Abstract
In this paper analytical solutions to the radiative transport equation are derived for the angular resolved single scattered radiance in a semi-infinite turbid medium having depth dependent optical properties. Explicit formulas are given for a two-layered turbid medium. A difference in the refractive index between the surrounding non-scattering medium and the two-layered medium is considered. The result displays a linear relationship between the phase functions of both layers and the radiance. In order to verify the results, the Monte Carlo method is used to compare calculations for varying configurations of the medium and phase functions. For all cases, the analytical solution and the Monte Carlo simulations show excellent agreement with one another.
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