Reflectometry sounding of inhomogeneities in periodic multilayer structures

In this paper, a reflectometry method of sounding of layers' parameters in periodic multilayered dielectric structures is proposed and applied to the study of X-ray optics structures. It is based on angular and spectral (multi-frequency) measurements of a studied structure. Angular measurements of the reflection coefficient are used to determine the period of a structure; the spectrum is in use to study the inhomogeneity of layers - the effective profile of dielectric permittivity related to the diffusion of material at the epitaxy and to the roughness of layers' interfaces. An integral equation has been obtained to solve this inverse scattering problem. An algorithm of the solution based on the Tikhonov's method of generalized discrepancy has been worked out, and the theory has been applied to study inhomogeneities of multilayer structures manufactured for the X-ray optics.