Solutions of the Diffusion Equation for Homogeneous Media

doi:10.1117/3.2624517.ch5

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.ch5

Author Affiliations +

Abstract

In this chapter, an overview of solutions of the diffusion equation for homogeneous geometries is provided. Green’s functions for the infinite medium, the laterally infinitely extended slab, the semi-infinite medium, the parallelepiped, the infinite and finite cylinder, and the sphere are presented. The solutions are obtained with the method of images, the eigenfunctions method, the integral transform method, or the separation of variables method. The solutions of the DE are approximate solutions of the RTE. Information on the accuracy of the solutions can be obtained from comparisons with the results of MC simulations that will be presented in Ch. 17.