Diffuse reflection from a stochastically bounded, semi-infinite medium

Abstract

In order to determine the diffuse reflection from a medium bounded by a rough surface, we consider the problem of radiative transfer in a boundary layer characterized by a statistical distribution of heights. For the case that the surface is defined by a multivariate normal probability density, we derive the propagation probability for rays traversing the boundary layer and, from that probability, a corresponding radiative transfer equation. A solution of the Eddington (two stream) type is found explicitly, and examples are given. The results should be applicable to reflection from the regoliths of solar system bodies, as well as from a rough ocean surface.