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

Abstract

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.

There’s plenty of light at the bottom: statistics of photon penetration depth in random media

“…The overall performance of this approach is strongly dependent on the exact physical description of the light-matter interaction, and this is more effectively provided within the framework of the radiative transport theory4. Usually, the medium is addressed in reflectance geometry, where light, injected and collected from the same side of its external surface, carries information on the medium optical properties encoded along photons random paths.…”

Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm

“…39 Given the complexity of solving the RTE, analytical solutions rely on numerous simplifying assumptions, which typically result in loss of accuracy at subdiffusion lengthscales. 40 Although improved analytical solutions, such as the phase function corrected diffusion approximation by Vitkin et al 1 and modified spherical harmonic method by Liemert and Kienle 41 , have demonstrated excellent accuracy at subdiffusion lengthscales, these results are still limited to a scalar approximation that is only strictly applicable for unpolarized light. For this reason, we choose to take a more brute force approach by solving for pðr s Þ with electric field Monte Carlo simulation.…”

Analytical solution of the simplified spherical harmonics equations in spherical turbid media

“…The RTE is an integro-partial-differential equation for which few analytical solutions in 3D have been found for infinite or semi-infinite media, see for instance [13,21,23] and the references therein. However, for practical applications, it is burdensome to solve numerically [14], as is its high order so-called P N approximation [4] for which also only few analytical solutions are known [22].…”