Analytical solution of the vector radiative transfer equation for the double scattered radiance of semi-infinite media containing polydisperse particle distributions

Abstract

Within the context of this work, the analytical solution of the angular resolved radiance in the spatial domain for double scattered photons based on the vector radiative transfer equation is derived. The solution is obtained for semi-infinite scattering media which have no refractive index mismatch to the surrounding nonscattering medium. Analytical solutions are provided for scattering media which exhibit monodisperse and polydisperse particles distributions. Verification is performed using an electric field Monte Carlo method. Overall, an excellent agreement between the analytical solutions and the Monte Carlo method was found.