Analytic relationships for the statistical moments of scattering point coordinates for photon migration in a scattering medium

Abstract

Some statistical relationships relating the optical properties of the diffusing medium to the first and second moments of the coordinates of the points at which the different scattering orders occur are presented. These relationships give qualitative information on the spatial broadening of a light beam propagating in a diffusive medium and can be very useful to test the reliability of Monte Carlo codes: the correctness of the calculation procedure used to determine the scattering points can be checked comparing the statistical moments of coordinates with the values given by the analytical expressions.