Effects of nonlocalized target shape in the random walk description of transillumination experiments for optical imaging

A lattice random walk theory has been successfully used to interpret and analyze a variety of experimental data related to applications in optical imaging. A major advantage of the lattice theory is that it replaces cumbersome eigenfunction expansions resulting from diffusion theory by simpler relations expressed in terms of generating functions. The transillumination experiment has previously been analyzed by representing a region of increased absorptive properties in tissue by a single anomalous point. Here we extend the analysis to allow for $k$ anomalous sites, thus providing a tool for studying the effects of nonlocality of the anomalous region. We show that if the absorption coefficient in the anomalous region is sufficiently small, the simple approximation based on the use of a single point with an anomalous absorption coefficient yields quite good results as compared to data obtained from phantoms. It is shown that the neglect of correlation effects leads to an underestimate of the absorption coefficient in an anomalous region.