The Radiative Transfer Equation

doi:10.1117/3.2624517.ch2

Book: Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Validation, Second Edition

Author(s): Fabrizio Martelli, Tiziano Binzoni, André Liemert, Samuele Del Bianco, Alwin Kienle

Published: 2022

https://doi.org/10.1117/3.2624517.ch2

Author Affiliations +

Abstract

The radiative transfer equation (RTE) (also called the transport equation in other fields where the generic transport of particles is considered) is a phenomenological and heuristic theory describing the transport of energy through a scattering medium that lacks a rigorous mathematical formulation able to account for all the physical effects involved in light propagation. The RTE is actually obtained with the assumption that the intensities, not the fields, add up at a point in the medium. However, it has been demonstrated that under certain simplifying assumptions, the RTE can be derived from the electromagnetic theory of multiple scattering in discrete random media. Solutions of the RTE have been compared with analytical solutions of Maxwell’s equations, and a pretty good agreement was found between the two theories for relatively low scatterer concentrations, with the exception of interference effects, such as speckles or coherent back scattering. Despite the fact that the RTE is less rigorous than Maxwell’s equations for light propagation, the former has led to useful models for many practical problems.