Boundary conditions for diffusion of light

Abstract

In connection with recent work on remote imaging of random media by light, a straightforward generalization of the proper diffusion boundary conditions is presented that takes into account Fresnel reflection. The Milne problem at exterior boundaries is solved for various values of index of refraction, absorption, and scattering anisotropy parameters to yield extrapolated end points and extrapolation distances. A generalized interface condition is derived to replace the usual condition of continuity of intensity. Benchmark-quality numerical results are given for the extrapolation distance and for the new index-dependent parameter in the interface conditions. Difficulties in using the extrapolated end point when the index is sufficiently large are discussed, and a new image procedure suitable for this case is presented.