## Abstract

Lunar calibration has the potential to put all participating instruments on the same long-term stable radiometric scale. Realizing this involves significant effort on the part of instrument teams and calibration community. Among the challenges are: improving the lunar spectral-irradiance model, extracting the measured irradiance from an instrument observation, and understanding any response differences between a normal nadir observation and a lunar view. This work addresses the first of these; this year’s CALCON workshop will help address the other two.

A problem with the ROLO lunar calibration model is ’jumps’ between its underlying 32 bands, especially at longer wavelengths. This issue is also contained in the initial version of the SLIM (Spacecraft and earth- base Lunar Irradiance Model); a band-by-band methodology. By normalizing instrument measurements to a high-spectral-resolution lunar reflectance spectrum, a model has now been developed that is continuous in wavelength as well as geometry.

The SLIM system allows scaling each instrument band by a constant gain factor, which is found by iterative modeling. SLIM models can be polynomial to a modest power in each of the five geometric angles; phase angle, selenographic solar longitude and latitude, selenographic viewer longitude and latitude; and each of these terms can be independently be multiplied by a polynomial up to cubic in ’wave’; wavelength λ in µm, 1/λ or ln λ. A variety of numerical tools have been developed to aid in choosing which combination from this large zoo of terms works well in minimizing both residuals and the number of coefficients.

Currently, data from ROLO, Landsat-8 OLI, Hyperion, MODIS-Aqua, MODIS-Terra, SNPP-VIIRS, SeaW-IFS, PLEIADES-A, PLEIADES-B go into the model, about 87,000 points. If the instrument team supplies trends that they feel should be applied to the measurements, that is done at data ingest. Data are automatically processed for wild-points. Overall weights can be assigned to each instrument, and relative weights to each band.

After a model fit, all instruments are calibrated with that model, the empirical gain factors for each band and instrument are revised, trends can be assessed (five possible models) and applied; weights can also be revised. Residual seasonal oscillations can be quantified and applied. Then the fit process is iterated until convergence.

The calibration spectrum of all instruments mentioned plus five GOES instruments and NIST telescope observations, will be presented, revealing their relative scales. All spacecraft teams with lunar observations are invited to participate.

A Lunar Calibration Model Based on Many Instruments and One Moon

Lunar calibration has the potential to put all participating instruments on the same long-term stable radiometric scale. Realizing this involves significant effort on the part of instrument teams and calibration community. Among the challenges are: improving the lunar spectral-irradiance model, extracting the measured irradiance from an instrument observation, and understanding any response differences between a normal nadir observation and a lunar view. This work addresses the first of these; this year’s CALCON workshop will help address the other two.

A problem with the ROLO lunar calibration model is ’jumps’ between its underlying 32 bands, especially at longer wavelengths. This issue is also contained in the initial version of the SLIM (Spacecraft and earth- base Lunar Irradiance Model); a band-by-band methodology. By normalizing instrument measurements to a high-spectral-resolution lunar reflectance spectrum, a model has now been developed that is continuous in wavelength as well as geometry.

The SLIM system allows scaling each instrument band by a constant gain factor, which is found by iterative modeling. SLIM models can be polynomial to a modest power in each of the five geometric angles; phase angle, selenographic solar longitude and latitude, selenographic viewer longitude and latitude; and each of these terms can be independently be multiplied by a polynomial up to cubic in ’wave’; wavelength λ in µm, 1/λ or ln λ. A variety of numerical tools have been developed to aid in choosing which combination from this large zoo of terms works well in minimizing both residuals and the number of coefficients.

Currently, data from ROLO, Landsat-8 OLI, Hyperion, MODIS-Aqua, MODIS-Terra, SNPP-VIIRS, SeaW-IFS, PLEIADES-A, PLEIADES-B go into the model, about 87,000 points. If the instrument team supplies trends that they feel should be applied to the measurements, that is done at data ingest. Data are automatically processed for wild-points. Overall weights can be assigned to each instrument, and relative weights to each band.

After a model fit, all instruments are calibrated with that model, the empirical gain factors for each band and instrument are revised, trends can be assessed (five possible models) and applied; weights can also be revised. Residual seasonal oscillations can be quantified and applied. Then the fit process is iterated until convergence.

The calibration spectrum of all instruments mentioned plus five GOES instruments and NIST telescope observations, will be presented, revealing their relative scales. All spacecraft teams with lunar observations are invited to participate.