 3 4 3 3 3 4 244 255 255 3 4 3 3 3 3 3 3 3 3 3 4 3 3 3 4 4 3 4 4 4 3 4 4 3 4 4 4 4 4 245 255 255 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 4 4 3 4 4 4 4 4 3 3 4 3 4 4 246 255 255 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 4 3 3 4 4 3 3 3 4 3 3 4 4 247 255 255 3 3 3 3 3 3 4 3 4 3 4 4 4 3 3 4 3 3 3 3 3 4 3 3 3 3 3 3 3 4 248 255 255 3 3 3 3 3 3 4 4 3 3 3 3 4 3 3 3 3 5 5 3 3 4 3 3 3 4 3 3 4 3 249 255 255 3 4 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 6 4 3 3 3 4 4 4 3 3 4 3 3 250 255 255 3 3 5 3 3 4 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 251 255 255 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 252 255 255 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 253 255 255 1 2 1 2 2 1 1 1 2 1 1 2 1 1 2 2 2 2 2 2 2 1 3 3 2 2 2 2 1 1 Table 1b. Columns 33-64 of the H ratio bin designator for the HRI. Table 1c. Columns 65-96 of the H ratio bin designator for the HRI. Table 1d. Columns 97-128 of the H ratio bin designator for the HRI. Table 1e. Columns 129-159 of the H ratio bin designator for the HRI. Table 2a. Columns 0-32 of the H ratio bin designator for the MRI. Table 2b. Columns 33-64 of the H ratio bin designator for the MRI. Table 2c. Columns 65-96 of the H ratio bin designator for the MRI. Table 2d. Columns 97-128 of the H ratio bin designator for the MRI. Table 2e. Columns 129-160 of the H ratio bin designator for the MRI. Table 2f. Columns 161-175 of the H ratio bin designator for the MRI. Table 3a. Columns 0-32 of the H ratio bin designator for the SLI. Table 3b. Columns 33-64 of the H ratio bin designator for the SLI. Table 3c. Columns 65-96 of the H ratio bin designator for the SLI. Table 3d. Columns 97-128 of the H ratio bin designator for the SLI. Table 4.1.2.4-2 Weighted coefficients for the HRI, MRI and SLI. Color has been added to this table to avoid confusion and facilitate reading of numbers. The HRI is coded green, the MRI pink and the SLI yellow. Wavelengths in increments of 50 nm are underlined. HRI HRI HRI MRI MRI MRI SLI SLI SLI Wave a b c a b c a b c 600 3.288974 -1.32550E-02 1.665190E-05 5.111286 -2.809130E- 4.752022E- 4.916132 -2.681690E- 4.555899E-05 02 05 02 610 2.418571 -5.19748E-03 -1.911770E-06 2.120584 1.272830E- -1.805949E- 1.894906 2.022280E-03 -2.202743E- 04 05 05 620 3.036622 -1.04974E-02 9.139965E-06 3.864251 -1.649534E- 1.951607E- 3.786977 -1.582640E- 1.810568E-05 02 05 02 630 6.932502 -3.73153E-02 5.388908E-05 8.363853 -4.863792E- 7.649633E- 8.709702 -5.101840E- 8.062100E-05 02 05 02 640 11.550716 -6.75313E-02 1.011196E-04 18.958386 -1.220593E- 2.003961E- 19.757071 -1.272160E- 2.084717E-04 01 04 01 650 4.280622 -1.43356E-02 4.494052E-06 9.466947 -4.964568E- 6.302795E- 9.767006 -5.147660E- 6.560333E-05 02 05 02 660 1.218266 3.43220E-03 -1.758690E-05 1.783594 1.757473E- -1.995971E- 1.846405 1.377690E-03 -1.943957E- 03 05 05 670 1.13103 1.06200E-03 -6.576115E-06 1.119748 1.949033E- -1.001173E- 1.128906 1.883840E-03 -9.890641E- 03 05 06 680 1.14824 1.55337E-05 -2.600322E-06 1.169833 1.036833E- -2.951323E- 1.178632 -7.962670E- -2.723885E- 05 06 05 06 690 1.132828 -2.06158E-04 -1.417045E-06 1.170288 -4.830111E- -9.209733E- 1.180867 -5.909070E- -6.526977E- 04 07 04 07 700 1.095146 -8.66387E-05 -1.270609E-06 1.132769 -3.923761E- -6.570176E- 1.144507 -5.056740E- -3.868393E- 04 07 04 07 710 1.063243 5.74426E-05 -1.325585E-06 1.09917 -2.378110E- -7.248308E- 1.111581 -3.528090E- -4.583687E- 04 07 04 07 720 1.051643 6.57093E-05 -1.164638E-06 1.083889 -1.953717E- -6.395075E- 1.093074 -2.935570E- -3.879672E- 04 07 04 07 730 1.025303 1.90553E-04 -1.232495E-06 1.050522 -4.726235E- -8.583844E- 1.058149 -9.856340E- -5.981789E- 06 07 05 07 740 1.005586 2.18169E-04 -1.009786E-06 1.018717 1.166237E- -8.143735E- 1.025921 2.198150E-05 -5.432133E- 04 07 07 750 0.963112 3.84177E-04 -9.665908E-07 0.967982 3.423563E- -8.754751E- 0.976417 2.372720E-04 -5.817663E- 04 07 07 760 0.908761 5.94740E-04 -9.090922E-07 0.901442 6.413009E- -9.714695E- 0.91181 5.295140E-04 -6.841600E- 04 07 07 770 0.863176 7.54517E-04 -7.824690E-07 0.856536 8.049467E- -8.741732E- 0.867289 6.878980E-04 -5.716742E- 04 07 07 780 0.85718 6.48941E-04 -2.357488E-07 0.842646 7.681261E- -4.748638E- 0.851954 6.652280E-04 -2.078589E- 04 07 07 790 0.828506 7.47089E-04 -1.525834E-07 0.816895 8.593257E- -4.153557E- 0.82361 7.673580E-04 -1.475281E- 04 07 07 800 0.833012 5.98054E-04 3.903167E-07 0.811271 7.923628E- -3.375598E- 0.820289 6.842670E-04 2.598304E-07 04 08 810 0.808892 6.40763E-04 6.342086E-07 0.784474 8.523508E- 1.858560E- 0.796538 7.196040E-04 5.305716E-07 04 07 820 0.804004 5.19249E-04 1.218913E-06 0.775586 7.501205E- 7.592601E- 0.782894 6.574500E-04 1.017625E-06 04 07 830 0.769592 5.84289E-04 1.548489E-06 0.741416 8.179728E- 1.071970E- 0.751243 7.056300E-04 1.370365E-06 04 06 840 0.768034 3.81093E-04 2.422684E-06 0.724258 7.302301E- 1.739966E- 0.729972 6.607260E-04 1.932139E-06 04 06 850 0.715047 5.58351E-04 2.603638E-06 0.676204 8.734291E- 1.977582E- 0.684124 7.785580E-04 2.234335E-06 04 06 860 0.746674 1.15022E-04 3.917412E-06 0.687043 6.302120E- 2.817308E- 0.69328 5.559430E-04 3.018810E-06 04 06 870 0.551166 1.42498E-03 1.902245E-06 0.534266 1.601658E- 1.457453E- 0.541877 1.511700E-03 1.703015E-06 03 06 880 0.538356 1.27811E-03 2.751388E-06 0.518945 1.458275E- 2.336711E- 0.525667 1.380230E-03 2.549068E-06 03 06 890 0.531977 1.02575E-03 3.889665E-06 0.506863 1.255058E- 3.369906E- 0.510508 1.191200E-03 3.578455E-06 03 06 900 0.705137 -8.16463E-04 8.586537E-06 0.664135 -4.605281E- 7.821583E- 0.674648 -5.741800E- 8.117875E-06 04 06 04 910 0.59218 -8.57303E-05 7.513227E-06 0.54541 2.972283E- 6.736824E- 0.551387 2.246860E-04 6.941266E-06 04 06 920 0.560715 -1.62827E-04 8.374011E-06 0.507345 2.745011E- 7.489396E- 0.515397 1.744900E-04 7.769978E-06 04 06 930 0.605488 -9.09530E-04 1.069717E-05 0.531685 -3.019800E- 9.462133E- 0.536014 -3.668970E- 9.661755E-06 04 06 04 940 0.621983 -1.40141E-03 1.249612E-05 0.540727 -7.312909E- 1.113373E- 0.547967 -8.261790E- 1.140822E-05 04 05 04 950 0.646745 -1.95553E-03 1.441543E-05 0.544412 -1.134064E- 1.279101E- 0.54783 -1.194410E- 1.299115E-05 03 05 03 960 0.611102 -2.11004E-03 1.565419E-05 0.52158 -1.389899E- 1.422808E- 0.525755 -1.452950E- 1.442346E-05 03 05 03 970 0.675438 -3.15991E-03 1.892512E-05 0.577255 -2.363779E- 1.733266E- 0.578638 -2.412710E- 1.751903E-05 03 05 03 980 0.683064 -3.86779E-03 2.178988E-05 0.600222 -3.184212E- 2.039689E- 0.60699 -3.275410E- 2.066598E-05 03 05 03 990 0.676964 -4.55704E-03 2.478376E-05 0.596667 -3.909083E- 2.349562E- 0.596966 -3.934840E- 2.360497E-05 03 05 03 1000 0.693957 -5.69615E-03 2.923833E-05 0.628506 -5.165556E- 2.817695E- 0.634181 -5.236900E- 2.838410E-05 03 05 03 1010 0.80112 -7.82353E-03 3.630920E-05 0.742488 -7.332771E- 3.529279E- 0.747447 -7.390910E- 3.545725E-05 03 05 03 1020 0.930916 -1.03893E-02 4.483759E-05 0.868927 -9.864173E- 4.374059E- 0.877364 -9.942390E- 4.392786E-05 03 05 03 1030 1.119663 -1.38032E-02 5.583123E-05 1.050266 -1.317542E- 5.442762E- 1.056694 -1.322710E- 5.454070E-05 02 05 02 1040 1.572806 -1.98429E-02 7.314089E-05 1.497343 -1.916700E- 7.163924E- 1.502572 -1.917750E- 7.160510E-05 02 05 02 1050 2.91639 -3.29331E-02 1.047122E-04 2.818997 -3.202886E- 1.026359E- 2.78034 -3.163270E- 1.016520E-04 02 04 02 1060 2.393062 -2.80499E-02 9.323775E-05 2.326112 -2.742079E- 9.177578E- 2.314316 -2.729240E- 9.145683E-05 02 05 02 1070 2.199146 -2.67789E-02 9.133312E-05 2.089045 -2.571144E- 8.878625E- 2.056294 -2.537580E- 8.795805E-05 02 05 02 1080 2.482303 -2.99791E-02 9.979281E-05 2.395833 -2.915238E- 9.783855E- 2.373029 -2.892280E- 9.728562E-05 02 05 02 1090 2.732143 -3.27908E-02 1.072091E-04 2.560594 -3.113325E- 1.032658E- 2.513793 -3.067560E- 1.021747E-04 02 04 02 In Tables 4.1.2.4-3 through 4.1.2.4-5, the HRI is again color coded green, the MRI pink and the SLI yellow, and wavelengths in increments of 50 nm are underlined. Table 4.1.2.4-3 Mean within a bin for the HRI at a base temperature of 239K. HRI 239 HRI Wave bin1 bin2 bin3 bin4 bin5 bin6 bin7 bin8 bin9 bin10 600 0.000409 0.000403 0.000403 0.000403 0.000401 0.000400 0.000396 0.000387 0.000385 0.000296 610 0.000630 0.000624 0.000610 0.000606 0.000604 0.000601 0.000597 0.000536 0.000550 0.000499 620 0.001248 0.001227 0.001195 0.001179 0.001170 0.001158 0.001144 0.001116 0.001091 0.000979 630 0.003808 0.003765 0.003650 0.003590 0.003552 0.003512 0.003481 0.003323 0.003287 0.003143 640 0.026109 0.025735 0.025155 0.024793 0.024607 0.024537 0.024395 0.023536 0.023267 0.022056 650 0.174333 0.172120 0.168724 0.167026 0.166515 0.167335 0.167036 0.163012 0.159064 0.155990 660 0.447086 0.441074 0.433138 0.430408 0.430460 0.434243 0.434258 0.425884 0.415512 0.408875 670 0.648236 0.638821 0.626193 0.622814 0.623542 0.629313 0.629097 0.617304 0.601251 0.592584 680 0.787447 0.777250 0.759335 0.753728 0.752734 0.755740 0.753524 0.734957 0.716742 0.704198 690 0.879738 0.868918 0.849413 0.840739 0.836303 0.833192 0.827833 0.807952 0.790720 0.772165 700 0.918463 0.909638 0.890858 0.879939 0.872526 0.865013 0.857343 0.840918 0.827005 0.808520 710 0.923696 0.915492 0.900927 0.891204 0.884286 0.877994 0.872686 0.862698 0.852849 0.840423 720 0.932059 0.925570 0.913844 0.906791 0.902232 0.898618 0.895133 0.891142 0.886042 0.878857 730 0.951119 0.945691 0.937716 0.933349 0.931049 0.930548 0.928845 0.926405 0.925087 0.925376 740 0.980878 0.977423 0.973106 0.971251 0.970386 0.971148 0.970291 0.968028 0.966026 0.966936 750 0.999771 0.999617 0.998925 0.998946 0.999117 0.999391 0.999161 0.997790 0.997351 0.997619 760 0.990232 0.993136 0.995833 0.995901 0.995648 0.994920 0.995460 0.993539 0.998128 0.998882 770 0.946463 0.950959 0.956434 0.957210 0.957326 0.956071 0.957144 0.958673 0.965342 0.971307 780 0.889420 0.895235 0.902805 0.904380 0.905862 0.906951 0.910360 0.915311 0.922163 0.940552 790 0.842642 0.849113 0.858790 0.862722 0.866081 0.869741 0.874523 0.888691 0.894859 0.920377 800 0.817516 0.824518 0.834855 0.840813 0.846278 0.852696 0.858932 0.878682 0.887412 0.910429 810 0.811005 0.818270 0.829138 0.836304 0.842207 0.848907 0.856188 0.878371 0.890237 0.917457 820 0.813526 0.820729 0.830570 0.839112 0.846843 0.854271 0.862701 0.885135 0.893815 0.933281 830 0.811992 0.819161 0.828532 0.836226 0.842058 0.845376 0.850877 0.876276 0.894654 0.925405 840 0.791726 0.799769 0.807962 0.813692 0.817752 0.817268 0.821787 0.848021 0.866133 0.902996 850 0.751840 0.759320 0.766570 0.770680 0.773018 0.769036 0.772069 0.800082 0.819727 0.850050 860 0.685450 0.692679 0.698824 0.701057 0.702244 0.697388 0.700049 0.726437 0.748975 0.775509 870 0.615174 0.622489 0.628267 0.630006 0.630846 0.625993 0.628488 0.657810 0.681479 0.706108 880 0.550480 0.557107 0.562798 0.565156 0.566730 0.562914 0.565744 0.593554 0.612059 0.648066 890 0.488361 0.493855 0.500562 0.503975 0.506348 0.503576 0.506393 0.533218 0.554863 0.581582 900 0.429571 0.434530 0.441399 0.445232 0.447702 0.445821 0.448710 0.473166 0.492249 0.516137 910 0.380195 0.384712 0.392209 0.396785 0.399630 0.398650 0.401828 0.423951 0.442078 0.465881 920 0.333609 0.338381 0.346722 0.352007 0.355087 0.354559 0.357606 0.376994 0.394518 0.417340 930 0.291900 0.296693 0.305195 0.310488 0.313647 0.313721 0.316598 0.334764 0.350289 0.370821 940 0.255753 0.260061 0.268504 0.273875 0.276902 0.277173 0.279744 0.296105 0.308798 0.327094 950 0.225063 0.229117 0.237275 0.242423 0.245097 0.245268 0.247577 0.262212 0.272715 0.290766 960 0.197572 0.201310 0.208936 0.213721 0.216247 0.216417 0.218428 0.231823 0.241326 0.256447 970 0.172548 0.176090 0.182990 0.187463 0.189821 0.189788 0.191375 0.203094 0.211734 0.225728 980 0.148439 0.151369 0.157534 0.161378 0.163168 0.162711 0.163906 0.173642 0.181464 0.191741 990 0.125264 0.127708 0.132802 0.135883 0.137257 0.136542 0.137426 0.145674 0.152766 0.160607 1000 0.102344 0.104458 0.108514 0.110924 0.111958 0.111095 0.111739 0.118226 0.123865 0.131732 1010 0.079881 0.081472 0.084592 0.086457 0.087217 0.086368 0.086771 0.092417 0.097469 0.102306 1020 0.059610 0.060790 0.063143 0.064521 0.065101 0.064398 0.064721 0.069085 0.073212 0.077240 1030 0.042432 0.043235 0.044994 0.046004 0.046447 0.045958 0.046235 0.049620 0.052846 0.055973 1040 0.029308 0.029857 0.031138 0.031877 0.032192 0.031850 0.032065 0.034439 0.037101 0.039436 1050 0.019027 0.019354 0.020257 0.020783 0.021020 0.020816 0.020988 0.022780 0.024377 0.026204 1060 0.014123 0.014390 0.015100 0.015541 0.015744 0.015600 0.015736 0.017142 0.018529 0.019987 1070 0.010434 0.010629 0.011178 0.011530 0.011699 0.011603 0.011705 0.012809 0.013832 0.014959 1080 0.007944 0.008083 0.008522 0.008809 0.008947 0.008881 0.008966 0.009807 0.010684 0.011587 1090 0.006110 0.006215 0.006556 0.006789 0.006901 0.006854 0.006925 0.007619 0.008236 0.009022 Table 4.1.2.4-4a Mean within a bin at wavelength for the MRI. The MRI has 10 anomalous pixels, designated by bin numbers 20-29 and these are included in Table 7b7. MRI 239 MRI Wave bin1 bin2 bin3 bin4 bin5 bin6 bin7 bin8 bin9 bin10 600 0.00032 0.00024 0.00027 0.00025 0.00025 0.00025 0.00025 0.00026 0.00018 0.00031 610 0.00025 0.00025 0.00028 0.00027 0.00026 0.00026 0.00026 0.00026 0.00021 0.00031 620 0.00015 0.00029 0.00031 0.00031 0.00033 0.00033 0.00033 0.00033 0.00034 0.00037 630 0.00079 0.00067 0.00068 0.00067 0.00068 0.00069 0.00069 0.00068 0.00062 0.00069 640 0.00565 0.00594 0.00582 0.00577 0.00580 0.00585 0.00584 0.00571 0.00551 0.00527 650 0.07779 0.07776 0.07685 0.07600 0.07590 0.07615 0.07651 0.07573 0.07411 0.07298 660 0.34953 0.34653 0.34388 0.33971 0.33863 0.33901 0.34129 0.33931 0.33372 0.32781 670 0.60563 0.60701 0.60031 0.59236 0.58909 0.58883 0.59234 0.58904 0.57914 0.56809 680 0.77558 0.77094 0.76202 0.74995 0.74352 0.74088 0.74162 0.73410 0.72043 0.70245 690 0.87354 0.87191 0.85879 0.84479 0.83607 0.83041 0.82582 0.81247 0.79652 0.77555 700 0.92276 0.90942 0.89792 0.88473 0.87476 0.86641 0.85713 0.84295 0.82786 0.81085 710 0.91607 0.91268 0.90197 0.88976 0.88178 0.87550 0.86883 0.85944 0.84721 0.83612 720 0.92540 0.92249 0.91317 0.90281 0.89715 0.89276 0.88867 0.88436 0.87658 0.87428 730 0.95192 0.94522 0.93849 0.93151 0.92744 0.92440 0.92260 0.92075 0.91804 0.91480 740 0.97838 0.97701 0.97531 0.97160 0.96961 0.96824 0.96772 0.96741 0.96566 0.96430 750 0.99893 0.99992 0.99919 0.99891 0.99864 0.99863 0.99882 0.99783 0.99817 0.99534 760 0.99311 0.98808 0.99180 0.99357 0.99431 0.99431 0.99386 0.99493 0.99132 0.99378 770 0.94681 0.94055 0.94848 0.95126 0.95350 0.95503 0.95477 0.95870 0.95981 0.96839 780 0.88909 0.88175 0.89308 0.89791 0.90123 0.90367 0.90526 0.91317 0.91789 0.93217 790 0.83970 0.83750 0.85104 0.85794 0.86277 0.86688 0.87095 0.88273 0.89270 0.91558 800 0.81130 0.81497 0.82962 0.83918 0.84535 0.85104 0.85762 0.87281 0.88633 0.91356 810 0.81275 0.81167 0.82821 0.83895 0.84577 0.85242 0.85975 0.87662 0.89217 0.92306 820 0.81948 0.82058 0.83579 0.84491 0.85142 0.85874 0.86776 0.88693 0.90422 0.93574 830 0.83797 0.82700 0.84004 0.84961 0.85470 0.85915 0.86281 0.88052 0.89870 0.93518 840 0.80907 0.81289 0.82288 0.83104 0.83459 0.83676 0.83619 0.85206 0.87208 0.90484 850 0.77563 0.77312 0.78231 0.78942 0.79170 0.79183 0.78750 0.80261 0.82269 0.85805 860 0.70666 0.70776 0.71591 0.72235 0.72259 0.72140 0.71510 0.72949 0.75030 0.78191 870 0.64117 0.63618 0.64328 0.64902 0.65051 0.65016 0.64451 0.65983 0.67968 0.71331 880 0.57218 0.57310 0.57783 0.58241 0.58396 0.58453 0.58045 0.59477 0.61412 0.64837 890 0.51476 0.51156 0.51597 0.52026 0.52241 0.52346 0.52050 0.53423 0.55335 0.58589 900 0.45438 0.44996 0.45583 0.46079 0.46331 0.46506 0.46328 0.47631 0.49376 0.52519 910 0.39439 0.39966 0.40481 0.40985 0.41317 0.41560 0.41500 0.42703 0.44306 0.47365 920 0.35050 0.35166 0.35773 0.36330 0.36700 0.36950 0.36964 0.38095 0.39657 0.42162 930 0.31012 0.31035 0.31592 0.32181 0.32523 0.32754 0.32795 0.33845 0.35284 0.37572 940 0.27058 0.27222 0.27846 0.28435 0.28820 0.29079 0.29155 0.30147 0.31377 0.33515 950 0.23925 0.23924 0.24581 0.25165 0.25555 0.25836 0.25936 0.26794 0.27946 0.29863 960 0.20904 0.21077 0.21706 0.22232 0.22587 0.22836 0.22929 0.23675 0.24743 0.26385 970 0.18427 0.18578 0.19106 0.19587 0.19885 0.20102 0.20164 0.20804 0.21648 0.23164 980 0.16139 0.16112 0.16557 0.16952 0.17204 0.17372 0.17385 0.17921 0.18707 0.20029 990 0.13790 0.13639 0.14012 0.14337 0.14536 0.14669 0.14647 0.15070 0.15705 0.16773 1000 0.11222 0.11188 0.11471 0.11729 0.11882 0.11981 0.11936 0.12276 0.12791 0.13729 1010 0.08741 0.08796 0.08963 0.09158 0.09268 0.09335 0.09281 0.09546 0.09943 0.10670 1020 0.06634 0.06582 0.06717 0.06849 0.06929 0.06973 0.06922 0.07136 0.07449 0.08024 1030 0.04703 0.04710 0.04794 0.04892 0.04960 0.04994 0.04957 0.05118 0.05369 0.05806 1040 0.03232 0.03253 0.03313 0.03393 0.03446 0.03477 0.03452 0.03571 0.03749 0.04078 1050 0.02118 0.02103 0.02151 0.02208 0.02250 0.02274 0.02261 0.02348 0.02475 0.02698 1060 0.01561 0.01565 0.01599 0.01645 0.01682 0.01705 0.01699 0.01769 0.01877 0.02057 1070 0.01159 0.01153 0.01182 0.01219 0.01250 0.01270 0.01267 0.01321 0.01406 0.01549 1080 0.00874 0.00885 0.00905 0.00932 0.00958 0.00975 0.00974 0.01017 0.01084 0.01189 1090 0.00680 0.00685 0.00699 0.00721 0.00741 0.00754 0.00754 0.00790 0.00838 0.00929 Table 4.1.2.4-5a Mean within a bin at wavelength for the 10 anomalous pixels for the MRI, designated by bin numbers 20-29. MRI Wave bin20 bin21 bin22 bin23 bin24 bin25 bin26 bin27 bin28 bin29 600 0.00019 0.00050 0.00000 0.00043 0.00040 0.00024 0.00036 0.00060 0.00019 0.00020 610 0.00016 0.00042 0.00023 0.00000 0.00034 0.00000 0.00000 0.00051 0.00049 0.00034 620 0.00016 0.00042 0.00000 0.00037 0.00069 0.00021 0.00061 0.00017 0.00033 0.00052 630 0.00051 0.00090 0.00025 0.00118 0.00074 0.00089 0.00065 0.00055 0.00053 0.00073 640 0.00543 0.00437 0.00520 0.00380 0.00509 0.00552 0.00540 0.00529 0.00583 0.00557 650 0.07792 0.06648 0.07295 0.06790 0.06986 0.07798 0.07191 0.07347 0.07537 0.07488 660 0.35368 0.31290 0.33316 0.30081 0.31384 0.34097 0.32264 0.33308 0.33270 0.33343 670 0.61599 0.53131 0.58563 0.51627 0.54163 0.59742 0.56518 0.56611 0.57903 0.59105 680 0.76333 0.65879 0.70882 0.62965 0.67614 0.74691 0.71446 0.71241 0.73516 0.73027 690 0.83620 0.71619 0.76448 0.71234 0.74533 0.81500 0.78088 0.80043 0.82869 0.82845 700 0.86097 0.77356 0.79310 0.75452 0.78568 0.86137 0.83964 0.85116 0.85581 0.86336 710 0.87148 0.79531 0.83475 0.80742 0.82472 0.86724 0.85768 0.84337 0.87398 0.88373 720 0.88532 0.85533 0.86644 0.81462 0.86097 0.88901 0.90309 0.88147 0.89649 0.89385 730 0.91467 0.90703 0.90819 0.88318 0.90535 0.94378 0.93590 0.91312 0.91930 0.93736 740 0.96455 0.97005 0.95892 0.95126 0.95151 0.97245 0.95526 0.96179 0.97036 0.98657 750 1.00000 0.97756 1.00000 0.96730 0.98806 1.00000 0.99582 0.99672 1.00000 1.00000 760 0.98868 0.98409 0.98503 1.00000 1.00000 0.99781 1.00000 1.00000 0.99888 0.99360 770 0.94455 0.97068 0.93358 0.97896 0.96872 0.96937 0.97377 0.96899 0.96711 0.96026 780 0.88503 0.96256 0.89471 0.96001 0.95408 0.90399 0.94711 0.92300 0.92206 0.89967 790 0.84680 0.94651 0.88902 0.93532 0.93112 0.87747 0.91606 0.89952 0.88701 0.88605 800 0.82821 0.95499 0.89276 0.95525 0.91963 0.88006 0.93455 0.87711 0.87026 0.86336 810 0.83233 0.98139 0.90376 0.97320 0.93150 0.88441 0.94809 0.88866 0.88741 0.86702 820 0.82161 0.99994 0.88891 0.97302 0.95744 0.89269 0.97253 0.88511 0.88851 0.88889 830 0.81634 1.00000 0.89233 0.99432 0.96249 0.90446 0.99241 0.89199 0.89148 0.89372 840 0.78558 0.97110 0.86272 0.97048 0.93138 0.88036 0.98284 0.87559 0.87491 0.88331 850 0.74165 0.91343 0.79595 0.91742 0.90342 0.83139 0.92178 0.82844 0.83784 0.82694 860 0.65909 0.84857 0.72277 0.84954 0.81117 0.77543 0.84765 0.75310 0.76597 0.75853 870 0.58560 0.76361 0.65707 0.77438 0.74233 0.69239 0.76555 0.68921 0.68385 0.70302 880 0.53390 0.69184 0.59308 0.71296 0.68110 0.62259 0.68577 0.61137 0.62834 0.62143 890 0.47054 0.63247 0.54250 0.64782 0.62339 0.55062 0.63346 0.55022 0.56794 0.55470 900 0.41900 0.58120 0.47861 0.58271 0.55235 0.49053 0.56265 0.49433 0.49583 0.48924 910 0.37569 0.52099 0.43834 0.53677 0.49722 0.43670 0.50652 0.44214 0.45027 0.44858 920 0.33330 0.46632 0.39273 0.46842 0.44971 0.38625 0.44965 0.39169 0.40067 0.39544 930 0.29370 0.41183 0.34889 0.43207 0.40375 0.34922 0.40693 0.35286 0.35003 0.34941 940 0.26295 0.37580 0.30487 0.37865 0.35402 0.30956 0.36132 0.31549 0.31146 0.31112 950 0.23153 0.33792 0.27169 0.33957 0.32104 0.27495 0.31845 0.27860 0.27906 0.27466 960 0.20022 0.29457 0.24227 0.29992 0.28769 0.24392 0.28222 0.24551 0.25121 0.24415 970 0.18177 0.26033 0.21273 0.26285 0.24503 0.21448 0.24786 0.21429 0.22044 0.21397 980 0.15202 0.22908 0.18247 0.22673 0.21510 0.18360 0.21977 0.18632 0.18990 0.18760 990 0.13011 0.18477 0.14852 0.19372 0.18449 0.15598 0.18086 0.15687 0.15891 0.15514 1000 0.10392 0.15429 0.12518 0.16031 0.14845 0.12751 0.14957 0.13035 0.13164 0.12649 1010 0.08001 0.11941 0.09601 0.12700 0.11806 0.09921 0.11726 0.10013 0.10353 0.10146 1020 0.05961 0.08989 0.07214 0.09395 0.08909 0.07343 0.08798 0.07647 0.07623 0.07587 1030 0.04262 0.06524 0.05143 0.06829 0.06524 0.05370 0.06454 0.05392 0.05451 0.05393 1040 0.02964 0.04737 0.03726 0.04814 0.04466 0.03672 0.04427 0.03838 0.03935 0.03683 1050 0.01888 0.03093 0.02363 0.03276 0.02945 0.02501 0.03067 0.02471 0.02558 0.02445 1060 0.01441 0.02492 0.01826 0.02518 0.02328 0.01814 0.02360 0.01885 0.01905 0.01840 1070 0.01071 0.01856 0.01351 0.01876 0.01761 0.01329 0.01732 0.01434 0.01428 0.01390 1080 0.00822 0.01449 0.01081 0.01457 0.01368 0.01033 0.01332 0.01067 0.01084 0.01049 1090 0.00631 0.01160 0.00810 0.01169 0.01063 0.00800 0.01051 0.00834 0.00865 0.00810 Table 4.1.2.4-6 Mean within a bin at wavelength for the SLI at 239K. SLI 239 SLI Wave bin1 bin2 bin3 bin4 bin5 bin6 bin7 bin8 bin9 bin10 600 0.00022 0.00022 0.00024 0.00024 0.00024 0.00024 0.00023 0.00013 0.00044 0.00016 610 0.00023 0.00024 0.00024 0.00024 0.00024 0.00024 0.00026 0.00020 0.00038 0.00022 620 0.00031 0.00030 0.00029 0.00030 0.00030 0.00031 0.00031 0.00034 0.00019 0.00050 630 0.00057 0.00058 0.00060 0.00063 0.00063 0.00062 0.00063 0.00060 0.00040 0.00053 640 0.00528 0.00524 0.00539 0.00557 0.00555 0.00550 0.00550 0.00553 0.00509 0.00454 650 0.07757 0.07654 0.07618 0.07642 0.07635 0.07621 0.07575 0.07406 0.07306 0.07037 660 0.36147 0.35585 0.34943 0.34575 0.34580 0.34644 0.34481 0.34033 0.33652 0.32646 670 0.63748 0.62808 0.61247 0.60334 0.60308 0.60418 0.60102 0.59149 0.58921 0.57052 680 0.80040 0.78843 0.76804 0.75603 0.75366 0.75286 0.74752 0.73468 0.72620 0.70498 690 0.88591 0.87411 0.85339 0.84241 0.83715 0.83288 0.82588 0.80676 0.79854 0.78133 700 0.91507 0.90381 0.88652 0.87690 0.86900 0.86159 0.85420 0.83784 0.82828 0.80257 710 0.91908 0.90885 0.89391 0.88656 0.88080 0.87559 0.87071 0.86196 0.85985 0.83498 720 0.93256 0.92406 0.91136 0.90515 0.90110 0.89732 0.89399 0.89111 0.88838 0.87617 730 0.95809 0.95094 0.94099 0.93536 0.93281 0.93076 0.92936 0.92723 0.92655 0.91681 740 0.98678 0.98400 0.97871 0.97465 0.97318 0.97220 0.97122 0.97211 0.97949 0.97571 750 0.99986 0.99996 0.99982 0.99958 0.99944 0.99938 0.99883 0.99897 0.99970 0.99723 760 0.98057 0.98337 0.98796 0.99046 0.99131 0.99184 0.99265 0.99221 0.99195 0.99123 770 0.92944 0.93385 0.94257 0.94798 0.94938 0.95055 0.95294 0.95686 0.95938 0.96903 780 0.87267 0.87970 0.88888 0.89513 0.89834 0.90140 0.90485 0.91664 0.92727 0.92927 790 0.83168 0.83968 0.84964 0.85566 0.85971 0.86410 0.86977 0.88659 0.89833 0.90576 800 0.81268 0.82001 0.83056 0.83687 0.84164 0.84729 0.85451 0.87320 0.89013 0.90718 810 0.80792 0.81573 0.82756 0.83396 0.83869 0.84419 0.85189 0.87560 0.89814 0.91017 820 0.80719 0.81592 0.82745 0.83626 0.84301 0.85031 0.86010 0.88447 0.90618 0.91416 830 0.80024 0.81002 0.82248 0.83113 0.83424 0.83784 0.84661 0.87662 0.90457 0.90357 840 0.77198 0.78185 0.79438 0.80495 0.80688 0.80862 0.81753 0.84826 0.87179 0.88119 850 0.72303 0.73331 0.74589 0.75688 0.75770 0.75785 0.76677 0.80101 0.81883 0.83168 860 0.65497 0.66435 0.67543 0.68568 0.68616 0.68565 0.69377 0.72506 0.74801 0.75195 870 0.58580 0.59256 0.60385 0.61419 0.61489 0.61462 0.62329 0.65572 0.68685 0.67563 880 0.52243 0.52916 0.53971 0.54991 0.55147 0.55184 0.56019 0.59204 0.60801 0.61814 890 0.46445 0.46993 0.48057 0.49032 0.49204 0.49269 0.50058 0.53025 0.54593 0.55165 900 0.40910 0.41499 0.42464 0.43364 0.43541 0.43608 0.44351 0.47106 0.48566 0.49284 910 0.36275 0.36753 0.37778 0.38666 0.38879 0.38981 0.39636 0.42423 0.43838 0.44383 920 0.31915 0.32442 0.33448 0.34248 0.34450 0.34567 0.35170 0.37673 0.38852 0.39576 930 0.28166 0.28609 0.29557 0.30240 0.30411 0.30512 0.31072 0.33279 0.34458 0.35051 940 0.24717 0.25190 0.26104 0.26744 0.26890 0.26970 0.27502 0.29598 0.30396 0.31228 950 0.21771 0.22194 0.23062 0.23650 0.23780 0.23848 0.24307 0.26117 0.27277 0.27368 960 0.19139 0.19523 0.20285 0.20811 0.20930 0.20989 0.21382 0.22942 0.23823 0.23987 970 0.16745 0.17076 0.17757 0.18225 0.18316 0.18356 0.18696 0.20118 0.20801 0.21111 980 0.14397 0.14663 0.15252 0.15653 0.15704 0.15707 0.15996 0.17338 0.17888 0.18246 990 0.12069 0.12307 0.12784 0.13142 0.13178 0.13169 0.13416 0.14388 0.14960 0.15211 1000 0.09808 0.09975 0.10363 0.10675 0.10699 0.10682 0.10892 0.11735 0.12137 0.12326 1010 0.07585 0.07726 0.08019 0.08272 0.08291 0.08274 0.08441 0.09068 0.09344 0.09521 1020 0.05652 0.05734 0.05956 0.06147 0.06162 0.06149 0.06278 0.06815 0.06990 0.07225 1030 0.04007 0.04079 0.04241 0.04382 0.04393 0.04384 0.04479 0.04873 0.05044 0.05156 1040 0.02769 0.02812 0.02935 0.03040 0.03047 0.03041 0.03113 0.03409 0.03488 0.03657 1050 0.01797 0.01826 0.01912 0.01985 0.01991 0.01989 0.02041 0.02249 0.02301 0.02423 1060 0.01332 0.01353 0.01422 0.01481 0.01487 0.01488 0.01528 0.01697 0.01755 0.01884 1070 0.00981 0.00999 0.01053 0.01098 0.01104 0.01105 0.01136 0.01262 0.01312 0.01403 1080 0.00747 0.00762 0.00803 0.00838 0.00844 0.00845 0.00870 0.00976 0.01023 0.01085 1090 0.00577 0.00586 0.00619 0.00646 0.00650 0.00651 0.00672 0.00749 0.00778 0.00839 4.1.2.5. Location of Data and Supporting Programs The location of the average RSR at each temperature is listed in Table 4.1.2.5- 1. The program: yield_rsr.pro which exists in /users/lisa/RSR_model/ gives the RSR for any imager, any pixel and any temperature. To recreate the sample calculation in this document, type .run yield_rsr.pro then type: yield_rsr,'hri',208.,14,24,rsr The output (for all the wavelengths) is called rsr. The program g.pro and then o.pro were used initially as well. Table 4.1.2.5-1. Complete path to the RSR data at temperature averaged over all pixels. Temperature Data Path 171 /misc/RSR_03/SH3/29Jul96_S/ave2_dli1.dat 185 /misc/RSR_03/SH3/30Jul96.2/ave2_dli1.dat 201 /misc/RSR_04/SH3/1Aug96.1_/ave2_dli1.dat 225 /misc/RSR_04/SH3/1Aug96.2_/ave2_dli1.dat 239 /misc/RSR_04/SH3/31Jul96_S/ave2_dli1.dat 269 /misc/RSR_03/SH3/30Jul96.1/ave2_dli1.dat 294 /misc/RSR_03/SH3/26Jul96_S/ave2_dli1.dat 4.1.2.6. Model Performance The model is evaluated by computing the RMS (root mean square) between the RSR of a specific measured pixel and the RSR computed by the model (Equation 3). EQUATION_03.GIF (3) In equation 3, difference is defined as measured RSR- calculated RSR, and 49 is one less that the number of measurements (wavelengths in this case). Figures 11- 13 show the RMS results for the three imagers at all seven temperatures respectively. Figure 4.1.2.6-1 for the HRI shows that approximately 99% of the pixels have an RMS value of less than 1%. All pixels at all temperatures have an RMS residual less than 4% with one pixel at one temperature just under 5%. Figure 4.1.2.6-2 for the MRI demonstrates that approximately 99% of the pixels have an RMS value less than 1%. The error then creeps up, with a few pixels having an RMS residual as high as 8%. Figure 4.1.2.6-3 for the SLI shows that approximately 90% of pixels have an RMS value of 1%, while 99.9% of pixels have an RMS residual of approximately 2%. A few pixels at a couple of temperatures have an RMS residual as high as approximately 4%. The AR-RSR and Ave model RMS residuals are included in Figure 4.1.2.6-1 for comparison. The relevant comparison is between the AR-RSR, Ave and hump ratio model for 239K (the yellow line). While the result is better for many pixels using the AR-RSR and Ave model, the RMS residuals are much higher for some pixels toward the right of the graph. The cross over is at approximately 99%. Recall the HRI has 40,640 pixels such that 1% of the total pixels represent over 400 pixels. The 239K line never exceeds a 2% RMS residual, while a significant number of pixels have higher RMS residuals for both the AR-RSR and Ave model. Thus, the hump ratio model yields the lowest RMS residuals of the 3 models for all pixels in the HRI. Figure 4.1.2.6-1 A probability plot of the RMS residuals for the HRI for every pixel at the 7 measured temperatures. Also included are the RMS residuals from the AR-RSR and Ave models for a temperature of 239K. Figure 4.1.2.6-2 A probability plot of the RMS for the MRI for every pixel at the 7 measured temperatures. Figure 4.1.2.6-3 A probability plot of the RMS for the SLI for every pixel at the 7 measured temperatures. 4.1.3. Conclusion Although there is some correlation between AR and RSR, there is significant scatter, and the correlation is not strong. Both the AR-RSR model and the Ave model yield appropriate RSR values for most pixels. However, both models yield high RMS residuals for a significant number of pixels. A better method for yielding the RSR of any pixel is a model based upon the ratio of the RSR at two wavelengths corresponding to the humps surrounding the RSR peak. The use of this hump ratio model yields results in the RSR that do not deviate more than 2% for the HRI at 239K and 5% for all pixels at all temperatures, 4% for the MRI at 239K and 8% for all pixels at all temperatures, and 3% for the SLI and 4% for all pixels at all temperatures. 4.2. Image Absolute Responsivity Reductions The absolute responsivity of every pixel in all three imagers was measured at 15 temperatures ranging from 171.5K to 289.7K. The measurements were made in the large integrating sphere at the University of Arizona on July 24, 1996. The method of computing the absolute responsivities is described in detail below. An IDL program was used to compute the responsivities of all pixels. The absolute responsivities of two pixels (at different temperatures) were verified by detailed computations described below and carried out in an Excel spreadsheet. The IDL and Excel results for these pixels agree to 5 significant figures. The following section describes this verification and the reduction method. 4.2.1. Method and Verification of Absolute Responsivity Reductions Here we verify the reduction of absolute responsivity of two imager pixels, one from the DISR#3 HRI and one from the DISR#3 MRI. The "standard" reductions were done using IDL program imager_abs_resp_v4, located on cassini in directory /users/ldoose/idl_programs/imager_abs_resp_sw/new_2002. As mentioned above, we repeat the reduction for these two pixels using an Excel spreadsheet with the intention of obtaining a result independent of the IDL program. Verification will be achieved if we arrive at the same absolute responsivity using both methods. The count rate in an imager pixel in DN/sec is given by SECTION_4.2.1_EQU_1.GIF, (1) where A is the absolute responsivity I(lambda) is the intensity of the source which depends on wavelength and RSR(lambda) is the relative spectral response of the imager pixel The absolute responsivity is given by SECTION_4.2.1_EQU_4.GIF (2) We arbitrarily choose column 100 and row 100 at 290K for the HRI and column 50, row 150 at 172K for the MRI. Other specifics for the test pixels are given in the table below: Table 4.2.1-1 HRI verification information Item Test Log /disr3_cal/24Jul96/Log/absresp_cold_24Jul96.4 Bright exposure seq. 101 101 numbers Dark exposure seq. numbers 90 102 Bright 0 sec exposure seq. 98 98 numbers Dark 0 sec exposure seq. 95 107 numbers Exposure times of Bright 5.0 ms 5.0 ms exposure Exposure times of Dark 5.0 ms 5.0 ms exposure CCD temperatures for 289.73 289.73 Bright Exposure CCD temperatures for Dark 289.73 289.73 Exposure Bright DNs for HRI pixel 2448 2448 (100,100) Dark DNs for HRI pixel 38 35 (100,100) Bright DNs for 0 exp. HRI 139 139 pixel (100,100) Dark DNs for 0 exp. HRI 35 36 pixel (100,100) Sphere silicon detector 123401 123401 reading for bright exposure Sphere silicon detector 16289 16318 reading for dark exposures Table 4.2.1-2 MRI verification information Item Test Log /disr3_cal/24Jul96/Log/absresp_cold_24Jul96.1 Bright exposure seq. 9 9 numbers Dark exposure seq. numbers 2 14 Bright 0 sec exposure seq. 6 6 numbers Dark 0 sec exposure seq. 3 15 numbers Exposure times of Bright 12.0 ms 12.0 ms exposure Exposure times of Dark 12.0 ms 12.0 ms exposure CCD temperatures for 171.51 171.51 Bright Exposure CCD temperatures for Dark 171.39 171.51 Exposure Bright DNs for MRI pixel 2207 2207 (50,150) Dark DNs for MRI pixel 9 9 (50,150) Bright DNs for 0 exp. MRI 72 72 pixel (50,150) Dark DNs for 0 exp. MRI 9 9 pixel (50,150) Sphere silicon detector 124441 124441 reading for bright exposure Sphere silicon detector 16293 16293 reading for dark exposures For both pixels the absolute responsivities were computed for two sets of measurements listed in the two columns of tables 4.2.1-1 and 4.2.1-2. The relative spectral response of the imager pixels was measured for each pixel at several temperatures and about 50 wavelengths. It has also been modeled assuming the relative spectral response falls into a discrete number of categories, based on the relative height of the left and right "bumps" in a plot of response vs. wavelength. The model description and a comparison of the model and measurements is given in another document. The relative spectral response was measured at 171K, 185K, 201K, 225K, 239K, 269K, and 294K. The relative spectral response measurements at relevant temperatures are shown below in tabular and graphical form. Figure 4.2.1-1 Measured and model relative spectral responses for the HRI pixel. Table 4.2.1-3 Relative Spectral Response of HRI pixel (100,100) vs. Temperature Wavelength 269K 294K 289.73K Model at 289.73K 600 0.00022 0.00022 0.00022 0.00034 610 0.00047 0.00044 0.00045 0.00045 620 0.00094 0.00078 0.00081 0.00089 630 0.00291 0.00214 0.00227 0.00229 640 0.01730 0.01099 0.01207 0.01164 650 0.12050 0.08003 0.08694 0.08396 660 0.37222 0.30440 0.31598 0.31685 670 0.58265 0.53704 0.54483 0.55268 680 0.71644 0.69498 0.69865 0.70313 690 0.81114 0.78977 0.79342 0.79764 700 0.84711 0.83740 0.83906 0.84025 710 0.86408 0.84617 0.84923 0.85620 720 0.88271 0.87400 0.87549 0.87745 730 0.90994 0.90672 0.90727 0.90933 740 0.95680 0.94935 0.95062 0.95452 750 0.99001 0.98843 0.98870 0.99202 760 1.00000 1.00000 1.00000 1.00000 770 0.96272 0.97561 0.97341 0.97236 780 0.91849 0.92625 0.92492 0.92852 790 0.88535 0.89122 0.89022 0.89358 800 0.86488 0.87828 0.87599 0.87898 810 0.86694 0.88176 0.87923 0.88210 820 0.87306 0.89904 0.89460 0.89457 830 0.87713 0.90226 0.89797 0.89969 840 0.85709 0.88740 0.88222 0.88431 850 0.81556 0.85366 0.84715 0.84642 860 0.75204 0.78799 0.78185 0.77837 870 0.68397 0.71784 0.71206 0.70861 880 0.61653 0.65639 0.64958 0.64561 890 0.55652 0.59555 0.58888 0.58495 900 0.50429 0.54182 0.53541 0.53227 910 0.44692 0.49162 0.48399 0.47858 920 0.40274 0.44147 0.43485 0.43179 930 0.35822 0.39860 0.39170 0.38875 940 0.32116 0.35995 0.35332 0.35012 950 0.28805 0.32331 0.31729 0.31611 960 0.25589 0.29135 0.28529 0.28400 970 0.22766 0.26426 0.25801 0.25589 980 0.20008 0.23595 0.22982 0.22697 990 0.17252 0.20481 0.19929 0.19717 1000 0.14419 0.17588 0.17047 0.16765 1010 0.11491 0.14491 0.13979 0.13795 1020 0.09063 0.11622 0.11185 0.10963 1030 0.06759 0.08991 0.08610 0.08390 1040 0.04903 0.06772 0.06453 0.06318 1050 0.03417 0.04914 0.04658 0.04548 1060 0.02495 0.03576 0.03391 0.03294 1070 0.01873 0.02649 0.02516 0.02464 1080 0.01451 0.02137 0.02020 0.01944 1090 0.01148 0.01674 0.01584 0.01539 1100 0.00000 0.00000 0.00000 0.00034 Figure 4.2.1-2 Measured and model relative spectral responses for the MRI pixel. Table 4.2.1-4 Relative Spectral Response of MRI pixel (50,150) vs. Temperature Wavelength 171K 185K 171.51K Model at 171.51K 600 0.00039 0.00051 0.00039 0.00042 610 0.00045 0.00067 0.00046 0.00042 620 0.00045 0.00045 0.00045 0.00053 630 0.00157 0.00096 0.00155 0.00156 640 0.02565 0.01502 0.02526 0.02289 650 0.21618 0.16569 0.21434 0.21475 660 0.50008 0.46797 0.49891 0.51133 670 0.68313 0.66488 0.68247 0.68699 680 0.80203 0.78803 0.80152 0.80469 690 0.87495 0.87560 0.87497 0.87587 700 0.89993 0.88585 0.89942 0.89689 710 0.90701 0.90616 0.90698 0.90124 720 0.91172 0.91533 0.91185 0.91693 730 0.93554 0.93410 0.93549 0.94539 740 0.99089 0.97496 0.99031 0.98224 750 1.00000 1.00000 1.00000 1.00000 760 0.99296 0.96972 0.99211 0.97705 770 0.93001 0.92415 0.92980 0.92527 780 0.88023 0.87629 0.88009 0.86963 790 0.82808 0.81879 0.82774 0.82938 800 0.81022 0.79928 0.80982 0.81165 810 0.80750 0.81731 0.80786 0.80503 820 0.80577 0.81157 0.80598 0.80423 830 0.79316 0.78859 0.79299 0.78813 840 0.76898 0.75713 0.76855 0.75332 850 0.70633 0.70629 0.70633 0.69645 860 0.64816 0.64816 0.64816 0.62800 870 0.56424 0.58148 0.56487 0.54914 880 0.48534 0.51765 0.48652 0.48641 890 0.43408 0.44468 0.43447 0.42756 900 0.38219 0.39744 0.38275 0.37777 910 0.34170 0.34652 0.34188 0.32981 920 0.29125 0.30433 0.29173 0.28644 930 0.25317 0.26408 0.25357 0.24872 940 0.21869 0.22748 0.21901 0.21662 950 0.18958 0.19938 0.18994 0.18838 960 0.16541 0.17313 0.16569 0.16094 970 0.13747 0.14927 0.13790 0.13749 980 0.11548 0.12431 0.11580 0.11374 990 0.09054 0.10037 0.09090 0.09045 1000 0.06961 0.07775 0.06991 0.06822 1010 0.04905 0.05578 0.04930 0.04855 1020 0.03316 0.03768 0.03332 0.03211 1030 0.01942 0.02406 0.01959 0.01941 1040 0.01088 0.01431 0.01100 0.01096 1050 0.00749 0.00993 0.00758 0.00780 1060 0.00503 0.00687 0.00510 0.00549 1070 0.00351 0.00472 0.00355 0.00369 1080 0.00253 0.00352 0.00257 0.00267 1090 0.00172 0.00275 0.00176 0.00195 1100 0.00000 0.00000 0.00000 0.00000 The final quantity needed to determine the AR is the intensity of the integrating sphere. This is obtained from a scan of the sphere interior wall as illuminated by an incandescent lamp using the standard detector of the monochromator itself. Three bandpass detectors monitor the brightness of the sphere separately. The sphere brightness may change between the time of the monochromator scan and the DISR measurements. The brightness of the sphere is corrected for this change. Finally the spatial variations of intensity within the sphere are considered. The intensity is different in the direction of the imager pixels as compared to the field of view of the standard detector. A correction is applied to account for this difference. The brightness of the sphere interior is computed from readings on silicon and germanium detectors in the monochromator sensor. The intensity of the portion of the sphere viewed by the monochromator detector at wavelength, lambda, is computed as TABLE_4.2.1-4_EQU_2.GIF, where (3) D(lambda) is the detector reading at wavelength lambda c(lambda) is the monochromator calibration factor at wavelength, lambda , obtained from an appropriate calibration file Lo is the "luminosity constant" (e.g. = 12853) L_lambda is the luminosity constant actually measured during the determination of c(lambda) (e.g., usually 12853), so the quantity Lo/L(lambda) is taken to be unity Bt/Bo is the ratio of the brightness at time t to the brightness at time t0. This term allows for drift in the lamp between the times of the monochromator detector measurements and the DISR imager measurements. D(Lambda) is obtained from either the silicon or germanium standard detector of the monochromator. Only one detector is active at a given time. Values of D(Lambda) are obtained from the "cal" file taken close in time to the DISR measurements. The units of these measurements are Amperes. Generally the monochromator is configured to measure the sphere brightness at a uniformly spaced grid of wavelengths. c(lambda) is the detector responsivity in Amperes/[watt/(m2 micro-m str)]. These values are obtained from the monochromator manufacturer during absolute calibration of the detectors. c(Lambda) also depends on the slit configuration inside the monochromator. For the DISR#3 measurements the appropriate files are cassini:/local/cal.cal/New_Std_Si_(Calcal_vers) and cassini:/local/cal.cal/New_Std_Ge_(Calcal_vers). Only the slit configurations 5:5:5mm aperture for the Si detector and 5:5:3mm aperture for the Ge detector were used. Details of the absolute calibration can be found in the document "A New DISR Absolute Standard" by Bashar Rizk. Table 4.2.1-5, below, gives the intensity (in Watts/m^2-micron-str.) of the integrating sphere from the standard detector readings alone, i.e., without the corrections for time drift or spatial inhomogeneity. Table 4.2.1-5 Brightness of the Integrating Sphere from Monochrometer Scan Wavelength D(l) c(l) I(l) (nm) 600 8.269E-11 1.0459E-10 0.790611 610 9.749E-11 1.2036E-10 0.809987 620 9.852E-11 1.1846E-10 0.831673 630 9.388E-11 1.0988E-10 0.854387 640 9.249E-11 1.0470E-10 0.883381 650 1.136E-10 1.2550E-10 0.905179 660 1.284E-10 1.3863E-10 0.926206 670 1.310E-10 1.3816E-10 0.948176 680 1.271E-10 1.3129E-10 0.968086 690 1.208E-10 1.2214E-10 0.989029 700 1.140E-10 1.1321E-10 1.006978 710 1.072E-10 1.0460E-10 1.024857 720 1.006E-10 9.6846E-11 1.038763 730 9.428E-11 8.9465E-11 1.053820 740 8.799E-11 8.2488E-11 1.066701 750 8.199E-11 7.6033E-11 1.078348 760 7.616E-11 6.9893E-11 1.089666 770 7.063E-11 6.4270E-11 1.098958 780 6.553E-11 5.9079E-11 1.109193 790 6.081E-11 5.4488E-11 1.116026 800 5.686E-11 5.0673E-11 1.122097 810 5.378E-11 4.7783E-11 1.125505 820 5.170E-11 4.5872E-11 1.127049 830 5.076E-11 4.5038E-11 1.127048 840 5.095E-11 4.5303E-11 1.124650 850 5.222E-11 4.6628E-11 1.119928 860 5.439E-11 4.8841E-11 1.113614 870 7.085E-11 6.3255E-11 1.120070 880 9.348E-11 8.4091E-11 1.111653 890 1.224E-10 1.1135E-10 1.099237 900 1.577E-10 1.4541E-10 1.084520 910 1.997E-10 1.8575E-10 1.075101 920 2.525E-10 2.3586E-10 1.070550 930 3.236E-10 3.0449E-10 1.062761 940 4.032E-10 3.8449E-10 1.048662 950 4.686E-10 4.5668E-10 1.026101 960 5.186E-10 5.1171E-10 1.013465 970 5.569E-10 5.5491E-10 1.003586 980 5.917E-10 5.9505E-10 0.994370 990 6.210E-10 6.2993E-10 0.985824 1000 6.399E-10 6.5562E-10 0.976023 1010 6.444E-10 6.6810E-10 0.964526 1020 6.321E-10 6.6319E-10 0.953121 1030 6.001E-10 6.3821E-10 0.940286 1040 5.493E-10 5.9188E-10 0.928060 1050 4.852E-10 5.2955E-10 0.916250 1060 4.149E-10 4.5913E-10 0.903666 1070 3.572E-10 4.0006E-10 0.892866 1080 3.118E-10 3.5310E-10 0.883036 1090 2.709E-10 3.0874E-10 0.877437 1100 2.291E-10 2.6532E-10 0.863486 We first compute [TABLE_4.2.1-5_EQU_2.GIF] without the corrections for time drift and spatial inhomogeneity. Computations are done for the HRI pixel and the MRI pixel for both the interpolated (in temperature) measured and model RSR. Simpson's rule is used for the integration. The results (in Watts/m^2-str.) are: Table 4.2.1-6 [TABLE_4.2.1-6_EQU_1.GIF] (uncorrected) RSR HRI pixel MRI pixel (100,100) (50,150) Measured 0.254986 0.230221 Model 0.254939 0.228738 The count rates are obtained from TABLE_4.2.1-6_EQU_2.GIF, (4) where DNb is the number of bright (shutter open) counts at the full exposure time DBbo is the number of bright (shutter open) counts at zero exposure time DNd is the number of dark (shutter closed) counts at the full exposure time DNdo is the number of dark (shutter closed) counts at zero exposure time delta_t is the exposure time in seconds Where two measurements of the number of counts were1 made, we average them. The result for HRI pixel is r=461,600 DN/d [TABLE_4.2.1-6_EQU_8.GIF] (5) The result for the MRI pixel is r=177,917 DN/s [TABLE_4.2.1-6_EQU_9.GIF] (6) The resulting absolute responsivities (in (DN/s)/(Watts/m^2 str) ) are Table 4.2.1-7 Absolute responsivities (uncorrected) RSR HRI pixel MRI pixel (100,100) (50,150) Measured 1810295 772810 Model 1810629 777820 Current 1842440 753925 In this table the "Current" entry is from the files on cassini in /local. These values are from the reductions using the DISRSOFT program imager_abs_resp_v3, and they have been used in all reductions requiring absolute responsivity. They include the corrections mentioned below. Older algorithms were used for these corrections. As mentioned above, small corrections must be applied for drift in the lamp during the monochromator scan, the drift in the lamp between the times of the monochromator scan and the DISR exposure, and difference in intensity caused by the inhomogeneity of the integrating sphere. We consider these in this section. Early algorithms to correct for the lamp drift involved the consideration of three monitor detectors: a broadband silicon detector, a narrow band (violet) filtered silicon, detector, and an InGaAs detector (infrared). The three detectors theoretically provide information about the color temperature of the lamp as well as its luminosity. In practice it has been found that simple use of the broadband silicon detector as a scale factor correction is an adequate method. The broadband silicon detector output is found in column 10 of the "cal" file and in the header entry H_SPSI of the DISRSOFT image data sets. The first step is to correct all the standard silicon reference detector readings for drift during the monochromator scan itself. TABLE_4.2.1-7_EQU_1.GIF (7) where s_corr(lambda) is standard silicon reference detector reading at the standard time, t0 s(lambda) is the uncorrected standard silicon reference detector reading at the time wavelength, lambda, was measured (t_lambda) Si_mono-t0-b is the silicon monitor detector reading with the shutter open at t0 Si_mono-t0-d is the silicon monitor detector reading with the shutter closed at t0 Si_t_lambda-b is the silicon monitor detector reading with the shutter open at the time when wavelength, lambda, was measured (t_lambda) Si_t_lambda-d is the silicon monitor detector reading with the shutter closed at the time when wavelength, lambda, was measured (t_lambda) In practice dark measurements were not usually made during a monochromator scan, but they were2 measured during the imager exposures. The quantity Si_t_lambda-d should not vary with time, except due to statistical fluctuations. The figure below shows the variation of Si_t_lambda-d vs. time while the images were exposed on 24 July, 1996. Figure 4.2.1-3 Silicon monitor detector readings with the shutter closed during DISR image taking. The graph shows a cyclic change in the monitor detector dark readings, however the amplitude is very small. Typically the peak-to-peak variation is 30 counts. The bright readings are about 123000. The variation in the dark is about 0.03% of the signal. We choose to adopt a constant value for the dark readings equal to the average of the values in the plot. This average value is 16336. We define t0 by choosing the first DISR bright image as the reference, and we compute the silicon reference detector readings as if the whole monochromator scan were done at the time of this image, according to the equation above. From these readings we can compute the integrating sphere intensity I_lambda as if the whole monochromator scan had been done at time t0. Using the numbers from the monochromator file for the bright silicon monitor detector readings and 16336 for the dark silicon monitor detector reading during the monochromator scan, we can re-compute the integrating sphere intensities in table 4.2.1-8. Table 4.2.1-8 Brightness of the integrating sphere with drift corrections to HRI image Wavelength D(l) c(l) I(l) Bright Dark Correction Corrected (nm) Monitor Monitor Factor I(l) Reading Reading 600 8.269E-11 1.0459E-10 0.790611 123476 16336 0.999739 0.790404 610 9.749E-11 1.2036E-10 0.809987 123476 16336 0.999701 0.809745 620 9.852E-11 1.1846E-10 0.831673 123483 16336 0.999636 0.831370 630 9.388E-11 1.0988E-10 0.854387 123478 16336 0.999683 0.854116 640 9.249E-11 1.0470E-10 0.883381 123480 16336 0.999664 0.883084 650 1.136E-10 1.2550E-10 0.905179 123479 16336 0.999673 0.904883 660 1.284E-10 1.3863E-10 0.926206 123485 16336 0.999617 0.925852 670 1.310E-10 1.3816E-10 0.948176 123486 16336 0.999608 0.947804 680 1.271E-10 1.3129E-10 0.968086 123488 16336 0.999589 0.967688 690 1.208E-10 1.2214E-10 0.989029 123489 16336 0.999580 0.988614 700 1.140E-10 1.1321E-10 1.006978 123485 16336 0.999617 1.006593 710 1.072E-10 1.0460E-10 1.024857 123488 16336 0.999589 1.024436 720 1.006E-10 9.6846E-11 1.038763 123482 16336 0.999645 1.038395 730 9.428E-11 8.9465E-11 1.053820 123482 16336 0.999645 1.053446 740 8.799E-11 8.2488E-11 1.066701 123476 16336 0.999701 1.066382 750 8.199E-11 7.6033E-11 1.078348 123477 16336 0.999692 1.078016 760 7.616E-11 6.9893E-11 1.089666 123478 16336 0.999683 1.089320 770 7.063E-11 6.4270E-11 1.098958 123482 16336 0.999645 1.098568 780 6.553E-11 5.9079E-11 1.109193 123482 16336 0.999645 1.108800 790 6.081E-11 5.4488E-11 1.116026 123484 16336 0.999627 1.115609 800 5.686E-11 5.0673E-11 1.122097 123486 16336 0.999608 1.121657 810 5.378E-11 4.7783E-11 1.125505 123482 16336 0.999645 1.125106 820 5.170E-11 4.5872E-11 1.127049 123481 16336 0.999655 1.126660 830 5.076E-11 4.5038E-11 1.127048 123482 16336 0.999645 1.126648 840 5.095E-11 4.5303E-11 1.124650 123479 16336 0.999673 1.124283 850 5.222E-11 4.6628E-11 1.119928 123478 16336 0.999683 1.119573 860 5.439E-11 4.8841E-11 1.113614 123475 16336 0.999711 1.113292 870 7.085E-11 6.3255E-11 1.120070 123476 16336 0.999701 1.119735 880 9.348E-11 8.4091E-11 1.111653 123479 16336 0.999673 1.111290 890 1.224E-10 1.1135E-10 1.099237 123484 16336 0.999627 1.098827 900 1.577E-10 1.4541E-10 1.084520 123484 16336 0.999627 1.084115 910 1.997E-10 1.8575E-10 1.075101 123481 16336 0.999655 1.074730 920 2.525E-10 2.3586E-10 1.070550 123483 16336 0.999636 1.070160 930 3.236E-10 3.0449E-10 1.062761 123479 16336 0.999673 1.062414 940 4.032E-10 3.8449E-10 1.048662 123482 16336 0.999645 1.048290 950 4.686E-10 4.5668E-10 1.026101 123477 16336 0.999692 1.025785 960 5.186E-10 5.1171E-10 1.013465 123478 16336 0.999683 1.013143 970 5.569E-10 5.5491E-10 1.003586 123480 16336 0.999664 1.003249 980 5.917E-10 5.9505E-10 0.994370 123479 16336 0.999673 0.994045 990 6.210E-10 6.2993E-10 0.985824 123485 16336 0.999617 0.985447 1000 6.399E-10 6.5562E-10 0.976023 123490 16336 0.999571 0.975604 1010 6.444E-10 6.6810E-10 0.964526 123491 16336 0.999561 0.964103 1020 6.321E-10 6.6319E-10 0.953121 123496 16336 0.999515 0.952658 1030 6.001E-10 6.3821E-10 0.940286 123491 16336 0.999561 0.939874 1040 5.493E-10 5.9188E-10 0.928060 123482 16336 0.999645 0.927731 1050 4.852E-10 5.2955E-10 0.916250 123484 16336 0.999627 0.915908 1060 4.149E-10 4.5913E-10 0.903666 123488 16336 0.999589 0.903295 1070 3.572E-10 4.0006E-10 0.892866 123491 16336 0.999561 0.892474 1080 3.118E-10 3.5310E-10 0.883036 123486 16336 0.999608 0.882690 1090 2.709E-10 3.0874E-10 0.877437 123485 16336 0.999617 0.877101 1100 2.291E-10 2.6532E-10 0.863486 123485 16336 0.999617 0.863156 Table 4.2.1-9 [TABLE_4.2.1-9_EQU_1.GIF] for HRI with first drift correction RSR Uncorrected Corrected Measured 0.254986 0.254895 Model 0.254939 0.254834 Similarly we can compute the corrected monochromatic integrating sphere brightness for the MRI. We note that the brightness in the integrating sphere was slightly brighter (about 1%) for the MRI images, as indicated by the higher monitor detector reading (124441 vs. 123401). Table 4.2.1-10 Brightness of the integrating sphere with drift corrections to MRI image Wavelength D(l) c(l) I(l) Bright Dark Correction Corrected I(l) (nm) Monitor Monitor Factor Reading Reading 600 8.269E-11 1.0459E-10 0.790611 123476 16336 1.009408 0.798049 610 9.749E-11 1.2036E-10 0.809987 123476 16336 1.009408 0.817608 620 9.852E-11 1.1846E-10 0.831673 123483 16336 1.009342 0.839443 630 9.388E-11 1.0988E-10 0.854387 123478 16336 1.009389 0.862409 640 9.249E-11 1.0470E-10 0.883381 123480 16336 1.009371 0.891659 650 1.136E-10 1.2550E-10 0.905179 123479 16336 1.009380 0.913670 660 1.284E-10 1.3863E-10 0.926206 123485 16336 1.009323 0.934841 670 1.310E-10 1.3816E-10 0.948176 123486 16336 1.009314 0.957007 680 1.271E-10 1.3129E-10 0.968086 123488 16336 1.009295 0.977085 690 1.208E-10 1.2214E-10 0.989029 123489 16336 1.009286 0.998213 700 1.140E-10 1.1321E-10 1.006978 123485 16336 1.009323 1.016367 710 1.072E-10 1.0460E-10 1.024857 123488 16336 1.009295 1.034383 720 1.006E-10 9.6846E-11 1.038763 123482 16336 1.009352 1.048477 730 9.428E-11 8.9465E-11 1.053820 123482 16336 1.009352 1.063675 740 8.799E-11 8.2488E-11 1.066701 123476 16336 1.009408 1.076737 750 8.199E-11 7.6033E-11 1.078348 123477 16336 1.009399 1.088483 760 7.616E-11 6.9893E-11 1.089666 123478 16336 1.009389 1.099897 770 7.063E-11 6.4270E-11 1.098958 123482 16336 1.009352 1.109235 780 6.553E-11 5.9079E-11 1.109193 123482 16336 1.009352 1.119566 790 6.081E-11 5.4488E-11 1.116026 123484 16336 1.009333 1.126442 800 5.686E-11 5.0673E-11 1.122097 123486 16336 1.009314 1.132548 810 5.378E-11 4.7783E-11 1.125505 123482 16336 1.009352 1.136030 820 5.170E-11 4.5872E-11 1.127049 123481 16336 1.009361 1.137599 830 5.076E-11 4.5038E-11 1.127048 123482 16336 1.009352 1.137588 840 5.095E-11 4.5303E-11 1.124650 123479 16336 1.009380 1.135199 850 5.222E-11 4.6628E-11 1.119928 123478 16336 1.009389 1.130443 860 5.439E-11 4.8841E-11 1.113614 123475 16336 1.009418 1.124102 870 7.085E-11 6.3255E-11 1.120070 123476 16336 1.009408 1.130608 880 9.348E-11 8.4091E-11 1.111653 123479 16336 1.009380 1.122080 890 1.224E-10 1.1135E-10 1.099237 123484 16336 1.009333 1.109496 900 1.577E-10 1.4541E-10 1.084520 123484 16336 1.009333 1.094642 910 1.997E-10 1.8575E-10 1.075101 123481 16336 1.009361 1.085165 920 2.525E-10 2.3586E-10 1.070550 123483 16336 1.009342 1.080551 930 3.236E-10 3.0449E-10 1.062761 123479 16336 1.009380 1.072730 940 4.032E-10 3.8449E-10 1.048662 123482 16336 1.009352 1.058469 950 4.686E-10 4.5668E-10 1.026101 123477 16336 1.009399 1.035745 960 5.186E-10 5.1171E-10 1.013465 123478 16336 1.009389 1.022981 970 5.569E-10 5.5491E-10 1.003586 123480 16336 1.009371 1.012990 980 5.917E-10 5.9505E-10 0.994370 123479 16336 1.009380 1.003697 990 6.210E-10 6.2993E-10 0.985824 123485 16336 1.009323 0.995015 1000 6.399E-10 6.5562E-10 0.976023 123490 16336 1.009276 0.985077 1010 6.444E-10 6.6810E-10 0.964526 123491 16336 1.009267 0.973464 1020 6.321E-10 6.6319E-10 0.953121 123496 16336 1.009220 0.961909 1030 6.001E-10 6.3821E-10 0.940286 123491 16336 1.009267 0.949000 1040 5.493E-10 5.9188E-10 0.928060 123482 16336 1.009352 0.936739 1050 4.852E-10 5.2955E-10 0.916250 123484 16336 1.009333 0.924801 1060 4.149E-10 4.5913E-10 0.903666 123488 16336 1.009295 0.912066 1070 3.572E-10 4.0006E-10 0.892866 123491 16336 1.009267 0.901140 1080 3.118E-10 3.5310E-10 0.883036 123486 16336 1.009314 0.891261 1090 2.709E-10 3.0874E-10 0.877437 123485 16336 1.009323 0.885618 1100 2.291E-10 2.6532E-10 0.863486 123485 16336 1.009323 0.871537 Table 4.2.1-11 [TABLE_4.2.1-11_EQU_1.GIF] for MRI with drift correction RSR Uncorrected Corrected Measured 0.230221 0.232375 Model 0.228738 0.230878 The second part of the drift correction is to correct the image count rates to what their values would have been at t0. Because we have chosen to to be the time of the first (and only) bright image of the sequence, this correction is unnecessary. We already know the intensity in the integrating sphere at this time. The terms necessary to compute the absolute responsivity with the time drift corrections are now known, and equation 2 may be recomputed using the integrating sphere intensity at the time of the bright image. A = 1,811,375 (DN/s)/(W/sqm str) [TABLE_4.2.1-11_EQU_4.GIF] for the HRI (12) and A = 770,611 (DN/s)/(W/sqm str) [TABLE_4.2.1-11_EQU_5.GIF] for the MRI, (13) where we have used the measured (rather than model) RSR values. These represent changes of +0.08% for the HRI and -0.87% for the MRI compared to the values uncorrected for drift. Almost all of the drift correction comes from changes between t0 and the DISR image taking. The effect of the drift during the monochromator scan is negligible. The correction for non-uniformity of brightness in the integrating sphere begins with Bashar Rizk's document "Integrating Sphere Homogeneity and the Relative Brightness of each DISR Instrument's Calibration Field" (also available as http://disr.lpl.arizona.edu/Integrating%20Sphere%20Non-Uniformity%20Report.htm on the DISR team web site. This document describes the brightness in sphere- centered and DISR window-centered coordinate systems, concluding that the sphere is uniform to approximately 2% over most of the DISR fields of view. The intensity in the direction corresponding to each pixel must be compared to the intensity in the direction of the Silicon standard detector to obtain the actual sphere intensity for that pixel. A spreadsheet named Integrating_Sphere_Relative_Brightness.xls gives the sphere brightness on a 1 grid in zenith and azimuth angle over the entire sphere. This file is located on cassini in the directory /local/Integrating_Sphere. In this speadsheet the zenith angle varies from 0 to 180 with row number, and the azimuth angle increases counter-clockwise when looking down on the sphere (and DISR). 0 DISR azimuth corresponds to 90 sphere azimuth. The monochromater standard reference detector views the "front" of integrating sphere, an area opposite the mounting position of the DISR. It has a finite field of view. For purposes of standardization, we adopt the value used by M. Tomasko for the Solar Aureole absolute responsivity of 0.987988. TABLE_4.2.1-11_EQU_7.GIF, where (14) I(col,row)_corr is the corrected intensity seen by a given column and row of the imagers S(con,row) is the sphere intensity factor from Bashar Rizk's tables for that column and row I(col,row) is the original, uncorrected intensity measured by the standard reference detector The sphere inhomogeneity correction is assumed to be independent of wavelength. The elevation and azimuth of the two pixels in this study can be found in Appendix II. This appendix contains the coordinates of every pixel in all three imagers. These coordinates are nadir angle and azimuth angle. Azimuth angle increases clockwise when looking down on the top of DISR (opposite from the convention for the sphere azimuth). The conversion from DISR to sphere coordinates is as follows: TABLE_4.2.1-11_EQU_11.GIF (15) TABLE_4.2.1-11_EQU_12.GIF (16) For HRI (column 100, row 100), the DISR azimuth is 6.098ş, and the DISR nadir angle is 12.941ş. These convert to a relative brightness (rb) azimuth of 83.902ş and an rb zenith of 167.059ş. For MRI (column 50, row 150), the DISR azimuth is -7.711ş, and the DISR nadir angle is 34.506ş. These convert to rb azimuth of 97.711ş and rb zenith of 145.491ş. Tables 4.2.1-12 and 4.2.1-13, below give the percentage differences from the field of view of the reference detector of the normalized sphere intensity at the 4 points surrounding these two directions. Table 4.2.1-12 Sphere Intensity Factor for the HRI point Zenith\Azimuth 83ş 84ş 167ş -7.87774 -7.85185 168ş -8.12122 -8.09307 Table 4.2.1-13 Sphere Intensity Factor for the MRI point Zenith\Azimuth 97ş 98ş 145ş -1.71368 -1.78599 146ş -1.91588 -2.03303 Bilinear interpolation at the actual positions of the pixels yields -7.86863 for the HRI point and -1.88003 for the MRI point. Equation 14 becomes [TABLE_4.2.1-13_EQU_1.GIF] for the HRI pixel and [TABLE_4.2.1-13_EQU_2.GIF] for the MRI pixel. The absolute responsivities are divided by these factors to obtain the final calibration. A = 1,942,789 (DN/s)/(W/m^2 str) [TABLE_4.2.1-13_EQU_3.GIF] for HRI, and A = 775,943 (DN/s)/(W/m^2 str) [TABLE_4.2.1-13_EQU_4.GIF] for the MRI. As mentioned above, the IDL program reproduces these results to five significant figures. 4.2.2. Results The absolute responsivity of each pixel in all three imagers was computed using the method above. The results for the HRI at 236.84K, the MRI at 236.53K, and the SLI at 236.72K are given in tables X, Y, and Z below. Similar computations were made at each of the other 14 temperatures. The absolute responsivity for each pixel in the three imagers at all 15 temperatures can be found on cassini (the computer) in the directory local/Imagers/Abs_Resp/DISR#3/new_reductions_ Oct2002. The file names are given in table 4.2.2-1. Table 4.2.2-1 File Names of Absolute Responsivity Reductions Imager Temperature (K) File Name HRI 171.57 abs_resp_dli1_171.57 HRI 181.51 abs_resp_dli1_181.51 HRI 187.37 abs_resp_dli1_187.37 HRI 195.85 abs_resp_dli1_195.85 HRI 207.25 abs_resp_dli1_207.25 HRI 211.77 abs_resp_dli1_211.77 HRI 222.32 abs_resp_dli1_222.32 HRI 229.58 abs_resp_dli1_229.58 HRI 236.84 abs_resp_dli1_236.84 HRI 244.40 abs_resp_dli1_244.40 HRI 253.43 abs_resp_dli1_253.43 HRI 259.84 abs_resp_dli1_259.84 HRI 271.00 abs_resp_dli1_271.00 HRI 281.31 abs_resp_dli1_281.31 HRI 289.67 abs_resp_dli1_289.67 MRI 171.51 abs_resp_dli2_171.51 MRI 181.51 abs_resp_dli2_181.51 MRI 187.31 abs_resp_dli2_187.31 MRI 195.60 abs_resp_dli2_195.60 MRI 207.07 abs_resp_dli2_207.07 MRI 211.52 abs_resp_dli2_211.52 MRI 222.08 abs_resp_dli2_222.08 MRI 229.27 abs_resp_dli2_229.27 MRI 236.53 abs_resp_dli2_236.53 MRI 244.10 abs_resp_dli2_244.10 MRI 253.19 abs_resp_dli2_253.19 MRI 259.84 abs_resp_dli2_259.84 MRI 270.94 abs_resp_dli2_270.94 MRI 281.31 abs_resp_dli2_281.31 MRI 289.73 abs_resp_dli2_289.73 SLI 171.57 abs_resp_sli_171.57 SLI 181.39 abs_resp_sli_181.39 SLI 187.43 abs_resp_sli_187.43 SLI 195.66 abs_resp_sli_195.66 SLI 207.13 abs_resp_sli_207.13 SLI 211.65 abs_resp_sli_211.65 SLI 222.14 abs_resp_sli_222.14 SLI 229.46 abs_resp_sli_229.46 SLI 236.72 abs_resp_sli_236.72 SLI 244.28 abs_resp_sli_244.28 SLI 253.25 abs_resp_sli_253.25 SLI 259.84 abs_resp_sli_259.84 SLI 270.94 abs_resp_sli_270.94 SLI 281.31 abs_resp_sli_281.31 SLI 289.73 abs_resp_sli_289.73 These files are in DISRSOFT format, and they must be read with the d_read procedure through IDL. In these files bad pixels are given the flag value of -1.0. Constructing a model for the temperature dependence of the absolute responsivity can reduce the large quantity of numbers. We expect the temperature dependence for all pixels to be very nearly the same. Therefore we have modeled the temperature dependence of the average responsivity of all good pixels in each imager. A polynomial is fitted to the temperature dependence of each imager. The results are shown in figures 4.2.2-1, 4.2.2-2, and 4.2.2-3. Figure 4.2.2-1 Temperature model of the absolute responsivity for all good HRI pixels. Dots are the measurements, and the curve is a fourth-order polynomial fit. Figure 4.2.2-2 Temperature model of the absolute responsivity for all good MRI pixels. Dots are the measurements, and the curve is a fourth-order polynomial fit. Figure 4.2.2-3 Temperature model of the absolute responsivity for all good SLI pixels. Dots are the measurements, and the curve is a fourth-order polynomial fit. The principal temperature effect is a drop in the responsivity as the temperature increases. This is consistent with the narrowing of the imager relative spectral responses with decreasing temperature. We note that the responsivity of the HRI is a little over twice that of the other imagers. The HRI does not have the neutral density filter in the filter window that the other imagers have. An obvious question is whether all pixels really do have the same temperature dependence. This is investigated below by comparing the measured and modeled absolute responsivity for each pixel. The model responsivity is computed by assuming the same shape for the temperature dependence found for all pixels for each imager independently. The responsivity at approximately 237K is used as a basis, and the responsivity at the other 14 temperatures is predicted using the shape of the model temperature dependence. At each of these 14 temperatures there will be a residual, the measured responsivity - the predicted responsivity. For each temperature we examine the distribution of these residuals in figures 4.2.2-4, 4.2.2-5, and 4.2.2-6. Figure 4.2.2-4 The distribution of absolute responsivity residuals expressed in percent as (measured - model) for the temperature dependence of the HRI. Figure 4.2.2-5 The distribution of absolute responsivity residuals expressed in percent as (measured - model) for the temperature dependence of the MRI. Figure 4.2.2-6 The distribution of absolute responsivity residuals expressed in percent as (measured - model) for the temperature dependence of the SLI. The temperature model performs very well for almost all pixels. More than 98% of the pixels show residuals of 1.5%. The best performance is achieved for temperatures close to the base temperature of 237K, and the performance decreases as the temperature differs more from the base temperature. Errors exceed 10% for only a few pixels at the most extreme temperatures. To gain insight about the pixels which do not fit the temperature model well, we examine their spatial distribution within the imagers in figures 11, 12, and 13. In these images poorly fitting pixels are color coded according to table 14. Table 4.2.2-2 Color Codes of Poorly Fitting Pixels Range of Residual Color <-10% Blue -5% to -10% Blue-Green -3% to -5% Green +3% to +5% Magenta +5% to +10% Yellow >+10% Red Figure 4.2.2-7 Spatial Distribution of Pixels that1 Fit the Temperature Model Poorly for the HRI HRI at 171.57K HRI at 181.51K HRI at 187.37K HRI at 195.85K HRI at 207.25K HRI at 211.77K HRI at 222.32K HRI at 229.58K HRI at 236.84K HRI at 244.40K HRI at 253.43K HRI at 259.84K HRI at 271.00K HRI at 281.31K HRI at 289.67K Figure 4.2.2-8 Spatial Distribution of Pixels which Fit the Temperature Model Poorly for the MRI MRI at 171.51K MRI at 181.51K MRI at 187.31K MRI at 195.60K MRI at 207.07K MRI at 211.52K MRI at 222.08K MRI at 229.27K MRI at 236.53K MRI at 244.10K MRI at 253.19K MRI at 259.84K MRI at 270.94K MRI at 281.31K MRI at 289.73K Figure 4.2.2-9 Spatial Distribution of Pixels which Fit the Temperature Model Poorly for the SLI SLI at 171.57K SLI at 181.39K SLI at 187.43K SLI at 195.66K SLI at 207.13K SLI at 211.65K SLI at 222.14K SLI at 229.46K SLI at 236.72K SLI at 244.28K SLI at 253.25K SLI at 259.84K SLI at 270.94K SLI at 281.31K SLI at 289.73K Conclusions from figures 4.2.2-7, 4.2.2-8, and 4.2.2-9 are as follows: * Although many of the ill-fitting pixels are near the edges of the imagers, most of these pixels are distributed throughout the interior of each imager. * These interior pixels remain anomalous over a wide range of temperature, i.e., the same pixels fit the temperature model poorly2 over the whole temperature range. * Anomalous pixels occur in isolation or with anomalous neighbors with roughly the same frequency. The persistence of the identity of the anomalous pixels suggests a familiar method of improving the model. These pixels could be assigned to different "bin" numbers, which have different temperature models. At this point we simply recognize this fact without actually developing such a model. 5.0. Flight and Ground Software Processing The flight software both schedules the acquisition of images and processes the resulting data. Several types of image processing are possible, although during a descent all images are processed with hardware compressor. The ground software (GSE) decompresses the images but not in an optimal way for photometric analysis. 5.1. Measurement scheduling Images are taken according to cycle type, as described in Table 5.1-1. The target azimuths are referenced to the azimuth of the sun, and they can be achieved only when the Sun Sensor is locked on the sun. Table 5.1-1 Image Scheduling During Descents Cycle Type No. No. No. Target Azimuths HRIs MRIs SLIs Image A 12 12 12 2ş, 32ş, 62ş, 92ş, 122ş, 152ş, 182ş, 212ş, 242ş, 272ş, 302ş, 332ş Image B 12 12 12 17ş, 47ş, 77ş, 107ş, 137ş, 167ş, 197ş, 227ş, 257ş, 287ş, 317ş, 247ş High Near 12 12 12 2ş, 32ş, 62ş, 92ş, 122ş, Surface A 152ş, 182ş, 212ş, 242ş, 272ş, 302ş, 332ş High Near 12 12 12 17ş, 47ş, 77ş, 107ş, 137ş, Surface B 167ş, 197ş, 227ş, 257ş, 287ş, 317ş, 247ş Calibration 1 1 1 180ş Cycle A Calibration 1 1 1 180ş Cycle B Medium Near 1 1 1 Unconstrained Surface Low Near 1 0 0 Unconstrained Surface Surface C 1 1 1 Unconstrained Surface D 1 1 1 Unconstrained Actual azimuths of the images are typically 1ş - 2ş less than the target azimuths. 5.2. Bad Pixel Maps All descent images are processed by the flight software using the bad pixel maps. This is the first processing performed after the CCD readout. The bad pixel maps were intially created to remove hot pixels on the CCD. This removal is necessary to avoid poor performance of the hardware data compressor. A single hot pixel in a 16 x 16 block of pixels can produce a checkerboard pattern within that block on the decompressed image. As hot pixels develop during the mission modifications to the bad pixel map can be made to follow the changing spatial distribution of hot pixels. After the instruments were built another obvious use for the bad pixel maps was discovered. The fiber optic bundles carrying the images to the CCD had imperfections (usually broken fibers) near the edges of the fields, and the CCD pixels which they were supposed to feed received little, if any, light. This problem also impacts the data compression, so these pixels have been mapped out. Two of the DISR instruments have exhibited small changes in this pattern of poorly fed pixels, probably due to cracking of additional fibers at the edges of the fields. This effect may also require updating of the bad pixel maps. For the imagers bad pixel mapping really means bad pixel replacement. Each pixel identified as bad has its value replaced by the value of another pixel in the same row. A second method of accomplishing the same result is possible through the flat-fielding operation. A special flat fielding code specifies that the previous pixel's value should be used for the current pixel. Because the computer memory space for the bad pixel map is limited, much of the bad pixel mapping has been done using this flat-fielding function. True bad pixel replacement is specified through EEPROM uploads. No modifications to the initial uploads have been made as of this writing. The locations of these uploads (slots) are shown in table 5.2-1. Table 5.2-1 Bad Pixel Map Slots Imager EEPROM Slots HRI 0x019 and 0x219 MRI 0x01A and 0x21A SLI 0x01B - 0x029 and 0x21B and 0x229 The original bad pixel maps are given in tables 5.2-2, 5.2-3, and 5.2-4. Table 5.2-2 DLI1 (HRI) Map in Imager Coordinates Entry Column Replacement First Last No. Column Row Row 1 0 2 34 78 2 0 3 131 196 3 0 4 197 254 4 1 2 44 74 5 1 4 183 254 6 2 4 183 217 7 3 4 202 216 Table 5.2-3 DLI2 (MRI) Map in Imager Coordinates Entry Column Replacement First Last No. Column Row Row 1 0 13 0 254 2 1 13 0 112 3 27 25 162 163 4 28 25 162 163 5 172 170 193 193 Table 5.2-4 SLI Map in Imager Coordinates Entry Column Replacement First Last No. Column Row Row 1 87 86 73 254 2 0 122 0 7 3 0 3 34 253 4 1 3 93 253 5 2 3 151 253 6 76 74 62 63 7 77 74 62 63 8 1 122 -1 6 9 2 122 -1 5 10 3 122 0 4 11 4 122 0 4 12 5 122 0 4 13 6 122 0 3 14 7 122 0 3 15 8 122 0 3 16 9 122 0 2 17 10 122 0 1 18 11 122 0 1 19 12 122 0 1 20 13 122 0 1 21 14 122 0 1 22 15 122 0 1 23 16 122 0 1 24 17 122 0 1 25 18 122 0 1 26 19 122 0 1 27 20 122 0 1 28 21 122 0 1 29 22 122 0 1 30 23 122 0 1 31 24 122 0 1 32 25 122 0 1 33 26 122 0 1 34 27 122 0 1 35 28 122 0 1 36 29 122 0 1 37 30 122 0 1 38 31 122 0 1 39 32 122 0 1 40 33 122 0 1 41 34 122 0 1 42 35 122 0 1 43 36 122 0 1 44 37 122 0 1 45 38 122 0 1 46 39 122 0 1 47 40 122 0 1 48 41 122 0 1 49 42 122 0 1 50 43 122 0 1 51 44 122 0 1 52 45 122 0 1 53 46 122 0 1 54 47 122 0 1 55 48 122 0 1 56 49 122 0 1 57 50 122 0 1 58 51 122 0 1 59 52 122 0 1 60 53 122 0 1 61 54 122 0 1 62 55 122 0 1 63 56 122 0 1 64 57 122 0 1 65 58 122 0 1 66 59 122 0 1 67 60 122 0 1 68 61 122 0 1 69 62 122 0 1 70 63 122 0 1 71 64 122 0 1 72 65 122 0 1 73 66 122 0 1 74 67 122 0 1 75 68 122 0 1 76 69 122 0 1 77 70 122 0 1 78 71 122 0 1 79 72 122 0 1 80 73 122 0 1 81 74 122 0 1 82 75 122 0 1 83 76 122 0 1 84 77 122 0 1 85 78 122 0 1 86 79 122 0 1 87 80 122 0 1 88 81 122 0 1 89 82 122 0 1 90 83 122 0 1 91 84 122 0 1 92 85 122 0 1 93 86 122 0 1 94 87 122 0 0 95 88 122 0 0 96 89 122 0 0 97 90 122 0 0 98 91 122 0 0 99 92 122 0 0 100 93 122 0 0 101 94 122 0 0 102 95 122 0 0 103 96 122 0 0 104 97 122 0 0 105 98 122 0 0 106 99 122 0 0 107 100 122 0 0 108 101 122 0 0 109 102 122 0 0 110 103 122 0 0 111 104 122 0 0 121 105 122 0 0 123 106 122 0 0 124 107 122 0 0 125 108 122 0 0 126 109 122 0 0 127 110 122 0 0 128 111 122 0 0 129 112 122 0 0 130 113 122 0 0 131 114 122 0 0 132 115 122 0 0 133 116 122 0 0 134 117 122 0 0 135 118 122 0 0 136 119 122 0 0 137 120 122 0 0 138 121 122 0 0 The structure of the bad pixel map memory area is well described in the Experiment User's Manual. We note that two entries for the SLI bad pixel map contain possibly inconsistent data. These are entries 8 and 9, which specify a first row of -1. The consequences of this must be investigated. 5.3. Square-root processing The data compression hardware (DCS) is capable of processing only 8 bits/pixel data. The analog-to-digital converter for the CCD delivers 12 bits. A method of converting a 12-bit image to an 8-bit image was required. We noted that the inherent accuracy in the imager data was limited by Shot noise, and that for high data numbers the standard deviation of a pixel value would be several DN. We therefore decided on a mapping of 12 to 8 bit data numbers which took advantange of this noise property. The 12-to-8 bit transfer function used is approximately a square root function. It differs from a square root because we also imposed the condition that signal-to-noise ratios in excess of 100 need not be retained. This condition permits a less dense mapping of 12 bit states into 8 bit states for high data numbers. The final step was to make the transfer function adaptive in some cases. If an image has a narrow histogram, there is no point in assigning 8-bit codes to 12- bit DNs which do not occur. Higher signal-to-noise ratios can be achieved by mapping fewer 12-bit DNs to the 256 8-bit codes. If the histogram is too broad, the original transfer function is used. The non-adaptive transfer function is implemented as a lookup table in the flight software. Table 5.3-1 Non-adaptive square root table in the flight software 12 bit DNs 8 bit DN 12 bit DNs 8 bit DN 12 bit DNs 8 bit DN 12 bit DNs 8 bit DN 0 0 170 - 173 64 480 - 485 128 1261 - 1282 192 1 1 174 - 177 65 486 - 491 129 1283 - 1305 193 2 - 3 2 178 - 181 66 492 - 497 130 1306 - 1328 194 4 - 5 3 182 - 185 67 498 - 503 131 1329 - 1352 195 6 - 7 4 186 - 189 68 504 - 509 132 1353 - 1376 196 8 - 9 5 190 - 193 69 510 - 515 133 1377 - 1400 197 10 - 11 6 194 - 197 70 516 - 522 134 1401 - 1425 198 12 - 13 7 198 - 201 71 523 - 529 135 1426 - 1450 199 14 - 15 8 202 - 205 72 530 - 536 136 1451 - 1476 200 16 - 17 9 206 - 209 73 537 - 543 137 1477 - 1503 201 18 - 19 10 210 - 213 74 544 - 550 138 1504 - 1530 202 20 - 21 11 214 - 217 75 551 - 557 139 1531 - 1558 203 22 - 23 12 218 - 221 76 558 - 565 140 1559 - 1586 204 24 - 25 13 222 - 225 77 566 - 573 141 1587 - 1615 205 26 - 27 14 226 - 229 78 574 - 581 142 1616 - 1644 206 28 - 29 15 230 - 233 79 582 - 589 143 1645 - 1674 207 30 - 31 16 234 - 237 80 590 - 597 144 1675 - 1704 208 32 - 33 17 238 - 241 81 598 - 605 145 1705 - 1735 209 34 - 35 18 242 - 245 82 606 - 614 146 1736 - 1767 210 36 - 37 19 246 - 249 83 615 - 623 147 1768 - 1799 211 38 - 39 20 250 - 253 84 624 - 632 148 1800 - 1832 212 40 - 41 21 254 - 257 85 633 - 641 149 1833 - 1866 213 42 - 43 22 258 - 262 86 642 - 650 150 1867 - 1900 214 44 - 45 23 263 - 267 87 651 - 660 151 1901 - 1935 215 46 - 47 24 268 - 272 88 661 - 670 152 1936 - 1971 216 48 - 49 25 273 - 277 89 671 - 680 153 1972 - 2007 217 50 - 51 26 278 - 282 90 681 - 690 154 2008 - 2044 218 52 - 53 27 283 - 287 91 691 - 700 155 2045 - 2082 219 54 - 56 28 288 - 292 92 701 - 711 156 2083 - 2121 220 57 - 59 29 293 - 297 93 712 - 722 157 2122 - 2161 221 60 - 62 30 298 - 302 94 723 - 733 158 2162 - 2201 222 63 - 65 31 303 - 307 95 734 - 744 159 2202 - 2242 223 66 - 68 32 308 - 312 96 745 - 756 160 2243 - 2284 224 69 - 71 33 313 - 317 97 757 - 768 161 2285 - 2327 225 72 - 74 34 318 - 322 98 769 - 780 162 2328 - 2371 226 75 - 77 35 323 - 327 99 781 - 792 163 2372 - 2415 227 78 - 80 36 328 - 332 100 793 - 805 164 2416 - 2460 228 81 - 83 37 333 - 337 101 806 - 818 165 2461 - 2506 229 84 - 86 38 338 - 342 102 819 - 831 166 2507 - 2553 230 87 - 89 39 343 - 347 103 832 - 844 167 2554 - 2601 231 90 - 92 40 348 - 352 104 845 - 858 168 2602 - 2650 232 93 - 95 41 353 - 357 105 859 - 872 169 2651 - 2700 233 96 - 98 42 358 - 362 106 873 - 886 170 2701 - 2751 234 99 - 101 43 363 - 367 107 887 - 900 171 2752 - 2803 235 102 - 104 44 368 - 372 108 901 - 915 172 2804 - 2856 236 105 - 107 45 373 - 377 109 916 - 930 173 2857 - 2910 237 108 - 110 46 378 - 382 110 931 - 945 174 2911 - 2965 238 111 - 113 47 383 - 387 111 946 - 961 175 2966 - 3021 239 114 - 116 48 388 - 392 112 962 - 977 176 3022 - 3079 240 117 - 119 49 393 - 397 113 978 - 993 177 3080 - 3138 241 120 - 122 50 398 - 402 114 994 - 1010 178 3139 - 3198 242 123 - 125 51 403 - 407 115 1011 - 1027 179 3199 - 3259 243 126 - 128 52 408 - 413 116 1028 - 1044 180 3260 - 3321 244 129 - 131 53 414 - 419 117 1045 - 1062 181 3322 - 3385 245 132 - 134 54 420 - 425 118 1063 - 1080 182 3386 - 3450 246 135 - 137 55 426 - 431 119 1081 - 1098 183 3451 - 3516 247 138 - 141 56 432 - 437 120 1099 - 1117 184 3517 - 3583 248 142 - 145 57 438 - 443 121 1118 - 1136 185 3584 - 3652 249 146 - 149 58 444 - 449 122 1137 - 1156 186 3653 - 3702 250 150 - 153 59 450 - 455 123 1157 - 1176 187 3703 - 3794 251 154 - 157 60 456 - 461 124 1177 - 1196 188 3795 - 3867 252 158 - 161 61 462 - 467 125 1197 - 1217 189 3868 - 3941 253 162 - 165 62 468 - 473 126 1218 - 1238 190 3942 - 4017 254 166 - 169 63 474 - 479 127 1239 - 1260 191 4018 - 4095 255 The algorithm for selecting an adaptive transfer function is complex. The reader is referred to the flight software (object O350_Image_Pic) and to the IDL program new_sqrt_sim.pro. Note that each adaptive transfer function is defined entirely by two values in the data set header, H_SQRT_MIN (=img_min) and H_SQRT_MAX(=img_max). The adaptive transfer function calculation is described by the following steps. 1. Construct a histogram of frequency of occurrence of each 12-bit DN 2. Determine the 12-bit DN values: a. Above which 95% of the image DN values lie (img_min) b. Below which 95% of the image DN values lie (img_max) 3. Redefine img_min and img_max by extending the range ( = img_max - img_min) by 10%, i.e., a. (img_maxnew-img_minold-0.6*(img_max-img_min) b. (img_maxnew-img_minold+0.6*(img_max-img_min) 4. Under the following conditions, use the original transfer function in table 5.3-1: a. (img_maxnew-img_minnew) < 2000 b. img_maxnew = img_minnew c. All pixels have values < img_minnew 5. The range of 12-bit DNs is then divided into three sections: a. Lower (DN < img_minnew) b. Middle (img_minnew < DN < img_maxnew) c. Upper ( DN > img_maxnew) 6. The number of new 8-bit codes in the middle section is set to the lesser of a. 10 times the number of codes in the middle section for the non-adaptive transfer function b. 128 c. img_maxnew-img_minnew+1 7. If the non-adaptive transfer function contained more 8-bit codes than the adaptive transfer function, the non-adaptive function is used throughout 8. The DN value boundaries of the three sections are calculated a. The largest DN in the lower section is the larger of i. img_minnew-1 ii. 0 b. The smallest DN in the middle section is img_minnew c. The largest DN in the middle section is img_maxnew d. The smallest DN in the upper section is the lesser of i. img_maxnew+1 ii. 4095 9. Calculate the number of codes in the lower and upper sections a. Compute the fraction of all codes in the non-adaptive table for DN < img_min b. Set the number of codes in the lower section to this fraction times the number of codes left (256 - number of codes in the middle section) c. Set the number of codes in the upper section to the number of codes left (256 - number of codes in the middle section - number of codes in the lower section) d. Compute the number of codes in the non-adaptive table for DN > img_max e. If there are now more new codes in the upper section (from c) than there were old codes (from d): i. Reset the number of new codes in the upper section to be equal to the the old codes in the upper section ii. Reset the number of codes in the lower section to the number of codes left (256 - number of codes in the middle section - number of codes in the upper section f. Compute the number codes in the non-adaptive table for DN < img_min g. If there are now more new codes in the lower section than there were old codes (from f): i. Reset the number of new codes in the lower section to the number of old codes in the lower section 10. Generate the new codes in the lower section of the new table a. Compute the factor, f [TABLE_5.3-1_EQU_3.GIF] b. For all codes in the lower section [TABLE_5.3-1_EQU_4.GIF] 11. Generate the new codes in the middle section of the new table a. If the number of new codes in the middle section is equal to the number of data numbers in the middle section, then assign one code to each data number, beginning with the first unused 8-bit code b. If the number of new codes in the middle section is less than the number of data numbers in the middle section, new_code(DN)=... [TABLE_5.3-1_EQU_7.GIF] i. Compute the factor, f [TABLE_5.3-1_EQU_5.GIF] ii. Let start_code be the first unused 8-bit code iii. For all codes in the middle section iv. Reset the number of codes in the middle section to the total number of codes assigned so far less the number of codes in the lower section 12. Generate the new codes in the upper section of the new table a. Compute the number of codes left as 256 - number of codes already used b. If the number of codes left is greater than the number of codes in the upper section, reset the number of codes in the upper section to be the number of codes left c. Compute the factor f to be the lesser of: i. [TABLE_5.3-1_EQU_8.GIF] ii. 1.0 d. Let start_code be the first unused 8-bit code e. For all codes in the upper section set new_code(DN) to the lesser of i. [TABLE_5.3-1_EQU_11.GIF] ii. 255 13. Return to the middle section to fill in gaps, because the scheme of assigning codes above may skip some new code values a. Find the first DN values in the middle region which have code values larger than the code values for the previous DN, i.e., where new_code(DN) new_code(DN- 1) b. Reset the new_codes between the successive DN values found in a. using linear interpolation, i.e., [TABLE_5.3-1_EQU_12.GIF] 5.4. Flat-fielding During the DISR development phase when the first imaging system contained both a fiber optic conduit and processing by the hardware data compressor, we noticed a serious problem. The fiber optic conduit introduced a distinct high spatial frequency pattern into the images consisting of the hexagonal "chicken wire" pattern as well as many poorly illuminated pixels fed by fibers with low transmission. Figure X, which shows images from the three imagers of the inside of 20-inch integrating sphere, illustrates the problem. For low contrast scenes the data compressor tended to preserve this fiber optic pattern much better than many features in the scene. The only cure available in the original design was to reduce the compression ratio. With the low contrast scenes expected on Titan, compression ratios of only 2:1 would be required. HRI MRI SLI Fig. 5.4-1 Images of the 20-inch integrating sphere wall taken with the DISR flight model imagers. The contrast has been enhanced greatly to show the details of the flat field defects. The design of the DISR electronics was modified to include EEPROM containing an 8-bit number for each imager pixel. This number describes how to modify that pixel's DN to provide a flat field correction. The flat field algorithm is implemented in the flight software as follows. 5.4.1. Flat Field Table For each pixel in the three imagers a corresponding 8-bit code shall be stored in EEPROM. These codes shall be pre-loaded before instrument delivery. The flight software shall be capable of changing any of these codes by command upload. 5.4.2. Flat Field Lookup Table A translation table containing 256 16-bit entries shall be defined in PROM. It shall be copied to data RAM during initialization. The flight software shall be capable of changing any of these table entries by command upload through the normal EEPROM upload mechanism. Two table entries have special significance. A value of zero shall direct the flight software to make no alteration of the raw pixel value during the flat field correction operation. A value of 1 shall direct the flight software to replace the current pixel being corrected with the corrected value of the previous processed pixel. The remaining 254 table entries shall contain values representing 1024/(pixel transmission) according the following formula: [SECTION_5.4.2_EQU_1.GIF] where Entry is the table value and i is the table index (from 0 through 255). For i = 2, the table entry shall be 5120 and for i = 255 the table entry shall be 853. The table entries shall be evaluated using floating point arithmetic and rounded to the nearest integer. Figure X shows the relationship between flat field table entry and pixel correction factor, defined by [SECTION_5.4.2_EQU_2.GIF] Figure 5.4.2-1 The relationship between correction factor and the flat field table entry for tabular values 1. 5.4.3. Flat Field Correction Operation The entire flat field correction operation shall be optional, dependent on the setting of a flag in data RAM. By default the flat field correction shall be enabled. It may be disabled by resetting this flag through a memory upload. This operation shall be done prior to bad pixel replacement. For each pixel in the imaging area of the CCD the corresponding flat field table entry shall be examined. If the value of this entry is 0, the pixel shall be left unchanged. If the value of this entry is 1, the pixel value shall be replaced by the previously corrected pixel value. If the value of this entry is more than 1, the corresponding value in the flat field lookup table shall be retrieved. The raw pixel value shall first have a constant subtracted from it, then be multiplied by the flat field lookup table entry, and then shifted by 10 bits (to divide the result by 1024). If the result is larger than 4095, the result shall be set to 4095. The resulting value shall then replace the raw pixel value. 5.4.4. Method of Determining the Flat Field Table 20 sets of exposures of the 20-inch integrating sphere wall were made with each of the three imagers July 20, 1996. The test log for these data sets is flatfield_imagers_20July96.1. It is currently located on the computer cassini in directory /disr3_cal/20Jul96/Log. The brightness of a given pixel is taken to be proportional to (the bright DN - the dark DN) - the electronic shutter correction. The electronic shutter correction is caused by the charge picked up as the image is shifted from the image zone to the memory zone. This charge is different when the chip is illuminated from when it is not. Therefore, two additional exposures are taken with zero exposure time, with the chip illuminated and not illuminated, to derive the complete auto-exposure correction. The corrected DN for each pixel is [SECTION_5.4.4_EQU_1.GIF] The data sets, from the test log, used to derive the flat field correction are given in table 5.4.4. Table 5.4.4-1a Data Sets used to derive the High Resolution Imager flat field correction No Bright Dark . 1 V_00054I.MMX_01:42:34_7586_Img V_00048I.MMX_01:40:17_5079_Img 2 V_00060I.MMX_01:44:21_7577_Img V_00066I.MMX_01:46:38_7584_Img 3 V_00078I.MMX_01:52:51_2573_Img V_00072I.MMX_01:50:33_2585_Img 4 V_00084I.MMX_01:54:38_2584_Img V_00090I.MMX_01:56:55_0073_Img 5 V_00102I.MMX_02:03:49_0071_Img V_00096I.MMX_02:01:31_2586_Img 6 V_00108I.MMX_02:05:36_0096_Img V_00114I.MMX_02:07:52_7570_Img 7 V_00126I.MMX_02:12:45_0086_Img V_00120I.MMX_02:10:27_5077_Img 8 V_00132I.MMX_02:14:32_0091_Img V_00138I.MMX_02:16:48_2585_Img 9 V_00150I.MMX_02:22:44_5069_Img V_00144I.MMX_02:20:26_7584_Img 10 V_00156I.MMX_02:24:31_5080_Img V_00162I.MMX_02:26:48_2589_Img 11 V_00174I.MMX_02:31:40_5083_Img V_00168I.MMX_02:29:22_7574_Img 12 V_00180I.MMX_02:33:27_5074_Img V_00186I.MMX_02:35:44_2582_Img 13 V_00198I.MMX_02:42:44_2581_Img V_00192I.MMX_02:40:26_7575_Img 14 V_00204I.MMX_02:44:31_2572_Img V_00210I.MMX_02:46:48_2579_Img 15 V_00222I.MMX_02:52:28_0084_Img V_00216I.MMX_02:50:10_2582_Img 16 V_00228I.MMX_02:54:15_0082_Img V_00234I.MMX_02:56:32_0083_Img 17 V_00246I.MMX_03:02:28_2575_Img V_00240I.MMX_03:00:10_5088_Img 18 V_00252I.MMX_03:04:15_2584_Img V_00258I.MMX_03:06:31_7573_Img 19 V_00270I.MMX_03:11:18_7589_Img V_00264I.MMX_03:09:01_2580_Img 20 V_00276I.MMX_03:13:05_7602_Img V_00282I.MMX_03:15:22_5089_Img Table 5.4.4-1b Data Sets used to derive the High Resolution Imager electronic shutter correction No Bright - 0 Exposure Dark - 0 Exposure . 1 V_00059I.MMX_01:43:31_5081_Img V_00053I.MMX_01:41:14_2573_Img 2 V_00065I.MMX_01:45:18_5070_Img V_00071I.MMX_01:47:35_5079_Img 3 V_00083I.MMX_01:53:48_0103_Img V_00077I.MMX_01:51:30_0094_Img 4 V_00089I.MMX_01:55:35_0079_Img V_00095I.MMX_01:57:51_7587_Img 5 V_00107I.MMX_02:04:45_7587_Img V_00101I.MMX_02:02:28_0094_Img 6 V_00113I.MMX_02:06:32_7577_Img V_00119I.MMX_02:08:49_5087_Img 7 V_00131I.MMX_02:13:41_7581_Img V_00125I.MMX_02:11:24_2587_Img 8 V_00137I.MMX_02:15:28_7572_Img V_00143I.MMX_02:17:45_0079_Img 9 V_00155I.MMX_02:23:41_2584_Img V_00149I.MMX_02:21:23_5077_Img 10 V_00161I.MMX_02:25:28_2575_Img V_00167I.MMX_02:27:45_0082_Img 11 V_00179I.MMX_02:32:37_2578_Img V_00173I.MMX_02:30:19_5070_Img 12 V_00185I.MMX_02:34:24_2569_Img V_00191I.MMX_02:36:41_0077_Img 13 V_00203I.MMX_02:43:41_0076_Img V_00197I.MMX_02:41:23_5069_Img 14 V_00209I.MMX_02:45:28_0100_Img V_00215I.MMX_02:47:45_0074_Img 15 V_00227I.MMX_02:53:24_7586_Img V_00221I.MMX_02:51:07_0077_Img 16 V_00233I.MMX_02:55:11_7576_Img V_00239I.MMX_02:57:28_7584_Img 17 V_00251I.MMX_03:03:25_0089_Img V_00245I.MMX_03:01:07_2582_Img 18 V_00257I.MMX_03:05:12_0092_Img V_00263I.MMX_03:07:28_5089_Img 19 V_00275I.MMX_03:12:15_5084_Img V_00269I.MMX_03:09:58_0088_Img 20 V_00281I.MMX_03:14:02_5075_Img V_00287I.MMX_03:16:19_2584_Img Table 5.4.4-2a Data Sets used to derive the Medium Resolution Imager flat field correction No Bright Dark . 1 V_00056I.MMX_01:43:11_2582_Im V_00050I.MMX_01:40:54_0089_Img g 2 V_00062I.MMX_01:44:58_2573_Im V_00068I.MMX_01:47:15_2581_Img g 3 V_00080I.MMX_01:53:27_7570_Im V_00074I.MMX_01:51:09_7581_Img g 4 V_00086I.MMX_01:55:14_7581_Im V_00092I.MMX_01:57:31_5089_Img g 5 V_00104I.MMX_02:04:25_5089_Im V_00098I.MMX_02:02:07_7582_Img g 6 V_00110I.MMX_02:06:12_5079_Im V_00116I.MMX_02:08:29_2588_Img g 7 V_00128I.MMX_02:13:21_5084_Im V_00122I.MMX_02:11:04_0087_Img g 8 V_00134I.MMX_02:15:08_5074_Im V_00140I.MMX_02:17:24_7581_Img g 9 V_00152I.MMX_02:23:21_0086_Im V_00146I.MMX_02:21:03_2579_Img g 10 V_00158I.MMX_02:25:08_0090_Im V_00164I.MMX_02:27:24_7584_Img g 11 V_00176I.MMX_02:32:17_0081_Im V_00170I.MMX_02:29:59_2572_Img g 12 V_00182I.MMX_02:34:04_0083_Im V_00188I.MMX_02:36:20_7580_Img g 13 V_00200I.MMX_02:43:20_7579_Im V_00194I.MMX_02:41:03_2571_Img g 14 V_00206I.MMX_02:45:07_7588_Im V_00212I.MMX_02:47:24_7575_Img g 15 V_00224I.MMX_02:53:04_5088_Im V_00218I.MMX_02:50:46_7580_Img g 16 V_00230I.MMX_02:54:51_5079_Im V_00236I.MMX_02:57:08_5086_Img g 17 V_00248I.MMX_03:03:04_7570_Im V_00242I.MMX_03:00:47_0085_Img g 18 V_00254I.MMX_03:04:51_7581_Im V_00260I.MMX_03:07:08_2600_Img g 19 V_00272I.MMX_03:11:55_2586_Im V_00266I.MMX_03:09:37_7576_Img g 20 V_00278I.MMX_03:13:42_2577_Im V_00284I.MMX_03:15:59_0086_Img g Table 5.4.4-2b Data Sets used to derive the Medium Resolution Imager electronic shutter correction No Bright - 0 Exposure Dark - 0 Exposure . 1 V_00057I.MMX_01:43:31_5081_Im V_00051I.MMX_01:41:14_2573_Img g 2 V_00063I.MMX_01:45:18_5070_Im V_00069I.MMX_01:47:35_5079_Img g 3 V_00081I.MMX_01:53:48_0103_Im V_00075I.MMX_01:51:30_0094_Img g 4 V_00087I.MMX_01:55:35_0079_Im V_00093I.MMX_01:57:51_7587_Img g 5 V_00105I.MMX_02:04:45_7587_Im V_00099I.MMX_02:02:28_0094_Img g 6 V_00111I.MMX_02:06:32_7577_Im V_00117I.MMX_02:08:49_5087_Img g 7 V_00129I.MMX_02:13:41_7581_Im V_00123I.MMX_02:11:24_2587_Img g 8 V_00135I.MMX_02:15:28_7572_Im V_00141I.MMX_02:17:45_0079_Img g 9 V_00153I.MMX_02:23:41_2584_Im V_00147I.MMX_02:21:23_5077_Img g 10 V_00159I.MMX_02:25:28_2575_Im V_00165I.MMX_02:27:45_0082_Img g 11 V_00177I.MMX_02:32:37_2578_Im V_00171I.MMX_02:30:19_5070_Img g 12 V_00183I.MMX_02:34:24_2569_Im V_00189I.MMX_02:36:41_0077_Img g 13 V_00201I.MMX_02:43:41_0076_Im V_00195I.MMX_02:41:23_5069_Img g 14 V_00207I.MMX_02:45:28_0100_Im V_00213I.MMX_02:47:45_0074_Img g 15 V_00225I.MMX_02:53:24_7586_Im V_00219I.MMX_02:51:07_0077_Img g 16 V_00231I.MMX_02:55:11_7576_Im V_00237I.MMX_02:57:28_7584_Img g 17 V_00249I.MMX_03:03:25_0089_Im V_00243I.MMX_03:01:07_2582_Img g 18 V_00255I.MMX_03:05:12_0092_Im V_00261I.MMX_03:07:28_5089_Img g 19 V_00273I.MMX_03:12:15_5084_Im V_00267I.MMX_03:09:58_0088_Img g 20 V_00279I.MMX_03:14:02_5075_Im V_00285I.MMX_03:16:19_2584_Img g Table 5.4.4-3a Data Sets used to derive the Side-Looking Imager flat field correction No Bright Dark . 1 V_00058I.MMX_01:43:31_5081_Im V_00052I.MMX_01:41:14_2573_Img g 2 V_00064I.MMX_01:45:18_5070_Im V_00070I.MMX_01:47:35_5079_Img g 3 V_00082I.MMX_01:53:48_0103_Im V_00076I.MMX_01:51:30_0094_Img g 4 V_00088I.MMX_01:55:35_0079_Im V_00094I.MMX_01:57:51_7587_Img g 5 V_00106I.MMX_02:04:45_7587_Im V_00100I.MMX_02:02:28_0094_Img g 6 V_00112I.MMX_02:06:32_7577_Im V_00118I.MMX_02:08:49_5087_Img g 7 V_00130I.MMX_02:13:41_7581_Im V_00124I.MMX_02:11:24_2587_Img g 8 V_00136I.MMX_02:15:28_7572_Im V_00142I.MMX_02:17:45_0079_Img g 9 V_00154I.MMX_02:23:41_2584_Im V_00148I.MMX_02:21:23_5077_Img g 10 V_00160I.MMX_02:25:28_2575_Im V_00166I.MMX_02:27:45_0082_Img g 11 V_00178I.MMX_02:32:37_2578_Im V_00172I.MMX_02:30:19_5070_Img g 12 V_00184I.MMX_02:34:24_2569_Im V_00190I.MMX_02:36:41_0077_Img g 13 V_00202I.MMX_02:43:41_0076_Im V_00196I.MMX_02:41:23_5069_Img g 14 V_00208I.MMX_02:45:28_0100_Im V_00214I.MMX_02:47:45_0074_Img g 15 V_00226I.MMX_02:53:24_7586_Im V_00220I.MMX_02:51:07_0077_Img g 16 V_00232I.MMX_02:55:11_7576_Im V_00238I.MMX_02:57:28_7584_Img g 17 V_00250I.MMX_03:03:25_0089_Im V_00244I.MMX_03:01:07_2582_Img g 18 V_00256I.MMX_03:05:12_0092_Im V_00262I.MMX_03:07:28_5089_Img g 19 V_00274I.MMX_03:12:15_5084_Im V_00268I.MMX_03:09:58_0088_Img g 20 V_00280I.MMX_03:14:02_5075_Im V_00286I.MMX_03:16:19_2584_Img g Table 5.4.4-3b Data Sets used to derive the Side-Looking Imager electronic shutter correction No Bright - 0 Exposure Dark - 0 Exposure . 1 V_00058I.MMX_01:43:31_5081_Im V_00052I.MMX_01:41:14_2573_Img g 2 V_00064I.MMX_01:45:18_5070_Im V_00070I.MMX_01:47:35_5079_Img g 3 V_00082I.MMX_01:53:48_0103_Im V_00076I.MMX_01:51:30_0094_Img g 4 V_00088I.MMX_01:55:35_0079_Im V_00094I.MMX_01:57:51_7587_Img g 5 V_00106I.MMX_02:04:45_7587_Im V_00100I.MMX_02:02:28_0094_Img g 6 V_00112I.MMX_02:06:32_7577_Im V_00118I.MMX_02:08:49_5087_Img g 7 V_00130I.MMX_02:13:41_7581_Im V_00124I.MMX_02:11:24_2587_Img g 8 V_00136I.MMX_02:15:28_7572_Im V_00142I.MMX_02:17:45_0079_Img g 9 V_00154I.MMX_02:23:41_2584_Im V_00148I.MMX_02:21:23_5077_Img g 10 V_00160I.MMX_02:25:28_2575_Im V_00166I.MMX_02:27:45_0082_Img g 11 V_00178I.MMX_02:32:37_2578_Im V_00172I.MMX_02:30:19_5070_Img g 12 V_00184I.MMX_02:34:24_2569_Im V_00190I.MMX_02:36:41_0077_Img g 13 V_00202I.MMX_02:43:41_0076_Im V_00196I.MMX_02:41:23_5069_Img g 14 V_00208I.MMX_02:45:28_0100_Im V_00214I.MMX_02:47:45_0074_Img g 15 V_00226I.MMX_02:53:24_7586_Im V_00220I.MMX_02:51:07_0077_Img g 16 V_00232I.MMX_02:55:11_7576_Im V_00238I.MMX_02:57:28_7584_Img g 17 V_00250I.MMX_03:03:25_0089_Im V_00244I.MMX_03:01:07_2582_Img g 18 V_00256I.MMX_03:05:12_0092_Im V_00262I.MMX_03:07:28_5089_Img g 19 V_00274I.MMX_03:12:15_5084_Im V_00268I.MMX_03:09:58_0088_Img g 20 V_00280I.MMX_03:14:02_5075_Im V_00286I.MMX_03:16:19_2584_Img g The actual numbers in the flat field tables for the DISR flight model are contained in Appendix B. The flat field correction is assumed to be temperature independent, although this is not exactly the case. The calibration data used to derive the flat field was taken with focal plane temperatures in the range 240 - 251K. Figures 5.4-1, 5.4-2, and 5.4-3 show original image, the image with bad-pixel replacement, and the image with both bad pixel replacement and flat field processing for each of the three imagers. The three processing steps are all shown with the same highly stretched contrast. HRI original HRI bad pixel replacement HRI full processing Figure 5.4-1 Bad pixel replacement and flat-field processing for the High Resolution Imager MRI original MRI bad pixel replacement MRI full processing Figure 5.4-2 Bad pixel replacement and flat-field processing for the Medium Resolution Imager SLI original SLI bad pixel replacement SLI full processing Figure 5.4-3 Bad pixel replacement and flat-field processing for the Side- Looking Imager 5.4.5. Flat Field Performance at Other Temperatures As noted above the flat field was derived from measurements in the CCD temperature range 240 - 251K, and it is of interest to know how it performs at other temperatures. To investigate this we apply the flat field to images taken for the purpose of absolute responsivity calibration in the 20-inch integrating sphere at other temperatures. The figures below show images taken at different temperatures, then processed for the flat field correction and the bad pixel replacement. All images are scaled such that white is 10% larger than the image mean values and black is 10% less than the image mean value. Figure 5.4.5-1 HRI original image, flat field processing, and ff+bpm at 176K Figure 5.4.5-2 Same as figure 5.4.5-1 except at 208K Figure 5.4.5-3 Same as figure 5.4.5-1 except at 223K Figure 5.4.5-4 Same as figure 5.4.5-1 except at 245K Figure 5.4.5-5 Same as figure 5.4.5-1 except at 260K Figure 5.4.5-6 Same as figure 5.4.5-1 except at 281K Figure 5.4.5-7 MRI original image, flat field processing, and ff+bpm at 176K Figure 5.4.5-8 Same as figure 5.4.5-7 except at 208K Figure 5.4.5-9 Same as figure 5.4.5-7 except at 223K Figure 5.4.5-10 Same as figure 5.4.5-7 except at 245K Figure 5.4.5-11 Same as figure 5.4.5-7 except at 260K Figure 5.4.5-12 Same as figure 5.4.5-7 except at 281K Figure 5.4.5-13 SLI original image, flat field processing, and ff+bpm at 176K Figure 5.4.5-14 Same as figure 5.4.5-13 except at 208K Figure 5.4.5-15 Same as figure 5.4.5-13 except at 223K Figure 5.4.5-16 Same as figure 5.4.5-13 except at 245K Figure 5.4.5-17 Same as figure 5.4.5-13 except at 260K Figure 5.4.5-18 Same as figure 5.4.5-13 except at 281K Correction of the integrating sphere images using the standard flat field results in systematic changes with temperature. Not surprisingly, the best result occurs at 245K, which is approximately the temperature at which the flat field correction was derived. Hotter and colder exposures produce corrected images with more features, with the number and visibility of features increasing for larger temperature differences. The short conclusion from this study is that the flat field varies with temperature. The most accurate photometry from the images requires removing the flight software flat field correction and applications of the pixel-by-pixel responsivities to derive the intensities of field objects. It is possible to draw some conclusion about what is producing this temperature dependence. The changes are very systematic. The coldest images show blemishes with a dark part at about "4 o'clock", and the warmest images show blemishes with a dark part at about "10 o'clock". Apparently as the fiber optic/CCD assembly changes temperature the fibers move with respect to the CCD pixels in the 4 o'clock - 10 o'clock direction. All three imagers move in same direction, so the entire fiber optic bundle moves with respect to the CCD. Whatever the cause, removal of the flight software flat field correction followed by application of the pixel-by-pixel absolute responsivity at the focal plane temperature provides a fundamental correction. One aspect of the images above is worthy of further note. The MRI displays a prominent, large feature just to be upper left of the center of the images at all temperatures. This feature is about 23 pixels long and 5 pixels wide. It does not correlate well with any fiber-optic structures. It appears to be a variation in CCD responsivity between the two days (July 20, 1996 and July 24, 1996), with an amplitude of 1 - 2%. The origin of this feature is unknown. It does appear in the integrating sphere data on September 11, 1996, so it does appear to be a permanent feature. This feature is contained in the absolute responsivity data, so it should be possible to correct for this accurately. During the Titan descent no dark frames are available. For this reason the flight software "estimates" the dark DN to be 8 counts for each pixel, and it subtracts this number before applying the flat field correction. While this number may be close to accurate when the CCD is very cold, dark current growth during the mission will make it too small during a large part of the mission. Furthermore a wide variation in the dark currents of different pixels will exist. Both effects will degrade the flat field correction. The main effect of these will be to make images less compressible while the CCD cools. 5.5. Compression DISR offers two methods for compressing images. Software compression, based on a row-by-row applicaton of the Rice -f method, is available for lossless compression. It is used for compression of the Solar Aureole and spectrometer data sets during descent and will not be mentioned further here. By default, the imagers use the Data Compression Subsystem (DCS) compressor, which implements compression using a Discrete Cosine Transform method, for all image data sets during descent. Discrete cosine transform compression is similar to JPEG compression, although for most scenes it is not quite as efficient. It was chosen over JPEG, because no space-qualified JPEG hardware compressor was available at the time of the DISR design. The DCS hardware was furnished by the Technische Universit„t Braunschweig, under the direction of Professor Fritz Gliem. The hardware design was executed by Dr. Frank Rabe. The DISR implementation is described "A DCT Image Data Processor For Use On The Huygens Titan Probe", P. Rffer, F. Rabe, and F. Gliem, International Geoscience and Remote Sensing Symposium, pp. 678 - 680, 1992. The image is subdivided into 16x16 pixel blocks, and the discrete cosine transform of each is then computed. The resulting coefficients are then quantized (or eliminated) and coded using an arithmetic coding scheme. A traditional problem with image compression has been its susceptibility to telemetry dropouts. A single lost packet in the telemetry stream for an entire image could cause loss of the entire image. To contain this problem the DISR implementation contains added "sync" markers, which contain pointers to the addresses of previous blocks. This limits the data loss from lost telemetry packets. The DCS flight code and ground decompression software support dropped packet recovery only for version 3 of the algorithms. It is noted that the "gse" program, written by Martin Marietta, gives up trying to process any data set for which any data is missing. Therefore, the gse program will not currently process images with missing telemetry. The Technische Universit„t Braunschweig has provided code (in C) to reconstruct images with missing data. It is located on cassini in the directory /users/ldoose/TUB/source_Mar95. The main source code module is named dcs.c. Software has also been provided which simulates operation of the hardware compressor. This is in the same directory, and the main source code module is named disrcmp3.c. Mike Bushroe has recently and successfully undertaken the task is to integrate the dcs program with the image telemetry stream to produce recovered images. 5.5.1. DCS automatic bad pixel replacement A drawback of the DCS compression technique is its performance on hot pixels. If a 16x16 pixel block contains a single pixel very much brighter than the other pixels, the compressor/decompressor will produce a checker board pattern within the block. An example is shown in figure Z. Sources of hot pixels include cosmic rays and pixels made hot through enhanced dark current. Because the point spread function of the imagers is generally larger than one pixel, real features are unlikely to produce such disturbances. Figure 5.5.1-1 48x48 pixel sub-samples of an image before and after compression. The single bright pixel in the center causes the "checkerboard" pattern in its block. E. Karkoschka suggested a method of replacing pixels hot enough to disturb the compressor, and this method was implemented in the compressor software. The algorithm is applied to the data as the compressor receives it, i.e., after flat- fielding, bad pixel removal, and square root processing. The algorithm searches all 2x2 pixel squares. If the absolute difference between the sums of both diagonals is less than a given threshold, it does nothing. Otherwise it calculates for each of these four pixels the median of the four pixels directly bordering the offending pixel. If the absolute difference between the pixel value the median is less than the threshold, it again does nothing. Otherwise it changes the pixel value to the median plus threshold (if the pixel DN is too high) or the median minus threshold (if the pixel DN is too low). The DCS implementation of this algorithm limits the number replaced pixels to about 400 - 500. I believe the adopted threshold value was 40 DN, although I have no proof of this. 5.6. Imaging system performance A comprehensive look at the imaging system performance at different compression ratios is available in section 6 of this document, "Test for Suitable Selection of Compression Ratios for DISR Imagers", by Erich Karkoschka. Here we present a more limited study. DCS performance depends on several factors, including image contrast, compression ratio, flat-fielding performance, and dark current. Overall performance of the onboard image processing software is more important than the compressor performance alone. A software simulator has been written to reproduce the processing of the onboard and GSE software. This simulator has the advantage of operating on any concocted scene incident on the CCD. Prior to launch test exposures were made using the HRI aimed at a projected slide. Contrast of the scene was degraded by illuminating the screen with a lamp, until this diluting illumination made the scene contrast approach zero. Compression ratios of 2, 3, 6, and 8 were used. Figure 5.6-1 shows the unprocessed, onboard software/GSE-processed images, and simulator images for two of the five contrast levels at compression ratios of 8. The purpose of this figure is to demonstrate the accuracy of the simulator. Mean exposure levels are about 1800 DN. The detector temperature was about 277K for all exposures, so the dark current was only slightly above its nominal value of 8 DN. Figure 5.6-1a The original scene on the CCD (left), the image produced by the flight and GSE software (center), and the image produced by the simulator (right) for the highest contrast scene and compression ratio 8. The two right images are essentially identical, validating the simulator. For this high contrast scene a compression ratio of 8 is well tolerated. Figure 5.6-1b Same as figure 5.6-1a, except for a very low contrast scene. Reconstruction of the image suffers under the extreme contrast enhancement used to display this scene. The blockiness in the right two images is very obvious. Reconstruction quality from the original scene is still remarkable. Minor differences in the two right images are seen. These are expected, because the source images are different. In figure 5.6-1 the two processed images (on the right) have been divided by a best-fit cubic polynominal surface to remove large scale brightness gradients in the images. This division flattens the image brightness level and permits a higher contrast stretch. The histograms of the images with and without the division are shown in figure 5.6-2. Figure Z2 validates the simulator. Exact agreement between the DISR system and simulator images is not expected, because they originate from different exposures which will be slightly different due to noise. Figure 5.6-2a Histograms of the high contrast image at various stages of processing. Figure 5.6-2b Histograms of the low contrast image at various stages of processing. The histograms show significant changes during the processing. These are all expected. The flat field correction and bad pixel replacement alter the data number content substantially. Removal of the large scale gradients narrows the histograms. Square root processing reduces the number of permitted data numbers from 4096 to 256, and redistributes them so that relatively fewer high DN values are permitted. Compression certainly redistributes the data numbers; this will be shown better below. The adaptive square root algorithm allocates the number of DNs based on the flat-fielded, bad-pixel-replaced scene. For the low contrast image this means 128 8-bit DNs are assigned between approximate 1300 and 1900 12-bit DNs. On average one 8-bit DN covers about 5 12-bit DNs. This granularity of 5 DN in an image with a mean brightness of about 1600 DN does not significantly degrade the inherent 200:1 signal-to-noise ratio. We have removed the large scale gradients, which narrows the histogram dramatically. Most of the resulting image is then represented with only about 30 DN levels. This, combined with the compression, accounts for the contouring seen in parts of the 8:1 compressed image of this scene. Although the appearance of the images is very good except at the lowest contrasts and highest compression factors, it is important to know the quantitative size of the errors introduced by the onboard/GSE processing. We have no ground truth measurements of images containing structure. The closest we can come is to correct an unprocessed DISR image for dark current, flat field, and bad pixels. This can serve as our ground truth image, and it can be compared to DISR-processed images. The differences are presumably caused by square root processing, compression, inherent system noise, and any temporal differences between the two exposures. In figure 5.6-3 we compare our ground truth image to processed images at several steps during the processing for row 106, as indicated in the figure. The original data (red dashed line) is about 5% higher than all the other profiles. This is because the flat field for this line has a mean value of about 1.05. Dividing by the flat field correction leaves the result about 5% low. For the high contrast, 2X compression profile, errors introduced by both the square rooting and compression are very small. The errors introduced by the square rooting are also very small, causing the green line to cover the blue line almost everywhere. At 8X compression the compressor introduces errors as large as about 3%, seen as the difference between the orange and green lines. Typical errors are much smaller. There are differences also between the simulated compression and hardware-compressed images. As noted above some of these differences are caused by these images coming from different exposures. In the low contrast image the errors introduced by the processing remain small, typically a few DN. The amplitude of the features is much smaller. The feature at column 137 has a contrast of about 2.5% when measured as (I_max-I_min)/(I_max+I_min). The noise in the surrounding data is about 0.5% in these contrast units. The 2.5% feature is easily discernible. Figure 5.6-4 shows the errors from each stage of the flight/GSE software processing. For 2X compression square rooting errors dominate, while for 8X compression the compressor errors dominate. The optimum compression ratio for photometry should compress the image as much as possible without becoming a limiting error source. For the data studied here that compression ratio is certainly between 2X and 8X. Figure 5.6-3 The horizontal lines show the location of row 106 in the low contrast image. Figure 5.6-4a The data number in row 106 vs. column number in the HRI for four images (top to bottom): high contrast with 2X compression, high contrast with 8X compression, low contrast with 2X compression, and low contrast with 8X compression. Figure 5.6-4b Errors introduced by flight/GSE software for two scene contrasts and two compression ratios for HRI row 106. 5.6.1. Compression in the presence of increased dark current The mean CCD dark current has increased steadily during the mission. The dark current of some pixels has increased more than others, leading to a broadening of the image and memory zone dark current distributions. Although the dark current of each pixel is quite predictable, the onboard software does not have the capability to subtract dark current on a pixel-by-pixel basis - it simply subtracts 8 DN from all pixels. This may still be a reasonable correction when the CCD is very cold. At warmer temperatures the excess dark counts take the role of a scene-independent extra signal with a distribution similar to random noise. Because random noise is inherently incompressible, compression of the images suffers when the amplitude of the dark current is any significant fraction of the amplitude of the image scene. We have studied this effect in two ways. First, using real data from the in- flight Health Checks we have searched for degradation of compressed images of the calibration lamps, using unprocessed images as ground truth. Second, we have simulated high dark current cases by adding synthetic dark current to existing pre-launch image scenes. These images can be processed with software that simulates onboard and GSE processing and compared with the original image. Each in-flight Health Check contains an uncompressed image and a fully processed image with lamp B on. Each successive Health Check also contains more dark current than the previous one. The exposure times are 40 ms. At the present mean dark current rate of 25 DN/sec, the mean excess dark current is only about 1 DN, compared to mean signals of 600 to 1200 DN. The effect of the mean dark current will surely be negligible. Any visible effects must be caused by the smaller number of pixels with high dark current. We show the effect on compression of the growth of dark current from F1 to F7 in figures 5.6-5, below. In these figures the contrast is stretched to show the features with high contrast. The difference image is scaled such that black is 10% lower intensity in the compressed image and white is 10% higher intensity in the compressed image. Three points can be made from figure 5.6-5: 1. The quantitative measure of agreement between the unprocessed and compressed image is almost exactly the same (0.0143 in the fractional difference) for both the F1 and F7. This indicates the damage done to compression by the rise in dark current is minimal. 2. Vertical stripes are visible in the difference image are more visible for the F7 than for the F1. These stripes originate in the memory zone dark current. The compression does not follow these linear features perfectly. 3. The 8x compression used introduces artifacts visible in both the F1 and F7 images: a. The fiber "chicken wire" pattern is emphasized in the compressed image. b. Larger, low-contrast features are lost or diminished in the compressed image. Conclusions from HRI and SLI images are the same. The situation during descent may not be much different, except the scene will certainly be very different. Although the mean dark current rate may double, the exposure times will typically be shorter by a factor of two or more. The situation will be worse in the memory zone. Here a few hot pixels have been created which cause vertical lines in the image as the pixels are shifted through them. These will get more numerous as the mission progresses. If the probe is heated significantly prior to entry, as is now being discussed, the first images may contain more dark current and the period of "warm" images will be slightly extended. In order to extrapolate the dark current into the future, we build synthetic images. The true scenes for the three imagers are taken to be the projected slide images used in figure 5.6-1, above. The dark current is estimated from examination of the histograms of the dark current rates during the F3 (433 days after launch), F5 (841 days after launch), and F7 (1254 days after launch) checkouts. The descent occurs 2648 days after launch. Cumulative histograms of the dark rates may be formed for each of these three checkouts for both the image and memory zones. The largest number of counts/sec which is truly due to dark current rather than cosmic rays is estimated at 700. This number has not changed appreciably over the checkout duration. We project the dark rate distributions to the time of descent by projecting the cumulative histograms vs. time. The results are shown in Figure 5.6.1-1. Figure 5.6.1-1 Cumulative histograms giving the probability than a pixel has dark current less than the abscissa value. The Descent curve is computed by extrapolating the best linear fit through the F3, F5, and F7 data downward at each abscissa value. If the ordinate is divided by the number of pixels, the cumulative histogram shows the probability that a pixel will have a dark rate less than the ordinate. A dark rate "image" can then be constructed which satisfies these probabilities. That can be added to the "true scene", and the resulting image can be run through the onboard processing simulator. The exposure time multiplies the dark rate for the image zone. Likewise, the temperature dependence of the dark scene can be included using the "known" dependence of the dark current for the image zone, memory zone, and serial register. The bias is assumed to be 8.9 DN. Using these relationships a synthetic dark current at descent for any exposure time and temperature can be generated. This is added to the "true scene" image. For the projected slide images we perform the following steps in the simulation: 1. Generate the dark image for a specified exposure time and CCD temperature using the predicted descent dark rate probabilities. 2. Choose an unprocessed image of a projected slide with known scene contrast. (Here we have used only the 3% contrast images to provide worst case scenes). 3. Perform a flat field correction of the unprocessed image to eliminate blemishes. 4. Multiply the unprocessed, flat-fielded true scene image by a specified factor to control the brightness of the true scene. 5. Add the true scene image to the dark image. 6. Perform square root correction, compression by a specified factor, decompression, and "squaring" of the summed image, as the onboard and ground processing would do. 7. Subtract the dark image, leaving the reconstructed true scene. 8. Compare the original true scene to the reconstructed true scene. The specifiable parameters in this process are: 1. Exposure time (to control the image zone dark current) 2. CCD temperature (to control the image, memory, and serial register dark current rates) 3. "Brightness" factor (by which the flat-fielded true scene is multiplied) 4. Compression factor In the comparison images we fit a two-dimensional polynomial surface to the true scene to remove large-scale gradients. Both the true scene image and the reconstructed true scene image are divided by this fitted surface. Finally both scenes are contrast enhanced using the same linear stretch. This will likely be done during interpretation of the real images, so we felt it fair to do it here. In the study below we fix the exposure time at 50 msec. This is probably an upper limit on the exposure time as imposed by the spin rate. For compression factors of 3, 6, and 8, we vary the CCD temperature (266K, 250K, and 220K), brightness factor (0.1 and 0.4), and contrast (3% and 13%), for a total of 36 cases. For each we produce two pages of comparison images as well as a plot comparing the photometric profiles. We consider these figures of merit: the RMS and maximum photometric deviation in DN between the original and reconstructed scenes for row 106 only, shown in figures 5.6.1-2 through 5.6.1-5. During this study a minor flaw is the image decompression software was discovered. Dr. Frank Rabe graciously corrected this error, providing version 3.40 of the decompression software. In Table 5.6.1-1 we show a comparison of the decompression performance for version 3.30 vs. version 3.40. We also note that the version in the gse program which routinely decodes the telemetry is an earlier version yet. However we have no easy way to evaluate its performance. Table 5.6.1-1 Comparison of performance of version 3.30 and 3.40 of the DCS decompressor Sign Compression al Contra Ratio Temperatu Version Version Chang st re 3.30 RMS 3.40 RMS e Low Low 3 266K 1.27 1.27 0.00 Low Low 6 266K 2.03 2.03 0.00 Low Low 8 266K 2.26 2.26 0.00 High Low 3 266K 3.10 3.10 0.00 High Low 6 266K 3.95 3.95 0.00 High Low 8 266K 3.95 3.95 0.00 Low Low 3 250K 0.71 0.71 0.00 Low Low 6 250K 0.98 0.98 0.00 Low Low 8 250K 0.98 0.98 0.00 High Low 3 250K 2.85 2.85 0.00 High Low 6 250K 3.46 3.46 0.00 High Low 8 250K 3.46 3.46 0.00 Low Low 3 220K 0.67 0.67 0.00 Low Low 6 220K 0.94 0.94 0.00 Low Low 8 220K 0.94 0.94 0.00 High Low 3 220K 2.61 2.61 0.00 High Low 6 220K 3.25 3.25 0.00 High Low 8 220K 3.25 3.25 0.00 Low High 3 266K 2.04 2.04 0.00 Low High 6 266K 2.53 2.53 0.00 Low High 8 266K 2.53 2.53 0.00 High High 3 266K 4.37 4.37 0.00 High High 6 266K 5.40 5.40 0.00 High High 8 266K 5.61 5.45 -0.16 Low High 3 250K 1.03 1.03 0.00 Low High 6 250K 1.28 1.34 0.06 Low High 8 250K 1.41 1.39 -0.02 High High 3 250K 4.24 4.24 0.00 High High 6 250K 4.93 4.93 0.00 High High 8 250K 5.74 5.79 0.05 Low High 3 220K 1.06 1.06 0.00 Low High 6 220K 1.22 1.20 -0.02 Low High 8 220K 1.28 1.26 -0.02 High High 3 220K 4.08 4.08 0.00 High High 6 220K 4.63 4.63 0.00 High High 8 220K 5.13 5.32 0.19 Of 36 cases only 5 have difference RMS errors. Four of these are improvements with the newest software, and one is a degradation. Any changes are generally very small. Figure 5.6.1-2 Errors (RMS and maximum) in data number caused by compression for a low signal, low contrast scene for three different compression ratios and three different temperatures. Figure 5.6.1-3 Errors (RMS and maximum) in data number caused by compression for a low signal, high contrast scene for three different compression ratios and three different temperatures. Figure 5.6.1-4 Errors (RMS and maximum) in data number caused by compression for a high signal, low contrast scene for three different compression ratios and three different temperatures. Figure 5.6.1-5 Errors (RMS and maximum) in data number caused by compression for a high signal, high contrast scene for three different compression ratios and three different temperatures. 5.7. Auto-exposure calculation The flight software is capable of predicting the exposure time for the next exposure at the same azimuth (or at any azimuth if the azimuth of the next image is not constrained). This prediction is made if a flag (bit 3 in the general processing options word) is set. To make this prediction the flight software analyzes the histogram of DNs of the current image. A target is defined such that a specified fraction of the pixels exceeds a specified data number. For images 97% of the pixel DNs must be less than 60% of 4095 ( =2457 ). Normally the predicted exposure time is calculated using [IMAGE_610.GIF], where R = 0.6 F = 4095 X = the DN which 97% of the pixels are less than X is determined by analyzing the histogram. As an example suppose 97% of pixels are found to have DNs less than 1500 for an exposure time of 12 ms. Then the predicted exposure time will be [IMAGE_612.GIF]. Note that DNs actually contain a component which is independent of exposure time from the bias and memory zone dark current, whereas the algorithm above neglects this. This causes the algorithm to slightly underestimate the necessary change in exposure time. If a large fraction of the DN is generated by light and image zone dark current (components of the DN which do depend of exposure time), this underestimate makes a neglible error. However if a large fraction of the DN is generated by the bias and memory zone dark current, the underestimate of the correction will be larger. The auto exposure algorithm also contains special cases for extreme under exposure and over exposure. These are necessary for cases where the algorithm above has insufficient information to work correctly. An example is an image which is entirely saturated. If all data values are 4095, then the algorithm will decrease the exposure time by less than a factor of 2. In fact the image may be overexposed by many times. Therefore a special test is done to see if more than 92% of the pixels exceed DN 4088. If they do, the exposure time is decreased by a factor 10. The criterion for the lower limit is 92% of the pixels less than DN 7. If DCS compression is required, the pixel values have 8 subtracted from them before the tests are performed. If DCS compression is not required, the pixel values do not have 8 subtracted from them before the tests are performed. This appears to lead to some problems in the flight software. Table 5.7-1 Consequences of subtracting 8 DN from images Exp./Compression Min possible Max possible DN Status DN Under exposure with DCS 0 - OK compression Under exposure without 8 - Bad, because no pixel will have DN 7 DCS compression or less Over exposure with DCS - 4087 Bad, because no pixel will have DN compression 4088 or more Over exposure without - 4095 OK DCS compression The software does not provide for different limits depending on whether DCS compression is required or not. It should be designed for the case where DCS compression is required, because that it the case planned for descent. In this case the 4088 criterion should be reduce to (4087-8) = 4979. Probably this number should be reduced even more, because the fiber optic transmission is quite low for many pixels which are not mapped out in the bad pixel map. Fixing this flight software problem is currently under discussion. 5.8. Ground software processing 5.9. Photometric Reduction Summary For DCS-compressed images the flight software performs the following operations on the raw data numbers: 1. Bad pixel replacement 2. Flat field correction (after subtracting 8 DN from each pixel for "dark current") 3. (Adaptive) square root translation to 8-bits/pixel 4. DCS bad pixel replacement 5. DCS image compression The GSE software then 1. Decompresses the image 2. Translates from 8-bits/pixel back to 12-bits/pixel using the reverse square root table Some steps, such as compression, are not accurately reversible, of course. Otherwise this process works, except for three problems: 1) the flat field at the correct temperature should have been used, 2) the dark current is probably not 8 DN for each pixel, and 3) compressor introduces defects which can be minimized. An improvement over the standard GSE processing may be made by decompressing the image with more than 8-bit precision (i.e., keeping fractional DN values upon decompression), then interpolating in the reverse square root table. This results in more than 256 gray levels for the reconstructed image. A separate document on minimizing image defects, Processing of Compressed DISR Images, has been written by Erich Karkoschka. To enable use of Erich's algorithms, software has been written to extract the compressed data directly from the DISR data stream. Following ground-based reconstruction of the image one needs to performs the following steps to obtain a photometrically calibrated image: 1. multiply by the flat field used by the flight software 2. add 8 DN to each pixel 3. subtract the actual dark current (from a dark current model) from each pixel 4. divide by the exposure time in seconds 5. divide by the absolute responsivity of each imager pixel at the correct CCD temperature One might also consider flagging those image pixels which have been replaced, either through the bad pixel map or flat-fielding algorithm. Note that the derived radiance is within the spectral bandpass of the imager filter at the current temperature. 6.0. Improved Processing of Compressed DISR Images E. Karkoschka 6.1. Abstract DISR images of Titan will be transmitted with only about 1 bit/pixel, a compression ratio (CR) of 8. Most of our tests with such compression turned out more or less satisfactory, except that the compressed images contained many small-scale features that were not present in the original images. However, this unwanted property is not due to the compression but due to the decompression software that we used until now. By modifying the decompression algorithm, we successfully decreased or eliminated image defects and produced images resembling the original image significantly better. 6.2. The Discrete Cosine Transform DISR images get divided into 16x16 pixel blocks. In each block, a discrete cosine transform is performed by the compressor, which produces 256 coefficients resembling the amplitudes of various spatial frequencies. The lowest frequency, the constant, is always transmitted accurately. The three highest frequencies are never transmitted. The remaining 252 coefficients are grouped into 63 quadruples. If a quadruple contains a coefficient with an absolute value larger than a certain threshold (which depends on the image and the CR), all four coefficients of the quadruple are transmitted, otherwise none is transmitted. All transmitted coefficients are rounded down to a certain binary digit, called the quantization (which also depends on the image and the CR). By knowing the quantization and threshold for a compressed image, one knows the compression method and thus for each coefficient the possible range of values. The current decompression software chooses the middle of the range. Note that previous versions had some errors, or they made a less optimal choice. Choosing the middle of the range is often not the best choice as explained below. While the quantization is transmitted, the threshold is not, unfortunately. Thus, before one can give any uncertainty for a photometric or positional measurement, and before one can do image processing, one has to estimate the threshold. 6.3. Estimation of the Threshold At first, the maximum absolute value of the four coefficients in each quadruple is evaluated. A histogram of these maxima clearly shows the threshold to the size of the quantization. For example, if the transmitted values are 0, 4, 8, etc. , and no transmitted maximum is 0 or 4, but some are 8 and higher, then the threshold was between 6 and 10. The frequency of occurrence for the next three values (in our case 12, 16, and 20) is used to extrapolate for the frequency of occurrence between 6 and 10, using an almost exponential function. This yields to the estimation of threshold. For example, if values of 8 occur much less often than values of 12, then the cut-off was close to 10. On the other hand, if values of 8 occur as often as expected from the trend for 12, 16, and 20, then the cut-off was close to 6. Since an image has typically some 1000 transmitted quadruples, this statistical method works quite well. In some 100 test cases, the method found the exact threshold in 80 % of the cases and a value typically only some 5 % smaller or larger in the remaining cases, which is better than required for our purpose. 6.4. Unbiased Estimation of Coefficients All investigated images have a distribution of amplitude coefficients strongly peaked at zero. For the high frequencies, the peak is narrower and higher than for low frequencies. Therefore, the original estimation of each coefficient by the middle between the minimum and maximum possible value is not an unbiased estimation. In the new software, the estimation is closer to zero in order to account for the distribution peaked at zero. For high frequencies, the modification is larger than for low frequencies due to the stronger peaked distribution. For simplicity, the modification is not based on the image. This modification of coefficients is especially important for images with high dark current where the dark subtraction effectively adds a small constant to each amplitude. Thus, with the original decompression, all deleted coefficients are displayed in the final image as non-zero coefficients, producing high frequency noise. With the modification, the final amplitudes are much closer to zero. 6.5 Smoothing 16x16 Pixel Block Boundaries The last step yields acceptable images within each 16x16 pixel block. The images are about as smooth as allowed within the constraints from the transmitted data. However, this is not the case across block boundaries where the noise is uncorrelated, which causes unwanted artificial features along the block boundaries. In order to smooth the image across the block boundaries, the image is divided into 32x32 pixel blocks, shifted by multiples of 16 pixels. Thus, the 16x16 pixel blocks away from the edges appear in four 32x32 pixel blocks each. In each 32x32 pixel block, a discrete cosine transform is performed. The amplitudes are then decreased in a similar way as in the previous step. Then the image is transformed back. This method smoothes out the discontinuities across the two center boundaries in each 32x32 pixel block. The whole image is then constructed by weighted averaging the four data for each pixel from its four 32x32 pixel blocks. This smoothing operation decreases amplitudes of features that are close to the noise limit. Thus, features that almost could be noise or could be introduced by compression artifacts will appear with decreased amplitudes. Investigation of many images indicated that this is superior for most purposes since noise and image artifacts are strongly reduced while features well above the noise level are not affected. Nevertheless, the amount of smoothing is left as a free input parameter (a parameter of 1 means standard smoothing, 2 means twice as much smoothing, etc.). In cases where one is interested in very subtle features, the smoothing should be less. On the other hand, if one wants to be sure that there are no visible image artifacts, the smoothing should be larger. The smoothing operation actually takes place with square-rooted data numbers so that a specific amount of smoothing will causes the same amount relative to the CCD noise (which is constant in square-rooted data numbers). The software also evaluates how many more features there are across 16x16 block boundaries relative to the interior of a block. Based on this excess and on the known CCD noise, the program selects the standard amount of smoothing. 6.6 Rounding The original decompression algorithm rounds all pixel values to integers, between 0 and 255. This means that the data numbers in the final image have only 256 possible values between 0 and 4095. In regions of the image with slowly changing data numbers, this causes disturbing steps. In the new version, data numbers are multiplied by 8, square-rooted values are multiplied by 128 (range 0-32767 in both cases) before rounding to integers occurs. This decreases the steps so that they are invisible. 6.7 Bad Rows at Top/Bottom DISR gives images where a few CCD rows at the top and/or bottom are not exposed to light and thus have data numbers very different from the rest of the image, producing artificial sharp features. These edges do not exactly get transmitted causing ringing inside the exposed part of the image. The new decompression software has the ability to specify the number of bad rows at the bottom and top. This will cause the top and bottom 32x32 pixel blocks to be shifted accordingly towards the inside for smoothing so that the ringing is decreased. Therefore, accurate specification of the number of top and bottom bad rows is important. Some images have also bad areas close to the left and/or right edge. The software is not designed to handle those. These areas should be replaced by data numbers of neighboring valid pixels so that all the high frequency information of these boundaries do not need to be transmitted over and over again. 6.8 Figures The decompression algorithms are shown with three representative images: first, an image of a part of Ganymede taken by Galileo (which has higher contrasts than expected on Titan due to its low illumination angle), second, an image (repeated twice) of the forest in the Catalina Mountains (which also has higher contrasts than expected on Titan), and third, a low-contrast image with high dark current added, simulating the beginning of the descent. Each of the three images is shown in seven versions: 1: original CCD image 2: image with compression ratio of 4 with original decompression scheme 3: image with compression ratio of 8 with original decompression scheme 4: image with compression ratio of 8 with new decompression scheme, no smoothing 5: image with compression ratio of 8 with new decompression scheme, smoothing factor 0.5 6: image with compression ratio of 8 with new decompression scheme, nominal smoothing 7: image with compression ratio of 8 with new decompression scheme, smoothing factor 1.5. Figure 1a Original Mt. Bigelow scene. Figure 1b Compression ratio of 4 with original decompression scheme. Figure 1c Compression ratio of 8 with original decompression scheme. Figure 1d Compression ratio of 8 with new decompression scheme and no smoothing. Figure 1e Compression ratio of 8 with new decompression scheme and smoothing factor of 0.5. Figure 1f Compression ratio of 8 with new decompression scheme and nominal smoothing. Figure 1g Compression ratio of 8 with new decompression scheme and smoothing factor of 1.5. Figure 2a Original Ganymede scene. Figure 2b Compression ratio of 4 with original decompression scheme. Figure 2c Compression ratio of 8 with original decompression scheme. Figure 2d Compression ratio of 8 with new decompression scheme and no smoothing. Figure 2e Compression ratio of 8 with new decompression scheme and smoothing factor of 0.5. Figure 2f Compression ratio of 8 with new decompression scheme and nominal smoothing. Figure 2g Compression ratio of 8 with new decompression scheme and smoothing factor of 1.5. Figure 3a Original LANDSAT scene. Figure 3b Compression ratio of 4 with original decompression scheme. Figure 3c Compression ratio of 8 with original decompression scheme. Figure 3d Compression ratio of 8 with new decompression scheme and no smoothing. Figure 3e Compression ratio of 8 with new decompression scheme and smoothing factor of 0.5. Figure 3f Compression ratio of 8 with new decompression scheme and nominal smoothing. Figure 3g Compression ratio of 8 with new decompression scheme and smoothing factor of 1.5. These examples show that features from the dark image (vertical stripes and black dots) are significantly suppressed with the new scheme even without smoothing. However, block boundaries require at least a smoothing factor of 0.5 in order to be reasonably suppressed. With a smoothing factor of unity, they are almost invisible. A smoothing factor of 1.5 makes them completely invisible, but it typically comes with the cost of reducing the visibility of real features more than necessary. Some images look better with compression ratio of 8 and a smoothing factor of unity than with the original scheme at compression ratio of 4, although in other images, the higher compression ratio looses fine detail that cannot be brought back. 6.8. Equations and the Fortran Code 6.8.1. Estimation of Threshold We denote hk as the number of times in the image that the maximum absolute value of a transmitted quadruple has the smallest absolute maximum within the image. hk+1, hk+2, and hk+3 are the number of times in the image that the maximum absolute values of a transmitted quadruple has the next values. Thus, the index denotes the rounded absolute maximum of a quadruple (which is multiplied by a power of 2 which respect to real amplitudes according to the quantization q where q takes values of 1, 2, 4, etc.). The threshold t is then between k-0.5 and k+0.5. It is estimated the following way: t = k - 0.5 -ln{1+[1-exp(-fq)] hk / hk+1} / fq where f = 0.75 ln[(1+hk+1) / (1+hk+3)] /(q+0.2). t is then rounded to the next possible value. 6.8.2. Decrease of Small Amplitudes We denote the amplitude as a, and half of the possible range as d. Thus, the amplitude before compression must have been between a-d and a+d. We denote i and j are the frequency indices in both axes, ranging between 1 and 16. To calculate decreased amplitudes, the following iteration is performed twice: anew = 0.2 aold + 0.8 aold / max [ 1 , (aold/d)2 16/max(i,j)]. Note that in cases with a non-zero dark image, the zero amplitude is based with respect to the un-square-rooted image, and the scaling of amplitudes between the square-rooted and un-square-rooted image is based on the average bin size of data numbers. Since the bin size is not constant, the first estimate may not be perfect, but by the second iteration, it is close to perfect. 6.8.3. Determination of Standard Smoothing Amplitude The standard smoothing amplitude s, used in the 32x32 pixel block smoothing, is determined by the rms of the CCD noise and a value dependent on the size of excessive features at block boundaries. Thus, s = (2 + 32). The CCD noise was assumed to be 1 data number for an exposure level of 30 data numbers, increasing with the square-root of the exposure level. The horizontal and vertical feature size at each pixel is evaluated by DN(i,j) - 0.5 DN(i-1,j) - 0.5 DN(i+1,j) and DN(i,j) - 0.5 DN(i,j-1) - 0.5 DN(i,j+1), respectively, where DN(i,j) is the data number at pixel i,j. The rms of all feature sizes where the three pixels go across a 16x16 pixel block boundary is called e. The rms of all remaining feature sizes is called i. Then: = e - i. 6.8.4. Decrease of amplitudes in 32x32 pixel blocks Again, we denote the amplitude as a and the frequency indices i and j, now ranging between 1 and 32. Then, the amplitudes are decreased according to the equation: anew = aold - aold / max [ 1 , (aold/s)2 32/max(i,j)]. This calculation is performed on an image where all data numbers have been square-rooted (the mathematical square-root). 6.8.5. Interpolation between neighboring 32x32 pixel blocks For the horizontal interpolation, the contribution from each 32x32 pixel square is unity at the center of the square and zero at the edge. The contribution function is cos2(r 90) where r goes from -1 at the left edge of the square to 0 at the center to 1 at the right edge. The vertical interpolation is performed in the same way. 7.0. Test for Suitable Selection of Compression Ratios for DISR Imagers November 2001, by Erich Karkoschka with help by Martin Tomasko, Lyn Doose, and Bashar Rizk 7.1. Scientific Background 7.1.1. Introduction The DISR imagers were designed to be used with compression ratio (CR) 8(1 bit/pixel) in order to give sufficient coverage for the limited data rate. However, in 1995, we found that for low-contrast scenes, images compressed with CR 8 looked very bad since almost all compressed data were data about the flatfield, not data about the scene. Only at CR2-3 did the images look good. Thus, we considered CR of 3 and 6 for half of the images each. This way, at least half of the images would look good, and we would get half of the original coverage. Fortunately, flatfielding was installed before compression which caused some low-contrast scenes returned at CR 16 to look as well as scenes obtained at CR 3 without the flatfielding. During the last years, we collected many image sequences on the roof of the building, on a fire tower in the forest, and on a helicopter. These tests raised our appetite for higher quality since CR of 8 give some unwanted artifacts. The worst artifacts are discontinuities at16x16 pixel block boundaries. They are always bad at CR 16, they can be disturbing at CR 8, and they may be noticeable at CR 4. An example is shown in figure 7.1.1-1. Figure 7.1.1-1a An original test image with low signal and high contrast. Figure 7.1.1-1b The scene in figure 1a with a compression ratio of 16. Recently, we created software which smoothes the images at those boundaries in such a way that the resulting image is still consistent with the compressed data, which means that the unsmoothed and the smoothed images would give exactly the same compressed data stream. With images run through our software, 16x16 block boundaries cannot be detected any more even at CR 16, not even by detectives who are trained to detect those boundaries. Details on the software which removes the artifacts are found in a separate document. Other artifacts are periodic features introduced by incomplete transmission of the CCD noise. We created software which targets specific coefficients in order to reduce those artifacts. Further reduction of these artifacts is possible by setting a parameter in our software, but this would decrease the visibility of small, real features. For about the first half hour of the descent, the dark current is expected to be significant. This causes damage in low-contrast scenes which are expected during the beginning of the descent. We created software which lets the decompressor "know" about the dark current. This way, we can decrease this damage to insignificant levels. In studying image artifacts introduced by compression, it became clear that the resulting image becomes better and better the more the parameters of the software are tuned to the appropriate values. This can be done by testing the software with a few representative test images, which have similar noise, similar range of data numbers, similar contrast, and similar types of features as the compressed images. Currently, we do not have images representative of Titan's surface. However, these images could be taken during the descent by using low CR for 5-10 percent of the images. We expect that those images will tell what the compressor does at higher CR which then can be used to significantly improve the other images and to yield error estimates for measurements of features such as photometry or position measurements. Without a few very good representative images, the decompression software produces "mean" images but does not provide any information about the uncertainty of each data number. We think that a sufficient set of "perfect" representative images would be obtained by setting the CR for one or two out of the 24 azimuths to a value 1.5-2 times lower than for most of the other azimuths. This would only cost about 3-6 percent of the data rate. We propose to use two azimuths with low CR. Our image sequences during the past years were all taken with an essentially stationary camera where lower CR produce better images, of course. However, on Titan, the expected strong wind carries Huygens over the terrain so that lower CR give less coverage. Actually, we don't expect to lose many features by using low CR, but the imaged resolution is expected to decrease due to further distance, due to imaging in a camera of worse pixel scale (e.g. MRI instead of HRI), or due to less optimal positioning within the field of view (each imager produces sharper images near the center of the field of view than towards the corners). Furthermore, even if the coverage were perfect, higher CR would yields more images of the same feature which would increase the signal-to-noise (S/N) ratio. There is clearly a trade-off. At very low CR, the compressor produces little damage, but the resolution is so bad that even uncompressed images do not show much. At very high CR, the compressor produces only disappointing images. In order to find the best compromise, we designed a set of test images which show the degradation due to compression, resolution, and noise at the same time. For our test, we consider the area of the terrain which is visible to the HRI between the first and last panorama. The area outside the visibility of the HRI is imaged reasonably well, and the resulting resolution is not very dependent on the choice of the CR. The terrain imaged after the last panorama has such a poor coverage that we never considered lowering the CR below the original number of 8. 7.2. Resolution The imaged resolution of a feature depends on the distance between the feature and the camera, on the image scale (degrees/pixel) of the camera, and the width of the point spread function (pixels) at that location. For features close to the horizon, foreshortening decreases the resolution in the vertical direction. The best resolution is achieved when imaging is in the center of the HRI. The shortest distance is achieved when looking back about 75 degrees below horizontal since the descent angle is typically about 15 degrees down from horizontal. The resolution for all images of the same feature is expressed here relative to the best resolution, thus this number is 1.0 or larger. For the descent angle of 15 degrees, the resolution in the HRI can vary between 1.0 and 1.8 due to a factor of 1.3 in the variation of distance and a similar factor for the variation of the point-spread- function. The median value is about 1.3. The relative resolution in the MRI can vary between 2.2 and 11 due to variations of factors of about 2 in distance and in point-spread-function each. The median is about 4. The relative resolution in the SLI is 5 or more. According to simulated descent runs, the coverage is about CR times 10 percent for the HRI and about four times as much for the MRI. Thus, for CR = 8, for example, about 80 percent of the terrain is imaged by the HRI and about 320 percent by the MRI which means that for most surface features, one gets one HRI image and three MRI images (again, these numbers are valid for the terrain which is visible to the HRI between the first and last panorama). The HRI image will have a relative resolution between 1.0 and 1.8, the MRI images between 2.2 and 11. If we only consider the image of best resolution, then 80 percent of the features have a relative resolution between 1.0 and 1.8 and the remaining 20 percent above 2.2, but probably not much above 2.2 since we chose the best of the three MRI images. We now divide the terrain in eight parts: one eighth which happened to be imaged at the best relative resolution (1.0), one eighth which happened to be imaged close to the best resolution (1.1), and so on until the last eighth which happened to be imaged at a resolution of about 2.3. In our test image, each eighth is represented by a 32-pixel wide stripe, ordered from the best to the worst. In reality, the terrain will be irregularly divided up with regions well resolved bordering regions very poorly resolved. We estimated the distribution of relative resolutions for each eighth of the terrain for CR of 2, 3, 4, 6, 8, 12, and 16 (Table 7.4-1). Is obvious that for low CR, the relative resolution for part of the terrain is 4 or more and thus so bad that many features are lost. For CR of 8, the relative resolution becomes good for most of the terrain. For higher CR, the relative resolution does not improve much further. 7.3. Noise A specific scene can give high or low data numbers (DN) depending on the exposure time. The scene can also give high or low contrast depending on the amount of haze between Huygens and the ground, since haze absorbs some of the signal and adds an additional signal which we will assume to be featureless for the test. While the DN for a dark high-contrast scene and a bright low-contrast scene are very different, it turns out that the 8-bit numbers the compressor sees may be almost identical because the adaptive square-root scheme. What matters is the size of the noise relative to the full range of data numbers, or the numbers of noise steps between the minimum and maximum DN. For example, an image with DN between 20 and 40 has 20 noise steps since the noise is about 1 DN, while an image with DN between 2900 and 3100 has also 20 noise steps since the noise is about 10 DN. The number of noise steps is critical to the amount of damage the compressor does. As a rough guide, the mean error due to compression is almost negligible as long as it is smaller than the noise, but the error due to compression is roughly proportional to CR once it is larger than the noise. Thus, an image with twice the noise can roughly be compressed twice as much before the damage due to compression becomes noticeable. Note, however, that twice the CR allows transmission of two images which cuts the noise by the square-root of 2. Thus, twice the noise causes only a loss of a factor of square-root of 2 if the CR is adjusted. The optimal CR for each image is in the transition region where the error by compression is similar to the noise. The exact optimum depends slightly on other factors such as relative resolution, but it never makes sense to have a much lower CR where one uses most of the data stream to transmit noise, nor does is make sense to have a much higher CR where one loses many features. In principle, a compressor could use the optimal CR if it knew the size of the noise. However, the design of the data transmission called for a predetermined CR. Thus, we have to estimate how many noise steps we expect in the images in order to design the CR for near optimal performance. The basis of our estimation is a model of Titan's atmosphere with aggregate particles which predicts the amount of light from the atmosphere in the appropriate passband for several altitudes and several directions. These numbers were fit to simple functions of altitude for evaluation at each altitude. The predicted intensities are tabulated as I/F values with the flux taken from the surface (Table 7.3-1). Table 7.3-1 Estimation of brightness, data numbers, and signal-to-noise ratios for a bright surface (top), average surface (middle), and dark surface (bottom) for various altitudes. 1) Surface geometric albedo = 0.5 # Alt Exp I/F (-90) I/F (-45) I/F(5 DN (-90) DN (- DN(5) S/ N 0.4* S/N . ) 45) km ms surf haze surf haze haze surf haze sur haze haze -90 -45 -90 -45 f A 146 7 0.035 +1.168 0.019 +1.606 2.998 39 1308 11 +899 1679 6 2 2 1 B 139 7 0.037 +1.112 0.021 +1.529 2.990 41 1245 12 +856 1674 6 2 2 1 C 94 11 0.059 +0.752 0.040 +1.034 2.624 104 1324 35 +910 2309 15 6 6 2 D 66 10 0.078 +5.28 0.060 +0.726 2.154 125 845 48 +581 1723 22 10 9 4 E 42 23 0.108 +3.36 0.083 +0.462 1.600 397 1236 153 +850 2944 54 26 22 10 F 33 31 0.110 +2.64 0.095 +0.363 1.260 546 1309 236 +900 3125 69 38 28 15 G 27 38 0.115 +2.16 0.103 +0.297 1.184 699 1313 313 +903 3599 85 49 34 20 H 21 44 0.122 +1.88 0.112 +0.231 1.004 859 1324 394 +813 3534 101 62 40 24 I 15 52 0.129 +1.20 0.122 +0.165 0.812 1073 998 508 +686 3378 129 81 52 32 J 12 55 0.133 +0.96 0.127 +0.132 0.714 1170 845 559 +581 3142 143 91 57 36 K 9 61 0.137 +0.72 0.132 +0.099 0.614 1337 703 644 +483 2996 162 105 65 42 L 6 64 0.141 +0.48 0.138 +0.066 0.512 1444 492 707 +338 2621 180 120 72 48 M 3 68 0.146 +0.24 0.144 +0.033 0.408 1588 261 783 +180 2220 202 138 81 55 N 1 70 0.149 +0.08 0.148 +0.011 0.336 1669 90 829 +62 1882 218 152 87 61 2) Surface geometric albedo = 0.2 # Alt Exp I/F (-90) I/F (-45) I/F(5 DN (-90) DN (- DN(5) S/ N 0.4* S/N . ) 45) km ms surf haze surf haze haze surf haze sur haze haze -90 -45 -90 -45 f A 146 7 .012 +1.168 .006 +1.606 2.998 13 +1308 3 +899 1679 2 1 1 0 B 139 7 .012 +1.112 .007 +1.529 2.990 13 +1245 4 +856 1674 2 1 1 0 C 94 11 .020 +.752 .013 +1.034 2.624 35 +1324 11 +910 2309 5 2 2 1 D 66 10 .026 +.528 .020 +.726 2.154 42 +845 16 +581 1723 8 4 3 2 E 42 23 .036 +.336 .028 +.462 1.600 132 +1236 52 +850 2944 20 9 8 4 F 33 31 .037 +.264 .032 +.363 1.260 184 +1309 79 +900 3125 26 14 11 6 G 27 38 .038 +.216 .034 +.297 1.184 231 +1313 103 +903 3599 32 18 13 7 H 21 44 .041 +.188 .037 +.231 1.004 289 +1324 130 +813 3534 39 23 16 9 I 15 52 .043 +.120 .041 +.165 .812 358 +998 171 +686 3378 53 32 21 13 J 12 55 .044 +.096 .042 +.132 .714 387 +845 185 +581 3142 60 37 24 15 K 9 61 .046 +.072 .044 +.099 .614 449 +703 215 +483 2996 72 45 29 18 L 6 64 .047 +.048 .046 +.066 .512 481 +492 236 +338 2621 84 54 34 22 M 3 68 .049 +.024 .048 +.033 .408 533 +261 261 +180 2220 104 68 42 27 N 1 70 .050 +.008 .049 +.011 .336 560 +90 274 +62 1882 120 82 48 33 3) Surface geometric albedo = 0.05 # Alt Exp I/F (-90) I/F (-45) I/F(5 DN (-90) DN (- DN(5) S/ N 0.4* S/N . ) 45) km ms surf haze surf haze haze surf haze sur haze haze -90 -45 -90 -45 f A 146 7 .0014 +1.168 .0008 +1.606 2.998 2 +1308 0 +899 1679 0 0 0 0 B 139 7 .0015 +1.112 .0009 +1.529 2.990 2 +1245 0 +856 1674 0 0 0 0 C 94 11 .0023 +.752 .0016 +1.034 2.624 4 +1324 1 +910 2309 1 0 0 0 D 66 10 .0031 +.528 .0024 +.726 2.154 5 +845 2 +581 1723 1 0 0 0 E 42 23 .0039 +.336 .0033 +.462 1.600 14 +1236 6 +850 2944 2 1 1 0 F 33 31 .0043 +.264 .0038 +.363 1.260 21 +1309 9 +900 3125 3 2 1 1 G 27 38 .0046 +.216 .0041 +.297 1.184 28 +1313 12 +903 3599 4 2 2 1 H 21 44 .0049 +.188 .0045 +.231 1.004 34 +1324 16 +813 3534 5 3 2 1 I 15 52 .0052 +.120 .0049 +.165 .812 43 +998 20 +686 3378 7 4 3 2 J 12 55 .0053 +.096 .0051 +.132 .714 47 +845 22 +581 3142 9 5 4 2 K 9 61 .0055 +.072 .0053 +.099 .614 54 +703 26 +483 2996 11 6 4 2 L 6 64 .0057 +.048 .0055 +.066 .512 58 +492 28 +338 2621 14 8 6 3 M 3 68 .0058 +.024 .0058 +.033 .408 63 +261 32 +180 2220 19 12 8 5 N 1 70 .0059 +.008 .0059 +.011 .336 66 +90 33 +62 1882 29 19 12 8 Column header explanations: #: Panorama number for CR = 4 Alt: Altitude (km) Exp: Exposure time for constant image smear (ms) I/F: Reflectivity between straight down (-90) and 5 degrees up (5) surf: Contribution from the surface haze: Contribution from the haze DN: Data number S/N: Signal from the surface divided by the CCD noise 0.4*S/N: Number of noise steps for +/- 20 percent contrast The model also predicts the extinction between the surface and Huygens. The light from the surface is estimated by phase functions of asteroids with three cases, one of the brightest asteroids, (44) Nysa, with a geometric albedo of 0.5 and a relatively flat phase function, asteroids with a geometric albedo of 0.2 (which is close to Titan's geometric albedo) and a slightly steeper phase function, and a dark asteroid (53) with a geometric albedo of 0.05 and a steep phase function. Since the current landing site is expected to be in the dark terrain, one can expect an albedo somewhere between the average and dark case, but the bright case is still possible on small scales. The bright case is typical of relatively clean, icy surfaces, while some satellites are still brighter. The dark case matches Hyperion's dark side, Titan's outer neighbor. There are a few satellites and a fair fraction of asteroids with geometric albedos less than 0.05. We assumed that half of the light is direct sunlight and half of the light is diffuse skylight, although resulting numbers are very insensitive to this assumption. For an object at Titan's surface with an I/F = 1, we assume a sensitivity of 160 DN/ms for the HRI and 80 DN/ms for the MRI and SLI because of their filters with 50 percent transmission. We then calculated the expected DN for various altitudes for the three kinds of surfaces and for three directions: straight down (representative for all HRI images), 45 degrees down with am azimuth 90 degrees away from the azimuth of the sun (representative of most of the MRI and SLI images, although in some directions, DN can easily get twice as high and half as high), and 5 degrees up with an azimuth 90 degrees away from the azimuth of the sun (representative for the sky in the SLI). We then calculated S/N values where the signal is the contribution of DN from the surface and the noise is the CCD noise. The S/N data show that there is a very large increase from the highest to the lowest altitudes, but the actual values are difficult to predict since they depend a lot on the surface albedo which we do not know (Table 7.3-1). We assume that the albedo varies between the assumed value minus 20 percent and the assumed value plus 20 percent in every image. The true contrasts can easily be twice as high, but much higher contrasts are rare with the sun high in the sky and with part of the illumination from diffuse skylight. The contrast can be easily half as much as the ń 20 percent, but much lower contrasts would mean that we are exceptionally unlucky. I/F variations due to topography with moderate slopes are on the order of 10 percent. The last columns of Table 7.3-1 show the number of noise steps for each considered case. For altitudes above 20 km, the number of noise steps will probably stay below 20 (HRI) and 10 (MRI) with more typical numbers on the order of 4 (HRI) and 2 (MRI). Below 20 km altitude, the typical number of noise steps will be about 20 (HRI) and 10 (MRI), but there is a good chance that it can get as high as about 100 (HRI) and 50 (MRI). Table 7.3-1 shows that the noise for the MRI is typically twice as high as for the HRI. Thus, for a test images, we use twice the noise for the terrain which is not imaged by the HRI. The right side of Table 7.4-1 lists the scaled noise, usually 1.0 for the HRI and 2.0 for the MRI. For high CR, one gets several images at similar scales which can be used to decrease the noise. The lower adopted values on the right side of Table 7.3-1 account for this fact. For the test, we use three images. The first image is based on a Ganymede scene imaged by Galileo with 100 noise steps (HRI) and 50 noise steps (MRI). Such a case is possible at the lowest altitudes with the brightest surface. The second image is the same as the first one but with five times the noise which is typical for intermediate altitudes (0 km for the dark case, 15 km for the average case, and 40 km for the bright case). The last image is a different scene with only 4 and 2 noise steps (HRI and MRI, respectively). This is typical for higher altitudes (10 km for the dark case to 100 km for the bright case). This artificial scene, looking like a set of many lakes, was chose since it has most DN near the maximum or near the minimum DN and thus the best chance to be recognized under very noisy conditions. The three test images are listed in Table 7.3-2. This table also lists some previous test images. Note that most of the test images including most of the images from the building roof, fire tower, and helicopter have many more noise steps than what we can expect. Table 7.3-2 Noise steps for test images Image HRI MRI Object Low Noise Image 100 50 Ganymede Medium Noise Image 20 10 Ganymede High Noise Image 4 2 Lakes Previous tests: 620 Jupiter 420 Forest 250-300 Ganymede 140 Dark test 45 Dark test + noise The HRI and MRI have a significant overlap. If features are imaged at the HRI and MRI simultaneously, the HRI collects eight times as much signal than the MRI because its aperture area is four times as much as that of the MRI and because of the filter with 50 percent transmission in front of the MRI. Thus, very large features are imaged with one HRI image as well as eight repetitions with the MRI. For smaller features, the ratio is much higher since the MRI smoothes out features much more due to its point-spread-function which is about three times as wide as that of the HRI in the overlapping region. This consideration shows the most important aspect of the choice of CR, the loss from an HRI image to an MRI image of the same terrain. 7.4. Evaluation We have not found a parameter which describes how much an image has been degraded due to worse image scale, due to CCD noise, and due to compression. Thus, the evaluation has to be done by comparing images. However, we have a parameter which gives a rough guide about the damage. We take the root mean square of the DN between the original image at the best scale (1.0) without noise and the final image. We use averages of 2x2 pixels for this comparison since this is about the size of the point-spread-function. For each 2x2 pixel square, we calculate the difference between the DN in the original image at resolution 1.0 and the DN in the actual image (which may have worse resolution, which has added CCD noise and compression artifacts). We then calculate the root-mean-square of these differences across each eighth of the image. We scale this value to the value expected for the CCD noise of a single HRI image. The bottom part of Table 7.4-1 lists this number for each section of each of the three images and each CR. Table 7.4-1 Relative distribution of resolution, noise, and total damage parameter for each of the eight panels of terrain, ordered from best to worst resolution, and the total damage Relative resolution distribution Noise CR 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 2 1.3 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 3 1.2 1.5 2.2 2.8 3.4 4.0 4.8 5.6 1.0 1.0 2.0 2.0 2.0 2.0 2.0 2.0 4 1.1 1.3 1.6 2.0 2.5 3.0 3.5 4.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 2.0 6 1.1 1.2 1.3 1.5 1.8 2.2 2.6 3.0 1.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 8 1.0 1.1 1.2 1.3 1.4 1.6 2.0 2.3 1.0 1.0 1.0 1.0 1.0 1.0 1.6 1.6 12 1.0 1.1 1.1 1.2 1.3 1.4 1.5 1.6 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 16 1.0 1.0 1.1 1.1 1.2 1.2 1.3 1.3 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 Total damage for low noise image CR 1 2 3 4 5 6 7 8 Average Weighted scheme Average 2 4.6 8.6 12 15 18 23 21 14 14.5 11.4 3 4.5 5.5 10 13 15 21 19 14 12.7 9.7 3,6 4.1 4.0 6.7 10 13 20 17 12 10.8 7.9 2-6 4.1 4.0 6.7 10 13 20 17 12 10.8 7.9 4 4.1 3.9 6.8 10 13 20 17 12 10.8 7.9 6 4.5 3.7 4.9 7.0 9.9 16 15 12 9.0 6.9 8 3.2 4.1 5.2 6.5 7.4 11 13 11 7.7 6.1 12 4.9 5.9 6.1 7.3 8.0 10 11 9.3 7.8 7.3 16 6.5 6.2 7.8 7.7 9.0 9.3 10 8.9 8.2 8.0 Total damage for medium noise image CR 1 2 3 4 5 6 7 8 Average Weighted scheme Average 2 1.4 2.8 3.4 3.8 4.5 5.4 4.8 3.9 3.7 3.2 3 1.5 1.8 3.2 3.6 4.1 5.0 4.7 4.0 3.5 3.0 3,6 1.5 1.5 2.0 3.5 3.8 5.0 4.7 3.8 3.2 2.6 2-6 1.5 1.5 2.0 3.5 3.8 4.9 4.7 3.8 3.2 2.6 4 1.4 1.4 2.0 3.1 3.5 4.8 4.4 3.5 3.0 2.5 6 1.4 1.4 1.6 2.1 2.6 4.0 3.5 3.3 2.5 2.1 8 1.1 1.3 1.5 1.7 1.9 2.6 3.1 2.6 2.0 1.8 12 1.1 1.4 1.4 1.7 1.8 2.3 2.3 2.0 1.7 1.6 16 1.3 1.3 1.6 1.6 1.8 1.9 2.0 1.8 1.7 1.6 Total damage for high noise image CR 1 2 3 4 5 6 7 8 Average Weighted scheme Average 2 1.0 2.3 2.5 2.9 3.2 3.0 3.0 3.0 2.6 2.3 3 0.9 1.0 2.2 2.7 2.8 2.6 3.1 3.3 2.3 1.9 3,6 1.0 1.0 1.1 2.7 3.0 3.2 3.1 3.2 2.3 1.7 2-6 1.0 1.0 1.0 2.8 2.9 3.1 3.0 3.0 2.2 1.7 4 0.9 0.9 0.9 2.3 2.5 2.5 2.5 2.5 1.9 1.5 6 0.9 1.0 1.0 1.1 1.3 2.4 2.3 2.6 1.6 1.3 8 0.8 0.8 0.9 1.1 1.1 1.1 1.7 1.7 1.2 1.1 12 0.8 0.8 0.7 0.9 0.9 1.0 1.0 1.0 0.9 0.9 16 0.7 0.7 0.7 0.8 0.9 0.9 0.9 0.9 0.8 0.8 This parameter may be a rough guide, but we have found cases where the subjective judgment does not agree with the results based on this parameter. The last two rows give the average of the preceding eight values and a weighted average, the inverse of the average of the inverse values. The latter average is strongly weighted towards values with little damage which is probably appropriate since good images will be more looked at than bad ones. After looking at the test images, it is clear that some types of features or regions improve with higher CR, other degrade. Thus, depending on each person's subjective preference, the votes for optimal CR will definitely scatter. Nevertheless, there are certain cases which look so bad that most people will agree that those cases need to be avoided. The images with CR of 2 and 3, and probably even 4, have very poor resolution for some of the terrain. This can be significantly improved with higher CR without losing much. For the low noise image, CR of 12 and 16 loses too many small features. Thus, for low altitudes, the CR probably should be around 6 or 8. By setting a higher priority for quality than for quantity, the preferred choice is 6. For higher altitudes, higher CR give the better images overall, but the gain is small, so that it is not clear how much one should push for higher CR. Taking the total-damage parameter one step further, one can define the image quality as the number of noise steps divided by the weighted average damage. Table 7.4-2 lists those values for the case of average surface albedo (0.2). Again, it is clear that one gains a lot by increasing the CR from 2 to 8, but there is no significant gain for CR larger than 8. Table 7.4-2 Expected quality as function of altitude and compression ratio for average surface brightness (geometric albedo 0.2) # Alt Noise (Noise steps)/ for Weighted Average Damage steps CR = km -90 2 3 3,6 2-6 4 6 8 12 16 A 146 1 1 1 1 1 1 1 1 1 1 B 139 1 1 1 1 1 1 1 1 1 1 C 94 2 1 1 2 2 2 2 2 2 2 D 66 3 1 2 2 2 2 3 3 3 3 E 42 8 3 3 4 4 4 5 6 7 7 F 33 11 4 5 5 5 6 6 7 8 8 G 27 13 4 5 6 6 6 7 8 9 9 H 21 16 5 6 6 6 7 8 10 12 12 I 15 21 6 7 8 8 8 10 12 13 13 J 12 24 6 7 8 8 9 11 13 13 13 K 9 29 7 8 9 9 9 11 13 14 13 L 6 34 8 9 10 10 10 12 14 14 13 M 3 42 8 9 10 10 10 12 14 14 13 N 1 48 9 10 11 11 11 13 15 14 13 7.5. Variation of CR We also tested two alternatives for CR of 4 which produce the same number of images (the same time-averaged CR): the first alternative is half the azimuths at CR of 3 and half at CR of 6. With respect to the CR = 4 case, one seems to lose more between CR of 4 and 6 than one gains between CR of 4 and 3. However, a variation of CR has some benefit. For example, some complicated feature many never be clear at one specific CR but at a somewhat smaller CR. Thus, by varying the CR, one gets the feature at least half the time. Currently, we feel that some smaller variation, say half of the images at about 1.5 times the CR than the other half, has still advantages, but a variation by a factor of two loses too much for the higher CR. The other tested alternative for an average CR of 4 is 1/7 at CR of 2, 3/7 at CR of 4, and 3/7 at CR of 6. With respect to the all CR of 4 case, only a small region is improved but a large region degraded. Thus, such a distribution is probably not recommended unless the small region with low CR is important. As stated near the beginning, we prefer to have a few percent of the images at a low CR, but these are so few images that they hardly affect the coverage of the remaining ones. We do not show the images with mixed CR, since variation of the CR is much less important than selection of the average CR. During the descent, the best and probably second-best image of the area only visible to the MRI and SLI are taken at azimuths more than 90 degrees away from the direction of motion. This is simply due to the angle of descent where the closest approach to any feature occurs by looking back. Furthermore, the forward-looking azimuths see the surface at higher phase angles which makes the I/F lower. Together with the larger distance, the best views will almost certainly occur looking back. Thus, if one chooses to vary the CR somewhat, the backward azimuths should probably get the lower CR. 7.6. Additional Considerations This test is designed for interpretations which require just one good image of any region. However, some studies, such as stereo imaging or studies of phase functions, require more than one image. In that case, a slightly higher CR may be preferable so that the second best image of a region is at least at somewhat similar resolution. This test does not consider a variation of haze within each test case. However, especially at higher altitudes, the regions imaged from larger distances will not only have worse resolution but also lower contrast due to the additional haze. Thus, the real loss at the poorly resolved regions is larger than in the test images. This may favor slightly larger CR at higher altitudes than the test suggests, but the change is expected to be minimal. 7.7. The Test There are three images, a Ganymede image of low noise (figure 7.7-1), a Ganymede image of moderate noise (figure 7.7-2), and an image of lakes of high noise (figure 7.7-3). Each image comes in seven different compression ratios (CR) of 2, 3, 4, 6, 8, 12, and 16, in addition to the uncompressed image. While we cannot control the scene we get, we can choose the CR. Thus, the question is: which is the best choice of CR? This may difficult to judge since some parts of the terrain improve with higher CR, others improve with lower CR. Nevertheless, we need to choose. Which one is the best compromise for each of the three images? Or better, which range of CR is acceptable for each of the three images? Figure 7.7-1a Original Ganymede image smoothed with no noise Figure 7.7-1b Low noise with CR 2 Figure 7.7-1c Low noise with CR 3 Figure 7.7-1d Low noise with CR 4 Figure 7.7-1e Low noise with CR 6 Figure 7.7-1f Low noise with CR 8 Figure 7.7-1g Low noise with CR 12 Figure 7.7-1h Low noise with CR 16 Figure 7.7-2a Moderate noise with CR 2 Figure 7.7-2b Moderate noise with CR 3 Figure 7.7-2c Moderate noise with CR 4 Figure 7.7-2d Moderate noise with CR 6 Figure 7.7-2e Moderate noise with CR 8 Figure 7.7-2f Moderate noise with CR 12 Figure 7.7-2g Moderate noise with CR 16 Figure 7.7-3a Original "lakes" image smoothed with no noise Figure 7.7-3b High noise with CR 2 Figure 7.7-3c High noise with CR 3 Figure 7.7-3d High noise with CR 4 Figure 7.7-3e High noise with CR 6 Figure 7.7-3f High noise with CR 8 Figure 7.7-3g High noise with CR 12 Figure 7.7-3h High noise with CR 16 Add images lakwg2-16 Also include original (uncompressed) image of all 3 and include it in the blinking sequence. Add captions to all 3 blinking sets. Table 7.7-1 File names, all in pirl:/pirl1/erich/mrim/: Original 2x 3x 3x & 6x 2,4,6x* 4x 6x 8x 12x 16x #1: ganzh ganvg2 ganvg3 ganvg36 ganvg26 ganvg4 ganvg6 ganvg8 ganvg12 ganvg16 #2: ganzh ganwg2 ganwg3 ganwg36 ganwg26 ganwg4 ganwg6 ganwg8 ganwg12 ganwg16 #3: lakeh lakwg2 lakwg3 lakwg36 lakwg26 lakwg4 lakwg6 lakwg8 lakwg12 lakwg16 * 1/7 at 2x (top), 3/7 and 4x (middle), and 3/7 at 6x (bottom) 8.0. Area Coverage and Image Statistics for a Simulated Descent The simulated descent of 17 Sept. 1996 was performed with the flight-model, DISR#3, in the calibration laboratory a few days before ship. The sensor head and flight electronics were mounted so as to receive a simulated image of the Sun at Titan moving past the field of view. The speed of the moving solar image was adjusted so as to mimic the nominal predicted rate of the rotation of the Huygens descent module within Titan's atmosphere. Hence, a realistic lock was achieved by the Sun Sensor, which performed flawlessly under these simulated conditions, and provided a baseline for the scheduling of all DISR measurements. A full suite of DISR measurements was acquired. Some 13 image panoramas were recorded under these simulated conditions and they were fully flight-processed using the current hardware compression scheme (compression ratios alternating between 3 and 6) and tagged with the simulated altitudes of the nominal time-altitude table. Table 1 shows their locations in time, vertical and horizontal space. Figures 8.0-1 through 8.0-9 show the same information in graphical form. After modifying the image compression scheme as described above (alternating between compression ratios of 6 and 8 with a single image at a compression ratio of 4 acquired per panorama), the arrangement of panoramas listed in Table 8.0-2 and displayed in Figures 8.0-10 through 8.0-20 resulted. Only the HRI image footprints are shown. Table 8.0-1 List of Panoramas acquired during simulated descent of 17 Sept. 1996, along with times, altitudes (km) and estimated sub-probe longitudes on Titan assuming an entry point of 162o E longitude and a nominal Flasar et al wind model. Panorama Time (min) Altitude Sub-P Lng A 1.7-3.7 143-150 162.2-162.5 B 3.8-6.0 135-142 162.6-162.9 C 18.3-20.4 90-98 164.6-164.8 D 27.9-29.9 64-68 165.7-165.9 E 46.9-49.2 41-43 167.6-167.8 F 58.2-60.4 32-34 168.5-168.7 G 68.0-70.5 26-27 169.2-169.3 H 78.3-80.8 21-22 169.8-169.9 I 91.7-94.1 14.5-16 170.4-170.6 J 98.5-100.7 11.8-12.7 170.7-170.8 K 107.1-109.2 8.4-9.4 171.1 L 114.3-117.0 5.8-6.8 171.2-171.3 M 123.4-125.8 2.8-3.6 171.4 Figure 8.0-3 Histogram of image compression ratios for original compression scheme. Figure 8.0-4 Distribution of image acquisition times for original compression scheme. Figure 8.0-5 Distribution of image acquisition altitudes for original compression scheme. Figure 8.0-6 Distribution of image sub-probe longitudes for original compression scheme. Figure 8.0-7 HRI footprint outlines for all HRI images for original compression scheme. Figure 8.0-8 HRI footprint outlines for all HRI images (magnified view) for original compression scheme. Figure 8.0-9 HRI footprint outlines for mid to low altitude panoramas for original compression scheme. Figure 8.0-10 HRI footprint outlines for low panoramas for original compression scheme. Figure 8.0-11 HRI footprint outlines for lowest panoramas and non-panoramic images for original compression scheme. Table 8.0-2 List of Panoramas acquired during simulated descent of 17 Sept. 1996, along with times, altitudes (km) and estimated sub-probe longitudes on Titan assuming an entry point of 162o E longitude and a nominal Flasar et al wind model for the modified compression scheme. Panorama Time (min) Altitude Sub-P Lng A 2.52-4.64 146.7-139.6 162.4-162.7 B 4.92-6.95 138.8-132.6 162.7-163.0 C 8.5-10.5 128.3-123.1 163.2-163.5 D 16.8-18.8 105.5-96.3 164.3-164.6 E 23.4-25.4 80.2-74.6 165.2-165.4 F 29.9-31.9 64.2-60.7 165.9-166.1 G 36.7-38.8 53.8-51.2 166.6-166.8 H 46.7-48.8 42.8-41.0 167.6-167.7 I 53.4-55.7 37.2-35.4 168.1-168.3 J 58.8-61.0 33.2-31.8 168.5-168.7 K 65.5-68.0 28.8-27.4 169.0-169.2 L 71.1-73.3 25.6-24.4 169.4-169.5 M 78.5-80.6 21.7-20.6 169.8-169.9 N 87.9-90.3 17.2-16.2 170.3-170.4 O 92.9-95.5 15.1-14.0 170.5-170.6 P 97.8-100.0 13.0-12.2 170.7-170.8 Q 102.6-104.8 11.1-10.3 170.9-171.0 R 109.7-112.2 8.4-7.6 171.1-171.2 S 114.6-117.2 6.7-5.8 171.2-171.3 T 121.8-124.4 4.2-3.3 171.4 Figure 8.0-12 Distribution of image acquisition times for new compression scheme. Figure 8.0-13 Distribution of image compression ratio (with raw image data sets included) for new compression scheme. Figure 8.0-14 Distribution of image acquisition times for new compression scheme. Figure 8.0-15 Distribution of image acquisition altitudes for new compression scheme. Figure 8.0-16 Distribution of image sub-probe longitudes for new compression scheme. Figure 8.0-17 HRI footprint outlines for all HRI images for new compression scheme. Figure 8.0-18 HRI footprint outlines for all HRI images (magnified view) for new compression scheme. Figure 8.0-19 HRI footprint outlines for mid to low altitude panoramas for new compression scheme. Figure 8.0-120 HRI footprint outlines for low panoramas for new compression scheme. Figure 8.0-21 HRI footprint outlines for lowest panoramas and non-panoramic images for new compression scheme. Figure 8.0-22 HRI footprint outlines for lowest panoramas and non-panoramic images (magnififed) for new compression scheme.