Anisotropic diffusive transport: connecting microscopic scattering and macroscopic transport properties

Abstract

This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and the macroscopic diffusion tensor, in the limit of independent scatterers, is presented. The theory is accompanied by a numerical method capable of performing the calculations. In addition, a boundary condition appropriate for modeling systems with anisotropic radiance is derived. It is shown that anisotropic diffusion theory, when based on these developments, indeed can describe radiative transfer in anisotropic turbid media. More specifically, it is reported that solutions to the anisotropic diffusion equation are in excellent agreement with Monte Carlo simulations, both in steady-state and time-domain. This stands in contrast to previous work on the topic, where inadequate boundary conditions and/or incorrect relations between microscopic scattering properties and the diffusion tensor have caused disagreement between simulations and diffusion theory. The present work thus falsify previous claims that anisotropic diffusion theory cannot describe anisotropic radiative transfer, and instead open for accurate quantitative diffusion-based modeling of anisotropic turbid materials.