**Monte-Carlo Simulations of Bi-Directional Surface Reflection and Comparisons with Photometric Model Predictions**

**D. L. Domingue (LPI), A. F. Cheng (APL)**

The reflectance properties of a scattering surface are governed by the surface porosity, the single scattering albedo of the particles composing the surface, the single scattering function of the particles, the relative percentage of different particle types (distinguished by differences in their single scattering albedo and single scattering function) within the surface, and the physical relationship between particles (i.e. is the surface layer randomly filled with material or is there a structure to the filling of the surface layer). We have developed a Monte-Carlo simulation of radiative transfer through a particulate surface layer where the above parameters are varied. Photometric phase curves are constructed to examine variations in brightness of the particulate surface as functions of photon incidence and emission angles, for various types of surface microscopic structure and particle scattering properties. The results are compared with the predictions from photometric theory (e.g., Hapke's model). The scattered photons are divided into two groups, singly scattered and multiply scattered, in order to examine the relative importance of multiple scattering as a function of single scattering albedo. The single vs multiple scattering results from the Monte-Carlo simulation are also compared to predictions from photometric theory.