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(-alpha r)/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.
Highlights
Light diffusion in strongly scattering media is of primary importance in several fields, including spectroscopy of highly turbid media and optical imaging of thick tissues. 7 After a few scattering events the light propagation process can be treated as a transport of particles that undergo a large number of collisions, performing a random walk through the scattering medium
The diffusion approximation to the Boltzmann transport equation fully describes our experiments of propagation of photons in macroscopically homogeneous infinite media for all the absorptions investigated
The range of absorption and transport scattering coefficients that we have studied is typical of many animal tissues in the nearinfrared region.[6]
Summary
Light diffusion in strongly scattering media is of primary importance in several fields, including spectroscopy of highly turbid media and optical imaging of thick tissues. 7 After a few scattering events the light propagation process can be treated as a transport of particles that undergo a large number of collisions, performing a random walk through the scattering medium. 7 After a few scattering events the light propagation process can be treated as a transport of particles that undergo a large number of collisions, performing a random walk through the scattering medium. It has been suggested that the use of short light pulses can provide a better approach to the identification of different macroscopic regions with different optical properties, since the time of photon propagation through a strongly scattering medium is related to the effective optical path, which is dependent on the absorption and transport scattering coefficients of the medium. For most applications to the medical field, the use of unscattered light for optical imaging is restricted to only a few tissues such as the eye or to tissues that are at most a few millimeters thick.'[4]
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