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Time-dependent equation for the intensity in the diffusion limit

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Abstract

The first two terms in the spherical-harmonics expansion (the P1 approximation) of the radiative transfer equation yield the diffusion equation. This approximation applies to multiple scattering and results in a solution for the energy density, the gradient of which is proportional to the light intensity. In this work a higher-order spherical- harmonics expansion of the radiative transfer equation is developed. Using the Fourier transform, an approximation based on expanding at small wave vectors k leads to an equation similar to the diffusion equation. This equation applies to the radiant intensity rather than the energy density. The equation is expected to predict the intensity for multiple scattering at earlier times and shorter distances than the DE can. The notion of an equivalent wave field is introduced.

© 1998 Optical Society of America

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