Comparison of PN or spherical harmonics approximation for scattering media with spatially varying and spatially constant refractive indices

In this paper, we derive the PN or spherical harmonics approximation to the radiative transport equation for a medium with a spatially varying refractive index. We compare the analytical solutions of the coupled system of partial differential equations corresponding to the PN approximation in a spherically symmetric geometry for spatially varying and spatially constant case. We show that the PN model with spatially varying refractive index for photon transport is substantially different than the spatially constant model.