Fermat photons in turbid media: an exact analytic solution for most favorable paths-a step toward optical tomography

Photon propagation in a turbid medium characterized by highly forward-directed light scattering can be described by a generalized Fermat principle, a counterpart of the conventional Fermat principle for transparent media. An exact analytic solution for the most favorable photon paths (Fermat paths) has been found and is investigated. An analysis intended to encourage and facilitate experimental observation of Fermat photons is presented. The feasibility of using the theory in time-resolved optical tomography for the recognition of objects hidden in turbid media is discussed.