Related Experiment Video
Updated: Jun 22, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Heuristic Green's function of the time dependent radiative transfer equation for a semi-infinite medium
Fabrizio Martelli1, Angelo Sassaroli, Antonio Pifferi
1Dipartimento di Fisica dell'Università degli Studi di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy. fabrizio.martelli@unifi.it
Abstract:
The Green's function of the time dependent radiative transfer equation for the semi-infinite medium is derived for the first time by a heuristic approach based on the extrapolated boundary condition and on an almost exact solution for the infinite medium. Monte Carlo simulations performed both in the simple case of isotropic scattering and of an isotropic point-like source, and in the more realistic case of anisotropic scattering and pencil beam source, are used to validate the heuristic Green's function. Except for the very early times, the proposed solution has an excellent accuracy (> 98 % for the isotropic case, and > 97 % for the anisotropic case) significantly better than the diffusion equation. The use of this solution could be extremely useful in the biomedical optics field where it can be directly employed in conditions where the use of the diffusion equation is limited, e.g. small volume samples, high absorption and/or low scattering media, short source-receiver distances and early times. Also it represents a first step to derive tools for other geometries (e.g. slab and slab with inhomogeneities inside) of practical interest for noninvasive spectroscopy and diffuse optical imaging. Moreover the proposed solution can be useful to several research fields where the study of a transport process is fundamental.
Related Concept Videos
Extended Versions of Green’s Theorem
Green’s Theorem
Vector Forms of Green’s Theorem
Absorption of Radiation
Debye–Huckel–Onsager Conductance Equation
Conduction, Convection and Radiation: Problem Solving
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
