Light propagation in very turbid media can be described as a diffusion process.' Light in the near-infrared is multiply scattered in tissues. The scattering coefficient, is on the order of 103 to 104 per mm and is essentially forward scattering.2,3,4,5,6,7 Taking into account the average of the cosine of the scattering angle, g, it is possible to define a reduced scattering coefficient, !Zs= (1-g)Ã‚Âµs, which is still on the order of 1 per mm. Typical values of the absorption coefficient, ga, in animal tissues are on the order of 0.01 per mm.7 Under the above conditions, the Boltzman transport equation for photons in tissues can be solved in the diffusion approximation.' Several researchers have experimentally demonstrated the validity of the diffusion approximation in typical tissues.4,9,10,11,12 Once we have achieved a fairly good understanding of the physical nature of light propagation in tissues, the question remains as to how best to determine the parameters that appear in the diffusion approximation solution, i.e., the scattering and the absorption coefficient. In general these values are a function of the location in the tissue and they can vary with time. Ideally, we want to reconstruct a 3-D map of the scattering and absorption coefficients with the highest possible spatial resolution from time-resolved measurements of light intensity performed at the surface of the object being investigated." At this point several questions arise as to the mathematical possibility of the reconstruction of the map of scattering and absorption, the ultimate resolution achievable, the size of differences in scattering and absorption coefficients that can be measured, the best measurement method, and the best reconstruction algorithm to name a few.