Geodesic
Statement and solution of сollimation problems in small angle X-ray scattering by anisotropic systems
Nanosistemy: fizika, himiâ, matematika, Tome 2 (2011) no. 2, pp. 32-47.

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А problem of taking into account collimation distortions of small angle X-ray scattering intensity for anisotropic objects has been considered. Mathematical statement of the problem is presented and two methods of desmearing the experimental scattering intensity have been described. The first method – the method of basic functions – consists that the experimental scattering intensity is represented as a linear combination of the two-dimensional basic functions (B-splines). The modified method of least squares has been developed. It allows to achieve the best agreement between the original experimental scattering intensity and the intensity obtained by expanding the basic functions. The second approach is based on the iterative Friedman method that was substantially modified in accordance with the features of problem considered. We introduce a function that takes into account the influence of local values of the scattering intensity that is sought for on the value of the function approximating the experimental intensity. This “influence function” enables to precisely adjust the current approach at each step of the iterative process that leads to significant improvement of convergence. Shown that both approaches give a rather high accuracy collimation correction as in the case of anisotropic scattering on the number of model objects, as well as in the case of the experimental scattering curves on annealed films of highly oriented polyethylene.
Keywords: small-angle X-ray scattering, anisotropic objects, expansion of scattering intensity in the basic functions, iterative Friedman method, highly oriented polyethylene.
Mots-clés : collimation correction 
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     author = {D. D. Zakharov and A. V. Smirnov and B. A. Fedorov},
     title = {Statement and solution of {\cyrs}ollimation problems in small angle {X-ray} scattering by anisotropic systems},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {32--47},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/NANO_2011_2_2_a2/}
}
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D. D. Zakharov; A. V. Smirnov; B. A. Fedorov. Statement and solution of сollimation problems in small angle X-ray scattering by anisotropic systems. Nanosistemy: fizika, himiâ, matematika, Tome 2 (2011) no. 2, pp. 32-47. http://geodesic.mathdoc.fr/item/NANO_2011_2_2_a2/