Generalized diffusion theory for radiative transfer in fully anisotropic scattering media

TL;DR

This paper introduces a generalized anisotropic diffusion framework for radiative transfer in media with tensorial scattering, providing explicit formulas and validation against simulations for complex anisotropic scattering scenarios.

Contribution

It develops a comprehensive anisotropic diffusion theory with explicit expressions, validated by simulations, for media with tensorial scattering coefficients and phase-function asymmetry.

Findings

Excellent agreement with Monte Carlo simulations across anisotropy ranges

Derived explicit formulas for diffusion tensor components and boundary conditions

Provides open-source tools for practical implementation

Abstract

A generalized anisotropic-diffusion framework is developed for transport problem in media described by a tensorial scattering coefficient and a scalar Henyey--Greenstein asymmetry factor. In this regime the classical similarity relation between scattering and transport parameters fails, and each principal diffusion coefficient depends on all components of the microscopic scattering rate. Explicit expressions are derived for the direction-averaged mean free path, the diagonal elements of the diffusion tensor, and boundary condition lengths via rapidly convergent spherical-harmonics expansions, along with open-source implementations. The resulting predictions are validated against anisotropic Monte Carlo simulations, showing excellent agreement across broad ranges of structural anisotropy and phase-function asymmetry factors. The theory provides a compact, general route connecting microscopic anisotropic scattering to macroscopic diffusion coefficients and boundary conditions in bounded geometries.