Prior to this reprocessing, the instrument model used in deriving the focal plane temperature corrections attributed the residuals of the lunar time series, with the long-term radiometric trend removed, to the varying temperature response only. This assumption resulted in the possibility that biases could arise in the temperature correction coefficients due to any remaining changes in the radiometric response of the instrument over time. To avoid such possible biases, the instrument model used in deriving the temperature correction coefficients for this reprocessing has been updated to simultaneously solve for the long-term radiometric response of the instrument and the dependence of the response on focal plane temperatures. Once the optimum focal plane temperature correction coefficients have been identified for each band, these coefficients are incorporated into the instrument calibration and the optimum long-term radiometric corrections are re-derived.
The function used in the regression fits for the long-term radiometric trend and the focal plane temperature dependence has the form:
where AX are the fit coefficients, to is the reference time for the mission, C1 is the short-period time constant, and Tref is the reference temperature for the calibration (16 C).
The focal plane temperature dependency analysis has involved the evaluation of the lunar residuals derived three ways: 1) without any temperature corrections; 2) using the measured prelaunch temperature corrections; and 3) using the temperature corrections derived from the on-orbit data using Eq. 1.
The dependencies of the radiometric response for Bands 1-5 on the focal plane temperatures are small relative to those observed for the other bands. The temperature corrections derived for these bands from the on-orbit data are smaller than the prelaunch corrections and the prelaunch corrections yield smaller lunar residuals than do the on-orbit values. Accordingly, for the reprocessing, the focal plane temperature corrections for Bands 1-5 have reverted to their prelaunch measured values.
The focal plane temperature corrections for Bands 6-8 derived from the on-orbit data are larger significantly different from the prelaunch values -- there are sign changes in the coefficients and the values for Bands 7 and 8 are larger than the prelaunch values. The lunar residuals for Band 6 and 7 warrant using focal temperature corrections for each band derived from the on-orbit data. The lunar residuals for Band 8 show a change in the focal plane temperature dependence over the mission, warranting the use of two focal temperature corrections for this band, with the temperature correction epoch boundary occurring in mid-2005.
The focal plane temperature corrections that will be used in the current reprocessing are shown in the following table:
412 nm | 443 nm | 490 nm | 510 nm | 555 nm | 670 nm | 765 nm | 865 nm | |
---|---|---|---|---|---|---|---|---|
1st Epoch | 0.0009010 | 0.0005850 | 0.0004200 | 0.0003900 | 0.0003910 | -0.0000830 | -0.0005316 | -0.0016348 |
2nd Epoch | 0.0009010 | 0.0005850 | 0.0004200 | 0.0003900 | 0.0003910 | -0.0000830 | -0.0005316 | -0.0026531 |