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Radiance Model

A spatially resolved lunar radiance model is under development at USGS. The model source data are the ROLO lunar images, co-registered in the ALEX projection and calibrated to exoatmospheric radiance. To accommodate limitations of computer memory and to facilitate individual pixel I/O, the radiance image dataset has been re-sampled and transposed, forming ALEX bricks. Data selection has drawn on the irradiance model criteria, with additional quality checks built into the fitting algorithm. This model also operates in reflectance, with individual pixels converted by:

A_k = pi * L_k / E_k

where Lk is the radiance of a pixel and Ek is the solar irradiance in band k, both at the standard Sun-Moon distance of 1 AU. Additionally, ephemeris information for each ROLO image is used to compute the incidence and emission angles and phase angle for each point on the (hemispheric) Moon.

Model coefficients are generated by fitting a user-defined photometric function to individual data pixels using linear least squares and SVD. The linear restriction was imposed for runtime considerations, and places limitations on the ability to fully model the lunar photometric behavior, e.g. the opposition effect. Even using a 3-parameter fit, given the ~200,000 pixels in 32 bands there are about 20 million coefficients to be found.

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