Simple algorithm for the measurement of absorption coefficients of a two-layered medium by spatially resolved and time-resolved reflectance

An inversion procedure for the recovery of absorption coefficients of a two-layered semi-infinite diffusive medium by use of time-resolved reflectance measured at two different source-detector distances is proposed. The inversion procedure is based on the property of the photon diffusion equation; i.e., the solution of the diffusion equation for the time-resolved reflectance measured at a longer source-detector distance coincides with that measured at a shorter one by a proper temporal, spatial, and intensity transformation. This inversion procedure, used together with the results of one set of Monte Carlo simulations, is validated as working well when the values of the scattering coefficients of the two layers and the thickness of the first layer are within a range of interest in tissue optics.