P3 solution for the total steady-state and time-resolved reflectance and transmittance from a turbid slab

In this paper, we derive some explicit analytical solutions to the P3 equations for the slab geometry that is illuminated by a collimated plane source. The resulting expressions for the total reflectance and transmittance are compared with the corresponding transport theory solution predicted by the Monte Carlo method. Further, for the special case of a non-absorbing anisotropically scattering slab, simple and accurate expressions in the P1 approximation are obtained, yielding for optically thick slabs, the typical behavior of Ohm’s law. In view of the time domain, we present an alternative method to the classical frequency-domain approach avoiding the use of complex numbers.