The phase problem for X-ray specular reflectivity from thin films: A new approach

• A new approach to solving the phase problem for X-ray specular reflectivity is proposed.
• An iterative Levenberg–Marquardt algorithm is used to solve the nonlinear Fredholm integral equation.
• Effectiveness of the proposed method was tested by numerical experiments for the thin film.
• We compare the results obtained for the Cr film experimental data using different approaches.

A new approach to solving the phase problem for X-ray specular reflectivity is proposed. An iterative algorithm is used to solve the nonlinear Fredholm integral equation describing the intensity of the X-rays reflection from the sample surface and to determine the concentration depth-profile of element. Effectiveness of the proposed method was tested by numerical experiments for the thin film. We compare the results obtained for the Cr film experimental data using the Parratt model, phaseless inverse scattering method (logarithmic dispersion relations), and the proposed method.