Telegrapher's equation for light derived from the transport equation

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Abstract

Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapher's equations in the well known P 1 approximation. The method used in this paper is different: it is based on the asymptotic evaluation of the solutions of the equation of radiative transport with respect to place and time for all values of the albedo. Various coefficients for the telegrapher's equations were derived, restricted to the case of isotropic scattering, and their properties are discussed. A correct diffusion coefficient for the stationary case could be obtained. However, this solution did not lead to the correct phase velocity. Correct phase velocities in combination with a correct diffusion coefficient were found for a dispersion relation that corresponds with anisotropic Henyey-Greenstein scattering with g = 0.22. It provides a time-dependent description of the fluence rate with validity for all values of the albedo. © 2005 Elsevier B.V. All rights reserved.

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Hoenders, B. J., & Graaff, R. (2005). Telegrapher’s equation for light derived from the transport equation. Optics Communications, 255(4–6), 184–195. https://doi.org/10.1016/j.optcom.2005.06.024

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