Iterative reconstruction of a refractive-index profile from x-ray or neutron reflectivity measurements

Analysis of x-ray and neutron reflectivity is usually performed by modeling the density profile of the sample and performing a least square fit to the measured (phaseless) reflectivity data. Here we address the uniqueness of the reflectivity problem as well as its numerical reconstruction. In particular, we derive conditions for uniqueness, which are applicable in the kinematic limit (Born approximation), and for the most relevant case of box model profiles with Gaussian roughness. At the same time we present an iterative method to reconstruct the profile based on regularization methods. The method is successfully implemented and tested both on simulated and real experimental data.