A quantitative test of the ability of models based on the equation of radiative transfer to predict the bidirectional reflectance of a well-characterized medium

Predictions of two widely-used regolith reflectance models, a numerically exact computer code and an approximate analytic equation, based on the equation of radiative transfer were tested against the measured reflectance of a medium of close-packed spheres, whose properties supposedly can be well-characterized. Surprisingly, the approximate analytic model was a better match to the experimental data than the numerically exact computer solution. Other approximate regolith models were tested briefly with similar results. Discrepancies between the two models and between models and experiment can be explained if the phase functions and albedos of the spheres are not the same as when the particles are isolated. Differences include the absence of the Fraunhoffer diffraction peak, which is an intrinsic assumption of the approximate analytical model but not the exact numerical model, and increased scattering in the mid-range of phase angles, which the approximate analytic model fortuitously describes more accurately than the exact numerical model. These changes may be caused by the close proximity of surrounding particles. If they are taken into account, models based on the radiative transfer equation appear able to quantitatively predict the reflectances of regoliths and other particulate media. Interparticle perturbations are also predicted to cause a coherent backscatter opposition effect in the backward direction that was observed, but its angular width was found to be much larger than predicted by theories for sparsely-packed media.