Velikhovskyi G. Dynamical scattering theory for non-crystalline multilayer objects of arbitrary shape

Thesis for a scientific degree of Candidate of Sciences in Physics and Mathematics (Philosophy Doctor) in specialty 01.04.07 – Solid-State Physics. G.V. Kurdyumov Institute for Metal Physics, National Academy of Sciences of Ukraine, Kyiv, 2019. The dissertation is devoted to the development of methods of X-ray diagnostics of the internal structure of multi-layered non-crystalline objects of arbitrary shape, namely the creation of theoretical bases for describing the processes of refraction and forming of phase-contrast images of such objects within the triple-axis scheme. Within the quantum-mechanical approach, using a column approximation, there was developed a model, which describes the influence of parameters of both the outer surface of the object and the surfaces between the substances inside it, and actually the substances themselves as well as the size and the shape of the object on the change of the characteristics of the scanning beam. Based on the constructed model and the obtained analytical formulas, a phase variational method for solving the inverse scattering problem was proposed. This method provides the possibility to solve the problem of protection against the parasitic influence of instrumental factors on the image. The numerical experiment confirmed the efficiency of the developed approach in the diagnostics of multilayer non-crystalline objects.