A measure of photon penetration into tissue in diffusion models

In application of laser-based techniques to estimate optical parameters of tissue it is necessary to know the parts of the tissue that have been sampled by the photons. Towards this end it is desirable to define an average depth of a photon trajectory. This has been done earlier for lattice random walk models of photon trajectories where one simply counts the number of visits to a given set of sites. Here we calculate the equivalent quantity in the diffusion picture by equating the average depth of penetration to the local time of a diffusion process. We show that for a semi-infinite medium bounded by a plane the average depth probed by a photon trajectory in a continuous-wave (cw) experiment has the same functional form as that calculated from a random walk model. The local time, or average depth is shown to take a very simple form in the case of a time-gated experiment. We extend our results to the cw transillumination experiment.