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The Kirchhoff approximation (KA) is used to find the double scatter contribution to the field scattered from a random rough surface. The method is to use the same approximation for each interaction with the surface as is normally used for the single scatter term. Solution of the double scatter term using a Monte-Carlo method shows a peak in the scattered intensity in the backscatter direction. This peak is approximately a factor of 2 greater in intensity than the background intensity agreeing with a simple multiple scattering ray picture.
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Neil Bruce, Christopher Dainty, "Multiple scatter from rough surfaces using the Kirchhoff approximation," Proc. SPIE 1319, Optics in Complex Systems, (1 July 1990); https://doi.org/10.1117/12.34851