Integral equations for radiative transfer with linear anisotropic scattering and Fresnel boundaries

Transformation of the integro-differential transport equation in terms of radiation intensity to integral equations in terms of moments of the radiation intensity reduces the computational labor because the former depends on position and direction and the latter depends on position only. Our analysis deals with two cases for which the scattering is linearly anisotropic. One involves radiative transfer in an arbitrary three-dimensional medium with a given inward boundary intensity and the other involves radiative transfer in a three-dimensional rectangular medium with Fresnel boundaries and the top surface exposed to normal incidence. Because the inward boundary intensity is unknown in the second case, an image technique is used to generate integral equations similar to those obtained in the first case. Numerical results for specific examples are given. Comparing the results for a slab with nonreflecting boundaries with existing exact solutions shows that our analysis works quite well.