Improved steady-state diffusion approximation with an anisotropic point source and the δ—Eddington phase function

Abstract

Using the algebra transformation method, we develop and demonstrate the use of the $\delta –P_1$ approximation to improve steady-state radiative-transfer estimates on spatial scales comparable to the mean free path. We show that the $\delta –P_1$ approximation agrees well with Monte Carlo simulation from source to infinity when we choose an appropriate parameter f (fractional portion that scatters directly forward) in the δ–Eddington phase function. We also provide the empirical formula to determine the parameter f.

© 2007 Optical Society of America