Profile determination of a stratified medium from reflectivity measurements: A regularized inverse problem

We deal with the determination of the profile of a stratified medium with the absolute intensities of the specularly reflected field as input. The measurements can be performed at different angles of incidence at a fixed wavelength or at various wavelengths if the medium is dispersionless. The forward problem is linearized to allow one to use a matrix formulation of the discretized direct operator and the inverse problem is solved by an iterative process. Since the problem belongs to the class of the so-called ill-posed or ill-conditioned problems, a regularization method based on Tikhonov's method of the stabilizing functional is implemented. We present a numerical test in the X-ray spectral range where the method offers a considerable field of application for structural analysis.