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A path-integral model of light scattered by turbid media

Imaging techniques involving transillumination require detailed knowledge of radiation path(s) between the source and the detector. When imaging with near-infrared light in tissue this is particularly problematic due to the high scattering cross section. The population of `direct-path' photons is so small that information must be gathered from the much larger (but still small) population of `snaked path' photons. Path-integral (PI) models, described in this paper, set out to find the most likely of these paths, not by random sampling as in Monte Carlo-based techniques, but directly by a cost function (Lagrangian). This is constructed based on the physics of the scattering processes/absorption and integrated along the photon path to generate a total cost (action). This is minimized using variational calculus to extract the most likely path. Whilst the PI approach is not new, the work presented here is novel in constructing the Lagrangian using local path descriptors. This allows explicit inclusion of an absorption term and also lends itself to arbitrary numbers of constraints on intermediate `visit' points, path directions and the overall path length. Scaling symmetries are used to further reduce the computational expense of the method.