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VMC in-flight characterisation and calibration
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Version 1. Date: 01.06.2015
Contact: VMC PI Wojtek J. Markiewicz (marko@mps.mpg.de)
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Basing on in-flight characterisation of the VMC sensitivity, two correction were
applied to the VMC radiometric calibration. VMC calibration was cross-checked
with Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) (and appropriate
correction to the VMC data was made), and the UV channel data were corrected for
the CCD sensitivity degradation.

1. The radiometric correction factors

The radiometric correction factors for four VMC spectral channels centered at
the wavelengths of 0.365 mkm (UV), 0.513 mkm (VIS), 0.965 mkm (NIR-1), and 1.010
mkm (NIR-2) were obtained from the comparison of almost simultaneous co-located
observations of Venus by VMC and (VIRTIS) and from observations of the bright stars with known
calibrated spectral flux density (see details in subsection 3.2 of [1]).

Values of the corrections factors are the following:

UV    : 2.34
VIS   : 1.45
NIR-1 : 1.66
NIR-2 : 2.01

This values were multiplied with the nominal RADIANCE_SCALING_FACTOR.

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2. Sensitivity degradation in the VMC UV channel

The degradation of UV channel sensitivity with time of mission was estimated
(see details in subsection 3.3 of [1]). The degradation is expected because the
plastic micro-lenses attached to the CCD surface (not the lenses of the VMC
optics) might become more and more opaque the more UV photons they were exposed
to.

We assume the channel sensitivity
S = S0 - kS * t,
where S0 is the initial sensitivity and kS is the rate of its degradation with
the mission time t (which is measured in VEx orbits). To account for the
degradation, one should recalculate B to the time moment t0, when there was no
degradation and when the camera was calibrated (B0). To obtain the value of
degradation coefficient kd,  the "brightness --- orbit number" dependencies
were fitted by a linear function [1]:
B(t) = B0*(1+kd*t),
where B0 is measured in watt/metre^2/steradian/mkm and t in VEx orbits.

Using data from the whole VMC data-set, the value kd was found to be -14.0e-5.
This value is slightly different from that in [1] (-16.2e-5), because here all
orbits (until 3154) were used while in [1] only orbits until 2352 were used.

The values of the RADIANCE_SCALING_FACTOR were corrected for the sensitivity
degradation.

[1] Shalygina et. al. (2014), Planetary and Space Science, DOI:
10.1016/j.pss.2014.11.012