Descriptive parameter for photon trajectories in a turbid medium

In many applications of laser techniques for diagnostic or therapeutic purposes it is necessary to be able to characterize photon trajectories to know which parts of the tissue are being interrogated. In this paper, we consider the cw reflectance experiment on a semi-infinite medium with uniform optical parameters and having a planar interface. The analysis is carried out in terms of a continuous-time random walk and the relation between the occupancy of a plane parallel to the surface to the maximum depth reached by the random walker is studied. The first moment of the ratio of average depth to the average maximum depth yields information about the volume of tissue interrogated as well as giving some indication of the region of tissue that gets the most light. We have also calculated the standard deviation of this random variable. It is not large enough to qualitatively affect information contained in the first moment.