A test of Hapke's model by means of Monte Carlo ray-tracing

One of the most applied solution of the radiative transfer equation for a particulate medium is the so called Hapke's model. It is widely used to describe the photometric output of the surfaces of atmosphereless bodies of the Solar System and to interpret remote sensing data. In this paper we use a Monte Carlo routine which simulates ray-tracing in particulate media to test three formulations of the Hapke's model: IMSA (Isotropic Multiple Scattering Approximation), AMSA (Anisotropic Multiple Scattering Approximation) and an updated version of the model described in Hapke (Hapke, B. [2008]. Icarus 195, 918-926) (from now on H2008). While IMSA and AMSA assume a continuos medium, H2008 accounts for the discreteness of a particulate medium (regolith) and introduces a dependence of the photometric output on the filling factor. Using Monte Carlo ray-tracing we have simulated photometric output of media with different porosities and scattering behaviors (isotropic, back-scattering and forward-scattering). The Shadow Hiding Opposition Effect (SHOE) has been investigated as well. What emerges from this analysis is that H2008 is the most appropriate model to describe the photometric output of particulate media with arbitrary porosities, far from the opposition effect regime, and it is also able to characterize anisotropic scattering, unless the medium exhibits a strongly forward-scattering behavior. On the contrary, IMSA and AMSA models are effective only for sparse materials with a filling factor of the order of 0.01. Surprisingly the former provides a better description also in the anisotropic scattering case.