Random walk analysis of the effects of the presence of abnormalities in a turbid medium on expressions for the time-of-flight

Time-gated transillumination techniques for detecting and resolving regions of abnormal absorption and/or scattering in a slab geometry are based on the ability to detect transmitted photons that are nearly ballistic, i.e., that arrive at relatively short times after initial injection at a detector. However, at short gating times, the detectable intensity quickly falls below a practical detection threshold with increasing slab thickness. A quantitative theory of this effect is easily developed within the framework of random walk theory. Such a theoretical development has been shown to yield quite good approximations for properties of photon transport in a homogeneous multiply-scattering medium. Mathematical solutions of the random walk model are used to suggest experimentally measurable parameters with potential applicability tot he detection of abnormalities when their optical coefficients differ form those of the background.