NONLINEAR EFFECTS OF LOCALIZED ABSORPTION PERTURBATIONS ON THE LIGHT-DISTRIBUTION IN A TURBID MEDIUM

A theoretical model of photon propagation in a scattering medium is pr esented, from which algebraic formulas for the detector-reading pertur bations (Delta R) produced by one or two localized perturbations in th e macroscopic absorption cross section (Delta mu(alpha)) are derived. Examination of these shows that when hp, is titrated from very small t o large magnitudes in one voxel, the curve traced by-the corresponding Delta R values is a rectangular hyperbola. Furthermore, while Delta R -infinity equivalent to Lim(Delta mu alpha -->infinity) Delta R is dep endent on the location of the detector with respect to the source and the voxel, the ratio Delta R/Delta R-infinity is independent of the de tector location. We also find that when Delta mu(alpha) is varied in t wo voxels simultaneously, the quantity Delta R(Delta mu(alpha,1) boole an AND Delta mu(alpha,2)) is a bilinear rational function of the Delta mu(alpha)s. These results apply not only in the case of steady-state illumination and detection but to time-harmonic measurements as well. The validity of the theoretical formulas is demonstrated by applying t hem to the results of selected numerical diffusion computations. Poten tial applications of the derived expressions to image-reconstruction p roblems are discussed. (C) 1998 Optical Society of America.