Asymptotic behavior and inverse problem in layered scattering media

The main challenge of noninvasive optical biopsy is to obtain an accurate value of the optical coefficients of an encapsulated organ (muscle, brain, etc.). The idea developed by us is that some interesting information could be deduced from the long-time behavior of the reflectance function. This asymptotic behavior is analyzed for layered media in the framework of the diffusion approximation. A new method is derived to obtain accurate values for the optical parameters of the deepest layers. This method is designed to work in a specific long-time regime that is still within the scope of standard time-of-flight experiments but far from being included in the mathematically defined asymptotic region. The limits of this method, linked to the cases where the asymptotic behavior is no longer governed by the deepest layer, are then discussed.