Bidirectional Reflectance of Gaussian Random Surfaces and Its Scaling Properties

Using rigorous probabilistic techniques we define and compute the shadowing factor, the conditional mean slope and the conditional standard deviation of the slope for a random rough surface described as an isotropic Gaussian stochastic process with Gaussian autocorrelation function. We use these quantities in order to obtain the bidirectional reflectance distribution function for incoherent light scattering by rough surfaces. The calculated quantities depend on reduced, affine invariant parameters, such that changing roughness is equivalent to rescaling the slopes of incident and emergent direction. We discuss some possible applications of these scaling properties to remote sensing.