Bidirectional reflectance of rough particulate media: Ray-tracing solution

Abstract

We investigate the volume and surface shadowing in particulate porous random media with macroscale surface roughness over the full scattering hemisphere using Monte-Carlo ray tracing. We also study the volume and rough-surface effects using two diffuse bidirectional reflectance models, namely, the Lambertian and Lommel–Seeliger models. First, we examine the volume effects arising from the porosity of the loosely packed particulate medium. Next, we consider additional shadowing due to the macroscale surface roughness modelled as two-dimensional random fields following Gaussian correlation and fractional-Brownian-motion statistics. We pay special attention to the relative difference of the reflectance as a function of angles of incidence and emergence from a particulate medium with and without macroscale roughness, since it is the major factor when considering what information can safely be deduced from measured reflectance data. The main conclusions of our study concern the distribution of the reflectance over the scattering hemisphere. The rough-surface shadowing due to macroscale roughness has a relatively small effect on the total reflectance of porous media for small emergent azimuth angles, but the importance of rough-surface shadowing increases for large angles. Also, when compared to a solid rough surface which shows a single extended brightness maximum at the opposition observation geometry, a particulate surface can have two separated maxima along the zero azimuth angle. Thus, observations at the azimuth angle of 180 ∘ and large emergence angle, and observations sampling well the azimuth angle for large values of incidence angle would seem to give optimal data when considering the inversion of the properties affecting the shadowing of regolith-covered surfaces.