# 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.