Analysis for nonlinear inversion technique developed to estimate depth-distribution of absorption by spatially resolved backscattering measurement

We have proposed a new nonlinear inversion technique to estimate the spatial distribution of the absorption coefficient (μa) in the depth direction of a turbid medium by spatially resolved backscattering measurement. With this technique, we can obtain cross-sectional image of μa as deep as the backscattered light traveled even when the transmitted light through the medium cannot be detected. In this technique, the depth distribution of absorption coefficient is determined by iterative calculation using the spatial path-length distribution (SPD) of traveled photons as a function of source-detector distance. In this calculation, the variance of path-length of many photons in each layer is also required. The SPD and the variance of path-length are obtained by Monte Carlo simulation using a known reduced scattering coefficient (μs€™). Therefore, we need to know the μs€™ of the turbid medium beforehand. We have shown in computer simulation that this technique works well when the μs€™ is the typical values of mammalian body tissue, or 1.0 /mm. In this study, the accuracy of the μa estimation was analyzed and its dependence on the μs€™ was clarified quantitatively in various situations expected in practice. 10% deviations in μs€™ resulted in about 30% error in μa estimation, in average. This suggested that the measurement or the appropriate estimation of μs€™ is required to utilize the proposed technique effectively. Through this analysis, the effectiveness and the limitation of the newly proposed technique were clarified, and the problems to be solved were identified.