Radiative transfer as a sum over paths

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Abstract
The radiative-transfer equation describes the collection of paths taken by an element of radiation as it travels from one location to another. When backscatter can be ignored, the exact solution is constructed as a formal sum (path integral) over all such paths. In the appropriate limit the usual (diffusive) small-angle solution and the multiple-scattering solution can be obtained. Another small-angle solution has also been found which includes some of the nonlinear and large-angle behavior not present in the diffusive solution. After several attenuation lengths, length scales are characterized by a parameter constructed out of the absorption and scattering coefficients, and the rms scattering angle per scattering event. The two solutions are compared in the case of a point beam.