Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge

TLDR

Light propagation in strongly scattering media is described by the diffusion approximation to the Boltzmann transport equation. Using the Green's function from that diffusion approximation with a sinusoidally modulated point source, the authors derived analytic expressions for diffraction and reflection of photon‑density waves from an absorbing and/or reflecting semi‑infinite plane bounded by a straight edge in a strongly scattering medium. These analytic expressions predict that photon density propagates outward as a spherical wave with amplitude decaying as exp(−αr)/r, agree with frequency‑domain experiments in skim‑milk media and Monte‑Carlo simulations, and provide a basis for optimizing resolution and penetration in optical tomography of such media.

Abstract

Light propagation in strongly scattering media can be described by the diffusion approximation to the Boltzmann transport equation. We have derived analytical expressions based on the diffusion approximation that describe the photon density in a uniform, infinite, strongly scattering medium that contains a sinusoidally intensity-modulated point source of light. These expressions predict that the photon density will propagate outward from the light source as a spherical wave of constant phase velocity with an amplitude that attenuates with distance r from the source as exp(−αr)/r. The properties of the photon-density wave are given in terms of the spectral properties of the scattering medium. We have used the Green's function obtained from the diffusion approximation to the Boltzmann transport equation with a sinusoidally modulated point source to derive analytic expressions describing the diffraction and the reflection of photon-density waves from an absorbing and/or reflecting semi-infinite plane bounded by a straight edge immersed in a strongly scattering medium. The analytic expressions given are in agreement with the results of frequency-domain experiments performed in skim-milk media and with Monte Carlo simulations. These studies provide a basis for the understanding of photon diffusion in strongly scattering media in the presence of absorbing and reflecting objects and allow for a determination of the conditions for obtaining maximum resolution and penetration for applications to optical tomography.