Revisiting the Rytov approximation in diffuse optics and its applications for the inverse and forward problems

We propose an overview of the Rytov approximation in diffuse optics of biological tissues, for the inverse and forward problems. First, we show a physical interpretation of the Rytov approximation as a type of partial pathlength (named fluence rate partial pathlength) which is distinct from the usual partial pathlength for reflectance measurements. Second, we study the accuracy of the Rytov approximation for the calculation of Jacobians considering absorption perturbations and reflectance measurements. For higher absorption and lower reduced scattering values the discrepancy between the true Jacobian (i.e., the reflectance partial pathlength) and that obtained with the Rytov approximation (i.e., the fluence rate partial pathlength) can be up to about 70% for diffusion theory calculations and up to about 25% for Monte Carlo simulations. For higher reduced scattering values, the discrepancies become less than 10%. Third, we propose a calibration method that can circumvent numerical inaccuracies when the calculation of Jacobians is carried out in presence of highly absorbing layers. Finally, fourth, we also propose an original formula derived from the Rytov approximation for reflectance measurements, and we show how it performs for the forward problem, when we consider defects with large absorption contrast with respect to the background.