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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Andreev A. B., Khachaturov R. V., Otrazhenie i rasseyanie rentgenovskogo izlucheniya mnogosloinymi nanostrukturami s sherokhovatymi poverkhnostyami, Soobsch. po prikl. matem., VTs RAN, M., 1996

[2] Khachaturov V. R., “Approksimatsionno-kombinatornyi metod dekompozitsii i kompozitsii sistem i konechnye topologicheskie prostranstva, reshetki, optimizatsiya”, Zh. vychisl. matem. i matem. fiz., 25:12 (1985), 1777–1794 | MR | Zbl

[3] Dietrich S., Haase A., “Scattering of X-Rays and neutrons at interfaces”, Phys. Repts., 260 (1995), 1–138 | DOI

[4] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989 | MR

[5] Khachaturov P. B., “Matematicheskoe modelirovanie samofokusirovki osesimmetrichnykh rentgenovskikh impulsov v plazme”, Zh. vychisl. matem. i matem. fiz., 39:12 (1999), 2086–2097 | MR | Zbl

[6] I. K. Kikoin (red.), Tablitsy fizicheskikh velichin. Spravochnik, Atomizdat, M., 1976

[7] Pinsker Z. G., Rentgenovskaya kristallooptika, Nauka, M., 1982

[8] Khachaturov V. R., “Approksimatsionno-kombinatornyi metod i nekotorye ego prilozheniya”, Zh. vychisl. matem. i matem. fiz., 14:6 (1974), 1464–1487 | Zbl

[9] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR