Correcting the diffusion approximation at the boundary

Abstract

The diffusion approximation to the radiative transport equation applies for light that has propagated deeply into an optically thick medium, such as biological tissue. It does not accurately model light near boundaries where measurements of scattered light are often taken. Here, we compute a correction to the diffusion approximation at the boundary. This correction requires only small modifications to the standard diffusion approximation used in biomedical optics. In particular, one needs only to compute the coefficients in the boundary condition for the diffusion approximation and an additive correction. We give explicit procedures for these computations. Using numerical results for the steady-state plane-parallel slab problem, we show that this corrected diffusion approximation is a much better approximation than the standard diffusion approximation for modeling the reflectance and transmittance.