The percent polarization of light reflected from a rough surface has been calculated using a two-dimensional, two-layer, dielectric model and the geometrical-optics approximation. The choice of this model was prompted by a desire to investigate the dependence of the percent polarization upon internal scattering and re-emission of light which has penetrated the top surface. The parameters of the model are the indices of refraction of the two layers, and the distribution of slopes of the top surface of the upper layer. Polarization curves that are qualitatively similar to lunar and laboratory-sample signatures (i.e., the percent polarization is negative at small phase angles and positive at larger phase angles) can be obtained with this model. The curves are very sensitive to changes of the distribution of slopes or the index of refraction of the upper layer, but not, for the cases considered, to changes of the index of refraction of the lower layer. For the range of parameters considered in this paper, a variation of the index of refraction of the upper layer produces a change of the albedo; the sign of the change is opposite to that of the change of the percent polarization at high phase angles (~90°). However, a variation of the structure (distribution of slopes) of the top surface produces changes of the albedo and percent polarization of the same sign.
G. C. McCoYD, "Polarization Properties of a Simple Dielectric Rough-Surface Model," J. Opt. Soc. Am. 57, 1345-1349 (1967)