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Collimation problem in small‐angle X‐ray scattering for anisotropic objects: statement and solution
Author(s) -
Zakharov Denis D.,
Smirnov Alexander V.,
Fedorov Boris A.
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576714017750
Subject(s) - collimated light , scattering , curvature , optics , anisotropy , statement (logic) , physics , basis (linear algebra) , intensity (physics) , distortion (music) , computational physics , mathematics , geometry , laser , law , amplifier , optoelectronics , cmos , political science
The problem of removal of collimation distortion due to employing a slit collimation system in small‐angle X‐ray scattering experiments is considered for anisotropic objects in general and for orientated macromolecules in particular. A mathematical statement of the problem is presented, and two approaches to `de‐smear' the experimental scattering intensity are described. The first method seeks the theoretical scattering intensity as a linear combination of two‐dimensional basis functions (B splines). The combination coefficients are found using the χ 2 and two‐dimensional curvature‐minimization criteria. The second approach is based on the iterative Friedman method, which was generalized to be effective for the problem of interest. The described methods are applied to simulated and experimental data, and the results are discussed.