Numerical method for the inverse problem of near field microscopy of layered media

We present the numerical method for retrieving of the profile of layered media permittivity from the near field microscopy data. The method is based on the minimization of the discrepancy function describing the difference between the experimental measured of the near field antenna impedance and the calculated one for given permittivity profile. Such calculation is based on the numerical algorithm which developed on the base of rigorous solution of corresponding direct problem. We suppose that the profile to be retrieved is described by the function with finite number of unknown parameters and the discrepancy is minimized with respect of these parameters. We present some results of numerical experiments with method suggested.