Analytical solution of the radiative transfer equation of light radiance in a turbid slab with an inner-medium source under the P3-1D approximation

A generalized model of the 1-dimensional radiative transfer equation of the light radiance in a turbid slab is detailed, under the P-3 approximation, including the possibility to model a continuous plane-wave source located at any depth within the scattering slab. This analytical model, which requires significant evolution of the P3-1D model, is extensively described and validated by comparison with Monte-Carlo numerical experiments. A series of numerical simulations illustrates some of the modeling possibilities offered by this extended model, which makes it possible to continuously model the transition between a classical slab geometry and a semi-infinite geometry.