Light propagation in turbid media: A generalization of the solution given by the diffusion approximation, based on the moments of multiple scattering

In this work we propose a generalization of the solution for light propagation in turbid media given by the diffusion approximation (DA), based on the calculus of the photon coordinates momenta. The main results of the proposed approach are: (1) the contributions of the scattering coefficient μs and the anisotropy factor g are explicitly separated, and (2) the minimum number of collisions N for which the DA is valid can be inferred. We demonstrate that when the number of collisions, N, is large our solution tends to that of the diffusion equation, but for those cases with small N or when the absorption coefficient, μa, cannot be considered as much smaller than the reduced scattering coefficient, μs', our solution remains useful. Validation using Monte Carlo simulations, taken as a standard, is presented for both situations. Comparisons with results from other authors are also provided.