Statistical properties of the penetration of photons into a semi-infinite turbid medium: a random-walk analysis

Statistical properties of the expected amount of time spent by a photon at different depths of a semiinfinite turbid medium are derived with formalism based on the continuous-time random walk. The formalism is applied to the study of both cw and time-gated experiments. Earlier analytical results relating to cw experiments are reproduced with a single approximation, rather than the more complicated approach used in earlier research based on the discrete-time random walk. The distribution of the occupancy of different depths in a time-gated experiment is found to have a convenient scaling form.