Analytical solution of the radiative transfer theory for the coherent backscattering from two-dimensional semi-infinite media

Abstract

An analytical solution for coherent backscattering (CBS) in two dimensions was derived by solving the radiative transfer equation. Particularly, the single scattered radiance from a semi-infinite medium containing perpendicularly illuminated cylinders was obtained. At the boundary, a refractive index mismatch was taken into account. Furthermore, the link between the radiance and the CBS was shown in the small angle approximation. An excellent agreement was found between Monte Carlo simulations and the analytical solution. Additionally, it was shown that the often applied solution in the spatial frequency domain for quantifying the CBS delivered significantly different results compared to the derived exact analytical solution.