Generalized diffusion model in optical tomography with clear layers.

Abstract

We introduce a generalized diffusion equation that models the propagation of photons in highly scattering domains with thin nonscattering clear layers. Classical diffusion models break down in the presence of clear layers. The model that we propose accurately accounts for the clear-layer effects and has a computational cost comparable to that of classical diffusion. It is based on modeling the propagation in the clear layer as a local tangential diffusion process. It can be justified mathematically in the limit of small mean free paths and is shown numerically to be very accurate in two- and three-dimensional idealized cases. We believe that this model can be used as an accurate forward model in optical tomography.