Radiative Transport Equation in Rotated Reference Frames

TL;DR

This paper introduces a spectral method for solving the 3D radiative transport equation in homogeneous media, offering computational efficiency and applicability to inverse problems with arbitrary phase functions depending only on the angle between directions.

Contribution

A new spectral approach for the 3D RTE that simplifies computations and handles arbitrary phase functions depending solely on the angular difference.

Findings

Efficient spectral expansion reduces computational complexity.

Method applicable to boundary conditions in slab and half-space geometries.

Suitable for inverse radiative transfer problems.

Abstract

A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the constraint that it depends only on the angle between the angular variables s and s'. This corresponds to spherically symmetric (on average) random medium constituents. Boundary conditions are considered in the slab and half-space geometries. The approach developed in this paper is spectral. It allows for the expansion of the solution to the RTE in terms of analytical functions of angular and spatial variables to relatively high orders. The coefficients of this expansion must be computed numerically. However, the computational complexity of this task is much smaller than in the standard method of spherical harmonics. The solutions obtained are especially convenient for solving inverse problems associated with radiative transfer.