Geodesic
Direct and inverse problems of determining the parameters of multilayer nanostructures from the angular spectrum of the intensity of reflected X-rays
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 10, pp. 1860-1867 
R. V. Khachaturov. Direct and inverse problems of determining the parameters of multilayer nanostructures from the angular spectrum of the intensity of reflected X-rays. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 10, pp. 1860-1867. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_10_a11/
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     title = {Direct and inverse problems of determining the parameters of multilayer nanostructures from the angular spectrum of the intensity of reflected {X-rays}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Mathematical models and methods for determining the degree of roughness and other parameters of multilayer nanostructures from the angular spectrum of the intensity of the reflected X-rays are studied. The proposed mathematical model for solving the direct problem of x-ray propagation and the distribution of their electromagnetic field within a multilayer nanostructure takes into account the refraction effect due to the inclusion of the second derivative with respect to the structure depth. A numerical method for solving the resulting problem is developed, and the numerical results are analyzed. The approximation-combinatorial method of the decomposition and composition of systems is used to solve the inverse problem.

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