Statistical properties of the expected amount of time spent by a photon at different depths of a semi-infinite 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.
[Optical Society of America ]
(030.6600) Coherence and statistical optics : Statistical optics
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.5280) Medical optics and biotechnology : Photon migration
George H. Weiss, "Statistical Properties of the Penetration of Photons into a Semi-Infinite Turbid Medium: A Random-Walk Analysis," Appl. Opt. 37, 3558-3563 (1998)