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.