Light transport with the equation of radiative transfer: The Fourier Continuation – Discrete Ordinates (FC–DOM) Method

Abstract

We present a method for the treatment of the time dependent radiative transfer equation under the discrete ordinate approximation. The novelty of the proposed approach stems, in part, from the incorporation of a spectral method for the calculation of the spatial differential operators based on the Fourier Continuation procedure introduced recently by Bruno and co–authors. This is a spatially dispersionless and high order method, which can handle arbitrary geometries, including those encountered in the forward model of light transport in optical tomography. We validate our theoretical results by comparison with analytic and experimental outcomes of the fluence measurements on tissue-like phantoms. The method makes it possible to calculate the time of flight of photons in random media efficiently and with high accuracy.