Extrapolation distance for diffusion of light

Raphael Aronson et al. (1993)

Summary

Abstract. Diffusion theory has been useful and frequently applied analytical method to study the transport of light in random media. The diffusion equation requires unphysical boundary conditions. This is reflected in the fact that the diffusion solution must differ from the exact solution in a boundary region a few mean free paths thick. Exact transport theory indicates that for particle diffusion the true boundary is to be replaced by an extrapolated boundary 0.71 transport mean free paths outside of it. This is the number that has universally been used in treating light diffusion, although it is sometimes neglected because it is often a very short distance. However, because there is reflection at the boundary due to a mismatch in the index of refraction, the extrapolation distance for diffusion of light is longer than that for particles, and this must be taken into account. The correction is large, even for modest indices of refraction. We show here that the appropriate boundary condition is given in terms of an extrapolation distance and tabulate this quantity as a function of relative scattering probability and index of refraction of the medium.