A discrete method for anisotropic angular sampling in Monte Carlo simulations

A discrete method is presented for sampling anisotropic angular scattering distributions in Monte Carlo simulations. Derived from fundamental transport considerations, this method is based on equating the moments of a given distribution with those of a discrete distribution consisting of a sequence of Dirac delta spikes. The discrete method is slightly faster and, for a given scoring accuracy, more flexible than the tabular sampling method. Tests indicate that accuracy better than 1 % in calculated transmittances is generally obtainable using only 4 spikes, provided the single scattering albedo exceeds 0.7. Conditions are described under which this method can be applied to heterogeneous media.