Calibration Report for the Solar Aureole Camera of the Descent Imager/Spectral Radiometer aboard the Huygens Probe of the Cassini Mission 27 April 2006 (Rev. 17 Jan. 2007) By M. G. Tomasko and L. E. Dafoe Table of Contents 1 Introduction 2 System Overview 3 The Titan Descent As It Occurred 4 Methodology for Analyzing Solar Aureole Data 4.1 Generation of Solar Aureole Data Numbers 4.2 Computing Solar Aureole Calibrated Intensities in Each Pixel 4.3 Combining Intensities in Each Pixel to Result in Total Absolute Calibrated Intensities and Degree of Polarization 5 Calibration Verification 6 Stability of SA Response with Time from Cruise Measurements 7 Some Operational Points of Note 8 Geometry and Field of View 9 Relative Spectral Response 9.1 The Form of Relative Spectral Response Model 9.2 The SA Interference Filter Transmissions 9.3 The SA RSR Thermal Coefficients, a, b, c, and d 9.4 The SA RSR Column Variation Coefficients, M0, M1, M2, and M3 10 Absolute Response 10.1 Mean Absolute Response 10.2 Thermal Variation in Pixel Maps 11 Polarization Sensitivity 12 Temperature Dependence of Dark Current 13 Appendices 13.1 Calibration Verification - Simulation Descent Reduction Paper 13.1.1 Introduction 13.1.2 Approach 13.1.3 Results - Absolute Calibration 13.1.4 Results - Relative Calibration across Columns 13.1.5 Results - Relative Calibration across Rows 13.1.6 Definition of SNR 13.1.7 Conclusion - Relative Calibration 13.1.8 Overall Conclusion 13.2 Several Operational Points of Note 13.2.1 Software 13.2.2 Timing 13.2.3 Electronic Shutter Effect 13.2.4 Lossless Compression 13.2.5 Auto Exposure Control 13.2.6 Noise Model 13.2.7 Linearity 13.2.8 Self Bleedthrough 13.3 Geometry and Field of View Derivations 13.3.1 Conversion between Row, Column and DISR Zenith, Azimuth 13.3.2 Conversion between DISR Zenith, Azimuth to True Zenith, Azimuth 13.4 Relative Spectral Response 13.4.1 Transmission of Filters as Functions of Temperature 13.4.2 Transmission of Filters as Functions of Angle of Incidence. 13.4.3 Relative Spectral Response of Solar Aureole System versus Temperature 13.5 Absolute Responsivity 13.5.1 Introduction 13.5.2 Approach for Absolute Response Computation at One Temperature 13.5.3 Thermal Modeling 13.5.4 Model Results 13.6 Polarization Sensitivity 13.6.1 Test Configuration 13.6.2 Polarization Calibration of the 500 nm SA Channels 13.6.3 Polarization Calibration of the 935 nm SA Channels Table of Figures Figure 2-1 The schematic layout of the components of the Solar Aureole system. The beamsplitter is used to introduce light from the inflight calibration system into the four channels of the Solar Aureole system. Figure 2-2 The field of view of the Solar Aureole camera is shown relative to the shadow bar of the sensor head. The center of the field of view is tipped by 6 degrees in the direction of increasing azimuth. The shadow bar shades the entire window of the Solar Aureole system when the Solar Aureole makes its measurement, since the measurement starts at an azimuth of about 2.5 degrees and extends to increasing azimuth. Figure 8-1 The centers of the pixels at the edge of the four solar arrays are shown in azimuth and zenith angle. Note that the arrays do not overlap exactly, and that care will have to be taken in interpolation in an array at one polarization state to obtain the intensity in the other polarization state at the same location. The azimuths shown are relative to the sun if the data were obtained when the instrument crossed the exact azimuth of the sun. In fact, Solar Aureole exposures begin when the instrument is 2.5 to 2.9 degrees past the azimuth of the sun and will continue for a maximum of 3.5 degrees of rotation. Figure 8-2 The effective field of view for the blue Solar Aureole channels if all columns are used. The horizontal and vertical channels do not overlap perfectly, so a smaller field is used to combine the intensities from both channels to result in total intensity and polarization. The + signs indicate locations where physical quantities are reported in the University of Arizona Lunar and Planetary Lab analysis for data sets that are delivered in full 24 by 50 pixel format. The diamonds indicate locations where physical quantities are reported for data sets that are summed on board before sending them to earth. Care must be taken to exclude pixels where the absolute responsivity is poorly known as mentioned in the section on the Titan descent. Figure 8-3 Same as previous figure, but for the red. Figure 10-1 Mean Absolute Response versus Temperature Figure 11-1 We show the position angle as a function of row number for the Blue Vertical and Horizontal channels in the SH03 flight Solar Aureole system. The retardance is taken as 90 degrees for the flight prism in the blue channel. Figure 11-2 The position angle (Psi, left scale, blue dots) and the degree of retardance (tau, right scale, red squares) as functions of row in the horizontal channel of the flight sensor head. Figure 11-3 Like Figure 11-2 but for the vertical channel of the flight SA in the red. Figure 13-1 Drawing of the fiber optic conduit showing that the face of the surface to which the Solar Aureole optical input optics are attached is tipped up by 40 degrees from horizontal, 50 degrees from vertical. Figure 13-2 Drawing along section V-V shown in Figure 5-1 that shows that the surface to which the input optics of the Solar Aureole system is fastened is tipped by 6 degrees in the direction of increasing azimuth. Figure 13-3 This figure shows the relationship of the x, y, z coordinate system of the sensor head to the x', y', z' system in which the y' axis is pointed at the zenith angle of the center of the array (50 degrees). Figure 13-4 This figure shows the relationship of the x", y", z" system after rotation by 6 degrees in the direction if increasing azimuth to the x', y', z' system. Figure 13-5 The relationship of the x"', y"', z"' system to the x", y", z" system is shown in this figure. The transformation consists of a small rotation about the y" axis as shown. Figure 13-6 The coordinates Da and Db form a latitude-longitude grid in the x"", y"', z"' system, where the pole of the system is the +z"' axis, the Da represents increasing southern latitude, and Db represents the direction of increasing longitude. Figure 13-7 The observed centroid in row and column is plotted by blue circles, while the model location of each point is plotted by red squares for each of the points observed in the four channels of the Solar Aureole system. Figure 13-8 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 0 to 5. The rms residual is about 0.07 in columns and 0.11 in row. Figure 13-9 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 6 to 11. The rms residual is about 0.12 in columns and 0.15 in row. Figure 13-10 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 12 to 17. The rms residual is about 0.08 in columns and 0.08 in row. Figure 13-11 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 18 to 23. The rms residual is about 0.09 in columns and 0.09 in row. Figure 13-12 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed column for the model to the Solar Aureole geometry for columns 18 to 23. The rms residual is about 0.08 in columns and 0.09 in row. Note that the points with centroids at observed columns within 0.5 column of the edge of the array have been omitted because of the systematic errors in locating the centroid of points where the peak of light is within 0.5 pixel of the edge of the array. 109 Figure 13-13 The transmission of the red Solar Aureole filter as a function of wavelength as measured by Bernard Schmitt at three different temperatures. The three measurements show rather little dependence on temperature. 114 Figure 13-14 The difference in the measured transmission of the red filter from the average of the measurements at three temperatures from the data of Table 13-7. Note that the difference of a measurement at any of the three temperatures from the average is less than 1% at all wavelengths, and usually less than a few tenths of a percent. Figure 13-15 Measured transmission of blue Solar Aureole filter at four temperatures, as labeled. Figure 13-16 The difference in the transmission measurements at each of the four temperatures from the average of the measurements at all four temperatures is shown as a function of wavelength. Note that the differences do not vary monotonically with temperature, and that the differences are within about 2% of the mean value at all wavelengths. We conclude that the transmission of the blue filter has little real variation in transmission with temperature even over the large range from 70 K to 300 K. Figure 13-17 Test setup schematic for measuring the filter transmission as a function of angle of incidence. Figure 13-18 A view of the laboratory setup used to measure the transmission of the Solar Aureole filters as a function of the angle of incidence of the collimated beam. The monochrometer and the collimating reflex telescope are visible at the left in the image. The filter holder mounted on a calibrated angle stage is visible at center. The standard silicon detector is visible at the right. Figure 13-19 Like Figure 13-18 but showing the baffle between the filter holder and the standard silicon detector. Figure 13-20 Measurements of the transmission of the blue Solar Aureole filter from the flight lot for different angles of incidence of collimated light, as labeled. Note the shift in the transmission of the filter with different incidence angles. Figure 13-21 Like Figure 13-20 but for the red Solar Aureole filter. Note the shift in the transmission of the filter with different incidence angles. 124 Figure 13-22 Side Looking Imager Spectral Response Figure 13-23 Red Horizontal NFM Curves Figure 13-24 Red Vertical NFM Curves Figure 13-25 Derived Blue Horizontal Filter Curves Figure 13-26 Derived Blue Horizontal Filter Curves, Log Scale Figure 13-27 Derived Blue Vertical Filter Curves Figure 13-28 Derived Blue Vertical Filter Curves, Log Scale Figure 13-29 Derived Red Horizontal Filter Curves Figure 13-30 Derived Red Horizontal Filter Curves, Log Scale Figure 13-31 Derived Red Vertical Filter Curves Figure 13-32 Derived Red Vertical Filter Curves, Log Scale Figure 13-33 Derived Red Horizontal Column 0 Filter Curves Figure 13-34 Derived Red Horizontal Column 0 Filter Curves, Log Scale Figure 13-35 Derived Red Horizontal Column 1 Filter Curves Figure 13-36 Derived Red Horizontal Column 1 Filter Curves, Log Scale Figure 13-37 Derived Red Vertical Column 0 Filter Curves Figure 13-38 Derived Red Vertical Column 0 Filter Curves, Log Scale Figure 13-39 Blue Horizontal Non-Filter Model Thermal Performance for Reference Column Figure 13-40 Blue Vertical Non-Filter Model Thermal Performance for Reference Column Figure 13-41 Red Horizontal Non-Filter Model Thermal Performance for Reference Column Figure 13-42 Red Vertical Non-Filter Model Thermal Performance for Reference Column Figure 13-43 Red Horizontal Non-Filter Model Thermal Performance for Column 0 Figure 13-44 Red Horizontal Non-Filter Model Thermal Performance for Column 1 Figure 13-45 Blue Horizontal Non-Filter Model Column Performance Figure 13-46 Blue Vertical Non-Filter Model Column Performance Figure 13-47 Red Horizontal Non-Filter Model Column Performance Figure 13-48 Red Vertical Non-Filter Model Column Performance Figure 13-49 Blue Horizontal Relative Spectral Response Modeling Results - Set of Nineteen Plots Figure 13-50 Blue Vertical Relative Spectral Response Modeling Results - Set of Nineteen Plots Figure 13-51 Red Horizontal Relative Spectral Response Modeling Results - Set of Nineteen Plots Figure 13-52 Red Vertical Relative Spectral Response Modeling Results - Set of Nineteen Plots Figure 13-53 Number of Relative Spectral Response Fliers versus Temperature 212 Figure 13-54 Frequency of Blue Horizontal Pixels Having RSR with RMS Deviation over 1% Figure 13-55 Frequency of Blue Vertical Pixels Having RSR with RMS Deviation over 1% Figure 13-56 Frequency of Red Horizontal Pixels Having RSR with RMS Deviation over 1% Figure 13-57 Frequency of Red Vertical Pixels Having RSR with RMS Deviation over 1% Figure 13-58 Sequence Numbers of Data Sets Used in Absolute Responsivity Derivation Figure 13-59 Mean Absolute Response versus Temperature Figure 13-60 The setup used to measure the polarization of the SH03 Flight Instrument. Figure 13-61 The intensity measured in the Blue Horizontal Channel as a function of the orientation of the polarization of the incident light as measured by the angle of the Glan-Thompson prism. The points are the observations at the columns 1 or 2 and at rows 4, 13, 24, and 43. The curves are cosine squared models that do not fit the observations well. Figure 13-62 Same as Figure 13-61 but for the Blue Vertical channel. Figure 13-63 Diagram of test setup for measuring the properties of a spare prism of the type used in the flight model of the DISR Solar Aureole system. Polarizer 1 was set to introduce linearly polarized at an angle of 0, 45, or 90 degrees from the horizontal direction. The intensity is measured by the photodiode detector after the light is passed through polarizer 2. The orientation of polarizer 2 is varied in 10 degree steps from the horizontal increasing in the CCW direction looking toward the source. Data were collected with the prism oriented perpendicular to the incident beam or at an angle of + or - 30 degrees from the direction. At a reading of 29.5 degrees on polarizer 2 the plane of polarization is oriented parallel to the Y axis (vertical). Figure 13-64 The intensity as a function of position angle when the spare Solar Aureole prism was illuminated by horizontally polarized light. The Glan- Thompson analyzer is positioned after the light passes through the flight prism. Note that a reading of 29.5 degrees corresponds to vertically polarized light. The points are observations, and the curves are models for a retardance, tau, and position angle, psi, of the incident light from the principal axis of the retarder that arises from the partially silvered beam splitter in the prism. Note that the fits are quite good. Figure 13-65 Same as Figure 13-62 but for light initially polarized at an angle of 45 degrees from the vertical. Note that when this purely polarized light is incident perpendicular to the prism (black curve) the output intensity is only modulated by some 10% after passing through the Glan- Thompson prism. This is an indication that the input polarized light is converted to a significant component of circular polarization in passing through the flight prism. The retardance of the flight prism must be nearly 90 degrees in this case. Figure 13-66 Like Figure 13-65 but for vertically polarized light incident on the flight prism. While the light is highly modulated, the phase of the light is shifted, again indicating strong retardance in the flight prism. Figure 13-67 This figure shows the retardance of the flight prism necessary to fit the observations in the last three figures as a function of the angle of the incident light to the perpendicular to the prism. Note that the retardance is near 90 degrees, and the flight prism acts similar to a quarter-wave plate. Figure 13-68 This figure shows the angle of the polarized light from the principal axis of the retarder as a function of the angle of the beam from the perpendicular to the prism. In the flight configuration, light in each row of the detector will enter the prism at a different angle, spanning the range from about -25 to + 25 degrees. Figure 13-69 We show the modulation of intensity caused by a rotated analyzer at the location of DISR in the test setup used for polarization measurements for different orientations of the plane of polarization of the input light. Note that for some orientations of the incident polarization a significant intensity leaks through the analyzer at the output of the test setup, indicating that a significant conversion from linear to circular polarization is occurring in the test setup is some orientations. Figure 13-70 We show the angle of the polarized light relative to the principal axis of the retarder in the test setup for different orientations of the Glan-Thompson prism at the input to the test setup. The angle is near 0 or 90 degrees when the Glan-Thompson prism polarizes the light vertically or horizontally, but at intermediate angles, significant angles from the axis of the retarder are reached. Figure 13-71 The retardance introduced by the test setup is shown as a function of the angle of the Glan-Thompson prism. There is little sensitivity at angles near 0 or 90 degrees, but near 45 or 135 degrees the retardance is some 50 or 60 degrees. Figure 13-72 The measured variation in intensity of the Blue Horizontal channel as a function of the setting of the Glan-Thompson prism is shown for various columns and rows. The curves are functions including the retardance of the test setup as well as a variable retardance and position angle of the flight prism. Note that the fits are much better than in Figure 13-61. Figure 13-73 Same Figure 13-72 but for the Blue Vertical channel. Again note the improved quality of the fit compared to Figure 13-62. Figure 13-74 We show the position angle as a function of row number for the Blue Vertical and Horizontal channels in the SH03 flight Solar Aureole system. The retardance is taken as 90 degrees for the flight prism in the blue channel. Figure 13-75 Intensity as a function of analyzer angle when spare prism is illuminated with linearly polarized light at an angle of 45 degrees. Figure 13-76 Like Figure 13-75 but for incident light polarized at an angle of 0 degrees (parallel to long axis of prism.) Figure 13-77 Like Figure 13-76 but for light polarized at an angle of 90 degrees (perpendicular to long axis of prism). Figure 13-78 Position angle of polarization relative to principal axis of retarder as a function of angle of illumination relative to perpendicular to spare prism (left scale and open symbols.) Right scale shows the degree of retardance of the spare prism as a function of the angle of illumination to the perpendicular to the prism. Note that the retardance of the prism is some 30 degrees, much less than the prism as measured in blue light. Figure 13-79 Intensity as a function of angle from horizontal direction when the test setup used to measure the flight instrument in red light is illuminated by linearly polarized light oriented as shown in the caption (caption angle is from horizontal increasing CCW looking toward the source.) Note that the intensity does not go to zero near 45 and 135 degrees indicating some amount of circular polarization in the beam under these conditions. Figure 13-80 The angle of the polarized beam relative to the principal axis of the retarder in the test setup used to measure the flight SA instrument in red light. Figure 13-81 The retardance of the test setup used to measure the properties of the flight SA instrument as a function of the angle of polarization produced by the Glan-Thompson prism. The polarization angle is measured CCW from horizontal looking toward the source. Figure 13-82 The position angle (Psi, left scale, blue dots) and the degree of retardance (tau, right scale, red squares) as functions of row in the horizontal channel of the flight sensor head. Figure 13-83 Like Figure 13-82 but for the vertical channel of the flight SA in the red. Figure 13-84 The intensity measured by the flight SA in the red vertical channel as a function of the setting of the Glan-Thompson prism in the test setup when different rows were illuminated as indicated. Note that the curves are in good agreement with the measured points. Figure 13-85 Like Figure 13-84 but for the red horizontal channel of the flight SA instrument. The fits are quite good except for the extreme corner of the field of view (column 22, row 3). Since the instrument will be used near the peak of the curve (near 30 degree Glan-Thompson angle), the agreement of the curves with the measured points is considered acceptably good. Table of Tables (Note: Many of the tables are in separate files and not imbedded in this document) Table 2-1 Solar Aureole CCD Row and Column Designations Table 3-1 Solar Aureole CCD Row and Column Designations for Columns that Should Be Omitted From Analysis Table 8-1 Blue Horizontal Solar Aureole Azimuth and Zenith Angles for Every Pixel Table 8-2 Blue Vertical Solar Aureole Azimuth and Zenith Angles for Every Pixel Table 8-3 Red Horizontal Solar Aureole Azimuth and Zenith Angles for Every Pixel Table 8-4 Red Vertical Solar Aureole Azimuth and Zenith Angles for Every Pixel Table 9-1 Table of NFMini Quadratic Coefficients Table 9-2 Table of Blue Horizontal Filter Curves Table 9-3 Table of Blue Vertical Filter Curves Table 9-4 Table of Red Horizontal Filter Curves Table 9-5 Table of Red Vertical Filter Curves Table 9-6 Table of Red Horizontal Filter Curves, Column 0 Table 9-7 Table of Red Horizontal Filter Curves, Column 1 Table 9-8 Table of Red Vertical Filter Curves, Column 0 Table 9-9 Thermal Coefficients for All SA Channels Table 9-10 Blue Horizontal Column Coefficients Table 9-11 Blue Vertical Column Coefficients Table 9-12 Red Horizontal Column Coefficients Table 9-13 Red Vertical Column Coefficients Table 10-1 Polynomial Coefficients for the Mean Absolute Response versus CCD Temperature Table 10-2 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M0 Coefficients Table 10-3 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M1 Coefficients Table 10-4 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M2 Coefficients Table 10-5 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M3 Coefficients Table 10-6 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M0 Coefficients Table 10-7 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M1 Coefficients Table 10-8 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M2 Coefficients Table 10-9 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M3 Coefficients Table 10-10 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M0 Coefficients Table 10-11 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M1 Coefficients Table 10-12 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M2 Coefficients Table 10-13 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M3 Coefficients Table 10-14 Coefficients for Thermal Variation of Pixel Map: Red Vertical M0 Coefficients Table 10-15 Coefficients for Thermal Variation of Pixel Map: Red Vertical M1 Coefficients Table 10-16 Coefficients for Thermal Variation of Pixel Map: Red Vertical M2 Coefficients Table 10-17 Coefficients for Thermal Variation of Pixel Map: Red Vertical M3 Coefficients Table 12-1 Solar Aureole CCD Image Section Map of Dark Current Rates Table 12-2 Solar Aureole CCD Memory Section Map of Dark Current Rates Table 12-3 Mean CCD Dark Rate, Bias, Serial Register Table 13-1 Self Bleedthrough Measurement Details Table 13-2 Parameters of geometrical transformation of SA observations Table 13-3 Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Table 13-4 Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Table 13-5Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Table 13-6 Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Table 13-7 Transmission of the Red Solar Aureole Filter at Three Temperatures Table 13-8 Transmission of the Blue Solar Aureole Filter at Four Temperatures Table 13-9Spectral Transmission of Blue Filter for Various Angles of Incidence Table 13-10 Spectral Transmission of Red Filter for Various Angles of Incidence Table 13-11 Dates, File Names, and Detector Temperatures of Relative Spectral Response Measurements of the SN03 Solar Aureole System Table 13-12 Reference Columns Used in Relative Spectral Response Model Derivation Table 13-13 Table of NFMini Quadratic Coefiicients Table 13-14 Thermal Coefficients for All SA Channels Table 13-15 Blue Horizontal Column Coefficients Table 13-16 Blue Vertical Column Coefficients Table 13-17 Red Horizontal Column Coefficients Table 13-18 Red Vertical Column Coefficients Table 13-19 Relative Brightness at the Location of Blue Horizontal Pixel to the Brightness at the Front of the Integrating Sphere Table 13-20 Relative Brightness at the Location of Blue Vertical Pixel to the Brightness at the Front of the Integrating Sphere Table 13-21 Relative Brightness at the Location of Red Vertical Pixel to the Brightness at the Front of the Integrating Sphere Table 13-22 Relative Brightness at the Location of Red Horizontal Pixel to the Brightness at the Front of the Integrating Sphere Table 13-23 Polynomial Coefficients for the Mean Absolute Response versus CCD Temperature Table 13-24 Portion of Modeled Data that Match Measured to within Noise 1 Introduction This document describes the Solar Aureole (SA) system on the flight model (SN03) of the Descent Imager/Spectral Radiometer (DISR) flown on the Huygens Probe of the Cassini Mission. An overview of the SA system is given, followed by a section on the actual Titan descent. Next follows the overall methodology of the reduction of Solar Aureole data to measured calibrated intensity and degree of polarization and the verification of that calibration. The following sections provide detail necessary to reduce the Solar Aureole data, including tables of values. Finally, the Appendices include reports on different aspects of the Solar Aureole system, often deriving the equations used in the analysis, describing test setups for the calibration, and noting the quality of modeling fits to the measured calibration data. 2 System Overview The Solar Aureole system uses four channels to measure the brightness of a vertical strip of sky some 6 degrees wide by 50 degrees long within a few degrees of the sun and opposite to the sun in the sky. The field of view is centered at 50 degrees zenith angle, the zenith angle of the sun in the sky of Titan during the nominal entry. Each of the four channels includes a linear sheet polarizer and an interference filter. The four channels thus consist of measurements centered at 500 or 935 nm in both vertically and horizontally polarized light. The schematic layout of the optical system is shown in Figure 2-1 . Lens elements in each of the four channels focus light onto the ends of fiber optic ribbons that bring the light to four 6 by 50 pixel arrays on the CCD sensor. The optical system also includes a beamsplitter that permits light from an onboard calibration source to illuminate the SA system through all optical elements except the outside window. Figure 2-2 shows the field of view of the SA system relative to the shadow bar on the DISR sensor head. The field is centered at 50 degrees zenith angle and is tipped 6 degrees toward the direction of increasing azimuth. The shadow bar prevents direct light from the sun from illuminating the SA window during the SA integrations. The software permits integrations to begin at azimuth angles between about 2.5 and 2.9 degrees. Thus the 6 degree-wide field of view of the SA system includes measurements from at least 6 - 3 + 2.5 or 5.5 degrees to 11.5 degrees azimuth from the sun at the start of the integration. The azimuth at the end of the integration depends on the integration time and the rotation rate, but the rotation during the integration is limited to a maximum of 3.5 degrees. In these measurements near the sun, all 300 elements in each of the four Solar Aureole channels are included in the telemetry stream. In addition to the measurements near the sun, the SA system makes a measurement centered at an azimuth angle between 172 and 176 degrees from the sun. In these measurements, the signals in all six columns in each SA channel are summed before transmission to the ground. The integration time for these measurements is limited so that the probe rotates through no more than 20 degrees during the exposure. The measurements through two orthogonal linear polarizers are not sufficient to uniquely determine the position angle and degree of linear polarization for light of an arbitrary state of linear polarization. Rather, we will assume that the light in Titan's atmosphere is partially linearly polarized with the position angle perpendicular to the scattering plane. This is sufficient to determine both the total intensity and the degree of polarization from the measurements made opposite to the sun. We plan to simply add the horizontal and vertical components of intensity near the sun to obtain the total intensity as a function of angular distance from the sun. FIG_2-1 Figure 2-1 The schematic layout of the components of the Solar Aureole system. The beamsplitter is used to introduce light from the inflight calibration system into the four channels of the Solar Aureole system. FIG_2-2 Figure 2-2 The field of view of the Solar Aureole camera is shown relative to the shadow bar of the sensor head. The center of the field of view is tipped by 6 degrees in the direction of increasing azimuth. The shadow bar shades the entire window of the Solar Aureole system when the Solar Aureole makes its measurement, since the measurement starts at an azimuth of about 2.5 degrees and extends to increasing azimuth. As described above, the Solar Aureole system consists of four 6 by 50 pixel cameras. These cameras have focal planes on the CCD detector array. The following table shows the row and column numbers of each camera. The data from the cameras is delivered in one of two data set types, Solar Aureole data sets or part of the Full CCD data sets. The table addresses both instances. Note also that rows 0:49 in a Solar Aureole data set correspond to rows 204:253 in a Full data set. In the DISRsoft files, the header entries that designate CCD column and row numbers for the lower left corner designate row 203 instead of 204, but this is incorrect. Table 2-1 Solar Aureole CCD Row and Column Designations SA data set columns 0:5 6:11 12:17 18:23 Full data set columns 40:45 31:36 23:28 14:19 Filter Blue Blue Red Red Polarization Horizontal Vertical Vertical Horizontal Designation sometimes Blue Perpendicular Blue Parallel Red Parallel Red Perpendicular used 3 The Titan Descent As It Occurred While much of the Huygens mission went as planned, the actual descent yielded some surprises. The most significant impact on the Solar Aureole measurements of the actual descent relative to what was expected was that the real time knowledge of azimuth failed throughout the descent. This was caused by the DISR Sun Sensor failing to lock onto the solar signal as the probe rotated. Its locking on the sun was intended to provide an effective trigger for scheduling all DISR measurements in azimuth, but the Solar Aureole measurement was particularly dependent on the Sun Sensor because of the desire to measure the aureole adjacent to the sun, but not including the solar disk. The timing on this measurement is especially critical. The Sun Sensor failed because of probe dynamics and the detector reaching colder than expected temperatures. Because real time azimuthal knowledge was not available, the Solar Aureole measurements were taken at random azimuths rather than at 2.5 degrees and 174 degrees as planned. Because the azimuths were random, the auto-exposure algorithm did not work as designed, and saturation occurred in some data sets. There is a single red unsaturated data set near the sun over the course of the mission. It occurs at around 60 km altitude and around 8.5 degrees from the sun. There are more blue data sets near the sun that are unsaturated. However, one can be grateful that the Sun Sensor detection failed because if it had succeeded, the Solar Aureole measurements near the sun would all have had the direct solar beam in them. The probe rotated backwards over most of the descent. The Shadow Bar was designed to shield the SA field from the direct solar beam as the probe rotated counter clockwise as viewed from above. This was the spin direction for the first roughly 10 minutes of the descent, but then the direction reversed and stayed clockwise throughout. Therefore, if the Sun Sensor had given stable and reliable triggers, which are not dependent on the direction of probe rotation, all the near sun measurements would have been taken with the sun in the field. Another difference between the Solar Aureole measurements as planned and the measurements achieved relates to the absolute calibration of edge rows and columns. Recall that the Solar Aureole is comprised of four optical channels, each fed via a fiber ribbon conduit to a CCD detector. The fiber ribbons are thin (under 140 microns thick) and delicate. The fiber polishing on the end of the ribbon resulted in small chips and fractures on the ribbon edges. The effect of these chips is to cause the edge columns of several of the four channels to have structure in their absolute response along the column. It becomes clear upon observing the computed absolute intensity over the course of the descent for each column that a slight shift in fiber location over the CCD array occurred. This shift is not seen in the cruise phase data (which includes active optical stimulation of the SA system). It is believed that the shift occurred during entry into Titan's atmosphere. The result is that several columns (not pixels) of the Solar Aureole system should be omitted from the data reduction. Additionally, row 0 has not had sufficient illumination to be useful throughout the program, so this row should be deleted. The columns and rows to be omitted are indicated below. Table 3-1 Solar Aureole CCD Row and Column Designations for Columns that Should Be Omitted From Analysis Instrument Blue Horizontal Blue Vertical Red Vertical Red Horizontal SA data set designation Column 0 Column 6 Column 12 Column 18 Column 5 Row 0 Column 17 Row 0 Row 0 Row 0 CCD data set Column 40 Column 31 Column 23 Column 14 designation Column 45 Row 204 Column 28 Row 204 Row 204 Row 204 SA channel designation Column 0 Column 0 Column 0 Column 0 (columns 0 to 5 and Column 5 Row 0 Column 5 Row 0 rows 0 to 49) Row 0 Row 0 Note that the following methodology and plans for data analysis assume the measurements will be taken as planned, and that all the SA pixels have accurate calibration. Special care should be taken in reducing the actual mission data regarding saturation, correct geometric viewing angles including probe tip and tilt, and careful combination of the two SA channels in each color because of field of view overlap and polarization/retarder effects using only the good columns. 4 Methodology for Analyzing Solar Aureole Data 4.1 Generation of Solar Aureole Data Numbers For every SA pixel, the number of counts generated at temperature T and exposure time ti in the presence of intensity I(lambda,theta,phi,altitude) is given by IMAGE_008.GIF 1. where: Abs_Resp(T) is absolute responsivity of the SA pixel in (DN/sec) / Watts/(m2-micron-str); I(lambda,theta,phi,altitude) is the intensity (Watts/(m2-micron-str)) in the atmosphere at wavelength lambda, zenith angle theta, azimuth angle phi, and the specified altitude in the Titan atmosphere; RSR(lambda,T) is the relative spectral response of the SA pixel at wavelength lambda and temperature T; IMAGE_020.GIF is the integral of the intensity times the RSR over the spectral band integrated over the field of view of the SA pixel over the course of the exposure time; DN_dark(T,ti) is the dark current of the SA pixel at that temperature and for that integration time, plus the CCD bias; Noise(T,ti,DN_nom) is the noise in the measurement at that temperature, integration time, and nominal incident energy. The absolute response, relative spectral response, dark current, and noise are all models as described later in this document. 4.2 Computing Solar Aureole Calibrated Intensities in Each Pixel Consider the above equation with the following substitution, IMAGE_027.GIF = IMAGE_028.GIF * IMAGE_029.GIF 2. where I_std_wave(lambda0,theta,phi,altitude) is the intensity at wavelength lambda0 at zenith angle theta, azimuth angle phi, and the specified altitude and I_shape is the normalized spectral shape of the intensity at that location where I_shape equals 1.0 at lambda0. This substitution results in the following: IMAGE_034.GIF 3. For every SA pixel (or row in the case of summed data sets), the intensity I_std_wave(lambda0,theta,phi,altitude) in units of Watts/(m2-micron-str) at wavelength lambda0, zenith angle theta, azimuth angle phi, and the altitude in the Titan atmosphere is computed from the number of counts generated at temperature T and exposure time ti by: IMAGE_037.GIF 4. where: DN is the measured counts for that Solar Aureole measurement; DN_dark(T,ti) is the dark current of the SA pixel at that temperature and for that integration time, plus the CCD bias; Abs_Resp(T) is absolute responsivity of the SA pixel in (DN/sec) / Watts/(m2-micron-str); is the relative spectral response of the SA pixel at wavelength lambda and temperature T; I_shape(lambda0,theta,phi,altitude) is the spectral shape of the intensity (unitless and normalized to 1.0 by definition) at the specified altitude in the Titan atmosphere. It is defined by dividing the Titan model by the intensity at that wavelength as in equation 2. It is important to note that the computation of calibrated intensities at a specific wavelength is an iterative process. The I_shape is model dependent, so a proposed model must be introduced, which creates an I_shape, which then must result in correct SA intensity predictions. This I_shape must be consistent with the polarizing affects of both Titan's atmosphere and the SA instrument as noted in the next section. 4.3 Combining Intensities in Each Pixel to Result in Total Absolute Calibrated Intensities and Degree of Polarization Recall that each pixel includes only the intensity in one polarization state. Therefore, the total Titan intensity and the degree of polarization measured in one data set must be computed using both polarization channels in each color. As can be seen in the sections and appendices regarding field of view and polarization, the combination of the intensities in each color is complex. First note that the four Solar Aureole channels do not have aligned fields of view - each channel looks at a slightly different angle and thus has a slightly different field of view. Therefore, the calibrated I_std_wave which has been computed for every pixel in a data set must be interpolated in space to some internal standard grid that has data from both polarization states (where the fields of view overlap). Care must be taken to omit columns and rows that have faulty calibration due to fiber ribbon shift upon Titan entry. Care must also be taken to ensure one knows where in Titan's sky each theoretic grid point is pointed. Second, note that the in flight calibration beamsplitter at the front of the optical train of the SA system acts as a retarder, with a different retardance and a different optical axis position angle for each row in each channel. The book Polarimeters for Optical Astronomy by K. Serkowski contains on pages 144 and 145 an excellent section on detection of light through a retarder and analyzer. If one defines the Stokes parameters of elliptically polarized light by IMAGE_040.GIF then the intensity of light transmitted through a retarder with the optical axis at position angle Psi followed by an analyzer with the principal plane at position Phi=0 (upper signs, horizontal Solar Aureole channels) or Phi=0 (lower signs, vertical Solar Aureole channels) can be obtained by: IMAGE_042.GIF Note that these retardances and retarder optical axes must be interpolated to the internal standard grid defined by the field of view overlap and carefully combined with the I_std_wave functions for each data set for accurate calculation of the intensity and degree of polarization. Because this combination can be complex, some correct IDL code lines are added here for user's verification of their understanding. ; First, consider the data sets that are summed across the rows. These have their own ; geometries since all 6 rows are included in each data set before telemetering to earth. for i=0,num_summed-1 do begin ; Interpolate to internal standard zenith angles b_per_interp=interpol(I_std_wave(sum_idx(i),0,*),mean_blu_per_ze,blu_za) b_par_interp=interpol(I_std_wave(sum_idx(i),1,*),mean_blu_par_ze,blu_za) r_par_interp=interpol(I_std_wave(sum_idx(i),2,*),mean_red_par_ze,red_za) r_per_interp=interpol(I_std_wave(sum_idx(i),3,*),mean_red_per_ze,red_za) ; Compute intensity blue(sum_idx(i),*)=2.0*(b_per_interp+b_par_interp+b_per_interp*cos(4.*b_par_psi)+ $ b_par_interp*cos(4.*b_per_psi))/(2.+cos(4.*b_per_psi)+cos(4.*b_par_psi)) red(sum_idx(i),*)=r_per_interp+r_par_interp+(r_per_interp-r_par_interp)* $ (Gv+Hv*cos(4.*r_par_psi)-Gh-Hh*cos(4.*r_per_psi))/(Gv+Hv*cos(4.*r_par_psi)+Gh+Hh*cos(4.*r_per_psi)) ; Compute degree of polarization blu_deg_pol(i,*)=2.*(b_per_interp-b_par_interp)/$ (b_per_interp+b_par_interp+b_per_interp*cos(4.*b_par_psi)+b_par_interp*cos(4.*b_per_psi)) red_deg_pol(i,*)=(r_per_interp-r_par_interp)/ $ (r_per_interp*(Gv+Hv*cos(4.*r_par_psi))+r_par_interp*(Gh+Hh*cos(4.*r_per_psi))) endfor ; Next consider the data sets that are contour, with 6x50 pixel aspects. for z=0,49 do begin for i=0,num_unsummed-1 do begin ; Interpolate to internal standard zenith angles, blue first blu_per_cont=interpol(unsum_data(i,0:5,z),blu_per_az_cont(*,z),blu_az(*,z)) blu_par_cont=interpol(unsum_data(i,6:11,z),blu_par_az_cont(*,z),blu_az(*,z)) b_per_interp=mean(blu_per_cont) b_par_interp=mean(blu_par_cont) ; Compute intensity for both contour and summed geometries blue(unsum_idx(i),z)=2.0*(b_per_interp+b_par_interp+b_per_interp* $ cos(4.*b_par_psi(z))+b_par_interp*cos(4.*b_per_psi(z)))/ $ (2.+cos(4.*b_per_psi(z))+cos(4.*b_par_psi(z))) blu_contour(i,*,z)=2.0*(blu_per_cont+blu_par_cont+blu_per_cont* $ cos(4.*b_par_psi(z))+blu_par_cont*cos(4.*b_per_psi(z)))/ $ (2.+cos(4.*b_per_psi(z))+cos(4.*b_par_psi(z))) endfor ; Interpolate to internal standard zenith angles, red next for i=0,num_unsummed-1 do begin red_par_cont=interpol(unsum_data(i,12:17,z),red_par_az_cont(*,z),red_az(*,z)) red_per_cont=interpol(unsum_data(i,18:23,z),red_per_az_cont(*,z),red_az(*,z)) r_per_interp=mean(red_per_cont) r_par_interp=mean(red_par_cont) red(unsum_idx(i),z)=r_per_interp+r_par_interp+(r_per_interp-r_par_interp)* $ (Gv(z)+Hv(z)*cos(4.*r_par_psi(z))-Gh(z)-Hh(z)*cos(4.*r_per_psi(z)))/ $ (Gv(z)+Hv(z)*cos(4.*r_par_psi(z))+Gh(z)+Hh(z)*cos(4.*r_per_psi(z))) red_contour(i,*,z)=red_per_cont+red_par_cont+(red_per_cont-red_par_cont)* $ (Gv(z)+Hv(z)*cos(4.*r_par_psi(z))-Gh(z)-Hh(z)*cos(4.*r_per_psi(z)))/$ (Gv(z)+Hv(z)*cos(4.*r_par_psi(z))+Gh(z)+Hh(z)*cos(4.*r_per_psi(z))) endfor endfor Also note that the effects of the retarder on the I_shapes used in the basic calculation of intensity falling on each SA pixel must also be included. Because Titan's atmosphere is polarized, the spectral shape of the intensity field falling on a SA pixel will vary over the SA field of view dependent on the direction the pixel is looking, the shape of the intensity field, and the shape of the Q intensity affected by the retarder in the appropriate manner. 5 Calibration Verification As may be becoming apparent, the calibration of the Solar Aureole system is quite involved, including careful combination of the geometric fields of the different instruments, variations of relative spectral response over the spatial field and temperature, variation of the absolute response on a pixel by pixel basis with temperature, variation of polarization qualities over the instrument field, and accurate handling of dark current and the basics of instrument performance. Therefore, verification of the calibration effort was desired. This was achieved using a simulated Titan descent performed in the lab using the flight model DISR inside a calibrated integrating sphere, with varying CCD temperature along the expected thermal profile for the descent. The Solar Aureole data created in this calibrated environment was reduced to result in computed intensities in the integrating sphere (which had spatial inhomogeneities which had been previously mapped). These computed intensities were then compared to the known intensity and found to be within 2% over all temperatures and every pixel. This is fully documented in an appendix. 6 Stability of SA Response with Time from Cruise Measurements Over the seven year cruise phase, sixteen instrument checkouts were performed. In each checkout, the In Flight Calibration System was used to stimulate the Solar Aureole cameras. The resulting measurements were tracked over time to detect any optical or electronic changes after the lab calibration. The changes in Solar Aureole response were less than 2% throughout cruise. These checkouts are all reported in detail in the In Flight Checkout documents that were submitted for each test. The latest, most complete Solar Aureole Responsivity verification was from F13. 7 Some Operational Points of Note Some operational points of note are included in an appendix. 8 Geometry and Field of View As mentioned above, the four Solar Aureole channels point at slightly different angles. Below is a figure of the fields of view for the four channels. Derivations of these angles and equations for converting from DISR to Titan coordinates are in an appendix. FIG_8-1.GIF Figure 8-1 The centers of the pixels at the edge of the four solar arrays are shown in azimuth and zenith angle. Note that the arrays do not overlap exactly, and that care will have to be taken in interpolation in an array at one polarization state to obtain the intensity in the other polarization state at the same location. The azimuths shown are relative to the sun if the data were obtained when the instrument crossed the exact azimuth of the sun. In fact, Solar Aureole exposures begin when the instrument is 2.5 to 2.9 degrees past the azimuth of the sun and will continue for a maximum of 3.5 degrees of rotation. The azimuth and zenith angles for each SA pixel are given in the following four tables. Table 8-1 Blue Horizontal Solar Aureole Azimuth and Zenith Angles for Every Pixel Table 8-2 Blue Vertical Solar Aureole Azimuth and Zenith Angles for Every Pixel Table 8-3 Red Horizontal Solar Aureole Azimuth and Zenith Angles for Every Pixel Table 8-4 Red Vertical Solar Aureole Azimuth and Zenith Angles for Every Pixel Because the physical quantities measured by the Solar Aureole combine data from both polarization states, there is an effective field of view created by the intersection of the two fields of view for each color. This effective field of view is smaller than 6 by 50 degrees, and it can have an irregular shape. The following two figures show the effective fields of view for the blue and red SA channels if all pixels can be used. As discussed in the section about the Titan descent, several columns must be omitted, which further constrains the effective field of view. FIG_8-2.GIF Figure 8-2 The effective field of view for the blue Solar Aureole channels if all columns are used. The horizontal and vertical channels do not overlap perfectly, so a smaller field is used to combine the intensities from both channels to result in total intensity and polarization. The + signs indicate locations where physical quantities are reported in the University of Arizona Lunar and Planetary Lab analysis for data sets that are delivered in full 24 by 50 pixel format. The diamonds indicate locations where physical quantities are reported for data sets that are summed on board before sending them to earth. Care must be taken to exclude pixels where the absolute responsivity is poorly known as mentioned in the section on the Titan descent. FIG_8-3.GIF Figure 8-3 Same as previous figure, but for the red. 9 Relative Spectral Response 9.1 The Form of Relative Spectral Response Model A model of the Relative Spectral Response (RSR) was derived from measured DISR Solar Aureole data. The details of the model derivation, as well as the quality of the model fits, are shown in an appendix. The form of the RSR model includes a foundational set of spectrally varying curves, filter, whose characteristics are largely due to the interference filters in each channel but also have contributions from the beamsplitter. The filter curves are functions of the row number (angle of incidence) for each pixel. To result in the RSR model, the filter curves are multiplied by a polynomial function that includes all thermally varying effects and some spatial effects, all of which are presumed to reside in the CCD chip and fiber bundle since the filters have been shown to have no temperature dependence (see appendix). This latter function is called the "non-filter model", or NFM, because it is derived analytically by eliminating the interference filter effects from the measured relative spectral response. It includes some spatial variation on a columnwise basis. As derived, the RSR for each of the four SA channels can be found by the following equation. IMAGE_050.GIF 5. The form of the NFM is the following polynomial equation, where the thermal coefficients, a, b, c, and d, are properties of the SA channel, and the column coefficients, M0 through M3, are column dependent for each channel. IMAGE_052.GIF 6. Due to fiber ribbon/CCD misalignments, a few columns do not match their neighbors in RSR shape. These columns are treated in the manner described above, but with their own set of filters and coefficients. Additional localized spatial effects are found throughout the system - the CCD has some pixel to pixel variation and the optical train has obvious illumination variations over the field due to the cameras and fiber ribbon underfilling the CCD - but the number of pixels affected and the degree of modeling error are small. The initial NFM, NFM_ini(lambda), is an underlying spectrally varying function which includes structure in the CCD quantum efficiency. The blue channels have no underlying structure, so NFMini is defined to be unity. The red channels, on the other hand, do have some structure over the SA bandpass, and this structure can be modeled as follows. A known bump in the CCD quantum efficiency can be seen in the red SA RSR, so it is modeled empirically in the initial NFM as a lorentzian function with a center wavelength of 854 nm, a full-width at half maximum response of 15 nm, and a peak amplitude of 0.4, as follows. IMAGE_054.GIF 7. The coefficients of the initial NFM quadratic fit of the quantum efficiency rolloff for the red horizontal and vertical channels are as follows. Table 9-1 Table of NFMini Quadratic Coefficients Red Horizontal Red Vertical nfm0 67.900400 25.311233 nfm1 -0.13372830 -0.043105799 nfm2 6.6157520e-005 1.8006592e-005 Thus, the initial NFM is as follows for the blue or red channels. IMAGE_056.GIF 8. Thus, the Solar Aureole Relative Spectral Response is modeled in the following forms. For the blue channels, the final equation is as follows, IMAGE_058.GIF 9. where the filter and the coefficients M0 through M3 and a through d are in the tables below. For the red channels, the final equation is as follows, IMAGE_060.GIF 10. where the filter and the coefficients M0 through M3 and a through d are in the tables below, and the Bump function and nfm0 through nfm2 are in this section. Care must be taken to use the correct filters and coefficients for the columns 0 and 1 as appropriate. It should be noted that the complexity of the modeling is due to both systematic effects such as the filter transmission variation with angle of incidence and the CCD quantum efficiency changing with temperature, and to pixel to pixel variations largely caused by the fiber ribbons. These ribbons have imperfections throughout their thin "bulk" and along their edges. It is these effects that create such model complexity. 9.2 The SA Interference Filter Transmissions Recall that while these are designated "filter transmissions," they include effects from the filters and the beamsplitters and possibly other sources. Therefore, the full zenith angle field of view is characterized rather than just angles from the optic axis. Table 9-2 Table of Blue Horizontal Filter Curves Table 9-3 Table of Blue Vertical Filter Curves Table 9-4 Table of Red Horizontal Filter Curves Table 9-5 Table of Red Vertical Filter Curves Table 9-6 Table of Red Horizontal Filter Curves, Column 0 Table 9-7 Table of Red Horizontal Filter Curves, Column 1 Table 9-8 Table of Red Vertical Filter Curves, Column 0 9.3 The SA RSR Thermal Coefficients, a, b, c, and d The thermal variations in the RSR are modeled using polynomials as shown in the equation for the NFM (non filter model). These polynomials are characteristic of each SA channel, with two columns requiring their own temperature dependence because of edge chips on the fiber ribbon. The coefficients are as follows. Table 9-9 Thermal Coefficients for All SA Channels Channel a b c d Blue Hor 2.0519205 -0.012112786 2.3854392e-005 -1.5672918e-008 Blue Ver 2.6717794 -0.015919638 3.1632590e-005 -2.0960937e-008 Red Hor 4.1627853 -0.013355480 1.4316606e-005 -5.1278929e-009 Red Ver 0.46694120 -0.0014621260 1.5654954e-006 -5.7336477e-010 Red Hor, col 0 5.2851043 -0.016804565 1.7844364e-005 -6.3286793e-009 Red Hor, col 1 4.9409769 -0.015830010 1.6938123e-005 -6.0531465e-009 9.4 The SA RSR Column Variation Coefficients, M0, M1, M2, and M3 Given the initial NFM and filter models, and the thermal variations represented by the polynomials in the previous section, there remain column to column variations in the non filter models. These are mapped by other polynomials, as shown in the NFM model equation in Section 9.1 The column coefficients M0 through M3 for each channel are in the following tables. Table 9-10 Blue Horizontal Column Coefficients M0 M1 M2 M3 Column 0 -1.576161E+01 6.991217E-02 -7.261663E-05 0.000000E+00 Column 1 -1.120476E+02 6.776472E-01 -1.348858E-03 8.917191E-07 Column 2 -5.451464E+01 3.371992E-01 -6.802498E-04 4.559225E-07 Column 3 1.0 0.0 0.0 0.0 Column 4 7.670377E+01 -4.607676E-01 9.324273E-04 -6.274879E-07 Column 5 1.279626E+02 -7.734728E-01 1.566727E-03 -1.055404E-06 Table 9-11 Blue Vertical Column Coefficients M0 M1 M2 M3 Column 0 1.287794E+02 -7.803157E-01 1.587449E-03 -1.075872E-06 Column 1 1.076329E+02 -6.419133E-01 1.287519E-03 -8.604670E-07 Column 2 1.0 0.0 0.0 0.0 Column 3 1.033230E+01 -5.103488E-02 9.152373E-05 -5.362022E-08 Column 4 4.158349E+01 -2.413895E-01 4.777937E-04 -3.147463E-07 Column 5 1.067493E+02 -6.317197E-01 1.256640E-03 -8.324925E-07 Table 9-12 Red Horizontal Column Coefficients M0 M1 M2 M3 Column 0 -6.951670E+01 2.272747E-01 -2.440805E-04 8.734615E-08 Column 1 9.833868E+00 -2.762700E-02 2.874322E-05 -9.946730E-09 Column 2 1.0 0.0 0.0 0.0 Column 3 -8.488152E+01 2.770449E-01 -2.980202E-04 1.069016E-07 Column 4 -1.488555E+02 4.824542E-01 -5.178775E-04 1.853475E-07 Column 5 -9.319383E+01 3.022677E-01 -3.235209E-04 1.154941E-07 Table 9-13 Red Vertical Column Coefficients M0 M1 M2 M3 Column 0 9.037937E+00 -2.485048E-02 2.555993E-05 -8.744530E-09 Column 1 3.750232E+02 -1.205694E+00 1.293924E-03 -4.622855E-07 Column 2 9.085585E+01 -2.906646E-01 3.126092E-04 -1.117840E-07 Column 3 1.0 0.0 0.0 0.0 Column 4 1.899895E+01 -6.003125E-02 6.722727E-05 -2.525717E-08 Column 5 2.436124E+01 -7.513855E-02 8.203623E-05 -3.038352E-08 10 Absolute Response The absolute responsivity of the SA cameras was measured in the lab as described in an appendix. Once this absolute response was measured, a model could be generated that would be a general representation of the absolute response. The details of the model derivation, as well as the quality of the model fits, are shown in an appendix. 10.1 Mean Absolute Response Because the absolute response varies with temperature, it is helpful to have a thermal model. As a base for the model, the mean absolute response for each channel is computed versus CCD chip temperature, and it is fit with a fifth or sixth order polynomial. Column 0 is excluded from the mean because it lies at the edge of the fiber ribbon illumination and is impacted by mechanical changes with temperature that are different from the rest of the array. Creating a thermal model using the detector temperature for the mean and initial pixel map derivation, but using the optics temperature for pixel-to-pixel variations over temperature (which makes more physical intuitive sense), resulted in a model with poorer performance than just using CCD temperature. The pixel-to-pixel variation with temperature is likely due to thermal variance of the separation between the CCD and the fiber ribbon, which is better modeled by the CCD temperature than the optics temperature since that temperature sensor is closer than the one on the optical bench. The results are in the following plot and table. Table 10-1 Polynomial Coefficients for the Mean Absolute Response versus CCD Temperature Blue Horizontal Blue Vertical Red Horizontal Red Vertical A0 -1.320628900000e+8 -1.043157230000e+8 -6.342293175000e+7 -4.764707846875e+7 A1 3.439118281250e+6 2.708450062500e+6 1.392982078125e+6 1.053106603516e+6 A2 -3.693190771484e+4 -2.898806738281e+4 -1.200406482697e+4 -9.126064826965e+3 A3 2.100620784760e+2 1.643101100922e+2 5.120302107930e+1 3.914550912380e+1 A4 -6.678061112761e-1 -5.205441340804e-1 -1.080477217911e-1 -8.309265802382e-2 A5 1.125490496634e-3 8.742839563638e-4 9.032962566380e-5 6.989951356218e-5 A6 -7.858712436359e-7 -6.084150783181e-7 0.000000000000e+0 0.000000000000e+0 FIG10-1.GIF Figure 10-1 Mean Absolute Response versus Temperature 10.2 Thermal Variation in Pixel Maps The next step in the generation of a thermal model is the formation of a pixel map at the coldest temperature. This map is the computed absolute response from the previous sections divided by the polynomial fit at the coldest temperature. This map then represents the pixel-to-pixel variations. IMAGE_064.GIF 11. If the pixel-to-pixel variations were thermally invariant, one could then compute the absolute response of any pixel at any temperature by the following equation. IMAGE_066.GIF 12. Unfortunately, this is not the case. The pixel-to-pixel variations do vary also with temperature. Several physical mechanisms may be contributing to this variation, but one effect is that the separation between the fiber ribbon bundle and the CCD appears to vary slightly with temperature. The pixel-to-pixel variation with temperature is modeled by an additional set of polynomial coefficients for each pixel in the map. Two temperatures were considered in this polynomial fit - the detector temperature and the optics temperature. The detector temperature yields the better performance, probably because the detector temperature sensor is closer to the gap between the fiber ribbon and CCD and thus models the temperature of that gap more accurately. In this way, the absolute response for any pixel at any temperature can be computed by the following equation. IMAGE_068.GIF 13. This equation can be simplified by multiplying the Map and the "p" polynomial coefficients to result in the final model for the thermal variation of the absolute response. IMAGE_070.GIF 14. The "M" coefficients for the thermal variation of the pixel map are in the following tables. Care should be taken not to confuse these M coefficients with those for the Relative Spectral Response model. Table 10-2 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M0 Coefficients Table 10-3 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M1 Coefficients Table 10-4 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M2 Coefficients Table 10-5 Coefficients for Thermal Variation of Pixel Map: Blue Horizontal M3 Coefficients Table 10-6 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M0 Coefficients Table 10-7 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M1 Coefficients Table 10-8 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M2 Coefficients Table 10-9 Coefficients for Thermal Variation of Pixel Map: Blue Vertical M3 Coefficients Table 10-10 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M0 Coefficients Table 10-11 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M1 Coefficients Table 10-12 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M2 Coefficients Table 10-13 Coefficients for Thermal Variation of Pixel Map: Red Horizontal M3 Coefficients Table 10-14 Coefficients for Thermal Variation of Pixel Map: Red Vertical M0 Coefficients Table 10-15 Coefficients for Thermal Variation of Pixel Map: Red Vertical M1 Coefficients Table 10-16 Coefficients for Thermal Variation of Pixel Map: Red Vertical M2 Coefficients Table 10-17 Coefficients for Thermal Variation of Pixel Map: Red Vertical M3 Coefficients 11 Polarization Sensitivity The four Solar Aureole channels include two channels in each of two colors. The two channels for a given color are identical with the exception of the orientation of polarizers in the optical path, one parallel to the Shadow Bar (vertical) and one perpendicular to the Shadow Bar (horizontal). During the test and calibration phase of the DISR program, several unexpected effects were noticed regarding the polarization sensitivity of the SA cameras. The details of these effects and their cause are included in an appendix. The bottom line result is that the beamsplitter prism which introduces calibration light into the SA optical train acts as a retarder in the system. It re-orients the principal plane over the field of view of each SA channel. The action of this retarder must be included in the SA data analysis. It is interesting to understand how the instrument came to have these properties. One requirement of the in flight calibration system was that it pass light through all the optical elements of a system except for the front window. This requirement allowed for accurate tracking of any radiation darkening of optics or changes in alignments over the launch or cruise environments. However, because of the design of the Solar Aureole optical system, it implied a beamsplitter to introduce the calibration signal. The blue beamsplitter acts nearly as a quarter-wave retarder. Its position angle as a function of row number is given in the following figure. The retardance is taken as 90 degrees for the blue prism. FIG_11-1.GIF Figure 11-1 We show the position angle as a function of row number for the Blue Vertical and Horizontal channels in the SH03 flight Solar Aureole system. The retardance is taken as 90 degrees for the flight prism in the blue channel. The retardance of the flight prism is less in the red than in the blue channel. Note that the retardance of the prism alone in the red channels is approximately 30 degrees compared to the 90 degrees measured in the blue channel. Since the dichroic beam splitter is much more reflective in the blue than in the red, this is not surprising. Below are two figures which include the retardance and the angle of the principal plane in both channels of the red Solar Aureole system. FIG_11-2.GIF Figure 11-2 The position angle (Psi, left scale, blue dots) and the degree of retardance (tau, right scale, red squares) as functions of row in the horizontal channel of the flight sensor head. FIG_11-3.GIF Figure 11-3 Like Figure 11-2 but for the vertical channel of the flight SA in the red. 12 Temperature Dependence of Dark Current The CCD has a temperature dependent dark current which must be removed from all measurements. This dark current can be computed in the following manner: 1.) Read in matrices mapping pixel to pixel variations for the Solar Aureole portion of the CCD. These are designated f1 and f2, and are attached as Table 12-1 and Table 12-2. 2.) Read the file with Mission Time, Mean CCD Dark, Bias + Serial Register. This is often designated CC_MST_MDK_BSR.dat, and is listed as Table 12-3. 3.) Interpolate the mean dark to the specific mission time of a data set. 4.) Interpolate the bias+sr to the specific mission time of a data set. 5.) Change bias+sr to spectral read mode using mbias = ((bias- 8.9)*(0.976/8.384))+8.9 > 0.0. 6.) Calculate memory zone dwell time array (mz) array for each row according to mz = (row+1)*0.000976 seconds where "row" is in Full CCD units (i.e. 204 through 253). 7.) Change the exposure time of data set to seconds. 8.) Calculate dark + bias pixel value for data set's specific mission time and exposure time using: dark + bias = (exptime * f1 * mdark) + (mz * mdark * f2) + mbias Table 12-1 Solar Aureole CCD Image Section Map of Dark Current Rates Table 12-2 Solar Aureole CCD Memory Section Map of Dark Current Rates Table 12-3 Mean CCD Dark Rate, Bias, Serial Register The derivation of the CCD dark current for all CCD measurements is contained in a separate report. 13 Appendices 13.1 Calibration Verification - Simulation Descent Reduction Paper 13.1.1 Introduction After the recent revelation that the Solar Aureole absolute response model needed refinement, the model was updated and a simulated descent was analyzed. This document describes the results from the recent simulated descent analysis. The simulated descent analyzed is that performed on August 7, 1996. It is the best descent to study for the SA because its window was not covered with alumalloy. 13.1.2 Approach The basic approach to this analysis is to compute the predicted intensity given the SA counts and the models derived elsewhere, followed by computation of the true intensity in the integrating sphere derived from the calibration files. The ratio of the predicted intensity to the true intensity is the figure of merit for this analysis, and we would hope this ratio would be unity over the descent and thus over temperature. The code descent_analysis, which inputs an entire descent's worth of Solar Aureole data and computes calibrated intensities at specific locations on the sky over the descent, is used to compute the predicted intensity. Total intensity cuts across zenith angle are computed for every data set returned in the descent, and contour maps are computed where the full format data is available. To compute the predicted intensity, we input the counts measured in the SA, subtract the dark counts and CCD bias using Andrew Eibl's dark model, and then divide this by the product of the integration time, model absolute response, and integral of the model relative spectral response times the shape of the monochromator scan (During the mission, the base shape for the input intensity will be derived from the ULVS measurements.). This quantity, Istd_wave, is the calibrated intensity at a specific wavelength: 492nm in the blue and 934nm in the red. Mathematically, we do the following: IMAGE_078.GIF To compute the true intensity in the sphere, we take the monochromator scan performed for this log, correct for lamp drift during the scan and during the descent, and correct for spatial variations in the integrating sphere. For comparison with the data produced by the descent_analysis code, which sums the two polarization states, the effects of pixel registration must be carefully performed since the interior of the integrating sphere is not perfectly uniform. 13.1.3 Results - Absolute Calibration Before describing the results in detail, we consider the overall results in the table below. This table indicates that for the total intensity data, the ratio of the predicted intensity at a specific zenith angle to the measured intensity at that angle, averaged over every data set in the descent is 0.997 for the blue and 1.005 for the red. This corresponds to an average model fidelity of a fraction of a percent. The minimum and maximum ratios for every zenith angle over the descent are also given. They indicate a maximum dispersion of 5% in the blue and 4% in the red. The contour data results in larger dispersion around nominal, which is expected due to noise. Minimum Maximum Mean Blue Total Intensity 0.953 1.052 0.997 Red Total Intensity 0.981 1.042 1.005 Blue Contour 0.898 1.077 0.996 Red Contour 0.967 1.076 1.005 It should be noted that the SNR has not been incorporated explicitly in these results. The SNR for data that has not been summed increases to around 100 for the blues and around 230 for the reds in the central pixels. It should also be noted that the lamp used for the test failed for a short period of the descent. This causes the lamp drift equation to yield unrealistic values. Data taken during this period is not included in this analysis, nor is the data from three instances of saturation which occurred due to auto-exposure when the lamp came back on. As will be seen later, the lamp failure contributes to an overall question to the true accuracy of the absolute response calibration for this test, but it is useful to see how well the Solar Aureole models perform even in this condition. Consider the following two plots of model performance for the total intensity cuts. These plots show the ratio of predicted to measured intensities in the blue and red channels. They include every zenith angle in every appropriate data set in the descent. One can note the minima and maxima as described in the table above. The three plotting styles (asterisks, diamonds, and plus signs) indicate regions of model performance, which will now be addressed. Note that for historical reasons there are three plotting styles. There are actually only two regions of performance. The third "region" was an artifact of incorrect handling of the bias in the CCD. After correction of this error, the three regions collapsed into two. FIG_13-0-A.GIF FIG_13-0-B.GIF 13.1.3.1 Red Summed Data The red channel shows the most obvious splitting of performance, so it is addressed first. It was found that the regions of performance related to periods of time during the descent. The CCD temperature is plotted versus mission time below. The plotting styles here correspond to those in the model performance plot above. FIG_13-0-C.GIF It is seen that the majority of the temperature range is in the first of the three regions. While the splitting of performance could in fact be due to poor thermal modeling of the SA response, another explanation is more convincing. The measured calibrated intensity in the integrating sphere at the location seen by the red horizontal channel central pixel is plotted versus mission time below. Again, the plotting styles here correspond to those in the model performance plot above. The large gap between the asterisks and the line is when the light failed and then came on again. One can see that the lamp does not really become stable again until later in the descent. It is clear that the model performance correlates with the lamp regions of operation. FIG_13-0-D.GIF The question arises, then, about the fidelity of the measured calibrated intensity values for this particular descent run. The measured intensity values are derived from two monochromator scans, one for the blue and one for the red, which were performed at 14:40 and 15:02 hours respectively, on 7 Aug 96. The descent occurred between 10:54 and 13:28 hours, and it included a lamp failure. The notes file from this log also indicates some "cal crashes" prior to the actual descent, and the dark readings for the calibrated detector system are very difficult to find through that entire day's work. Therefore, it could be argued fairly convincingly that the values taken for the true intensities for the descent could be off by a couple of percent due to lamp variations over a period of almost 5 hours which was known to include a lamp failure, and due to possible recent power cycles in the calibration equipment and due to misrepresentation of the dark readings in the calibration detector. 13.1.3.2 Blue Summed Data Switching to the blue channel, the plots of CCD temperature and measured intensity versus mission time are below. The boundary between the first and second performance regions occurs at a different place for the blue than the red. The boundary between the second and third regions occurs at the same time as the red (the red data point is not plotted because of saturation in that data set). FIG_13-0-E.GIF FIG_13-0-F.GIF In the blue case, it could be argued more convincingly that the variation in model performance is in fact due to the thermal modeling. The first region corresponds to temperatures over about 290K. The highest temperature for the absolute response original data is 289K. Therefore, it is reasonable that the model performance above 290K could diverge from the true response. Fortunately, the flight instrument is not expected to see this high temperature during its remaining lifetime. While the lower performance region could be due to poor models as well, its correlation with the red channel and the lamp re-stabilization makes it more likely that this third region is due to lamp effects. Therefore, the blue model appears to be working fairly well over its temperature region, within about 2%, 0.4% of which is due to noise (SNR in un-summed data rises to 100 over the descent.). 13.1.3.3 Blue Un-Summed Data Now that the summed data resulting in total intensity cuts has been analyzed, attention can be turned to the un-summed data, whose model performance is plotted below. Like the total intensity data, every appropriate data set in the descent is represented. For the contour data, only one column is plotted at a time for simplicity. However, the numerical data values in the table at the beginning of this section and duplicated on the plots for column 2 do include every pixel from every data set. Therefore, the minima and maxima are not necessarily included in the plotted lines since they could be from columns other than column 2. Turning first to the blue, the performance for column 2 is plotted below. Six different plotting points are included, with 10 consecutive data sets in each plot style. The order of the plot styles in the descent is: +, *, diamond, triangle, square, X. FIG_13-0-G.GIF We see that the blue intensity model for this central column is good to roughly 2% over temperature, with 1% of that error due to measurement noise in the original data. The other 5 columns in the blue are plotted below. We see that columns 1 through 4 show the same 2% error, with 1% due to noise. Column 0 has a slightly larger variation, roughly 3%. However, the SNR for this column at row 23 starts at 75 and rises to 90, so its measurement noise will be larger than the 1% seen in the central columns. Column 5 has the most variation of performance, but its SNR starts down around 60, so this makes sense. Column 5 has significant features due to fiber ribbon chips. FIG_13-0-H.GIF FIG_13-0-I.GIF FIG_13-0-J.GIF FIG_13-0-K.GIF FIG_13-0-L.GIF If we average over the rows and plot this mean ratio versus CCD temperature, we get the following result. There appears to be some systematic variation on the order of +/-2%. FIG_13-0-M.GIF The plot styles are as follows: Column Number Plot Symbol 0 + 1 * 2 Diamond 3 Triangle 4 Square 5 X The two vertical lines delineate the regions of performance noted in the discussion of total intensity results. 13.1.3.4 Red Un-Summed Data Now attention is turned to the red channel. Column 2 performance is plotted below. Again, six different plotting points are included, with 10 consecutive data sets in each plot style. The order of the plot styles in the descent is: +, *, diamond, triangle, square, X. FIG_13-0-N.GIF Fewer data sets are appropriate for the contour plotting than for the total intensity plots, but nevertheless, the performance regions are still visible. The same effects due to the lamp and calibration system would logically affect this data as well, and the model performance for the red column 2 is believed to be better than 2% overall. The other columns are plotted in the next 5 plots. Columns 2 through 5 show roughly the same 2% performance, but columns 0 and 1 have slightly worse performance. Column 0 has lower SNR than the others, starting at about 180 and falling to 130. This can explain some of the poorer performance, but not all. FIG_13-0-O.GIF FIG_13-0-P.GIF FIG_13-0-Q.GIF FIG_13-0-R.GIF FIG_13-0-S.GIF Again, averaging the ratios over the rows, we see the following. The vertical lines delineate the performance regions, and the column symbols are like those used in the similar blue plot. Recall that the lamp failed when the CCD was roughly 210K. There appears to be some systematic variation on the order of +/- 2% for most columns, with a larger deviation for column 0. FIG_13-0-T.GIF There is a slight upward slope in most red plots of performance. This could be due to model errors in the zenith direction, to variations in the relative brightness in the integrating sphere in the zenith direction, or to errors in the pixel registration code in descent_analysis. These errors are slight, but worth noting. If the error is in the pixel registration, the test cases using the constant and the "ramp zenith" input intensities will indicate the errors, which will then be corrected. 13.1.3.5 Conclusion - Absolute Calibration The test results of the DISR undergoing a thermally accurate simulated descent while placed in the calibrated integrating sphere indicate response models accurate to 2% in both the red and blue channels for un-summed data in almost all pixels. Column 0 in the red results in poorer performance than the other cases. Both the horizontal and vertical red channels have dark regions in column 0 due to fiber ribbon misalignments. The absolute response model for the red horizontal channel column 0 is worse than all other models. Consideration could be made to exclude it from the summed data returned in DISR telemetry. Care should also be taken in using this extreme column toward the sun in the contour analyses. A slight variation in red performance with zenith angle will be monitored. 13.1.4 Results - Relative Calibration across Columns Another interesting figure of merit is the relative calibration from pixel to pixel in a Solar Aureole channel. One would hope that although the absolute calibration may be off by several percent, the relative response of the pixels within a single data set would be closer. 13.1.4.1 Blue Summed Data Summed data implies the relative calibration will be along the column direction only. Consider the following 5 plots of the blue relative calibration. These plots are taken throughout the descent. There are roughly 100 data sets, and every 20th data set is plotted below. Each plot consists of the following. Plot Symbol Definition + Solar Aureole predicted calibrated intensity * Measured sphere calibrated intensity lines SNR 1-sigma band around the SA data diamond Measured sphere calibrated intensity normalized to the mean of the SA data FIG_13-0-U.GIF FIG_13-0-V.GIF FIG_13-0-W.GIF FIG_13-0-X.GIF FIG_13-0-Y.GIF We can see that in most cases, the relative calibration is within about 1%, and there are no systematic variations over column number. 13.1.4.2 Red Summed Data Turning now to similar plots in the red, we see the same results, relative calibration within 1%, though there does seem to be a slight systematic trend toward lower measured values for lower row numbers, and higher measured values for higher row numbers. FIG_13-0-Z.GIF FIG_13-0-AA.GIF FIG_13-0-AB.GIF FIG_13-0-AC.GIF FIG_13-0-AD.GIF 13.1.4.3 Blue Un-Summed Data Now we turn to the un-summed data. First, consider the relative response along the column direction for column 2 for the blue channel. The plotting styles are the same as in the previous sections. There are roughly 60 contour data sets in the descent, and every 10th one is plotted below. FIG_13-0-AE.GIF FIG_13-0-AF.GIF FIG_13-0-AG.GIF FIG_13-0-AH.GIF FIG_13-0-AI.GIF FIG_13-0-AJ.GIF We see that in the blue channel, the normalized response falls almost entirely in the noise band of the SA measurement. This implies a good relative calibration of the blue channel in column 2. 13.1.4.4 Red Un-Summed Data Turning to the red, we see the following plots along column 2. FIG_13-0-AK.GIF FIG_13-0-AL.GIF FIG_13-0-AM.GIF FIG_13-0-AN.GIF FIG_13-0-AO.GIF FIG_13-0-AP.GIF We see that much of the time, the normalized intensity is within the noise band of the measured data, which indicates a good relative calibration. Occasionally, a few pixels could be off by as much as 2%. The higher row numbers often have higher measured intensities than the true intensities. Because column 0 in the red has poorer performance in absolute calibration, this same set of plots is given below for column 0. This column has poorer results, sometimes as bad as 3%. FIG_13-0-AQ.GIF FIG_13-0-AR.GIF FIG_13-0-AS.GIF FIG_13-0-AT.GIF FIG_13-0-AU.GIF FIG_13-0-AV.GIF 13.1.5 Results - Relative Calibration across Rows Now we turn to relative calibration across the rows instead of the columns. The summed data does not lend itself to this section, so we consider only the data returned in full format. 13.1.5.1 Blue Un-Summed Data We make similar plots to those above for different rows. Consider row 23 near the center. The plots over the course of the descent are as follows. Note that in some cases, although the measured data may not be significantly out of the bounds of the noise band, the measured shape of the intensity field across those six pixels can be significantly different from the actual flat shape. Having only six pixels in this direction makes curve fitting difficult. There does not appear to be any systematic variation across the six pixels. FIG_13-0-AW.GIF FIG_13-0-AX.GIF FIG_13-0-AY.GIF FIG_13-0-AZ.GIF FIG_13-0-BA.GIF FIG_13-0-AB.GIF Also considering an extreme row is helpful to bound the performance. Here are the plots for row 48. Again, we sometimes see the possibility of vastly different measured shapes from the true ones, but there are no systematic errors. While the errors are not systematic, it is difficult to advertise greater than 2% relative calibration accuracy in this case. FIG_13-0-BC.GIF FIG_13-0-BD.GIF FIG_13-0-BE.GIF FIG_13-0-BF.GIF FIG_13-0-BG.GIF FIG_13-0-BH.GIF 13.1.5.2 Red Un-Summed Data Now we turn to the red channels, and we consider the same 10 plots as for the blue. Again, there can be vastly different shapes measured across the row, but the variations are under 1% in the central column, and there are no systematic variations. The extreme row shows 1% relative accuracy most of the time, but in some cases it decreases to 2% accuracy. FIG_13-0-BI.GIF FIG_13-0-BJ.GIF FIG_13-0-BK.GIF FIG_13-0-BL.GIF FIG_13-0-BM.GIF FIG_13-0-BN.GIF FIG_13-0-BO.GIF FIG_13-0-BP.GIF FIG_13-0-BQ.GIF FIG_13-0-BR.GIF FIG_13-0-BS.GIF FIG_13-0-BT.GIF 13.1.6 Definition of SNR Because the SNR bands are given on all these plots and are used as a figure of merit, the method of computing the SNR is described below. Note that for all the data returned from the descent_analysis code, the perpendicular and parallel channels are already registered in angle and summed. For the unsummed data, the SNR is defined as follows. The signal electrons are computed as the data numbers from the SA minus the dark plus bias model, times the electrons per data number: IMAGE_224.GIF 1. This is computed for each pixel in each channel. The noise electrons are computed as the root-sum-square of the shot noise and the read noise, all in electrons: IMAGE_226.GIF 2. This is also computed for each pixel in each channel. Finally, the total SNR is computed for the sum of the perpendicular and parallel channels on a pixel by pixel basis as: IMAGE_228.GIF 3. For the summed data, the SNR is defined as follows. First, the dark plus bias model must be summed across columns. IMAGE_230.GIF 4. Then, the signal electrons are computed: IMAGE_232.GIF 5. Next, the noise electrons are computed, dividing by the square root of 6 because of the summing of 6 columns: IMAGE_234.GIF 6. Finally, the SNR is computed in two steps. The data sets which are returned as sums have SNR computed using equation 3, with signal and noise electrons as computed in equations 5 and 6. The data sets which are given in full format have the following equation, with the signal and noise electron definitions given in equations 1 and 2 above. IMAGE_236.GIF 7. 13.1.7 Conclusion - Relative Calibration The relative calibration of the Solar Aureole appears in many cases to be good to 1%. However, in some cases it decreases to 2% or even 3%. Because of the many ways to consider relative calibration, the results are given in a summary table below. Type of Data Relative Calibration Along: Accuracy Summed Blue Column 1% Summed Red Column 1% Un-summed Blue Column 2 Within noise Un-summed Red Column 2 Much within noise, some within 1%, all within 2% Un-summed Red Column 0 Within 3% Un-summed Blue Row 23 Most within 1%, some within 2% Un-summed Blue Row 48 Most within 1%, some within 2% Un-summed Red Row 23 1% Un-summed Red Row 48 2% The signal shape versus column number is reasonably well represented in all cases, but there appears to be a small systematic increase in intensity for high row numbers in the red. The derived signal shape versus row number can vary significantly from the true shape, even though each data point may be close to the noise band. This is largely due to the small number of data points over which to make a "shape". However, the variations are only on the order of 1% to 2%. The central rows of the red are within 1%, but the outer rows do not match the true shape as well, with accuracy of 2%. One reason the relative calibration could be not as good across rows as across columns is that the relative spectral response model and the absolute response model are created for given columns. Therefore, there is more analytic independence between columns than between rows. 13.1.8 Overall Conclusion The overall conclusion of this analysis is that the absolute calibration models for the Solar Aureole instrument are good to roughly 2%. The relative calibration can be much better, but not in every case. Overall, the relative calibration accuracy is within the 2% region in almost all cases. 13.2 Several Operational Points of Note 13.2.1 Software With the exception of the timing considerations discussed below, the collection of data from the Solar Aureole system is routine relative to other DISR sub- instruments. Data from the DISR instrument is collected in different types of data cycles, limited in time to about three minutes. These cycles vary throughout the descent and attempt to optimize the mix of vertical and azimuthal resolution in the measurements. However, the Solar Aureole measurements are taken the same way in each standard cycle through the descent, one near the sun and one away from the sun as described in the overview section. 13.2.2 Timing The timing of the Solar Aureole measurement taken near the sun is especially critical. It is desirable to collect a measurement as near to the sun as possible to determine the aureole characteristics of Titan as a function of altitude. However, the direct solar beam must be kept from the field. As shown in the drawings and discussion in the overview section, a Shadow Bar shields the SA field from the direct solar beam. In fact, this Shadow Bar defines the SA field of view in that direction. The near sun measurement must be made beginning at a probe azimuth of 2.5 degrees to get as close to the sun as possible with the direct beam out of the field. If the measurement starts at an azimuth less than 2.5 degrees, the direct beam will enter the field. The probe can spin at a rate up to 15 RPM. Therefore, the timing of this measurement collection is critical. Azimuthal knowledge is provided real time during the descent by data collected from the DISR Sun Sensor. For highest accuracy, the most recent Sun Sensor pulse is used to schedule the SA measurement near the sun. In the case of 15 RPM spin rate, a Sun Sensor central pulse could occur within 28 milliseconds of the time the SA measurement should begin. Therefore, the software allows for scheduling the SA measurement near the sun before the third pulse of a valid Sun Sensor triplet is received. The geometric field of view of the Solar Aureole is mapped in calibration relative to the Sun Sensor central slit to accommodate this measurement. The Shadow Bar knife edge is adjusted during calibration to form the SA field of view. In short, the mechanical and software links between the Sun Sensor, the Shadow Bar, and Solar Aureole are tight to allow for this near sun measurement for mapping the aureole at Titan. 13.2.3 Electronic Shutter Effect The electronic shutter effect is caused by the lack of a mechanical shutter in any of the optical systems that use the CCD detector. Rapid shifts of the charge from the imaging half of the chip to the memory half of the chip serve to begin and end the integration. This shift is rapid, but not instantaneous, so a small accumulation of charge occurs during the shift which must be removed from short integrations. The Solar Aureole data is shifted through the Visible Spectrometer focal plane on its way to the memory zone. This effect was studied and found to be negligible for the Solar Aureole because of the relative brightness of the SA signal compared to the dim visible spectra. 13.2.4 Lossless Compression The SA data is compressed in a way that produces no loss in information. The compression technique is completely invertible; i.e., an inverse algorithm applied to the compressed data will exactly reproduce the original data. The algorithms designated Psi-14 and Psi-f are used; these algorithms also use Psi-0 and Psi-1 and optionally Psi-2. DISR uses the 8-option Psi-14 noiseless data compressor with lambda equal to 0; hence, DISR does not use Psi-2. These compression schemes will reduce the volume of data to near the intrinsic entropy level of the data in the range of 0 to 5 bits per sample. These schemes are described in the Practical Universal Noiseless Coding paper by Rice. 13.2.5 Auto Exposure Control Each Solar Aureole measurement, after the first cycle is complete, has an exposure time determined from previous measurements and the probe spin rate. There are two streams of exposure time computation, one for the measurements near the sun, and one for the measurements away from the sun. The first cycle initializes the automatic exposure algorithms for both streams. Note that there is a single exposure time for all four SA channels, so while the exposure time may be optimal for one channel, the other three may be underexposed. The exposure times are limited so that the probe rotates no more than 3.5 degrees for near the sun measurements and no more than 20 degrees for away from the sun measurements. However, the exposures are also limited by the full well of the CCD detector. The auto exposure algorithm attempts to have a signal at half the full well without saturating the field. It does this as follows: e_opt=e_old*(R*F)/X where: F is the full scale data value (4095) R is the target full well scale factor (50%) X is the pixel value at the Nth percentile desired (97%) E_old is the exposure time for the data used in the statistics E_opt is the calculated optimum exposure time. The CCD minimum and maximum exposure times are 0 and 32 seconds with a resolution of 0.5 milliseconds. Additionally, conditions exist in the exposure time algorithm for hard over- or under-saturation cases. 13.2.6 Noise Model The sources of noise in the Solar Aureole include the read noise, the quantization noise, and the shot noise. The variance in the measured quantity is the sum of the variances of each of these three quantities. Of course, the dark current must be subtracted from the measurements made in the atmosphere, and any uncertainty in the dark values is also included in the uncertainty of the measured intensities. The noise model is dominated by the signal shot noise for all but the lowest signal levels. The read noise has been determined from prelaunch and inflight tests to be about 17 electrons. The quantization scale is 30 electrons/data number (DN). The read noise is thus about 0.57 DN. The quantization noise is 1/sqrt(12), or 0.289 DN. The shot noise, be it from dark current or signal, in measuring N electrons is sqrt(N) in electrons, or sqrt (DN*30)/30 DN. 13.2.7 Linearity The DISR Solar Aureole system has linear response over its entire range from 0 to 4095 data numbers. This section of the report is added solely for clarification. There were some tests performed (June 26, 1996) on different cabling configurations before delivery of DISR to ESA. Some configurations had non-linear response. The non-linear response resulted in SA pixels never achieving the full 4095 scale because they would saturate at lower values. The cabling used in the mission did not have this problem, and over 96% of the SA pixels hit 4095 at some point in the Titan descent (due to lack of real time azimuthal knowledge). 13.2.8 Self Bleedthrough On 2 August 1996, a test was performed to measure the bleedthrough from one Solar Aureole color to the other. The test was performed in the integrating sphere. First, a red filter was introduced after the light source so that the red channels would be bright, but the blue channels dark. Brights and darks were taken at 4 exposure times. The same series was repeated with a blue filter in the source. The measurement specifics are in the table below. Table 13-1 Self Bleedthrough Measurement Details Measurement # Shutter State Exposure Time (ms) Filter Saturation Notes 0 Open (bright) 0 Red 1 Open 65 Red 2 Open 650 Red Red Saturated 3 Open 1300 Red Red Saturated 4 Closed (dark) 0 Red 5 Closed 65 Red 6 Closed 650 Red 7 Closed 1300 Red 8 Open 0 Blue 9 Open 170 Blue 10 Open 1740 Blue Blue Saturated 11 Open 3480 Blue Blue Saturated 12 Closed 0 Blue 13 Closed 170 Blue 14 Closed 1740 Blue 15 Closed 3480 Blue The method of analysis is to compute the count rates by subtracting bright from dark and removing the electronic shutter effect using the 0 msec exposures. IMAGE_238.GIF A base count rate in the bright channels was generated to compare with the bleedthrough count rates. This base count rate was derived using the vertical channels (the central two on the CCD). The count rates using measurements 1 and 9 are used since the others are saturated or 0ms exposures. For the bleedthrough into the blue channels from the red, the base count rate is the rate derived using the above equation for measurement 1, averaged over columns 12 through 17. For the bleedthrough into the red channels from the blue, the base count rate is the rate for measurement 9, averaged over columns 6 through 11. The percent bleedthrough then is the ratio of the count rate in the dark channels to the base count rate in the nearest bright channel. The following is a plot of this bleedthrough for all three integration times for row 23. The +'s are for measurement 1 (with poor SNR); the *'s are for measurement 2; the diamonds are for measurement 3. FIG_13-0-BU.GIF Over all rows and columns, the largest percent bleedthrough is 3.1%. There are 13 occurrences out of 3*24*50=3600 which have percent bleedthrough between 1 and 1.5%. One occurrence is 2.3%, and one is 3.1%. The remaining bleedthrough percentages are under 1%. The larger bleedthroughs occur in the blue vertical column 0 (column 6 in the plots) and the bottom rows of both red channels. The mean percent bleedthrough was computed as well. This figure of merit is the percent bleedthrough averaged over the rows. It is plotted below with the same legend as the previous plot. FIG_13-0-BV.GIF One can see that there is a systematic bleedthrough effect. The structure of this effect is not indicative of the clearing of the serial register, and it appears optical in nature. However, the largest mean bleedthrough is well under 0.5% and can be excluded from any further analysis. 13.3 Geometry and Field of View Derivations 13.3.1 Conversion between Row, Column and DISR Zenith, Azimuth The zenith and azimuth angles on the sky for each pixel in the 24-column by 50- row array of the Solar Aureole camera was determined by mounting the sensor head on the altitude-azimuth mount in the calibration lab with the system illuminated by light from the collimator. The collimation of the input beam was significantly better than the 1-degree spacing of the pixels of the Solar Aureole array. The sensor head was rotated through various azimuth and zenith angles, and data was recorded that showed the point of light from the collimator in each of the four channels of the Solar Aureole system. We determined the transformation from row and column to zenith and azimuth for each channel of the Solar Aureole system by comparing the centroid of light in row and column on the detector array with the azimuth and zenith at which the sensor head was pointed Most of the transformation from row and column to zenith and azimuth can be determined by adjusting the constants in the pointing of the Solar Aureole system relative to the coordinate system of the sensor head. The field of view of the Solar Aureole camera is centered at a zenith angle of about 50 degrees. The center of the field of view at this zenith angle is tipped by six degrees toward increasing azimuth, as seen from the drawings for the fiber optic conduit housing shown in Figure 13-2 . In the DISR imaging systems, where the angular resolution is up to a factor 15 higher than in the Solar Aureole system, distortions in the fiber optic conduit caused negligible distortions in the images. Thus, there is hope that a simple transformation from row and column to zenith and angle can be found by simply adjusting the pointing angles of the Solar Aureole system relative to the basic coordinate system of the sensor head. It is also possible that an additional factor will be necessary to account for the distortion of the field of view of the Solar Aureole optical system, especially in its long direction, where it extends some 50 degrees. We begin by considering the pointing of the Solar Aureole system as resulting from three separate rotations of coordinates from the basic coordinate system of the sensor head. Let us consider the basic right-handed coordinate system as one in which the z axis points up from the base of the instrument with the y axis pointing toward the direction of zero azimuth. (This system is fixed relative to the DISR sensor head. We will later consider the problem of accommodating situations where the Huygens probe is tipped or tilted relative to the local level.) In this DISR-fixed system, a vector pointing toward a particular zenith angle and azimuth angle will have x, y, z components given by x = -sin(Zenith angle) * sin(Azimuth angle) y = sin(Zenith angle) * cos(Azimuth angle) 15. z = cos(Zenith angle) FIG_13-1 Figure 13-1 Drawing of the fiber optic conduit showing that the face of the surface to which the Solar Aureole optical input optics are attached is tipped up by 40 degrees from horizontal, 50 degrees from vertical. FIG_13-2 Figure 13-2 Drawing along section V-V shown in Figure 5-1 that shows that the surface to which the input optics of the Solar Aureole system is fastened is tipped by 6 degrees in the direction of increasing azimuth. The first rotation (to the x', y', z' system) is shown in Figure 13-3 where the tilt of the axis of the Solar Aureole system is centered at 50 degrees zenith angle. In this system, x', y', and z' can be determined from x, y, and z by x' = x, y' = sin(a0) * y + cos(a0) * z, 16. z' = -cos(a0) * y + sin(a0) * z, a = alpha in figure 13-3 where a0 = 50 degrees is the zenith angle of the center of the Solar Aureole array. FIG_13-3 Figure 13-3 This figure shows the relationship of the x, y, z coordinate system of the sensor head to the x', y', z' system in which the y' axis is pointed at the zenith angle of the center of the array (50 degrees). Next we must account for the rotation by 6 degrees of the center of the Solar Aureole array toward the direction of increasing azimuth angle. The relationship of the rotated x", y", z" system after this rotation is performed to the x', y', z' system is shown in Figure 13-4 . The coordinates of a point in the x", y", z" system is given by x" = x' * cos(b0) + y' * sin(b0) y" = -x' * sin(b0) + y' * cos(b0) 17. z" = z' b = beta in figure 13-4 where b0 is the angle (6 degrees) of rotation toward the direction of increasing azimuth angle. FIG_13-4 Figure 13-4 This figure shows the relationship of the x", y", z" system after rotation by 6 degrees in the direction if increasing azimuth to the x', y', z' system. Finally, the optical assembly including the lenses, filters, and polarizers of the Solar Aureole system are bolted to the surface that has been tipped by angles a0 ,b0 from the sensor head coordinates system. When this assembly is bolted onto this surface, there is a possibility that the optical assembly will be rotated by a small amount about a line perpendicular to this surface. To account for this possibility, we permit a rotation about the y" axis by a small angle g. The relationship of this coordinate system x"', y"', z"' to the x", y", z" system is shown in Figure 13-5 . The transformation from the double primed system to the triple primed system is given by x"'= x" * cos(g) - z" * sin(g) y""=y" 18. z"" = x" * sin(g) + z" * cos(g) g = gama in figure 13-5 Here g is positive for a counterclockwise rotation looking at the instrument along the y" axis. FIG_13-5 Figure 13-5 The relationship of the x"', y"', z"' system to the x", y", z" system is shown in this figure. The transformation consists of a small rotation about the y" axis as shown. In the new triple-primed system, the center of the solar array field of view is on the equator of a sphere defined by the x'"-y'" plane. Different columns in the array are identified with different longitudes on this sphere. Different rows are identified with different latitudes on this sphere, with the pole of the sphere pointing in the z'" direction. FIG_13-6 Figure 13-6 The coordinates Da and Db form a latitude-longitude grid in the x"", y"', z"' system, where the pole of the system is the +z"' axis, the Da represents increasing southern latitude, and Db represents the direction of increasing longitude. Before we convert the angles Da and Db to row and column, we permit a stretch of the angular distance from the center of the array by an amount proportional to the cube of the angular distance from the center of the array. That is, we assume that the center of the array is at the location given by angles Dac and Dbc. The vector in this direction thus has components x"'c = -cos(Dac ) * sin(Dbc) y"'c = cos(Dac ) * cos(Dbc) 19. z"'c = -sin(Dac) The angular distance, d, of a point given by x"', y"', z"" from the center of the array is d = acos (x'" * x"'c + y'" * y"'c + z"' * z"'c) 20. This angular distance needs to be increased by an amount proportional to the cube of d. The direction of the increase is along the great circle from the center of the array to the point x"', y"', z"'. A vector perpendicular to this direction can be formed by computing the cross product of the vector to the center of the array and the x"', y"', z"' vector. This vector Vnx, Vny, Vnz is given by Vnx = (y"'c * z"' - z"'c * y"') Vny = (-x"'c * z"' + z"'c * x"') 21. Vnz = (x"'c * y"' - y"'c * x"') This vector needs to be normalized to unit length by setting Wnx = Vnx/(Vnx2+Vny2+Vnz2) Wny = Vny/(Vnx2+Vny2+Vnz2) 22. Wnz = Vnz/(Vnx2+Vny2+Vnz2) The vector in the direction of the increase is given by the cross product of the vector Wn with the vector x"', y"', z"' or Delta x = Wy * z"' - Wz * y"' Delta y = -Wx * z"' + Wz * x"' 23. Delta z = Wx * y"' - Wy * x"' Thus the stretched vector xs"', ys"', zs"' is given by adding the vector Delta times the cubic coefficient times the angular distance d3 to the vector x"', y"', z"'. This gives xs"' = x"' + tan[(d/20)^3 * CC] * Delta x ys"' = y"' + tan[(d/20)^3 * CC] * Delta y 24. s"' = z"' + tan[(d/20)^3 * CC] * Delta z The value CC is the size of the cubic coefficient per 20 degrees of distance off axis. This vector xs"', ys"', zs"' must be normalized to make it a unit vector by dividing each component by the magnitude of the vector to make components xsn"', ysn"', and zsn"'. Finally, the vector xsn"', ysn"', zsn"' can be projected onto a plane tangent to the sphere perpendicular to the y"' axis. We first evaluate the stretched values of a and b by as = - arc sin(zs"') 25. bs = atan2(ys"', -xs"') 26. This projection requires the scale factor of the optical system on axis, sc pixels/degree as well as the value of the central column, cc, and central row, cr. The final column and row numbers are given by Column = cc + tan(bs)/tan(1/sc) 27. Row = cr + tan(as)/tan(1/sc) 28. The same process can be reversed to transform from given column and row number to the zenith angle and azimuth angle of a particular pixel. The parameters required are collected into the table below. Table 13-2 Parameters of geometrical transformation of SA observations Color Blue Blue Red Red Direction of E vector Horizontal Vertical Vertical Horizontal Columns in SA read 0-5 6-11 12-17 18-23 Columns in full frame 40-45 31-36 23-28 14-19 Definition Parameter Central row cr 23.432 25.063 25.862 23.943 Central column cc 3.331 8.343 14.996 21.472 Scale factor sc 0.999 1.009 1.028 1.030 in pixels/deg Rotation angle Lambda 0.69 -0.90 -1.52 1.65 Cubic Coeff CC -0.0196 -0.022 -0.019 -0.020 per 20 degs. Center of CC Alpha_c -0.10 -0.60 -0.05 -1.00 in Alpha Center of CC Beta_c 0.0 0.0 0.0 0.0 in Beta rms dev. in cols 0.069 0.120 0.082 0.087 rms dev in rows 0.110 0.145 0.075 0.090 To make the computations in the reverse direction, from row and column to azimuth and zenith angle, we begin by finding the stretched values as and bs from the observed row and column by bs = atan[(column - cc) * tan(1/sc)] 29. as = atan[(row-cr) * tan(1/sc)] 30. The stretched vector to the point in the triple primed system is then xs"' = -cos(as) * sin(bs) ys"' = cos(as) * cos(bs) 31. zs"' = sin(as) We next must find the vector in the triple-primed system without the cubic stretch. To do this, we must find the components of the unit vector along which the change in position will be applied. This direction is given by a vector along the great circle connecting the center of the aberrations and the stretched vector. This direction is given by taking the cross product of the stretched vector with the vector in the direction of the center of the aberrations, normalizing it, and taking the cross product of this vector with the stretched vector. The first cross product vector is given by Vxn = (ys"' * zc"' - zs"' * yc"') Vyn = (-xs"' * zc"' + zs"' * zc"') 32. Vzn = (xs"' * yc"' - ys"' * xc"') This vector can be normalized to give Wxn = Vxn/(Vxn2 + Vyn2 + Vzn2) Wyn = Vyn/(Vxn2 + Vyn2 + Vzn2) 33. Wzn = Vzn/(Vxn2 + Vyn2 + Vzn2) The vector along the direction of the change to the stretched vector is given by the cross product of this vector with the stretched vector, or Delta x* = Wyn * zs"' - Wzn * y"' Delta y* = -Wxn * zs"' + Wzn * x"' 34. Delta z* = Wxn * ys"' - Wyn * xs"' The magnitude of the change is related to the angular distance between the stretched vector and the center of the field of aberrations given by equation 19. This angular distance is given by d* = acos(xs"' * x"'c + ys"' * y""c + zs"' * z"'c) 35. The cubic coefficient must be applied to the angular distance between the center of the array and the unstretched vector (d in equation 20.), not the angular distance between the center of the array and the stretched vector (d* in equation 35.). The relation between these two angles is given by the cubic expression d* = d - atan((d/20)^3 * CC) 36. In order to proceed in the reverse direction, we need an approximation for the difference between the unstretched and the stretched angular distances. The zero-level approximation is to take the unstretched distance as the stretched distance in the expression for the difference between these angular distances, or (d-d*)0 = atan((d*/20)^3 * CC) 37. The higher-level approximations are given by (d-d*)n = atan[{d*+(d-d*)n-1}/20)^3 * CC] 38. We continue to the third-order approximation, where the error is less than 0.01 degrees. The unstretched vector in the triple primed system is then x"' = xs"' + tan[({d*+(d-d*)^3}/20)^3 * CC] * Delta x* y"' = ys"' + tan[({d*+(d-d*)^3}/20)^3 * CC] * Delta y* 39. z"' = zs"' + tan[({d*+(d-d*)^3}/20)^3 * CC] * Delta z* This vector must be normalized to unit length to give the vector xn"', yn"', zn"' to the point in the triple primed system. Now this vector can be rotated from the triple primed system to the double primed system according to x" = xn"' * cos(g) - zn"' * sin(g) y" = yn"' 40. z" = xn"' * sin(g) + zn"' * cos(g) The vector can next be rotated from the double primed system to the primed system, and then to the unprimed system as follows. x' = x" * cos (b0) - y" * sin (b0) y' = x" * sin(b0) + y" * cos (b0) 41. z' = z" and x = x' y = y' * sin(a0) - z' * cos(a0) 42. z = y' * cos(a0) + z' * sin(a0) Finally, the azimuth and zenith angle of the point can be obtained from Zenith = acos(z) 43. Azimuth = atan2(y, -x) 44. In order to determine the constants required, we mounted the sensor head on the altitude-azimuth mount, illuminated the sensor head with collimated light, and recorded images in the Solar Aureole system for a range of zenith and azimuth angles of the incoming beam relative to the basic coordinate system of the sensor head. We then subtracted the dark current from each image and divided the net counts by the integration time and the pattern of absolute responsivity of each pixel in the Solar Aureole array obtained from the reduction of the absolute responsivity data shown in a section below. We next found the centroid of light in row and column for each azimuth and zenith angle at which the sensor head was illuminated. The data for each of the four SA channels is given in Table 13-3 through Table 13-6 . We next adjusted the pointing parameters to minimize the residuals between the observed location of the centroids of light from each measurement with the row and column number computed by the model equations describing the geometry above. Note that each of the parameters has a unique effect on the residuals. If the central row or column number is incorrect, the entire pattern of residuals is shifted up or down from zero. When the rotation angle g is changed, the pattern of column residuals rotates away from a horizontal line in the residual plot, either sloping up with column number or down with column number rather than remaining horizontal. When the scale factor is changed, the pattern of residuals in a plot of row residual plotted versus row is not flat near the central row, but slopes either upward or downward with row. When the cubic parameter for optical aberrations is changed, the row residuals at very small and very large row numbers move upward or downward by large amounts. Finally, the center of the aberrations in Da increases the residual at one end of the array while decreasing the residual at the other end. The value of the cubic coefficient and the direction of the center of the aberrations must both be adjusted together to minimize the residuals at both the low row and high row number ends of the array. When all six parameters are optimally adjusted, the root mean square residuals in both row and column can be decreased to about 0.1 pixel. This is about the accuracy to which the centroid algorithm gives the location of the center of light from the original data. Table 13-3 Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Azimuth Zenith Observed Observed Model Colmn Model Row Column Err Row Err Column Row 3.00 70.00 0.71 42.95 0.752 42.946 0.042 -0.004 4.00 70.00 1.76 42.91 1.687 42.912 -0.073 0.002 5.00 70.00 2.61 42.83 2.622 42.861 0.012 0.031 6.00 70.00 3.47 42.77 3.557 42.794 0.087 0.024 7.00 70.00 4.40 42.71 4.491 42.712 0.091 0.002 6.00 71.00 3.54 43.95 3.639 43.714 0.099 -0.236 6.00 71.50 3.76 44.09 3.681 44.170 -0.079 0.080 6.00 72.00 3.67 44.74 3.722 44.623 0.052 -0.117 6.00 72.50 3.85 45.01 3.762 45.073 -0.088 0.063 6.00 73.00 3.81 45.47 3.803 45.520 -0.007 0.050 6.00 73.50 3.90 45.98 3.844 45.964 -0.056 -0.016 6.00 74.00 3.90 46.23 3.885 46.404 -0.015 0.174 6.00 74.50 3.94 46.92 3.925 46.842 -0.015 -0.078 6.00 75.00 3.96 47.14 3.966 47.275 0.006 0.135 6.00 75.50 3.97 47.94 4.006 47.705 0.036 -0.235 6.00 76.00 3.98 48.09 4.046 48.131 0.066 0.041 10.00 27.00 2.04 0.77 2.073 0.873 0.033 0.103 10.00 27.50 2.06 1.22 2.135 1.317 0.075 0.097 10.00 28.00 2.13 1.84 2.197 1.763 0.067 -0.077 10.00 28.50 2.15 2.03 2.259 2.213 0.109 0.183 10.00 29.00 2.23 2.59 2.322 2.666 0.092 0.076 10.00 29.50 2.30 3.01 2.384 3.121 0.084 0.111 10.00 30.00 2.43 3.33 2.447 3.579 0.017 0.249 10.00 30.50 2.56 4.01 2.510 4.039 -0.050 0.029 4.00 60.00 0.98 33.38 1.005 33.318 0.025 -0.062 5.00 60.00 1.93 33.37 1.868 33.269 -0.062 -0.101 6.00 60.00 2.74 33.22 2.731 33.207 -0.009 -0.013 7.00 60.00 3.55 33.10 3.593 33.134 0.043 0.034 8.00 60.00 4.41 33.04 4.455 33.050 0.045 0.010 5.00 50.00 1.02 23.36 23.351 -0.009 6.00 50.00 1.99 23.35 1.924 23.295 -0.066 -0.055 7.00 50.00 2.80 23.18 2.686 23.230 -0.114 0.050 8.00 50.00 3.34 23.16 3.448 23.156 0.108 -0.004 9.00 50.00 4.16 23.05 4.209 23.074 0.049 0.024 5.00 40.00 0.60 13.40 0.515 13.435 -0.085 0.035 6.00 40.00 1.04 13.37 1.156 13.383 0.116 0.013 7.00 40.00 1.85 13.34 1.797 13.325 -0.053 -0.015 8.00 40.00 2.53 13.23 2.437 13.261 -0.093 0.031 9.00 40.00 3.02 13.24 3.076 13.191 0.056 -0.049 10.00 40.00 3.84 13.03 3.714 13.115 -0.126 0.085 11.00 40.00 4.34 12.99 4.351 13.033 0.011 0.043 7.00 30.00 1.01 3.91 0.957 3.753 -0.053 -0.157 8.00 30.00 1.52 3.92 1.454 3.699 -0.066 -0.221 9.00 30.00 2.00 3.85 1.951 3.641 -0.049 -0.209 10.00 30.00 2.57 3.81 2.447 3.579 -0.123 -0.231 11.00 30.00 3.00 3.66 2.942 3.513 -0.058 -0.147 12.00 30.00 3.49 3.45 3.436 3.443 -0.054 -0.007 13.00 30.00 4.00 3.24 3.929 3.370 -0.071 0.130 14.00 30.00 4.37 3.17 4.420 3.293 0.050 0.123 Note: Model and residual values are omitted for pixels near the edge of the array. Table 13-4 Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Azimuth Zenith Observed Observed Model Colmn Model Row Column Err Row Err Column Row 5.00 70.00 7.02 44.18 7.097 44.394 0.077 0.214 6.00 70.00 8.00 44.16 8.032 44.358 0.032 0.198 7.00 70.00 8.99 44.13 8.967 44.306 -0.023 0.176 8.00 70.00 9.99 44.06 9.901 44.237 -0.089 0.177 6.00 71.00 8.03 45.14 8.089 45.251 0.059 0.111 6.00 71.50 8.04 45.84 8.118 45.692 0.078 -0.148 6.00 72.00 8.08 46.05 8.146 46.130 0.066 0.080 6.00 72.50 8.07 46.86 8.174 46.563 0.104 -0.297 6.00 73.00 8.11 47.02 8.203 46.993 0.093 -0.027 6.00 73.50 8.14 47.48 8.231 47.418 0.091 -0.062 6.00 74.00 8.22 47.98 8.259 47.839 0.039 -0.141 6.00 74.50 8.25 48.23 8.288 48.255 0.038 0.025 10.00 25.50 7.43 0.67 7.562 1.057 0.132 0.387 10.00 26.00 7.57 1.21 7.611 1.485 0.041 0.275 10.00 26.50 7.69 1.95 7.660 1.917 -0.030 -0.033 10.00 27.00 7.75 2.22 7.710 2.353 -0.040 0.133 10.00 27.50 7.88 2.97 7.759 2.793 -0.121 -0.177 10.00 28.00 7.89 3.11 7.808 3.236 -0.082 0.126 10.00 28.50 7.91 3.86 7.858 3.684 -0.052 -0.176 10.00 29.00 7.97 4.01 7.908 4.134 -0.062 0.124 10.00 29.50 7.96 4.55 7.958 4.589 -0.002 0.039 10.00 30.00 7.99 5.00 8.008 5.046 0.018 0.046 10.00 30.50 7.99 5.54 8.058 5.506 0.068 -0.034 5.00 60.00 6.88 34.97 6.596 34.908 -0.284 -0.062 6.00 60.00 7.81 34.97 7.466 34.872 -0.344 -0.098 7.00 60.00 8.45 34.88 8.336 34.824 -0.114 -0.056 8.00 60.00 9.07 34.60 9.205 34.764 0.135 0.164 9.00 60.00 10.01 34.55 10.074 34.691 0.064 0.141 6.00 50.00 6.97 24.84 6.926 24.885 -0.044 0.045 7.00 50.00 7.93 24.80 7.698 24.841 -0.232 0.041 8.00 50.00 8.73 24.85 8.469 24.788 -0.261 -0.062 9.00 50.00 9.10 24.73 9.239 24.727 0.139 -0.003 10.00 50.00 10.00 24.71 10.008 24.657 0.008 -0.053 7.00 40.00 7.01 14.92 7.077 14.809 0.067 -0.111 8.00 40.00 7.96 14.96 7.725 14.763 -0.235 -0.197 9.00 40.00 8.11 14.94 8.372 14.711 0.262 -0.229 10.00 40.00 9.00 14.88 9.018 14.653 0.018 -0.227 11.00 40.00 9.69 14.62 9.664 14.589 -0.026 -0.031 12.00 40.00 10.15 14.30 10.308 14.519 0.158 0.219 8.00 30.00 6.94 5.14 7.007 5.135 0.067 -0.005 9.00 30.00 7.51 5.15 7.508 5.092 -0.002 -0.058 10.00 30.00 7.98 5.08 8.008 5.046 0.028 -0.034 11.00 30.00 8.44 5.05 8.508 4.995 0.068 -0.055 12.00 30.00 8.99 5.00 9.006 4.942 0.016 -0.058 13.00 30.00 9.43 4.99 9.503 4.884 0.073 -0.106 14.00 30.00 9.98 4.99 9.999 4.823 0.019 -0.167 Table 13-5Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Azimuth Zenith Observed Observed Model Colmn Model Row Column Err Row Err Column Row 5.00 70.00 13.53 45.78 13.492 45.856 -0.038 0.076 6.00 70.00 14.47 45.85 14.459 45.828 -0.011 -0.022 7.00 70.00 15.29 45.78 15.425 45.784 0.135 0.004 8.00 70.00 16.45 45.59 16.390 45.723 -0.060 0.133 6.00 71.00 14.48 46.75 14.507 46.785 0.027 0.035 6.00 71.50 14.53 47.27 14.531 47.259 0.001 -0.011 6.00 72.00 14.50 47.62 14.555 47.731 0.055 0.111 6.00 72.50 14.54 48.15 14.579 48.200 0.039 0.050 10.00 25.50 14.52 1.09 14.459 1.191 -0.061 0.101 10.00 26.00 14.57 1.45 14.505 1.644 -0.065 0.194 10.00 26.50 14.57 2.10 14.551 2.100 -0.019 0.000 10.00 27.00 14.59 2.51 14.597 2.560 0.007 0.050 10.00 27.50 14.64 2.97 14.643 3.023 0.003 0.053 10.00 28.00 14.64 3.48 14.689 3.488 0.049 0.008 10.00 28.50 14.75 3.94 14.735 3.957 -0.015 0.017 10.00 29.00 14.71 4.45 14.782 4.428 0.072 -0.022 10.00 29.50 14.82 4.82 14.828 4.902 0.008 0.082 10.00 30.00 14.78 5.38 14.874 5.379 0.094 -0.001 10.00 30.50 14.91 5.82 14.921 5.858 0.011 0.038 5.00 60.00 13.16 36.05 13.100 35.924 -0.060 -0.126 6.00 60.00 13.98 36.03 13.991 35.896 0.011 -0.134 7.00 60.00 14.81 35.93 14.881 35.856 0.071 -0.074 6.00 50.00 13.53 25.62 13.554 25.665 0.024 0.045 7.00 50.00 14.42 25.61 14.341 25.628 -0.079 0.018 8.00 50.00 15.30 25.64 15.127 25.583 -0.173 -0.057 9.00 50.00 16.05 25.59 15.912 25.529 -0.138 -0.061 6.00 40.00 13.20 15.42 13.158 15.438 -0.042 0.018 7.00 40.00 13.67 15.44 13.819 15.404 0.149 -0.036 8.00 40.00 14.48 15.44 14.480 15.365 0.000 -0.075 9.00 40.00 15.27 15.27 15.365 0.095 10.00 40.00 15.74 15.32 15.799 15.267 0.059 -0.053 7.00 30.00 13.38 5.52 13.333 5.493 -0.047 -0.027 8.00 30.00 13.66 5.53 13.847 5.459 0.187 -0.071 9.00 30.00 14.51 5.50 14.361 5.421 -0.149 -0.079 10.00 30.00 14.80 5.43 14.874 5.379 0.074 -0.051 11.00 30.00 15.56 5.44 15.387 5.333 -0.173 -0.107 12.00 30.00 15.84 5.40 15.898 5.283 0.058 -0.117 Note: The entry in red is believed to be in error, and has not been used in computing the residual in column. Table 13-6 Observed Centroids in Column and Row when the Solar Aureole was Stimulated by a Point Source at Various Azimuth and Zenith angles Azimuth Zenith Observed Observed Model Colmn Model Row Column Err Row Err Column Row 3.00 70.00 18.90 43.93 19.169 43.893 0.269 -0.037 4.00 70.00 20.05 43.90 20.124 43.842 0.074 -0.058 5.00 70.00 21.05 43.83 21.080 43.774 0.030 -0.056 6.00 70.00 22.01 43.79 22.035 43.690 0.025 -0.100 7.00 70.00 22.96 43.49 43.588 0.098 6.00 71.00 22.23 44.72 22.135 44.611 -0.095 -0.109 6.00 71.50 22.22 45.15 22.185 45.067 -0.035 -0.083 6.00 72.00 22.29 45.55 22.234 45.520 -0.056 -0.030 6.00 72.50 22.32 46.07 22.284 45.969 -0.036 -0.101 6.00 73.00 22.37 46.44 22.333 46.414 -0.037 -0.026 6.00 73.50 22.42 46.91 22.382 46.856 -0.038 -0.054 6.00 74.00 22.45 47.35 22.431 47.294 -0.019 -0.056 6.00 74.50 22.48 47.84 22.479 47.728 -0.001 -0.112 10.00 28.00 19.86 1.34 19.921 1.450 0.061 0.110 10.00 28.50 19.94 1.89 19.993 1.920 0.053 0.030 10.00 29.00 20.04 2.30 20.066 2.393 0.026 0.093 10.00 29.50 20.12 2.83 20.139 2.869 0.019 0.039 10.00 30.00 20.08 3.36 20.212 3.347 0.132 -0.013 10.00 30.50 20.31 3.83 20.285 3.828 -0.025 -0.002 5.00 60.00 20.03 33.99 20.138 34.061 0.108 0.071 6.00 60.00 21.03 33.92 21.024 33.984 -0.006 0.064 7.00 60.00 21.99 33.82 21.909 33.894 -0.081 0.074 8.00 60.00 22.59 33.73 33.792 0.062 9.00 60.00 22.97 33.52 33.678 0.158 6.00 50.00 19.92 23.77 20.019 23.825 0.099 0.055 7.00 50.00 20.86 23.70 20.804 23.745 -0.056 0.045 8.00 50.00 21.62 23.67 21.588 23.657 -0.032 -0.013 9.00 50.00 22.35 23.58 22.370 23.559 0.020 -0.021 10.00 50.00 22.71 23.41 23.453 0.043 11.00 50.00 22.99 23.36 23.338 -0.022 7.00 40.00 19.67 13.43 19.712 13.516 0.042 0.086 8.00 40.00 20.36 13.37 20.372 13.438 0.012 0.068 9.00 40.00 21.13 13.28 21.031 13.354 -0.099 0.074 10.00 40.00 21.88 13.18 21.689 13.264 -0.191 0.084 11.00 40.00 22.56 13.06 22.346 13.168 -0.214 0.108 12.00 40.00 22.81 12.82 13.065 0.245 8.00 30.00 19.12 3.65 19.186 3.492 0.066 -0.158 9.00 30.00 19.71 3.53 19.699 3.422 -0.011 -0.108 10.00 30.00 20.10 3.45 20.212 3.347 0.112 -0.103 11.00 30.00 20.66 3.37 20.723 3.269 0.063 -0.101 12.00 30.00 21.30 3.24 21.234 3.186 -0.066 -0.054 13.00 30.00 21.76 3.18 21.743 3.099 -0.017 -0.081 14.00 30.00 22.33 3.09 22.250 3.009 -0.080 -0.081 15.00 30.00 22.66 2.89 2.914 0.024 16.00 30.00 22.89 2.69 2.816 0.126 17.00 30.00 22.99 2.91 2.714 -0.196 Note: Model and residual values are omitted for pixels near the edge of the array. FIG_13-7-A.GIF FIG_13-7-B.GIF FIG_13-7-C.GIF FIG_13-7-D.GIF Figure 13-7 The observed centroid in row and column is plotted by blue circles, while the model location of each point is plotted by red squares for each of the points observed in the four channels of the Solar Aureole system. FIG_13-8.GIF Figure 13-8 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 0 to 5. The rms residual is about 0.07 in columns and 0.11 in row. FIG_13-9.GIF Figure 13-9 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 6 to 11. The rms residual is about 0.12 in columns and 0.15 in row. FIG_13-10.GIF Figure 13-10 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 12 to 17. The rms residual is about 0.08 in columns and 0.08 in row. FIG_13-11.GIF Figure 13-11 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed row for the model to the Solar Aureole geometry for columns 18 to 23. The rms residual is about 0.09 in columns and 0.09 in row. FIG_13-12.GIF Figure 13-12 The pattern of residuals in row (red squares) and column (blue circles) is plotted versus observed column for the model to the Solar Aureole geometry for columns 18 to 23. The rms residual is about 0.08 in columns and 0.09 in row. Note that the points with centroids at observed columns within 0.5 column of the edge of the array have been omitted because of the systematic errors in locating the centroid of points where the peak of light is within 0.5 pixel of the edge of the array. 13.3.2 Conversion between DISR Zenith, Azimuth to True Zenith, Azimuth In the DISR x, y, z coordinate system, z points upward from the baseplate of the instrument, and the sun is in the y-z plane. The DISR instrument (and the entire probe) is constrained by the parachute harness to rotate about the DISR z axis. The DISR measures the solar zenith angle of the sun from the DISR z axis, SZADISR, on every rotation of the probe. The vector to the sun in the x, y, z system is given by xsun = 0 ysun = sin(SZADISR) 45. sun = cos(SZADISR) Now suppose that the DISR z axis does not point vertically upward, but that the probe is tilted. Let the vector pointing vertically upward be at an angle q1 in the y-z plane (positive measured from the DISR z axis away from the vector to the sun), and at an angle q2 perpendicular to the plane containing the z axis and the vector to the sun. Let q2 be positive in the direction of decreasing azimuth. Now the vector to the vertical in the x, y, z system is given by xv = -sin(q2) yv = -cos(q2) * sin(q1) 46. zv = cos(q2) * cos(q1) We now define a new coordinate system x*, y*, z* where z* points vertically upward and the vector to the sun lies in the y*-z* plane. In this system, a unit vector i* in the direction x* is given by the (normalized) cross product of the vector to the sun and the vector to the vertical. The unit vector k* along the z* direction is given by the vertical vector. That is, i* = (ysun * xv - zsun * yv)/sin(SZADISR) i +(-xsun * zv + zsun * xv)/sin(SZADISR) j 47. +(xsun * yv - ysun * xv)/sin(SZADISR) k where i, j, k are unit vectors along the directions of the x, y, and z axes. Similarly, a unit vector j* along the y* axis is given by the cross product of the vertical vector crossed with i*. That is j* = (yv i*x - zv i*y) i + (-xv i*z + zv i*x) j 48. + (xv i*y - yv i*x) k Finally, the unit vector k* along the direction z* is given by the vertical vector, k* = xv i +yv j +zv k 49. Now any vector x i +y j +z k can be converted to the vector in the x*, y*, z* system by the use of equations 47. through 49., or x* = (ysun * xv - zsun * yv) x +(-xsun * zv + zsun * xv) y +(xsun * yv - ysun * xv) z y* = (yv i*x - zv i*y) x 50. + (-xv i*z + zv i*x) y + (xv i*y - yv i*x) z z* = xv x +yv y +zv z The true zenith and azimuth angles to the point at coordinates x, y, z can now be evaluated as Zenith Angletrue = acos(z*) 51. Azimuth Angletrue = atan2(y*, -x*) 52. The reverse transformation from the true zenith and angles on the sky to the x, y, z coordinates in the tipped DISR coordinate system is also possible given the relations above. Here we begin by determining the x*, y*, z* coordinates of the point at true zenith and true azimuth angle. We have x* = -sin (Zenith Angletrue) sin(Azimuth Angletrue) y* = sin(Zenith Angletrue) cos(Azimuth Angletrue) 53. z* = cos(Zenith Angletrue) These coordinates can be transformed to the x, y, z system by collecting the components from the relations in equations 47. through 49.. We have x = x* (ysun * xv - zsun * yv)/sin(SZADISR) +y*(yv i*x - zv i*y) 54. +z*xv y = x*(-xsun * zv + zsun * xv)/sin(SZADISR) +y*(-xv i*z + zv i*x) 55. +z*yv z = x*(xsun * yv - ysun * xv)/sin(SZADISR) +y*(-xv i*z + zv i*x) 56. +z*zv Now the zenith angle and the azimuth angle in the DISR coordinates are given by Zenith AngleDISR=acos(z) 57. Azimuth AngleDISR = atan2(y, -x) 58. 13.4 Relative Spectral Response 13.4.1 Transmission of Filters as Functions of Temperature The Solar Aureole system includes interference filters to limit the passband of the red and blue channels. The interference filters are at the very front of the optical system, close to the front windows of the sensor head. In this location, they will get very cold during the descent into the atmosphere of Titan. In our laboratory measurements of the relative spectral response of the entire Solar Aureole instrument on the flight model we were able to vary the temperature of the focal plane over the complete range of temperatures expected during the Titan entry, but we were not able to independently collect data with the filters near the front windows at the temperatures they will have during entry. Therefore, we arranged a special test after launch in which the transmissions of filters from the flight lot were measured over a wide range of temperature. Co- Investigator Bernard Schmitt made these measurements in his laboratory in Grenoble, France. A beam of about f/3 rather than collimated light was used to measure the transmission. The measurements of the red Solar Aureole filter are contained in Table 13-7 below at temperatures of 70 K, 180 K, and 301 K. The measured transmissions of the filter at the three temperatures are plotted in Figure 13-13 below. Fortunately, the plot shows that very little shift in the response of the filter occurs over this range of temperatures. Figure 13-14 shows the deviations in the transmissions at each temperature from the average of the transmission measurements at the three temperatures. We see that the deviations at any temperature are less than 1% of the peak transmission of the filter at all wavelengths, and are much less than this at most wavelengths. Hence, in considering the variations in the relative spectral response of the Solar Aureole instrument, the variation in response of the CCD detector will provide the major effect, and this effect was well measured in our laboratory before delivery. Table 13-7 Transmission of the Red Solar Aureole Filter at Three Temperatures Wavelength Average sigma average (nm) 70 K 180 K 301 K 850 0.00064 0.00076 0.00050 0.00063 0.00008 852 0.00096 0.00084 0.00063 0.00081 0.00010 854 0.00080 0.00101 0.00098 0.00093 0.00007 856 0.00115 0.00103 0.00100 0.00106 0.00004 858 0.00135 0.00115 0.00099 0.00117 0.00010 860 0.00155 0.00144 0.00114 0.00138 0.00012 862 0.00148 0.00173 0.00160 0.00160 0.00007 864 0.00181 0.00185 0.00161 0.00176 0.00007 866 0.00210 0.00197 0.00188 0.00198 0.00006 868 0.00251 0.00258 0.00230 0.00246 0.00008 870 0.00298 0.00300 0.00273 0.00290 0.00009 872 0.00363 0.00370 0.00330 0.00354 0.00012 874 0.00447 0.00454 0.00437 0.00446 0.00005 876 0.00598 0.00577 0.00553 0.00576 0.00013 878 0.00774 0.00744 0.00726 0.00748 0.00014 880 0.00988 0.00981 0.00948 0.00973 0.00012 882 0.01341 0.01304 0.01268 0.01305 0.00021 884 0.01813 0.01787 0.01762 0.01787 0.00015 886 0.02532 0.02502 0.02431 0.02488 0.00030 888 0.03566 0.03540 0.03463 0.03523 0.00031 890 0.05141 0.05105 0.05047 0.05098 0.00027 892 0.07503 0.07483 0.07399 0.07462 0.00032 894 0.11012 0.11085 0.10969 0.11022 0.00034 896 0.16176 0.16400 0.16279 0.16285 0.00065 898 0.23398 0.23925 0.23772 0.23698 0.00157 900 0.32830 0.33779 0.33646 0.33418 0.00297 902 0.43780 0.45136 0.45055 0.44657 0.00439 904 0.54775 0.56382 0.56363 0.55840 0.00533 906 0.64093 0.65583 0.65606 0.65094 0.00501 908 0.70772 0.71921 0.71958 0.71550 0.00389 910 0.74889 0.75639 0.75647 0.75392 0.00251 912 0.77096 0.77510 0.77504 0.77370 0.00137 914 0.78152 0.78319 0.78313 0.78261 0.00055 916 0.78594 0.78640 0.78633 0.78622 0.00014 918 0.78686 0.78695 0.78695 0.78692 0.00003 920 0.78651 0.78645 0.78663 0.78653 0.00005 922 0.78564 0.78537 0.78568 0.78556 0.00010 924 0.78439 0.78434 0.78476 0.78450 0.00013 926 0.78266 0.78288 0.78343 0.78299 0.00023 928 0.78076 0.78110 0.78188 0.78125 0.00033 930 0.77845 0.77921 0.78020 0.77929 0.00051 932 0.77540 0.77649 0.77760 0.77650 0.00064 934 0.77315 0.77478 0.77619 0.77471 0.00088 936 0.76964 0.77181 0.77345 0.77163 0.00110 938 0.76730 0.76969 0.77149 0.76949 0.00121 940 0.76507 0.76763 0.76964 0.76745 0.00132 942 0.76251 0.76460 0.76661 0.76457 0.00118 944 0.75998 0.76146 0.76351 0.76165 0.00102 946 0.75845 0.75901 0.76101 0.75949 0.00078 948 0.75732 0.75711 0.75893 0.75779 0.00057 950 0.75639 0.75499 0.75670 0.75603 0.00053 952 0.75547 0.75321 0.75493 0.75454 0.00068 954 0.75524 0.75227 0.75405 0.75385 0.00086 956 0.75437 0.75076 0.75267 0.75260 0.00104 958 0.75321 0.74928 0.75123 0.75124 0.00113 960 0.75129 0.74716 0.74921 0.74922 0.00119 962 0.74796 0.74386 0.74623 0.74602 0.00119 964 0.74253 0.73825 0.74066 0.74048 0.00124 966 0.73332 0.72875 0.73138 0.73115 0.00132 968 0.71740 0.71273 0.71567 0.71527 0.00136 970 0.68997 0.68518 0.68823 0.68779 0.00140 972 0.64661 0.64208 0.64549 0.64473 0.00136 974 0.58361 0.57985 0.58360 0.58235 0.00125 976 0.50244 0.50000 0.50388 0.50211 0.00113 978 0.41074 0.40956 0.41323 0.41118 0.00108 980 0.32006 0.31969 0.32284 0.32086 0.00099 982 0.23988 0.23983 0.24230 0.24067 0.00082 984 0.17533 0.17542 0.17717 0.17597 0.00060 986 0.12650 0.12659 0.12761 0.12690 0.00036 988 0.09108 0.09111 0.09171 0.09130 0.00020 990 0.06581 0.06571 0.06609 0.06587 0.00011 992 0.04791 0.04793 0.04812 0.04799 0.00007 994 0.03532 0.03538 0.03535 0.03535 0.00002 996 0.02636 0.02631 0.02627 0.02632 0.00003 998 0.01990 0.01991 0.01987 0.01990 0.00001 1000 0.01521 0.01528 0.01507 0.01519 0.00006 1002 0.01171 0.01198 0.01168 0.01179 0.00010 1004 0.00917 0.00937 0.00917 0.00923 0.00007 1006 0.00731 0.00747 0.00731 0.00736 0.00005 1008 0.00589 0.00613 0.00585 0.00595 0.00009 1010 0.00481 0.00497 0.00480 0.00486 0.00005 1012 0.00393 0.00423 0.00398 0.00405 0.00009 1014 0.00328 0.00360 0.00329 0.00339 0.00010 1016 0.00280 0.00295 0.00275 0.00283 0.00006 1018 0.00237 0.00260 0.00234 0.00244 0.00008 1020 0.00196 0.00224 0.00209 0.00210 0.00008 1022 0.00173 0.00193 0.00185 0.00184 0.00006 1024 0.00151 0.00172 0.00160 0.00161 0.00006 1026 0.00142 0.00156 0.00142 0.00147 0.00005 1028 0.00122 0.00140 0.00127 0.00130 0.00005 1030 0.00115 0.00132 0.00106 0.00118 0.00008 1032 0.00100 0.00112 0.00109 0.00107 0.00004 1034 0.00092 0.00108 0.00094 0.00098 0.00005 1036 0.00082 0.00102 0.00092 0.00092 0.00006 1038 0.00074 0.00080 0.00095 0.00083 0.00006 1040 0.00072 0.00071 0.00080 0.00075 0.00003 1042 0.00066 0.00081 0.00070 0.00072 0.00005 1044 0.00068 0.00073 0.00070 0.00070 0.00001 1046 0.00063 0.00067 0.00061 0.00064 0.00002 1048 0.00056 0.00068 0.00069 0.00064 0.00004 1050 0.00069 0.00066 0.00055 0.00063 0.00004 FIG_13-13.GIF Figure 13-13 The transmission of the red Solar Aureole filter as a function of wavelength as measured by Bernard Schmitt at three different temperatures. The three measurements show rather little dependence on temperature. FIG_13-14.GIF Figure 13-14 The difference in the measured transmission of the red filter from the average of the measurements at three temperatures from the data of Table 13-7. Note that the difference of a measurement at any of the three temperatures from the average is less than 1% at all wavelengths, and usually less than a few tenths of a percent. Table 13-8 shows the measurements of the blue Solar Aureole filter from the flight lot at four temperatures. Figure 13-15 shows the transmission of the filter at each temperature as a function of wavelength. Figure 13-16 shows the deviation at each temperature from the average of the measurements at the four temperatures. We note that the curves of the deviations do not change monotonically with temperature, but the curves often cross over each other. The deviations are not more than about 2% from the mean at any temperature. We conclude that the transmission of the blue filter does not change significantly with temperature even over the rather large temperature range of the measurements. Table 13-8 Transmission of the Blue Solar Aureole Filter at Four Temperatures Wavelength 70 K 150 K 220 K 300 K Average sigma average (nm) 450 0.0026 0.0051 0.0031 0.0008 0.0029 0.0009 451 0.0022 0.0029 0.0033 0.0012 0.0024 0.0005 452 0.0047 0.0040 0.0059 -0.0003 0.0035 0.0013 453 0.0038 0.0024 0.0031 0.0022 0.0029 0.0004 454 0.0030 0.0042 0.0040 0.0019 0.0033 0.0005 455 0.0036 0.0042 0.0032 0.0026 0.0034 0.0003 456 0.0042 0.0036 0.0037 0.0023 0.0035 0.0004 457 0.0046 0.0047 0.0053 0.0032 0.0044 0.0004 458 0.0056 0.0057 0.0063 0.0048 0.0056 0.0003 459 0.0069 0.0053 0.0067 0.0056 0.0061 0.0004 460 0.0077 0.0071 0.0059 0.0055 0.0065 0.0005 461 0.0091 0.0096 0.0094 0.0080 0.0091 0.0003 462 0.0119 0.0097 0.0108 0.0100 0.0106 0.0005 463 0.0142 0.0126 0.0124 0.0121 0.0128 0.0005 464 0.0176 0.0172 0.0154 0.0144 0.0161 0.0008 465 0.0236 0.0225 0.0205 0.0185 0.0213 0.0011 466 0.0293 0.0293 0.0272 0.0259 0.0279 0.0008 467 0.0416 0.0392 0.0371 0.0333 0.0378 0.0018 468 0.0613 0.0582 0.0528 0.0474 0.0549 0.0031 469 0.0893 0.0860 0.0782 0.0701 0.0809 0.0043 470 0.1331 0.1258 0.1174 0.1047 0.1202 0.0061 471 0.1938 0.1855 0.1701 0.1553 0.1762 0.0085 472 0.2648 0.2600 0.2414 0.2187 0.2462 0.0105 473 0.3386 0.3387 0.3217 0.2958 0.3237 0.0101 474 0.4062 0.4077 0.3929 0.3713 0.3945 0.0084 475 0.4547 0.4606 0.4458 0.4274 0.4471 0.0072 476 0.4841 0.4952 0.4817 0.4653 0.4816 0.0062 477 0.5056 0.5188 0.5063 0.4893 0.5050 0.0061 478 0.5213 0.5392 0.5267 0.5072 0.5236 0.0066 479 0.5399 0.5571 0.5476 0.5275 0.5430 0.0063 480 0.5628 0.5784 0.5676 0.5501 0.5647 0.0059 481 0.5868 0.6033 0.5899 0.5702 0.5875 0.0068 482 0.6096 0.6289 0.6142 0.5915 0.6111 0.0077 483 0.6309 0.6522 0.6378 0.6137 0.6336 0.0080 484 0.6492 0.6707 0.6575 0.6347 0.6530 0.0075 485 0.6641 0.6874 0.6729 0.6499 0.6686 0.0079 486 0.6748 0.6985 0.6852 0.6620 0.6801 0.0077 487 0.6809 0.7058 0.6927 0.6699 0.6873 0.0077 488 0.6839 0.7089 0.6972 0.6740 0.6910 0.0076 489 0.6831 0.7083 0.6966 0.6753 0.6908 0.0073 490 0.6798 0.7043 0.6934 0.6726 0.6875 0.0071 491 0.6736 0.6978 0.6875 0.6671 0.6815 0.0069 492 0.6658 0.6887 0.6780 0.6587 0.6728 0.0066 493 0.6557 0.6779 0.6668 0.6478 0.6620 0.0066 494 0.6426 0.6661 0.6549 0.6353 0.6497 0.0068 495 0.6299 0.6516 0.6426 0.6245 0.6371 0.0061 496 0.6179 0.6373 0.6287 0.6133 0.6243 0.0054 497 0.6082 0.6252 0.6156 0.6018 0.6127 0.0050 498 0.5983 0.6156 0.6048 0.5905 0.6023 0.0053 499 0.5901 0.6076 0.5971 0.5829 0.5944 0.0053 500 0.5846 0.6013 0.5916 0.5776 0.5888 0.0051 501 0.5816 0.5971 0.5876 0.5744 0.5852 0.0048 502 0.5812 0.5955 0.5862 0.5733 0.5840 0.0046 503 0.5831 0.5963 0.5862 0.5738 0.5848 0.0046 504 0.5862 0.5993 0.5876 0.5750 0.5870 0.0050 505 0.5907 0.6042 0.5920 0.5778 0.5912 0.0054 506 0.5942 0.6088 0.5978 0.5821 0.5957 0.0055 507 0.5992 0.6130 0.6025 0.5882 0.6007 0.0051 508 0.6056 0.6173 0.6060 0.5929 0.6055 0.0050 509 0.6109 0.6232 0.6095 0.5953 0.6097 0.0057 510 0.6129 0.6281 0.6141 0.5975 0.6131 0.0063 511 0.6138 0.6297 0.6181 0.6017 0.6158 0.0058 512 0.6160 0.6296 0.6187 0.6057 0.6175 0.0049 513 0.6174 0.6295 0.6166 0.6053 0.6172 0.0050 514 0.6157 0.6293 0.6152 0.6019 0.6155 0.0056 515 0.6096 0.6266 0.6132 0.5990 0.6121 0.0057 516 0.5998 0.6174 0.6078 0.5958 0.6052 0.0048 517 0.5883 0.6029 0.5954 0.5879 0.5936 0.0035 518 0.5718 0.5847 0.5754 0.5708 0.5757 0.0032 519 0.5449 0.5604 0.5502 0.5445 0.5500 0.0037 520 0.5058 0.5260 0.5192 0.5132 0.5160 0.0043 521 0.4580 0.4779 0.4770 0.4750 0.4720 0.0047 522 0.4057 0.4206 0.4226 0.4261 0.4187 0.0045 523 0.3496 0.3617 0.3622 0.3680 0.3604 0.0039 524 0.2913 0.3038 0.3034 0.3064 0.3012 0.0034 525 0.2349 0.2480 0.2492 0.2511 0.2458 0.0037 526 0.1859 0.1965 0.1994 0.2025 0.1961 0.0036 527 0.1459 0.1532 0.1565 0.1602 0.1539 0.0030 528 0.1145 0.1189 0.1205 0.1243 0.1195 0.0020 529 0.0894 0.0931 0.0936 0.0957 0.0930 0.0013 530 0.0695 0.0730 0.0733 0.0741 0.0725 0.0010 531 0.0541 0.0572 0.0575 0.0581 0.0567 0.0009 532 0.0431 0.0452 0.0456 0.0458 0.0449 0.0006 533 0.0345 0.0360 0.0361 0.0365 0.0358 0.0004 534 0.0283 0.0291 0.0289 0.0295 0.0290 0.0003 535 0.0231 0.0237 0.0236 0.0236 0.0235 0.0001 536 0.0190 0.0198 0.0195 0.0193 0.0194 0.0002 537 0.0159 0.0164 0.0162 0.0159 0.0161 0.0001 538 0.0132 0.0140 0.0134 0.0135 0.0135 0.0002 539 0.0111 0.0118 0.0118 0.0114 0.0115 0.0002 540 0.0098 0.0102 0.0101 0.0094 0.0099 0.0002 541 0.0085 0.0085 0.0084 0.0081 0.0084 0.0001 542 0.0072 0.0076 0.0073 0.0070 0.0073 0.0001 543 0.0065 0.0068 0.0064 0.0062 0.0065 0.0001 544 0.0053 0.0056 0.0057 0.0051 0.0054 0.0001 545 0.0047 0.0050 0.0048 0.0050 0.0049 0.0001 546 0.0044 0.0044 0.0043 0.0038 0.0042 0.0001 547 0.0039 0.0036 0.0035 0.0035 0.0036 0.0001 548 0.0034 0.0033 0.0031 0.0032 0.0032 0.0001 549 0.0032 0.0029 0.0031 0.0030 0.0030 0.0001 550 0.0027 0.0030 0.0026 0.0021 0.0026 0.0002 FIG_13-15.GIF Figure 13-15 Measured transmission of blue Solar Aureole filter at four temperatures, as labeled. FIG_13-16.GIF Figure 13-16 The difference in the transmission measurements at each of the four temperatures from the average of the measurements at all four temperatures is shown as a function of wavelength. Note that the differences do not vary monotonically with temperature, and that the differences are within about 2% of the mean value at all wavelengths. We conclude that the transmission of the blue filter has little real variation in transmission with temperature even over the large range from 70 K to 300 K. 13.4.2 Transmission of Filters as Functions of Angle of Incidence. While the Solar Aureole filters have essentially the same spectral transmission independent of temperature, we know that the transmission of the filter does depend significantly on the angle of incidence of the light beam. This effect is responsible for changing the relative spectral response of the Solar Aureole system as a function of row number (elevation) on the detector array. In fact the relative spectral response of the Solar Aureole system is a complex function of row number, column number, wavelength, and detector temperature. It was thought that we could separate the complex relative spectral response function into two parts by first characterizing the variation in filter spectral transmission with angle of incidence and then deriving the detector response as a function of wavelength and temperature. This, however, did not yield adequate results, so a different approach was pursued as discussed in the following section. However, the spectral transmission of a set of filters from the flight lot was characterized versus angle of incidence. The results of this test and analysis are included here. We measured the transmission of the red and blue Solar Aureole filters from the flight lot as a function of the angle of incidence of a collimated beam to the normal of the filter at the University of Arizona's Lunar and Planetary Lab clean room (room 222c) between the February 13 and March 13, 2001. Both the 'Red' (936 nm) and 'Blue' (500 nm) filters were measured. We used the high intensity light source to illuminate the input to the monochrometer. The output from the monochrometer was directed through the filter, to the Standard Silicon Detector. The reflex telescope was attached to the output of the monochrometer to collimate the monochromatic beam. The filter was attached to a holder that also served as a baffle. A baffle was also placed in front of the detector to reduce the stray light contamination. The filter holder was mounted to a rotary table to allow for accurate angular positioning of the sample relative to the collimated beam. An index datum was placed on the monochrometer directly below its output port so that the retro reflection from the filter holder could be used to determine the orthogonal orientation of the beam. FIG_13-17.GIF Figure 13-17 Test setup schematic for measuring the filter transmission as a function of angle of incidence. FIG_13-18 Figure 13-18 A view of the laboratory setup used to measure the transmission of the Solar Aureole filters as a function of the angle of incidence of the collimated beam. The monochrometer and the collimating reflex telescope are visible at the left in the image. The filter holder mounted on a calibrated angle stage is visible at center. The standard silicon detector is visible at the right. FIG_13-19 Figure 13-19 Like Figure 13-18 but showing the baffle between the filter holder and the standard silicon detector. For the measurements of the blue filter we covered the range from 420 to 570 nm in 5 nm steps. For the red measurements, we covered the range from 830 to 1020 nm in 5 nm steps. The scans were performed at incidence angles of 90, 85, 75, 65, 55, 100, 110, & 120 degrees relative to the plane of the filter in the direction of its long axis. The measurements were taken in three steps. First the beam was scanned over its entire wavelength range with the filter and holder removed. Second, the beam was again scanned over its wavelength range with the filter holder in place but with no filter installed. This scan was repeated at each incidence angle. Third, the beam was scanned over its wavelength range with the filter and holder installed, and this scan was repeated at each incidence angle. We calculated the transmission of the filter for each incidence angle by taking the ratio of the detector readings with the filter in place to the detector readings with only the filter holder in place and normalizing by the intensity of the beam during each measurement. IMAGE_286.GIF 59. The results, presented in terms of degrees from the normal to the filter, are shown in Table 13-9 and Table 13-10. Table 13-9 Spectral Transmission of Blue Filter for Various Angles of Incidence Wavelength 0 deg 5 deg 10 deg 15 deg 20 deg 25 deg 30 deg 35 deg (nm) 420 0.0000 0.0001 0.0000 0.0001 0.0000 0.0002 0.0000 0.0003 425 0.0000 0.0001 0.0000 0.0001 0.0000 0.0002 0.0001 0.0006 430 0.0000 0.0001 0.0000 0.0001 0.0000 0.0002 0.0004 0.0012 435 0.0000 0.0001 0.0000 0.0001 0.0001 0.0004 0.0010 0.0029 440 0.0000 0.0001 0.0001 0.0002 0.0003 0.0009 0.0028 0.0097 445 0.0001 0.0002 0.0002 0.0005 0.0010 0.0026 0.0109 0.0426 450 0.0005 0.0006 0.0008 0.0015 0.0034 0.0096 0.0512 0.1559 455 0.0016 0.0019 0.0026 0.0048 0.0143 0.0475 0.1836 0.3460 460 0.0059 0.0069 0.0107 0.0225 0.0752 0.1906 0.3994 0.4791 465 0.0319 0.0383 0.0628 0.1256 0.2646 0.4214 0.5471 0.5217 470 0.1710 0.1934 0.2514 0.3592 0.4900 0.5648 0.5872 0.5305 475 0.4086 0.4303 0.4753 0.5447 0.6069 0.6013 0.5858 0.5268 480 0.5614 0.5751 0.6027 0.6366 0.6399 0.5931 0.5752 0.5325 485 0.6480 0.6563 0.6614 0.6566 0.6222 0.5680 0.5778 0.5226 490 0.6696 0.6684 0.6538 0.6265 0.5937 0.5646 0.5784 0.5125 495 0.6340 0.6301 0.6133 0.5929 0.5909 0.5742 0.5760 0.4912 500 0.5954 0.5944 0.5913 0.5920 0.6027 0.5770 0.5460 0.3413 505 0.5911 0.5945 0.6000 0.6059 0.6052 0.5497 0.3871 0.1392 510 0.6044 0.6076 0.6090 0.6020 0.5512 0.3886 0.1683 0.0406 515 0.5912 0.5886 0.5677 0.5100 0.3590 0.1589 0.0500 0.0135 520 0.4749 0.4576 0.3997 0.2833 0.1417 0.0457 0.0156 0.0061 525 0.2521 0.2293 0.1764 0.0962 0.0416 0.0145 0.0064 0.0035 530 0.0857 0.0745 0.0539 0.0278 0.0133 0.0061 0.0033 0.0023 535 0.0254 0.0223 0.0166 0.0098 0.0055 0.0032 0.0020 0.0018 540 0.0094 0.0085 0.0067 0.0045 0.0028 0.0020 0.0015 0.0016 545 0.0042 0.0040 0.0032 0.0025 0.0017 0.0014 0.0012 0.0014 550 0.0022 0.0022 0.0018 0.0016 0.0012 0.0011 0.0010 0.0013 555 0.0014 0.0014 0.0012 0.0011 0.0009 0.0010 0.0009 0.0012 560 0.0009 0.0010 0.0009 0.0009 0.0008 0.0009 0.0008 0.0010 565 0.0007 0.0008 0.0007 0.0008 0.0007 0.0008 0.0007 0.0010 570 0.0006 0.0007 0.0006 0.0007 0.0006 0.0007 0.0006 0.0008 Table 13-10 Spectral Transmission of Red Filter for Various Angles of Incidence Wavelength 0 deg 5 deg 10 deg 15 deg 20 deg 25 deg 30 deg (nm) 830 0.0002 0.0003 0.0002 0.0003 0.0007 0.0022 0.0026 835 0.0002 0.0004 0.0003 0.0006 0.0011 0.0029 0.0038 840 0.0003 0.0006 0.0005 0.0010 0.0015 0.0036 0.0063 845 0.0006 0.0009 0.0009 0.0015 0.0019 0.0049 0.0116 850 0.0009 0.0013 0.0013 0.0019 0.0027 0.0073 0.0235 855 0.0012 0.0017 0.0016 0.0024 0.0043 0.0121 0.0535 860 0.0016 0.0021 0.0022 0.0034 0.0076 0.0236 0.1292 865 0.0033 0.0041 0.0044 0.0069 0.0163 0.0474 0.2112 870 0.0057 0.0068 0.0084 0.0141 0.0410 0.1221 0.4053 875 0.0111 0.0130 0.0183 0.0329 0.1064 0.2743 0.6216 880 0.0243 0.0286 0.0437 0.0842 0.2382 0.4979 0.7947 885 0.0596 0.0708 0.1088 0.2020 0.4353 0.7182 0.8959 890 0.1460 0.1707 0.2398 0.3992 0.6503 0.8624 0.9321 895 0.3091 0.3466 0.4362 0.6243 0.8151 0.9220 0.9391 900 0.5286 0.5684 0.6567 0.8109 0.9101 0.9360 0.9424 905 0.7362 0.7666 0.8314 0.9164 0.9472 0.9383 0.9460 910 0.8784 0.8967 0.9312 0.9587 0.9586 0.9404 0.9494 915 0.9491 0.9567 0.9668 0.9713 0.9589 0.9438 0.9485 920 0.9686 0.9723 0.9706 0.9729 0.9538 0.9435 0.9436 925 0.9699 0.9738 0.9648 0.9703 0.9458 0.9402 0.9277 930 0.9665 0.9682 0.9565 0.9607 0.9393 0.9317 0.8733 935 0.9599 0.9593 0.9487 0.9524 0.9356 0.9180 0.7489 940 0.9529 0.9519 0.9454 0.9459 0.9315 0.8760 0.5559 945 0.9473 0.9472 0.9449 0.9436 0.9115 0.7676 0.3495 950 0.9421 0.9439 0.9415 0.9354 0.8428 0.5781 0.1835 955 0.9364 0.9374 0.9264 0.8994 0.7064 0.3601 0.0833 960 0.9215 0.9180 0.8858 0.8042 0.5163 0.1847 0.0350 965 0.8748 0.8607 0.7918 0.6379 0.3178 0.0836 0.0151 970 0.7703 0.7413 0.6327 0.4330 0.1641 0.0370 0.0073 975 0.6045 0.5631 0.4336 0.2468 0.0744 0.0180 0.0039 980 0.4075 0.3625 0.2506 0.1192 0.0330 0.0100 0.0024 985 0.2299 0.1945 0.1237 0.0530 0.0156 0.0064 0.0016 990 0.1133 0.0930 0.0580 0.0248 0.0082 0.0047 0.0012 995 0.0527 0.0434 0.0278 0.0128 0.0047 0.0038 0.0010 1000 0.0255 0.0218 0.0144 0.0074 0.0030 0.0033 0.0008 1005 0.0134 0.0121 0.0081 0.0047 0.0021 0.0030 0.0007 1010 0.0079 0.0075 0.0050 0.0033 0.0016 0.0029 0.0007 1015 0.0050 0.0051 0.0034 0.0025 0.0013 0.0028 0.0007 1020 0.0034 0.0037 0.0025 0.0020 0.0011 0.0027 0.0007 FIG_13-20.GIF Figure 13-20 Measurements of the transmission of the blue Solar Aureole filter from the flight lot for different angles of incidence of collimated light, as labeled. Note the shift in the transmission of the filter with different incidence angles. FIG_13-21.GIF Figure 13-21 Like Figure 13-20 but for the red Solar Aureole filter. Note the shift in the transmission of the filter with different incidence angles. We note that the bandpass of both the red and blue Solar Aureole filters shift significantly with differing angle of incidence of the beam to the normal of the filter. 13.4.3 Relative Spectral Response of Solar Aureole System versus Temperature It has been shown above that while the bandpass filters do not show significant variations in their spectral transmissions with temperature, they do change strongly with angle of incidence (zenith angle or row number). The goal of this effort is to decompose the temperature dependent Solar Aureole Relative Spectral Response (SA RSR) into a relatively simple analytic function and table for each of the four channels. The model fit should match the original data with a root- mean-squared deviation over the bandpass of 1% or less for every pixel and every temperature. Measurements of the relative spectral response of the complete flight Solar Aureole system were made in the integrating sphere in July and August, 1996 at the detector temperatures shown in Table 13-11. The data was reduced by several individuals, and the final RSRs are located in /local/SA/Rel_Spec_Resp/DISR#3/output/save_files/. Table 13-11 Dates, File Names, and Detector Temperatures of Relative Spectral Response Measurements of the SN03 Solar Aureole System Date (1996) File Name Detector Temperature July 26 26Jul_2/ 293.869 K July 29 29Jul_1/ 168.197 K July 30 30Jul_1/ 267.683 K July 30 30Jul_2/ 184.082 K July 31 31Jul_1/ 237.042 K August 1 1Aug_1/ 200.855 K August 2 1Aug_2/ 224.700 K 13.4.3.1 The Form of Relative Spectral Response Model The form of the RSR model includes a foundational set of spectrally varying curves, filter, whose characteristics are largely due to the interference filters in each channel. The filter curves are functions of the row number (angle of incidence) for each pixel. To result in the RSR model, the filter curves are multiplied by a polynomial function that includes all thermally varying effects and some spatial effects, all of which are presumed to reside in the CCD chip and fiber bundle. This latter function is called the "non-filter model", or NFM, because it is derived analytically by eliminating the interference filter effects from the measured relative spectral response. It includes some spatial variation on a columnwise basis. As derived, the relative spectral response for each of the four SA channels can be found by the following equation. IMAGE_050.GIF 60. The form of the NFM is the following polynomial equation, where the thermal coefficients, a, b, c, and d, are properties of the SA channel, and the column coefficients, M0 through M3, are column dependent for each channel. IMAGE_052.GIF 61. Due to fiber ribbon/CCD misalignments, a few columns do not match their neighbors in RSR shape. These columns are treated in the manner described above, but with their own set of filters and coefficients. Additional localized spatial effects are found throughout the system - the CCD has some pixel to pixel variation and the optical train has obvious illumination variations over the field due to the cameras and fiber ribbon underfilling the CCD - but the number of pixels affected and the degree of modeling error are small. 13.4.3.2 Approach The following approach can be used to find the set of filter curves and NFMs whose product best matches the original data for each channel over temperature. 13.4.3.3 Step 1-Prepare Derived Data The previously derived SA RSR data, which is taken to be the "measured data" in this modeling exercise, is given at specific wavelengths. When fitting curves to this data, splining the data to a finer wavelength grid, 0.5 nm, and then normalizing the splined function to 1, improves the fit of the models. The normalization in the blue channels is best performed on the second hump in the response curve. The approach consists of polynomial fits to variations in the relative spectral response at a reference column and temperature. The reference columns and temperature can be varied to determine sensitivity on the modeling results. The central temperature, 224.7K, yields the best overall results. Little variation in results are indicated when any of the central columns are used. The following columns are used in this derivation. Table 13-12 Reference Columns Used in Relative Spectral Response Model Derivation Channel Reference Column Blue Horizontal 3 Blue Vertical 2 Red Horizontal 2 Red Vertical 3 13.4.3.4 Step 2-Find the Initial Non-Filter Models The initial NFM, NFMini(l), is an underlying spectrally varying function which includes structure in the CCD quantum efficiency. The blue channels have no underlying structure, so NFMini is defined to be unity. The red channels, on the other hand, do have some structure over the SA bandpass, and this structure can be modeled as follows. Analysis on the DISR Imager Relative Spectral Response indicates that there is a bump in the CCD spectral response around 854 nm. This can be seen in the following plot of the Side Looking Imager spectral response. FIG_13-22.GIF Figure 13-22 Side Looking Imager Spectral Response This bump can be seen in the SA RSR as well, so it is modeled empirically in the initial NFM as a lorentzian function with a center wavelength of 854 nm, a full- width at half maximum response of 15 nm, and a peak amplitude of 0.4, as follows. IMAGE_054.GIF 62. The quadratic shape of the falloff can also be modeled. We normalize the derived RSR data in the wavelength range from 922 to 938 nm, and then for each wavelength, we form the average for all rows with good response (greater than 50%). This average can then be fit by a quadratic to be used in the initial NFM. In mathematical terms, the quadratic portion of the initial NFM is as follows. IMAGE_294.GIF 63. This new array RSR' at the reference temperature is then averaged over the rows in the wavelength regions with good filter response and fit with a quadratic in wavelength to create the initial NFM. The coefficients of the initial NFM quadratic fit for the red horizontal and vertical channels are as follows. Table 13-13 Table of NFMini Quadratic Coefiicients Red Horizontal Red Vertical nfm0 67.900400 25.311233 nfm1 -0.13372830 -0.043105799 nfm2 6.6157520e-005 1.8006592e-005 Thus, the initial NFM is as follows for the blue or red channels. IMAGE_056.GIF 64. Below are plots of the RSR' curves and NFMini for both red channels. FIG_13-23.GIF Figure 13-23 Red Horizontal NFM Curves FIG_13-24.GIF Figure 13-24 Red Vertical NFM Curves 13.4.3.5 Step 3-Find the Filter Curves After finding the initial NFM, the filter curves can be determined. Because the filter transmission varies with incident angle, the filter shape is strongly dependent on row number. The beamsplitter in the optical train influences the shape as well, so the full field of view must be mapped rather than only half. A set of 12 curves can be chosen, at rows 0.5, 5, 10, 15, 20, 25, 30, 35, 40, 43, 45, and 48.5. These filter curves are defined at the reference temperature and column as the average of three adjacent measured RSRs. The filter curves for the top and bottom rows are defined as the average of the extreme two rows instead of three. The red channel filters can be derived as above, but using as the foundation the RSR' as defined in equation 63. instead of the measured RSRs. The RSR' can then be divided by NFMini to result in the filter set. It was found that the red channels have a few columns with RSR curves that do not match the rest of the channels. This is likely due to the fiber ribbon underfilling the fields of these channels. These columns have their own set of filter curves and coefficients. They are columns 0 and 1 for the red horizontal and column 0 for the red vertical. Below are plots of the filter curves for all four channels. The filters are plotted in linear and log forms for clarity at extreme wavelengths. Tabular values are given in the body of the text. FIG_13-25.GIF Figure 13-25 Derived Blue Horizontal Filter Curves FIG_13-26.GIF Figure 13-26 Derived Blue Horizontal Filter Curves, Log Scale FIG_13-27.GIF Figure 13-27 Derived Blue Vertical Filter Curves FIG_13-28.GIF Figure 13-28 Derived Blue Vertical Filter Curves, Log Scale FIG_13-29.GIF Figure 13-29 Derived Red Horizontal Filter Curves FIG_13-307.GIF Figure 13-30 Derived Red Horizontal Filter Curves, Log Scale FIG_13-31.GIF Figure 13-31 Derived Red Vertical Filter Curves FIG_13-32.GIF Figure 13-32 Derived Red Vertical Filter Curves, Log Scale FIG_13-33.GIF Figure 13-33 Derived Red Horizontal Column 0 Filter Curves FIG_13-34.GIF Figure 13-34 Derived Red Horizontal Column 0 Filter Curves, Log Scale FIG_13-35.GIF Figure 13-35 Derived Red Horizontal Column 1 Filter Curves FIG_13-36.GIF Figure 13-36 Derived Red Horizontal Column 1 Filter Curves, Log Scale FIG_13-37.GIF Figure 13-37 Derived Red Vertical Column 0 Filter Curves FIG_13-38.GIF Figure 13-38 Derived Red Vertical Column 0 Filter Curves, Log Scale 13.4.3.6 Step 4-Find the Thermal Variations of the Non-Filter Models To find the thermal variations in the NFM, we use the filter derived above as a base. Recall that for the blue, the filter is defined by averaging the surrounding rows in the original RSR measurement at a reference temperature and column. This average can be performed at each temperature and then divided by the filter (the result at the reference temperature). The resultant ratio can then be averaged over row in wavelengths with good filter response. In mathematical language, the following can be performed. IMAGE_328.GIF 65. Next, we form a ratio of NFM_ratio_avg to show the change in NFM per degree. This ratio can be averaged over temperature and then fit with a polynomial in wavelength. IMAGE_330.GIF 66. For the red, the process is identical, except the definition of NFM_ratio in equation 65. uses the RSR' in the numerator instead of the filter, and the bump is included, as follows. IMAGE_332.GIF 67. The result is a set of thermal coefficients in wavelength that can be used to find the non-filter model at any temperature. Recall that the reference temperature is 224.7K. IMAGE_334.GIF 68. The coefficients in all cases are in the following table. Red Horizontal columns 0 and 1 require their own set of thermal coefficients. These special coefficients are included here. Table 13-14 Thermal Coefficients for All SA Channels Channel a b c d Blue Hor 2.0519205 -0.012112786 2.3854392e-005 -1.5672918e-008 Blue Ver 2.6717794 -0.015919638 3.1632590e-005 -2.0960937e-008 Red Hor 4.1627853 -0.013355480 1.4316606e-005 -5.1278929e-009 Red Ver 0.46694120 -0.0014621260 1.5654954e-006 -5.7336477e-010 Red Hor, 0 5.2851043 -0.016804565 1.7844364e-005 -6.3286793e-009 Red Hor, 1 4.9409769 -0.015830010 1.6938123e-005 -6.0531465e-009 Following are plots of the thermal ratios and their polynomial fits for all channels. FIG_13-39.GIF Figure 13-39 Blue Horizontal Non-Filter Model Thermal Performance for Reference Column FIG_13-40.GIF Figure 13-40 Blue Vertical Non-Filter Model Thermal Performance for Reference Column FIG_13-41.GIF Figure 13-41 Red Horizontal Non-Filter Model Thermal Performance for Reference Column FIG_13-42.GIF Figure 13-42 Red Vertical Non-Filter Model Thermal Performance for Reference Column FIG_13-43.GIF Figure 13-43 Red Horizontal Non-Filter Model Thermal Performance for Column 0 FIG_13-44.GIF Figure 13-44 Red Horizontal Non-Filter Model Thermal Performance for Column 1 13.4.3.7 Step 5-Find the Column Variations of the Non-Filter Models At this point in the analysis, the relative spectral response is modeled for the reference column at all temperatures. The other columns can be modeled in a similar way by fitting a polynomial to the variation of the column RSR to the reference column RSR at the reference temperature. IMAGE_338.GIF 69. Now a polynomial can be fit to NFM_ratio_avg to result in the column coefficients that are used as M0(c), M1(c), M2(c), and M3(c). The curve fits are shown in the following plots. FIG_13-45.GIF Figure 13-45 Blue Horizontal Non-Filter Model Column Performance FIG_13-46.GIF Figure 13-46 Blue Vertical Non-Filter Model Column Performance The red channels have an additional complexity in their derivation as they did in the thermal fits. Instead of the measured RSR data, a normalized, averaged RSR function is used in the NFM_ratio in equation 69. IMAGE_354.GIF IMAGE_356.GIF 70. Then the NFM_ratio is averaged as in equation 69. and fit with a polynomial. The curve fits are shown in the following plots. FIG_13-47.GIF Figure 13-47 Red Horizontal Non-Filter Model Column Performance FIG_13-48.GIF Figure 13-48 Red Vertical Non-Filter Model Column Performance The column coefficients M0 through M3 for each channel are in the following tables. Table 13-15 Blue Horizontal Column Coefficients M0 M1 M2 M3 Column 0 -1.576161E+01 6.991217E-02 -7.261663E-05 0.000000E+00 Column 1 -1.120476E+02 6.776472E-01 -1.348858E-03 8.917191E-07 Column 2 -5.451464E+01 3.371992E-01 -6.802498E-04 4.559225E-07 Column 3 1.0 0.0 0.0 0.0 Column 4 7.670377E+01 -4.607676E-01 9.324273E-04 -6.274879E-07 Column 5 1.279626E+02 -7.734728E-01 1.566727E-03 -1.055404E-06 Table 13-16 Blue Vertical Column Coefficients M0 M1 M2 M3 Column 0 1.287794E+02 -7.803157E-01 1.587449E-03 -1.075872E-06 Column 1 1.076329E+02 -6.419133E-01 1.287519E-03 -8.604670E-07 Column 2 1.0 0.0 0.0 0.0 Column 3 1.033230E+01 -5.103488E-02 9.152373E-05 -5.362022E-08 Column 4 4.158349E+01 -2.413895E-01 4.777937E-04 -3.147463E-07 Column 5 1.067493E+02 -6.317197E-01 1.256640E-03 -8.324925E-07 Table 13-17 Red Horizontal Column Coefficients M0 M1 M2 M3 Column 0 -6.951670E+01 2.272747E-01 -2.440805E-04 8.734615E-08 Column 1 9.833868E+00 -2.762700E-02 2.874322E-05 -9.946730E-09 Column 2 1.0 0.0 0.0 0.0 Column 3 -8.488152E+01 2.770449E-01 -2.980202E-04 1.069016E-07 Column 4 -1.488555E+02 4.824542E-01 -5.178775E-04 1.853475E-07 Column 5 -9.319383E+01 3.022677E-01 -3.235209E-04 1.154941E-07 Table 13-18 Red Vertical Column Coefficients M0 M1 M2 M3 Column 0 9.037937E+00 -2.485048E-02 2.555993E-05 -8.744530E-09 Column 1 3.750232E+02 -1.205694E+00 1.293924E-03 -4.622855E-07 Column 2 9.085585E+01 -2.906646E-01 3.126092E-04 -1.117840E-07 Column 3 1.0 0.0 0.0 0.0 Column 4 1.899895E+01 -6.003125E-02 6.722727E-05 -2.525717E-08 Column 5 2.436124E+01 -7.513855E-02 8.203623E-05 -3.038352E-08 13.4.3.8 Detailed Results Thus, the Solar Aureole Relative Spectral Response is modeled. For the blue channels, the final equation is as follows, IMAGE_058.GIF 71. where the filter and the coefficients M0 through M3 and a through d are in the tables above. For the red channels, the final equation is as follows, IMAGE_060.GIF 72. where the filter and the coefficients nfm0 through nfm2, M0 through M3 and a through d are in the tables above, and the Bump function is in equation 7. Care must be taken to use the correct filters and coefficients for the columns 0 and 1 as appropriate. A useful figure of merit for the fit of the models is the root-mean-square deviation over wavelength for a pixel at a given temperature. The models were scaled up or down by up to three percent to minimize the root-mean-square deviations over wavelength from the measurements for each pixel and temperature. This scaling will be implicit in the absolute response values. The following sets of plots show the fidelity of the scaled models to the measured relative spectral responses. In the majority of the cases, the root- mean-square deviations are within 1%. Some pixels at some temperatures, however, have larger deviations. These are addressed in the appendix to this section. There is a plot set for each SA channel. Within each plot set are five types of plots. 1) The first plot is the bounds of the straight deviation (model minus measured) for all pixels in a column over all temperatures. This gives a feel for the fidelity of the model over wavelength and column. 2) The next plot is the root-mean-square deviation over rows of the root-mean- square deviation over wavelength for all columns and temperatures. This gives a feel for the overall fidelity of the model versus temperature. 3) The next set of two plots is the root-mean-square deviation over wavelength of every pixel for the extremes of the seven temperatures. This plot set shows the fidelity of each pixel's model RSR at these temperatures. 4) The next set of six plots is the measured and modeled RSRs for every pixel in column 4 at 168 K. The choice of this column and temperature was made to show the fidelity of the model prediction in column and temperature. The lines are the model, and the points are the measured points. 5) The final set of nine plots is the straight deviation (model minus measured) versus wavelength with error bars showing the measurement noise. A more detailed discussion of this noise and its impact on the modeling fidelity is in the appendix. The nine plots are for rows 5, 10, 15, 20, 25, 30, 35, 40, and 45 from column 4 at 168 K. FIG_13-49_A.GIF FIG_13-49_B.GIF FIG_13-49_C.GIF FIG_13-49_D.GIF FIG_13-49_E.GIF FIG_13-49_F.GIF FIG_13-49_G.GIF FIG_13-49_H.GIF FIG_13-49_I.GIF FIG_13-49_J.GIF FIG_13-49_K.GIF FIG_13-49_L.GIF FIG_13-49_M.GIF FIG_13-49_N.GIF FIG_13-49_O.GIF FIG_13-49_P.GIF FIG_13-49_Q.GIF FIG_13-49_R.GIF FIG_13-49_S.GIF Figure 13-49 Blue Horizontal Relative Spectral Response Modeling Results - Set of Nineteen Plots FIG_13-50_A.GIF FIG_13-50_B.GIF FIG_13-50_C.GIF FIG_13-50_D.GIF FIG_13-50_E.GIF FIG_13-50_F.GIF FIG_13-50_G.GIF FIG_13-50_H.GIF FIG_13-50_I.GIF FIG_13-50_J.GIF FIG_13-50_K.GIF FIG_13-50_L.GIF FIG_13-50_M.GIF FIG_13-50_N.GIF FIG_13-50_O.GIF FIG_13-50_P.GIF FIG_13-50_Q.GIF FIG_13-50_R.GIF FIG_13-50_S.GIF Figure 13-50 Blue Vertical Relative Spectral Response Modeling Results - Set of Nineteen Plots FIG_13-51_A.GIF FIG_13-51_B.GIF FIG_13-51_C.GIF FIG_13-51_D.GIF FIG_13-51_E.GIF FIG_13-51_F.GIF FIG_13-51_G.GIF FIG_13-51_H.GIF FIG_13-51_I.GIF FIG_13-51_J.GIF FIG_13-51_K.GIF FIG_13-51_L.GIF FIG_13-51_M.GIF FIG_13-51_N.GIF FIG_13-51_O.GIF FIG_13-51_P.GIF FIG_13-51_Q.GIF FIG_13-51_R.GIF FIG_13-51_S.GIF Figure 13-52 Red Vertical Relative Spectral Response Modeling Results - Set of Nineteen Plots FIG_13-52_A.GIF FIG_13-52_B.GIF FIG_13-52_C.GIF FIG_13-52_D.GIF FIG_13-52_E.GIF FIG_13-52_F.GIF FIG_13-52_G.GIF FIG_13-52_H.GIF FIG_13-52_I.GIF FIG_13-52_J.GIF FIG_13-52_K.GIF FIG_13-52_L.GIF FIG_13-52_M.GIF FIG_13-52_N.GIF FIG_13-52_O.GIF FIG_13-52_P.GIF FIG_13-52_Q.GIF FIG_13-52_R.GIF FIG_13-52_S.GIF Figure 13-51 Red Horizontal Relative Spectral Response Modeling Results - Set of Nineteen Plots 13.4.3.9 Appendix about the Fliers "RSR fliers" are defined as pixels whose root-mean-square deviation of the modeled RSR from the measured RSR is greater than 1% at some temperature. 13.4.3.9.1 Test Conditions The following plot shows the total number of fliers versus temperature for each channel. It is interesting to note the similarities in the relative number of fliers for each channel and to recall the order in which the data was taken, designated in text on the plot. The notes files from each of the tests indicate the possibility of systematic differences introduced into the data. FIG_13-53.GIF Figure 13-53 Number of Relative Spectral Response Fliers versus Temperature For example, at 293K where each channel has its highest number of fliers, the injection baffle was present at port 5 (the high intensity lamp port), but it was not present for the other tests. It is hard to see how the presence of this baffle would change the measured RSR shape in the SA channels, but it is worthy of note. At 267K, the maximum counts in the red channels were roughly 2200dN, the point at which the non-linearity occurs for some cable configurations. Therefore, some saturation could have occurred in the red channels for that temperature, causing readings slightly off from the true readings. At 184K, the three slits in the system were slightly different from the other tests - 5:5:2.5 versus 2.5:5:2.5 for the others. Notes files indicate that at 184K and possibly at 267K there were different exit slits than the rest of the days. As in the injection baffle case, it is not obvious how this would change the readings, but the difference in the test condition was worthy of mention. Also at 184K, the note is found, "We turned off the lamp providing a heat source under the integrating sphere. The light seemed to contaminate the SA darks." If contamination of the dark readings had occurred, this would certainly have changed the resultant measured RSR. It is unclear whether this lamp condition was in effect for the test at 184K and other tests, or just at 184K. By the last three days of testing, the setup had stabilized and the system was working smoothly. These latter three test days show the fewest fliers, and there is indication that the higher numbers of fliers for the other temperatures could be due partially to systematic test variations. Coincidentally, the RSR model reference data was taken on the last day of test. 13.4.3.9.2 Which Pixels Are Fliers Given the possibility that the test setup variations created some of the fliers, it is helpful to determine which pixels have root-mean-square deviations greater than 1% consistently over temperature and which pixels have a larger deviation only once or twice (i.e., at one or two temperatures). The following four plots show the total number of times each pixel has a root- mean-square deviation greater than 1%. There are 7 possible times. FIG_13-54.GIF Figure 13-54 Frequency of Blue Horizontal Pixels Having RSR with RMS Deviation over 1% FIG_13-55.GIF Figure 13-55 Frequency of Blue Vertical Pixels Having RSR with RMS Deviation over 1% FIG_13-56.GIF Figure 13-56 Frequency of Red Horizontal Pixels Having RSR with RMS Deviation over 1% FIG_13-57.GIF Figure 13-57 Frequency of Red Vertical Pixels Having RSR with RMS Deviation over 1% While these plots show the detail perhaps better than an image of the SA channel, it is often useful to see this data in image form. Displays were generated of the number of times each pixel has root-mean-square deviation greater than 1%. From these displays, the following conclusions were drawn. It is clear that the blue horizontal channel has some questionable RSR matches in the corners and on the edges, but fits well in the central region. There are a total of 14 pixels that are fliers for 4 or more temperatures out of 7. If one were to mask out or disregard data from the first few rows of column 0, there would be only 5. The blue vertical channel has a chip in the fiber ribbon on the left side causing a few poor fits, and the bottom rows are out of family, but the central region fits well. There are a total of 23 pixels that are fliers for 4 or more temperatures out of 7. If one were to mask out or disregard data from the first 3 rows, there would be only 6. The red horizontal channel column 0 has a number of pixels with out of family response, and several scattered throughout the channel with questionable RSR shape. There are a total of 20 pixels that are fliers for 4 or more temperatures out of 7. If one were to mask out or disregard data from the latter rows of column 0, there would be only 6. The red vertical channel is similar, with most variations in the bottom and corners. There are a total of 10 pixels that are fliers for 4 or more temperatures out of 7. If one were to mask out or disregard data from the first row, there would be only 4. Thus, there are specific regions on each SA channel that have RSR shapes that do not match the rest of the arrays. This is largely due to fiber ribbon misalignment on the CCD camera regions. Outside of these specific regions, each channel has 4 to 6 out of family pixels. 13.4.3.9.3 Signal to Noise Ratios of Relative Spectral Response Measurements The misalignment of the SA fiber ribbon on the CCD array causes pixels that are only partially illuminated. The partial illumination also results in poorer signal levels. It is interesting to note the signal to noise ratio of the measurements, and to fold that noise band back into the analysis. Any given pixel at a given temperature and wavelength has a known signal level and therefore a known theoretical noise. It is reasonable to say that the measured data fits the model if it matches the model to within this noise value. If the root-mean-square deviation of a pixel at a given temperature is greater than 1%, one can loop through the measurements at every wavelength, testing for the noise level. If the measured data matches the model within the noise, the deviation at that wavelength is defined to be zero. Then one can compute a new root-mean-square deviation for the pixel at that temperature. This gives a bound on how much the incorporation of the noise information can aid the model fidelity figure of merit. The number of times a given pixel has greater than 1% root-mean-square deviation from the model when the noise is incorporated as described above was plotted in image format and compared with the fliers results. The results are left largely unchanged. The pixels that are identified as having some out of family shape are classified as such whether noise based error bars are included or not. This is also seen in the deviations with error bars plotted in the detailed results section of this report. While some deviations at some wavelengths can be attributed to noise, there is genuine deviation between the measured data and the modeled results at other wavelengths. Fortunately the models match the measured data remarkably well over column and temperature, most of the time to within 1%. 13.5 Absolute Responsivity 13.5.1 Introduction The count rate generated in the Solar Aureole Cameras can be computed with the following equation. IMAGE_524.GIF 73. This section derives the Solar Aureole Absolute Responsivity, Abs(T,col,row). 13.5.2 Approach for Absolute Response Computation at One Temperature On July 24, 1996 the SA absolute response measurement test was performed with the DISR#3 sensor head in the integrating sphere. A broadband lamp illuminated the integrating sphere, and the calibrated monochromator viewed the sphere as a spectrum analyzer to determine the input intensity. A broadband silicon detector monitored the interior of the sphere throughout. The derivation of the SA absolute response is given by the following equation. IMAGE_526.GIF 74. 13.5.2.1 Count Rate The absolute response was measured at 31 temperatures in two separate logs listed below. The data sets for temperatures below 260K are in test log *.1, and those for temperatures over 260K are in test log *.4. /disr3_cal/24Jul96/Log/absresp_cold_24Jul96.1 /disr3_cal/24Jul96/Log/absresp_cold_24Jul96.4 For each one of 31 temperatures, there are six data sets - one each for bright and bright with 0 ms integration time, and two each for dark and dark with 0 ms integration time. The basic integration time was always less than a second, so the electronic shutter effect is significant. The 0 ms integrations remove any electronic shutter effect in the measurement. The two darks were taken on either side of the bright data sets. The temperature difference between each dark and its bright is under 0.5K, so the two are averaged to form an average dark measurement for each bright. The case at 205.3K is different, and the darks with temperatures closest to the bright are used. For each temperature, all data sets are taken within 90 seconds. If one sorts the files in the Solar Aureole directory of the log by mission time, one determines the sequence of the data set formation. The sequence numbers identifying the data sets for analysis are in the following table. Figure 13-58 Sequence Numbers of Data Sets Used in Absolute Responsivity Derivation Temperature Bright Dark #1 Dark #2 Bright 0ms Dark 0ms, #1 Dark 0ms, #2 171.260 5 0 6 3 2 8 171.390 11 6 12 9 8 14 174.560 20 15 21 18 17 23 175.050 26 21 27 24 23 29 179.440 35 30 36 33 32 38 180.050 41 36 42 39 38 44 186.030 50 45 51 48 47 53 186.390 56 51 57 54 53 59 191.030 65 60 66 63 62 68 191.760 71 66 72 69 68 74 205.300 80 75 none 78 none 77 205.670 86 81 87 84 83 89 209.210 95 90 96 93 92 98 209.690 101 96 102 99 98 104 218.600 110 105 111 108 107 113 219.330 116 111 117 114 113 119 225.800 125 120 126 123 122 128 226.410 131 126 132 129 128 134 233.000 140 135 141 138 137 143 233.480 146 141 147 144 143 149 240.680 155 150 156 153 152 158 241.410 161 156 162 159 158 164 250.080 170 165 171 168 167 173 250.690 176 171 177 174 173 179 260.200 5 0 6 3 2 8 260.450 11 6 12 9 8 14 270.690 20 15 21 18 17 23 270.820 26 21 27 24 23 29 280.820 35 30 36 33 32 38 280.940 41 36 42 39 38 44 289.600 50 45 51 48 47 53 It can be observed that two sets of data were taken at close to the same temperature throughout the test. Averaging the two sets reduces the statistical noise before using them to generate a model. Additionally, including the data sets taken at 186.39K and 191.03K caused errors in the models, so these data sets are discarded in the model generation. They are included below in the model performance section. The lamp illuminating the integrating sphere drifts over the course of the calibration and data collection, so normalization must occur. A broadband silicon detector monitored the sphere intensity throughout the test. One can reference all measurements to the intensity at a given time by computing a drift factor as follows. IMAGE_528.GIF 75. The count rate for a pixel is then computed by the following equation. IMAGE_530.GIF 76. 13.5.2.2 Relative Spectral Response The SA RSR has been derived above. The model SA RSR is used in this analysis for each temperature and pixel. 13.5.2.3 Sphere Intensity The sphere intensity must now be computed before the absolute response can be derived. The following equation is used. IMAGE_532.GIF 77. The factor of one-half in the equation is because the monochromator responds to all polarization states in the sphere, but the intensity entering each SA channel is that in one polarization state alone. The monochromator calibration function, C(l), in units of Amps/(W/sqm-m-sr), is in the file /local/cal.cal/Si_resp_5_5_5ap_dry_new.txt. The lamp drift must also be included. No dark values are available during the monochromator scan of the sphere, so the standard reference dark measurement is used. The integrating sphere spatial structure is included in the relative brightness ratio, rb/0.987988. The four tables below give rb(r,c) for every pixel in the Solar Aureole. Table 13-19 Relative Brightness at the Location of Blue Horizontal Pixel to the Brightness at the Front of the Integrating Sphere Row Col 0 Col 1 Col 2 Col 3 Col 4 Col 5 0 0.9813 0.9804 0.9792 0.9781 0.9772 0.9764 1 0.9817 0.9805 0.9792 0.9782 0.9775 0.9771 2 0.9814 0.9802 0.9790 0.9783 0.9780 0.9779 3 0.9807 0.9797 0.9789 0.9787 0.9786 0.9785 4 0.9801 0.9795 0.9792 0.9791 0.9789 0.9786 5 0.9799 0.9795 0.9792 0.9789 0.9785 0.9782 6 0.9798 0.9794 0.9789 0.9783 0.9778 0.9775 7 0.9794 0.9792 0.9788 0.9781 0.9774 0.9770 8 0.9790 0.9791 0.9789 0.9783 0.9775 0.9770 9 0.9786 0.9791 0.9794 0.9787 0.9779 0.9775 10 0.9788 0.9797 0.9800 0.9794 0.9787 0.9784 11 0.9797 0.9806 0.9809 0.9804 0.9800 0.9800 12 0.9810 0.9818 0.9820 0.9819 0.9820 0.9825 13 0.9825 0.9833 0.9838 0.9843 0.9850 0.9858 14 0.9843 0.9851 0.9859 0.9870 0.9879 0.9885 15 0.9866 0.9872 0.9878 0.9880 0.9887 0.9899 16 0.9889 0.9893 0.9898 0.9902 0.9902 0.9899 17 0.9910 0.9911 0.9915 0.9923 0.9925 0.9923 18 0.9926 0.9926 0.9929 0.9938 0.9945 0.9944 19 0.9937 0.9937 0.9940 0.9948 0.9957 0.9961 20 0.9944 0.9946 0.9948 0.9955 0.9964 0.9972 21 0.9950 0.9951 0.9954 0.9959 0.9968 0.9977 22 0.9954 0.9955 0.9957 0.9961 0.9969 0.9977 23 0.9959 0.9960 0.9961 0.9963 0.9968 0.9976 24 0.9965 0.9965 0.9965 0.9966 0.9970 0.9975 25 0.9971 0.9970 0.9969 0.9969 0.9971 0.9975 26 0.9979 0.9975 0.9973 0.9972 0.9973 0.9975 27 0.9986 0.9982 0.9978 0.9976 0.9975 0.9976 28 0.9993 0.9990 0.9985 0.9980 0.9978 0.9978 29 1.0000 0.9997 0.9992 0.9986 0.9982 0.9980 30 1.0007 1.0004 0.9999 0.9993 0.9987 0.9984 31 1.0013 1.0010 1.0006 1.0000 0.9993 0.9989 32 1.0018 1.0016 1.0012 1.0006 1.0000 0.9995 33 1.0023 1.0022 1.0018 1.0013 1.0007 1.0001 34 1.0028 1.0028 1.0025 1.0020 1.0014 1.0008 35 1.0034 1.0034 1.0032 1.0027 1.0021 1.0016 36 1.0040 1.0040 1.0039 1.0035 1.0030 1.0024 37 1.0045 1.0046 1.0045 1.0043 1.0038 1.0033 38 1.0051 1.0053 1.0052 1.0050 1.0047 1.0042 39 1.0056 1.0059 1.0059 1.0057 1.0055 1.0051 40 1.0061 1.0065 1.0065 1.0064 1.0062 1.0060 41 1.0064 1.0069 1.0071 1.0071 1.0069 1.0067 42 1.0070 1.0074 1.0076 1.0077 1.0076 1.0075 43 1.0078 1.0083 1.0085 1.0085 1.0084 1.0082 44 1.0088 1.0094 1.0096 1.0096 1.0094 1.0091 45 1.0096 1.0103 1.0107 1.0107 1.0104 1.0099 46 1.0101 1.0110 1.0115 1.0115 1.0111 1.0102 47 1.0102 1.0112 1.0117 1.0117 1.0110 1.0098 48 1.0097 1.0108 1.0113 1.0111 1.0102 1.0091 49 1.0089 1.0099 1.0102 1.0099 1.0091 1.0084 Table 13-20 Relative Brightness at the Location of Blue Vertical Pixel to the Brightness at the Front of the Integrating Sphere Row Col 6 Col 7 Col 8 Col 9 Col 10 Col 11 0 0.9777 0.9772 0.9766 0.9758 0.9748 0.9738 1 0.9792 0.9786 0.9778 0.9769 0.9759 0.9749 2 0.9805 0.9796 0.9786 0.9776 0.9766 0.9757 3 0.9812 0.9800 0.9788 0.9778 0.9770 0.9764 4 0.9812 0.9798 0.9787 0.9780 0.9775 0.9772 5 0.9806 0.9794 0.9786 0.9783 0.9781 0.9781 6 0.9800 0.9792 0.9789 0.9788 0.9787 0.9786 7 0.9797 0.9794 0.9792 0.9790 0.9787 0.9784 8 0.9797 0.9793 0.9789 0.9785 0.9781 0.9779 9 0.9794 0.9791 0.9785 0.9779 0.9774 0.9773 10 0.9792 0.9790 0.9785 0.9777 0.9771 0.9770 11 0.9791 0.9791 0.9787 0.9779 0.9772 0.9771 12 0.9792 0.9795 0.9793 0.9784 0.9778 0.9777 13 0.9798 0.9803 0.9800 0.9793 0.9789 0.9789 14 0.9809 0.9813 0.9811 0.9807 0.9806 0.9810 15 0.9823 0.9827 0.9827 0.9829 0.9834 0.9840 16 0.9839 0.9845 0.9852 0.9859 0.9866 0.9871 17 0.9859 0.9866 0.9874 0.9881 0.9890 0.9892 18 0.9881 0.9885 0.9887 0.9890 0.9896 0.9903 19 0.9901 0.9905 0.9911 0.9910 0.9906 0.9908 20 0.9918 0.9921 0.9929 0.9933 0.9931 0.9926 21 0.9932 0.9934 0.9941 0.9950 0.9951 0.9948 22 0.9941 0.9944 0.9950 0.9959 0.9966 0.9964 23 0.9948 0.9951 0.9956 0.9965 0.9974 0.9976 24 0.9953 0.9955 0.9960 0.9968 0.9977 0.9983 25 0.9957 0.9958 0.9962 0.9968 0.9977 0.9984 26 0.9962 0.9962 0.9964 0.9969 0.9976 0.9983 27 0.9967 0.9967 0.9968 0.9970 0.9975 0.9982 28 0.9972 0.9971 0.9970 0.9972 0.9975 0.9981 29 0.9978 0.9975 0.9974 0.9973 0.9976 0.9980 30 0.9985 0.9981 0.9977 0.9976 0.9977 0.9980 31 0.9992 0.9987 0.9982 0.9979 0.9978 0.9981 32 1.0000 0.9994 0.9988 0.9983 0.9981 0.9982 33 1.0006 1.0001 0.9995 0.9989 0.9986 0.9984 34 1.0013 1.0008 1.0001 0.9995 0.9991 0.9987 35 1.0018 1.0014 1.0008 1.0001 0.9996 0.9991 36 1.0025 1.0020 1.0014 1.0008 1.0003 0.9997 37 1.0031 1.0027 1.0022 1.0015 1.0010 1.0005 38 1.0037 1.0035 1.0030 1.0023 1.0018 1.0013 39 1.0043 1.0041 1.0038 1.0032 1.0027 1.0022 40 1.0050 1.0048 1.0046 1.0041 1.0036 1.0031 41 1.0057 1.0055 1.0053 1.0050 1.0045 1.0041 42 1.0063 1.0063 1.0060 1.0058 1.0055 1.0051 43 1.0069 1.0069 1.0068 1.0066 1.0063 1.0061 44 1.0074 1.0075 1.0074 1.0073 1.0071 1.0070 45 1.0083 1.0083 1.0082 1.0080 1.0079 1.0078 46 1.0094 1.0095 1.0093 1.0090 1.0087 1.0085 47 1.0105 1.0106 1.0104 1.0100 1.0094 1.0089 48 1.0113 1.0115 1.0113 1.0105 1.0095 1.0090 49 1.0116 1.0118 1.0113 1.0102 1.0092 1.0090 Table 13-21 Relative Brightness at the Location of Red Vertical Pixel to the Brightness at the Front of the Integrating Sphere Row Col 12 Col 13 Col 14 Col 15 Col 16 Col 17 0 0.9735 0.9737 0.9737 0.9734 0.9727 0.9719 1 0.9755 0.9754 0.9751 0.9745 0.9738 0.9729 2 0.9772 0.9768 0.9764 0.9758 0.9750 0.9741 3 0.9787 0.9783 0.9777 0.9770 0.9762 0.9752 4 0.9802 0.9796 0.9789 0.9780 0.9770 0.9761 5 0.9814 0.9806 0.9796 0.9785 0.9775 0.9766 6 0.9820 0.9809 0.9797 0.9787 0.9777 0.9770 7 0.9818 0.9807 0.9795 0.9785 0.9779 0.9775 8 0.9811 0.9801 0.9791 0.9786 0.9784 0.9783 9 0.9804 0.9796 0.9792 0.9790 0.9789 0.9787 10 0.9800 0.9796 0.9793 0.9791 0.9789 0.9786 11 0.9798 0.9795 0.9792 0.9787 0.9783 0.9780 12 0.9796 0.9793 0.9789 0.9783 0.9777 0.9773 13 0.9792 0.9791 0.9789 0.9783 0.9775 0.9770 14 0.9788 0.9791 0.9792 0.9786 0.9777 0.9772 15 0.9787 0.9794 0.9796 0.9791 0.9783 0.9778 16 0.9794 0.9801 0.9805 0.9800 0.9793 0.9790 17 0.9806 0.9813 0.9815 0.9811 0.9807 0.9808 18 0.9821 0.9827 0.9829 0.9830 0.9833 0.9838 19 0.9838 0.9845 0.9851 0.9858 0.9865 0.9870 20 0.9859 0.9865 0.9871 0.9875 0.9885 0.9893 21 0.9883 0.9886 0.9890 0.9891 0.9893 0.9897 22 0.9904 0.9905 0.9911 0.9914 0.9912 0.9909 23 0.9922 0.9921 0.9926 0.9933 0.9935 0.9932 24 0.9934 0.9934 0.9938 0.9946 0.9953 0.9952 25 0.9943 0.9944 0.9947 0.9955 0.9964 0.9967 26 0.9949 0.9950 0.9953 0.9960 0.9969 0.9976 27 0.9954 0.9955 0.9957 0.9963 0.9971 0.9980 28 0.9958 0.9959 0.9960 0.9964 0.9971 0.9980 29 0.9963 0.9963 0.9964 0.9966 0.9971 0.9979 30 0.9969 0.9968 0.9968 0.9969 0.9972 0.9978 31 0.9975 0.9973 0.9971 0.9971 0.9973 0.9977 32 0.9982 0.9978 0.9975 0.9974 0.9974 0.9977 33 0.9990 0.9985 0.9980 0.9977 0.9976 0.9978 34 0.9997 0.9992 0.9986 0.9982 0.9979 0.9980 35 1.0004 0.9999 0.9993 0.9987 0.9983 0.9982 36 1.0010 1.0006 1.0000 0.9993 0.9988 0.9986 37 1.0016 1.0012 1.0006 0.9999 0.9994 0.9990 38 1.0021 1.0018 1.0012 1.0006 1.0000 0.9995 39 1.0027 1.0024 1.0019 1.0013 1.0007 1.0002 40 1.0033 1.0031 1.0026 1.0020 1.0014 1.0009 41 1.0039 1.0038 1.0034 1.0028 1.0022 1.0017 42 1.0046 1.0044 1.0041 1.0036 1.0031 1.0026 43 1.0052 1.0051 1.0048 1.0045 1.0040 1.0035 44 1.0058 1.0058 1.0055 1.0053 1.0049 1.0044 45 1.0064 1.0065 1.0063 1.0060 1.0057 1.0054 46 1.0069 1.0070 1.0070 1.0068 1.0065 1.0063 47 1.0075 1.0076 1.0076 1.0074 1.0073 1.0071 48 1.0084 1.0084 1.0083 1.0082 1.0080 1.0079 49 1.0095 1.0096 1.0094 1.0092 1.0089 1.0086 Table 13-22 Relative Brightness at the Location of Red Horizontal Pixel to the Brightness at the Front of the Integrating Sphere Row Col 18 Col 19 Col 20 Col 21 Col 22 Col 23 0 0.9787 0.9782 0.9775 0.9767 0.9758 0.9749 1 0.9800 0.9793 0.9785 0.9775 0.9766 0.9757 2 0.9810 0.9800 0.9789 0.9779 0.9771 0.9764 3 0.9814 0.9801 0.9790 0.9781 0.9774 0.9770 4 0.9811 0.9799 0.9788 0.9782 0.9779 0.9778 5 0.9805 0.9795 0.9788 0.9786 0.9786 0.9785 6 0.9800 0.9794 0.9791 0.9790 0.9789 0.9787 7 0.9798 0.9795 0.9792 0.9789 0.9786 0.9783 8 0.9797 0.9794 0.9789 0.9784 0.9779 0.9776 9 0.9795 0.9792 0.9788 0.9781 0.9775 0.9771 10 0.9792 0.9790 0.9789 0.9781 0.9774 0.9770 11 0.9789 0.9791 0.9791 0.9785 0.9777 0.9773 12 0.9789 0.9795 0.9797 0.9791 0.9784 0.9780 13 0.9794 0.9802 0.9805 0.9800 0.9795 0.9794 14 0.9805 0.9813 0.9815 0.9812 0.9811 0.9814 15 0.9819 0.9827 0.9830 0.9832 0.9838 0.9845 16 0.9835 0.9843 0.9851 0.9859 0.9868 0.9875 17 0.9856 0.9863 0.9871 0.9876 0.9885 0.9895 18 0.9879 0.9883 0.9888 0.9891 0.9894 0.9895 19 0.9901 0.9902 0.9908 0.9914 0.9914 0.9912 20 0.9919 0.9919 0.9923 0.9931 0.9937 0.9935 21 0.9932 0.9932 0.9935 0.9943 0.9952 0.9955 22 0.9941 0.9942 0.9944 0.9951 0.9960 0.9968 23 0.9947 0.9948 0.9951 0.9956 0.9965 0.9974 24 0.9952 0.9953 0.9955 0.9959 0.9967 0.9976 25 0.9957 0.9957 0.9958 0.9961 0.9967 0.9975 26 0.9962 0.9962 0.9962 0.9964 0.9968 0.9974 27 0.9968 0.9967 0.9967 0.9967 0.9970 0.9974 28 0.9975 0.9973 0.9971 0.9971 0.9971 0.9974 29 0.9983 0.9979 0.9976 0.9974 0.9974 0.9975 30 0.9990 0.9987 0.9982 0.9979 0.9977 0.9976 31 0.9997 0.9994 0.9989 0.9984 0.9981 0.9979 32 1.0004 1.0001 0.9997 0.9991 0.9986 0.9983 33 1.0010 1.0008 1.0004 0.9998 0.9992 0.9988 34 1.0015 1.0014 1.0011 1.0005 0.9999 0.9994 35 1.0020 1.0020 1.0017 1.0012 1.0006 1.0000 36 1.0026 1.0026 1.0023 1.0018 1.0013 1.0007 37 1.0031 1.0031 1.0030 1.0026 1.0020 1.0014 38 1.0036 1.0037 1.0036 1.0033 1.0028 1.0023 39 1.0042 1.0043 1.0043 1.0041 1.0037 1.0032 40 1.0047 1.0050 1.0049 1.0048 1.0045 1.0041 41 1.0052 1.0056 1.0056 1.0055 1.0053 1.0050 42 1.0057 1.0061 1.0063 1.0062 1.0060 1.0058 43 1.0060 1.0066 1.0069 1.0069 1.0068 1.0066 44 1.0065 1.0070 1.0074 1.0075 1.0074 1.0073 45 1.0072 1.0078 1.0081 1.0082 1.0082 1.0081 46 1.0081 1.0088 1.0092 1.0093 1.0092 1.0091 47 1.0090 1.0098 1.0103 1.0105 1.0104 1.0101 48 1.0095 1.0105 1.0112 1.0114 1.0113 1.0107 49 1.0095 1.0107 1.0115 1.0118 1.0116 1.0106 13.5.2.4 Computation of SA Absolute Response The SA absolute response is then computed for every pixel at every temperature. This is the true, measured absolute response of the Solar Aureole. 13.5.3 Thermal Modeling 13.5.3.1 Mean Absolute Response Because the absolute response varies with temperature, it is helpful to have a thermal model. As a base for the model, the mean absolute response for each channel is computed versus CCD chip temperature, and it is fit with a fifth or sixth order polynomial. Column 0 is excluded from the mean because it lies at the edge of the fiber ribbon illumination and is impacted by mechanical changes with temperature that are different from the rest of the array. Creating a thermal model using the detector temperature for the mean and initial pixel map derivation, but using the optics temperature for pixel-to-pixel variations over temperature (which makes more physical intuitive sense), resulted in a model with poorer performance than just using CCD temperature. The pixel-to-pixel variation with temperature is likely due to thermal variance of the separation between the CCD and the fiber ribbon, which is better modeled by the CCD temperature than the optics temperature since that temperature sensor is closer than the one on the optical bench. The results are in the following plot and table. Table 13-23 Polynomial Coefficients for the Mean Absolute Response versus CCD Temperature Blue Horizontal Blue Vertical Red Horizontal Red Vertical A0 -1.320628900000e+8 -1.043157230000e+8 -6.342293175000e+7 -4.764707846875e+7 A1 3.439118281250e+6 2.708450062500e+6 1.392982078125e+6 1.053106603516e+6 A2 -3.693190771484e+4 -2.898806738281e+4 -1.200406482697e+4 -9.126064826965e+3 A3 2.100620784760e+2 1.643101100922e+2 5.120302107930e+1 3.914550912380e+1 A4 -6.678061112761e-1 -5.205441340804e-1 -1.080477217911e-1 -8.309265802382e-2 A5 1.125490496634e-3 8.742839563638e-4 9.032962566380e-5 6.989951356218e-5 A6 -7.858712436359e-7 -6.084150783181e-7 0.000000000000e+0 0.000000000000e+0 FIG_13-59.GIF Figure 13-59 Mean Absolute Response versus Temperature 13.5.3.2 Pixel Maps The next step in the generation of a thermal model is the formation of a pixel map at the coldest temperature. This map is the computed absolute response from the previous sections divided by the polynomial fit at the coldest temperature. This map then represents the pixel-to-pixel variations. IMAGE_064.GIF 78. 13.5.3.3 Thermal Variation in Pixel Maps If the pixel-to-pixel variations were thermally invariant, one could then compute the absolute response of any pixel at any temperature by the following equation. IMAGE_066.GIF 79. Unfortunately, this is not the case. The pixel-to-pixel variations do vary also with temperature. Several physical mechanisms may be contributing to this variation, but one effect is that the separation between the fiber ribbon bundle and the CCD appears to vary slightly with temperature. The pixel-to-pixel variation with temperature is modeled by an additional set of polynomial coefficients for each pixel in the map. Two temperatures were considered in this polynomial fit - the detector temperature and the optics temperature. The detector temperature yields the better performance, probably because the detector temperature sensor is closer to the gap between the fiber ribbon and CCD and thus models the temperature of that gap more accurately. In this way, the absolute response for any pixel at any temperature can be computed by the following equation. IMAGE_068.GIF 80. This equation can be simplified by multiplying the Map and the "p" polynomial coefficients to result in the final model for the thermal variation of the absolute response. IMAGE_070.GIF 81. The "M" coefficients for the thermal variation of the pixel map are in the tables in the main body of this document. 13.5.4 Model Results A figure of merit for the thermal model is the model divided by the true absolute response. Before applying this figure of merit to the model, the measurement uncertainty can be incorporated in the analysis by applying the theoretical signal to noise ratio for the original measurements of the absolute response. The measured "value" is actually a measured "band" consisting of the value plus and minus the noise. The model matches the measured absolute response if it falls within the band defined by the true absolute response and the measurement noise. The following table lists the portion of modeled pixels and temperatures (6*50*31 total samples for each channel) that match the measured values to within the measurement noise. Table 13-24 Portion of Modeled Data that Match Measured to within Noise Blue Horizontal Blue Vertical Red Horizontal Red Vertical 0.7045 0.7191 0.6043 0.6135 If one then adds an error band to the model to find the portion of the pixels that lie within a given percentage of the noise banded measured data, one gets the following plots (Figs 13_5_4_A thru M). The plots show the model performance overall, as well as broken out by column and by temperature. In the blue channels, 96% of the pixel/temperature combinations using the model are within 1% of the measured absolute response, and over 99% of the modeled pixels are within 1.7% of the measured data. In the red channels, over 99% are within 1%, and all are within 1.5%. In most cases, no particular column or temperature is worse performing than the others. However, in the blue channels, the data at 186K is not well modeled. There are two measurements at 186K, but they do not match the models well. The red horizontal column 0 is also poorly modeled. Figures 13.5.4A through 15.5.4M... FIG_13_5_4_A.GIF FIG_13_5_4_B.GIF FIG_13_5_4_C.GIF FIG_13_5_4_D.GIF FIG_13_5_4_E.GIF FIG_13_5_4_F.GIF FIG_13_5_4_G.GIF FIG_13_5_4_H.GIF FIG_13_5_4_I.GIF FIG_13_5_4_J.GIF FIG_13_5_4_K.GIF FIG_13_5_4_L.GIF FIG_13_5_4_M.GIF Following are four plots (Figs 13_5_4_N thru Q) of the root-mean-square deviation over temperature of the model from the measured absolute response, divided by the average response over temperature, for every pixel in each SA camera. For each plot the legend is the same. Point Style Column Number + 0 * 1 diamond 2 triangle 3 square 4 X 5 FIG_13_5_4_N.GIF FIG_13_5_4_O.GIF FIG_13_5_4_P.GIF FIG_13_5_4_Q.GIF The blue channels are modeled to about 1% accuracy, and the red are modeled to about half that, with the exception of the red horizontal column 0, which has known fiber ribbon chips. 13.6 Polarization Sensitivity 13.6.1 Test Configuration The Solar Aureole portion of the flight sensor head (SN03) was illuminated by a test setup in which the orientation of linearly polarized light could be changed. In this setup, light from the high intensity lamp passed through a spectral filter and then through a Glan-Thompson prism. The prism was mounted in a motor-driven rotating mount so the direction of linearly polarized light emerging from the prism could be changed during the test. The light emerging from the prism was turned through 90 degrees by reflection from a front surface mirror and was directed to an 8-inch diameter spherical mirror. Light reflected from the spherical mirror produced a collimated beam. The flight sensor head was mounted in a motor driven altitude-azimuth mount and was placed in this beam. A series of measurements was made while the Glan-Thompson prism was rotated. This series was repeated as the instrument was tipped so different columns and rows in the Solar Aureole camera were illuminated by the collimated beam. The instrument was removed from the beam and replaced by the standard silicon detector. This measured any variations in intensity presented to the instrument while the Glan-Thompson prism was rotated. Significant variations in intensity were measured at the location of the DISR sensor head. The DISR counts per second were divided by the signal of the standard detector to remove this modulation. FIG_13-60 Figure 13-60 The setup used to measure the polarization of the SH03 Flight Instrument. A second form of correction factor was also applied. The measurements made with the DISR instrument were separated in time from the measurements made using the standard detector in the collimated beam. It was possible that the brightness of the lamp might have drifted between these times. A partially-silvered beam splitter (actually an nd=1 neutral density filter) was used to pick off a portion of the beam emerging from the Glan-Thompson prism. This portion of the beam was measured by a second silicon detector. The ratio of the brightness measured by this detector at the times when the DISR measurements were taken and when the standard detector measurements were made was used to correct for drifts in the lamp with time. The test setup is shown in the figure. 13.6.2 Polarization Calibration of the 500 nm SA Channels Unfortunately, the partially silvered beam splitter and the front silvered mirror used to turn the direction of the beam acted to change the state of polarization of the light presented to the DISR instrument as a function of the rotation angle of the Glan-Thompson prism. The fact that this occurred can be seen in the corrected DISR intensities plotted as a function of the Glan- Thompson rotational position in Figure 13-61 and Figure 13-62. In these figures the points represent the measured intensities after the two correction factors were applied. The curves are attempts to fit the data with a cosine- squared law. Note that the fits are not very good. Also, it is not apparent why the peak intensity does not occur at the same Glan-Thompson angle regardless of row number of the SA instrument. In these measurements, a Glan-Thompson angle of 29.5 degrees corresponds to horizontally polarized light and 119.5 degrees corresponds to vertically polarized light. In both the vertical and horizontal channels the phase of apparent polarization varies significantly with row number in a manner that was totally unexpected. Further, at some rows (especially at small or large row numbers far off axis of the center of the SA field) the measurements seem to not go to zero for any orientation of the Glan-Thompson prism. FIG_13-60.GIF Figure 13-61 The intensity measured in the Blue Horizontal Channel as a function of the orientation of the polarization of the incident light as measured by the angle of the Glan-Thompson prism. The points are the observations at the columns 1 or 2 and at rows 4, 13, 24, and 43. The curves are cosine squared models that do not fit the observations well. FIG_13-62.GIF Figure 13-62 Same as Figure 13-61 but for the Blue Vertical channel. Even though the test setup likely produced light that was not completely linearly polarized at exactly the orientation of the Glan-Thompson polarizer, the shift of phase with location in the field (row number) was so striking and unexpected that a special set of measurements was made. These consisted of illuminating a spare beamsplitter of the type installed in the flight instrument by linearly polarized light and measuring the intensity emerging from the beam splitter as a function of the angular position of a sheet polarizer placed after the beam splitter. The test setup for this test is shown in Figure 13-63. FIG_13-63 Figure 13-63 Diagram of test setup for measuring the properties of a spare prism of the type used in the flight model of the DISR Solar Aureole system. Polarizer 1 was set to introduce linearly polarized at an angle of 0, 45, or 90 degrees from the horizontal direction. The intensity is measured by the photodiode detector after the light is passed through polarizer 2. The orientation of polarizer 2 is varied in 10 degree steps from the horizontal increasing in the CCW direction looking toward the source. Data were collected with the prism oriented perpendicular to the incident beam or at an angle of + or - 30 degrees from the direction. At a reading of 29.5 degrees on polarizer 2 the plane of polarization is oriented parallel to the Y axis (vertical). FIG_13-64.GIF Figure 13-64 The intensity as a function of position angle when the spare Solar Aureole prism was illuminated by horizontally polarized light. The Glan- Thompson analyzer is positioned after the light passes through the flight prism. Note that a reading of 29.5 degrees corresponds to vertically polarized light. The points are observations, and the curves are models for a retardance, tau, and position angle, psi, of the incident light from the principal axis of the retarder that arises from the partially silvered beam splitter in the prism. Note that the fits are quite good. In this test, horizontally polarized light was sent to the flight prism, and the state of polarization of the light that passed through the prism was measured by measuring the intensity that passed through the Glan-Thompson prism for each of many orientations of the prism. This test was repeated with the flight prism rotated so the light struck the prism perpendicular to the long axis of the prism, and also at + and - 30 degrees from this direction. The intensities measured as a function of Glan-Thompson analyzer orientation are shown in Figure 13-64. In addition to sending horizontally polarized light to the flight prism, the orientation of the sheet polarizer in front of the prism was rotated so that vertically polarized light could be used to illuminate the prism, and an orientation 45 degrees between horizontal and vertically polarized light could also be used. Figure 13-65 and Figure 13-66 show the results for these different orientations. The results for the 45 degree orientation of the incident beam are particularly revealing. Note that when light at 45 degrees orientation strikes the prism at 0 degrees from the perpendicular to the long axis of the prism that the light intensity is only very slightly modulated as a function of the orientation of the Glan-Thompson analyzer. For purely linearly polarized incident light to emerge almost unmodulated by the orientation of an analyzer requires the flight prism to act nearly as a quarter-wave retarder! In Figure 13-64, Figure 13-65, and Figure 13-66 the points are the measured intensities while the curves are the intensities expected from an ideal retarder with variable retardance and variable orientation of the incident polarized light from the principal axis of the retarder. FIG_13-65.GIF Figure 13-65 Same as Figure 13-62 but for light initially polarized at an angle of 45 degrees from the vertical. Note that when this purely polarized light is incident perpendicular to the prism (black curve) the output intensity is only modulated by some 10% after passing through the Glan-Thompson prism. This is an indication that the input polarized light is converted to a significant component of circular polarization in passing through the flight prism. The retardance of the flight prism must be nearly 90 degrees in this case. FIG_13-66.GIF Figure 13-66 Like Figure 13-65 but for vertically polarized light incident on the flight prism. While the light is highly modulated, the phase of the light is shifted, again indicating strong retardance in the flight prism. Figure 13-67 shows the retardance of the spare prism for the three orientations of the incident polarization and for the three angles of incidence of the light relative to the long axis of the prism. Note that the retardance is nearly 90 degrees in all cases. FIG_13-67.GIF Figure 13-67 This figure shows the retardance of the flight prism necessary to fit the observations in the last three figures as a function of the angle of the incident light to the perpendicular to the prism. Note that the retardance is near 90 degrees, and the flight prism acts similar to a quarter-wave plate. FIG_13-68.GIF Figure 13-68 This figure shows the angle of the polarized light from the principal axis of the retarder as a function of the angle of the beam from the perpendicular to the prism. In the flight configuration, light in each row of the detector will enter the prism at a different angle, spanning the range from about -25 to + 25 degrees. Figure 13-68 shows the angle of the polarized light from the principal axis of the retarder as a function of the angle of the incident beam from the perpendicular to the flight prism. The field of view in row number corresponds to angles within about + and - 25 degrees in this figure. Thus, the action of the flight prism corresponds to a roughly quarter wave plate with variable angles relative to the principal axes with different row numbers. This seems to be how the phase was shifted with row number in the original measurements in the test setup. In order to make use of the measurements made on the flight model before delivery, it is necessary to measure the properties of the test setup. This setup was reconstructed in the spring of 2004. We installed a sheet polarizer followed by the standard silicon detector at the location where the DISR sensor head had been placed in the collimated beam. We recorded the corrected intensity in this location for each orientation of the Glan-Thompson prism as a function of the orientation of the sheet polarizer. The results are shown in Figure 13-69 below. FIG_13-69.GIF Figure 13-69 We show the modulation of intensity caused by a rotated analyzer at the location of DISR in the test setup used for polarization measurements for different orientations of the plane of polarization of the input light. Note that for some orientations of the incident polarization a significant intensity leaks through the analyzer at the output of the test setup, indicating that a significant conversion from linear to circular polarization is occurring in the test setup is some orientations. Note that the intensity does not go to zero for any orientation of the sheet when the input polarization orientation is near 45 degrees from the horizontal. Near 0 and 90 degrees, the intensity does go to zero at the expected orientation of the sheet polarizer. In Figure 13-69, the points are the measured intensities and the curves are for an ideal retarder for fitted retardance and position angle relative to the principal axis of the retarder. The results are shown in Figure 13-70 and Figure 13-71. Figure 13-70 shows the variation of the position angle relative to the principal axis of the retarder as a function of the input polarization orientation. Figure 13-71 shows the retardance as a function of input polarization orientation. Note that the retardance is well constrained at input polarization angles of 45 and 135 degrees, and is poorly constrained near 0, 90, and 180 degrees since the polarization is nearly aligned with the principal axis of the retarder for these orientations. The retardance is approximately 60 degrees where it is well constrained. FIG_13-70.GIF Figure 13-70 We show the angle of the polarized light relative to the principal axis of the retarder in the test setup for different orientations of the Glan- Thompson prism at the input to the test setup. The angle is near 0 or 90 degrees when the Glan-Thompson prism polarizes the light vertically or horizontally, but at intermediate angles, significant angles from the axis of the retarder are reached. FIG_13-71.GIF Figure 13-71 The retardance introduced by the test setup is shown as a function of the angle of the Glan-Thompson prism. There is little sensitivity at angles near 0 or 90 degrees, but near 45 or 135 degrees the retardance is some 50 or 60 degrees. FIG_13-72.GIF Figure 13-72 The measured variation in intensity of the Blue Horizontal channel as a function of the setting of the Glan-Thompson prism is shown for various columns and rows. The curves are functions including the retardance of the test setup as well as a variable retardance and position angle of the flight prism. Note that the fits are much better than in Figure 13-61. Now that the characteristics of the test setup have been determined, it is possible to solve for the degree of retardance of the beam splitter in the flight model SA unit and the angle of the input polarization relative to the principal axis of the retarder as a function of row number in the blue horizontal and vertical channels. The best fits of the data to the observations are shown in Figure 13-72 and Figure 13-73. The points are the measurements while the curves are for a model of the sensor head. The fits are quite good. Figure 13-74 shows the position angle relative to the principal axis of the retarder of the sensor head as a function of row number in the blue vertical and horizontal channels. This angle varies from +10 to some - 15 degrees as the row number increases from 0 to 49 in the flight unit. Quadratic fits to the position angles as functions of row number in each blue channel are also given. It is interesting to understand how the instrument came to have these properties. One requirement of the in flight calibration system was that it pass light through all the optical elements of a system except for the front window. This requirement allowed for accurate tracking of any radiation darkening of optics or changes in alignments over the launch or cruise environments. However, because of the design of the Solar Aureole optical system, it implied a beamsplitter to introduce the calibration signal. FIG_13-73.GIF Figure 13-73 Same Figure 13-72 but for the Blue Vertical channel. Again note the improved quality of the fit compared to Figure 13-62. FIG_13-74.GIF Figure 13-74 We show the position angle as a function of row number for the Blue Vertical and Horizontal channels in the SH03 flight Solar Aureole system. The retardance is taken as 90 degrees for the flight prism in the blue channel. 13.6.3 Polarization Calibration of the 935 nm SA Channels A similar set of measurements of the full flight instrument as well as for the prism alone was made in the red Solar Aureole channel. Again, the measurements did not fit the corrected measurements made in the full instrument test. Measurements on the spare prism alone were repeated in the red channel using the test setup shown in Figure 13-63. The results for incident light at 45, 0, and 90 degrees from the horizontal are shown in Figure 13-75, Figure 13-76, and Figure 13-77. Points are measurements and the curves are fits for variable retardance and angle relative to the principal axis of the retardance introduced by the prism. FIG_13-75.GIF Figure 13-75 Intensity as a function of analyzer angle when spare prism is illuminated with linearly polarized light at an angle of 45 degrees. Note that the curve for 45 degrees incidence is much more highly modulated in the red channel than in the blue, indicating that the retardance of the flight prism is less in the red than in the 500 nm channel. Again, good fits are possible with adjustments of the retardance of the prism and the position angle. Results are shown in Figure 13-79. FIG_13-76.GIF Figure 13-76 Like Figure 13-75 but for incident light polarized at an angle of 0 degrees (parallel to long axis of prism.) FIG_13-77.GIF Figure 13-77 Like Figure 13-76 but for light polarized at an angle of 90 degrees (perpendicular to long axis of prism). FIG_13-78.GIF Figure 13-78 Position angle of polarization relative to principal axis of retarder as a function of angle of illumination relative to perpendicular to spare prism (left scale and open symbols.) Right scale shows the degree of retardance of the spare prism as a function of the angle of illumination to the perpendicular to the prism. Note that the retardance of the prism is some 30 degrees, much less than the prism as measured in blue light. Note that the retardance of the prism alone in the red channels is approximately 30 degrees compared to the 90 degrees measured in the 500 nm channel. Since the dichroic beam splitter is much more reflective in the 500 nm channel than in the red channel, this is not surprising. Also, the position angle relative to the principal axis of the retarder varies with row number in a similar manner to that measured for the measurements on the blue prism. Figure 13-79 shows the measurements made at the red channel wavelength on the test setup used for the measurements on the full flight Solar Aureole instrument. Again, the curves do not go to zero intensity near 45 and 135 degrees. The reduced position angle and retardance of the test setup in red light are shown in Figure 13-80 and Figure 13-81. With these measurements of the characteristics of the test setup in red light, the measurements made on the flight unit in this test can be analyzed. FIG_13-79.GIF Figure 13-79 Intensity as a function of angle from horizontal direction when the test setup used to measure the flight instrument in red light is illuminated by linearly polarized light oriented as shown in the caption (caption angle is from horizontal increasing CCW looking toward the source.) Note that the intensity does not go to zero near 45 and 135 degrees indicating some amount of circular polarization in the beam under these conditions. FIG_13-80.GIF Figure 13-80 The angle of the polarized beam relative to the principal axis of the retarder in the test setup used to measure the flight SA instrument in red light. FIG_13-81.GIF Figure 13-81 The retardance of the test setup used to measure the properties of the flight SA instrument as a function of the angle of polarization produced by the Glan-Thompson prism. The polarization angle is measured CCW from horizontal looking toward the source. The resulting position angle (Psi) and degree of retardance (Tau) as functions of row number are shown in Figure 13-82 and Figure 13-83 for red horizontal and vertical channels, respectively. The retardance is about 30 degrees, as measured for the prism alone. The position angle varies from some 80 degrees to near 20 degrees from row 0 to row 49 in both red channels. These values are slightly different than the values measured for the prism alone, but the full instrument is included in these tests. It seems necessary to accept these values of Psi as functions of row in the full flight assembly. Note that with a smaller degree of retardance in the prism in the red than the blue, more drastic values of Psi must be chosen to make the test measurements agree with the calculations. It may be that other portions of the optical system included in the full optical assembly require these values for the position angles in the red channels. FIG_13-82.GIF Figure 13-82 The position angle (Psi, left scale, blue dots) and the degree of retardance (tau, right scale, red squares) as functions of row in the horizontal channel of the flight sensor head. FIG_13-83.GIF Figure 13-83 Like Figure 13-82 but for the vertical channel of the flight SA in the red. The results of the model (curves) are compared to the observations made in the red full-instrument test setup are shown in Figure 13-84 and Figure 13-85 below. Again, the fits are quite good in both channels. Thus, it seems that the full flight Solar Aureole system can be modeled by an ideal variable retarder with position angle and retardance dependant on row number followed by an analyzer in the vertical or horizontal orientation. With this model, the intensity in the two instrument channels can be predicted for any orientation and degree of linear polarization in the incident light. Also, if the orientation of the polarization of the incident light is assumed, the total intensity and the degree of polarization can be found. FIG_13-84.GIF Figure 13-84 The intensity measured by the flight SA in the red vertical channel as a function of the setting of the Glan-Thompson prism in the test setup when different rows were illuminated as indicated. Note that the curves are in good agreement with the measured points. FIG_13-85.GIF Figure 13-85 Like Figure 13-84 but for the red horizontal channel of the flight SA instrument. The fits are quite good except for the extreme corner of the field of view (column 22, row 3). Since the instrument will be used near the peak of the curve (near 30 degree Glan-Thompson angle), the agreement of the curves with the measured points is considered acceptably good.