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A new iterative method for collimation correction in small‐angle scattering
Author(s) -
Glatter O.
Publication year - 1974
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/s0021889874008983
Subject(s) - smoothing , weighting , scattering , convergence (economics) , fortran , iterative and incremental development , algorithm , iterative method , iterative refinement , stability (learning theory) , mathematics , collimated light , optics , mathematical analysis , computer science , physics , statistics , laser , software engineering , machine learning , acoustics , economics , economic growth , operating system
A new iterative procedure for desmearing small‐angle scattering data including the three types of resolution errors and arbitrary weighting functions is presented. The statistical errors of the data are taken into account by a `weighted least‐squares' approximation, i.e. the accuracy of the data controls the iterative process. The degree of smoothing is dependent on a free smoothing parameter and on the accuracy of the data. The method is not restricted to special types of scattering functions. The termination error is negligible; therefore it is possible to correct parts of scattering distributions. This is of importance for investigations in biological substances where the scattering distribution must be determined in parts with different slit widths. No artificial oscillations are generated in the solution of the integral equation. To ensure the stability of the procedure a criterion for uniform convergence of the iterative process is involved. The results of several numerical tests are shown in the figures. The Fortran program was tested for several months with very satisfactory results.