Abstract

Mathematical expressions are obtained for various functions (e.g., path length and depth distributions, total reflectance, and its spatial distribution) associated with photon migration in turbid media. The models assume that photons are inserted at a point on the surface of a tissue and detected at another point on this surface (or the parallel lower surface of a slab) at a distance ρ from the point of insertion. For a homogeneous medium characterized by uniform absorption and scattering cross sections, an expression is derived for P(n|ρ), the probability density of photons emerging at surface point ρ whose path length within the media is n, given in units of rms distance between scattering events. The probability density of the corresponding transit times (t = n/c_i) in range-gating applications is also given by this expression. Expressions for spatial distribution of diffuse surface emission, mean path length, and penetration depth of emergent photons at ρ also are derived. Analogous quantities are calculated for photons migrating within a medium having a surface layer whose absorbance differs from that of the lower bulk material. The dependence of these parameters on surface thickness is illustrated.

© 1988 Optical Society of America