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New Approach to Solving the Radiative Transport Equation

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Abstract

We have proposed a novel method for solving the linear radiative transport equation (RTE) in a three-dimensional macroscopically homogeneous medium. The method utilizes the concept of locally rotated reference frames and can be used with an arbitrary phase function of a random medium consisting of spherically-symmetric microscopic scatterers. The angular dependence of the specific intensity written in the spatial Fourier representation is obtained as an expansion into spherical functions defined in reference frames whose z-axes coincide with the direction of the Fourier vector k. Coefficients of this expansion are obtained by numerical diagonalization of several k-independent tridiagonal matrices whose elements depend only on the form of the phase function. The inverse Fourier transform is then computed analytically. This results in a closed-form expression for the RTE Green’s function in infinite space. Further, the plane-wave decomposition of the 3D Green’s function is obtained. It is shown that the modes in this decomposition are the evanescent plane waves. These modes can be used to construct the solution to the boundary value problem in the slab and half-space geometries.

© 2006 Optical Society of America

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