Spatial sampling by diffuse photons

The contribution of some region in an opaque multiple-scattering sample to the detected signal is considered. Because diffusion theory gives only the total photon concentration and not the fraction of that which ultimately reaches the detector, it must be supplemented. We show how to do so by making further use of the assumption that photon migration is Markovian. This procedure is illustrated for illumination-detection geometries and scattering parameters of interest for diffusing-light spectroscopies. Specifically, we explore slab geometries with plane-wave illumination and detection as well as a semi-infinite sample with point illumination and detection. For the former the photon behavior as a function of slab thickness, scattering anisotropy, absorption, and boundary reflectivity is predicted and shown to compare well with Monte Carlo random-walk simulations.