Perturbation model to predict the effect of spatially varying inhomogeneities in diffusing media

An analitical approach is developed that allows for computing the time resolved transmittance signal through a slab of turbid material in presence of spatially varying Gaussian absorptive inhomogeneity included in thescattering slab.The perturbed time-resolved signal is calculated in the framework of the diffusion approximation up to the first order correction in the relative degree of the absrptive perturbation parameter. Numerical FEM simulations arecompared with the prediction of the perturbation-based approach for different values of the optical coefficients of the inhomogeneity and of the host medium and for different size of the inclusion