Analytical solution for the single scattered radiance of two-layered turbid media in the spatial frequency domain. Part 2: Vector radiative transfer equation

In this work, the analytical solution in the spatial frequency domain based on the vector radiative transfer equation is derived for the single scattered radiance of a scattering medium. A two-layer model with spherical scatterers is assumed as the scattering medium, where the second layer is infinitely extended and there is no refractive index mismatch between the two scattering layers. In contrast, a refractive index mismatch to the surrounding non-scattering medium is considered. The time-resolved and time-independent solutions are given and are verified using a self-implemented electrical field Monte Carlo method. Excellent agreement between the analytical solution and the Monte Carlo method is demonstrated. Possible errors due to discretizations in the Monte Carlo method are reduced, for example, by using the polarized last flight variance reduction method.