Exact and efficient solution of the radiative transport equation for the semi-infinite medium

An accurate and efficient solution of the radiative transport equation is proposed for modeling the propagation of photons in the three-dimensional anisotropically scattering half-space medium. The exact refractive index mismatched boundary condition is considered and arbitrary rotationally invariant scattering functions can be applied. The obtained equations are verified with Monte Carlo simulations in the steady-state, temporal frequency, and time domains resulting in an excellent agreement.