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A method for correcting slowly varying small‐angle scattering curves for collimation effects
Author(s) -
Walter G.,
Schmidt P. W.
Publication year - 1981
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/s0021889881008613
Subject(s) - scattering , collimated light , polynomial , curve fitting , optics , physics , small angle scattering , small angle x ray scattering , mathematical analysis , computational physics , geometry , mathematics , statistics , laser
A technique has been developed for correcting slowly varying small‐angle X‐ray scattering curves for the distortions produced by the length of the collimating slits when, as is very often true, slit‐width effects are negligible. The method, which is useful with measured scattering curves which decay so slowly with increasing scattering angle that the usual correction procedures do not converge, is based on approximating the measured curve by a polynominal in h 2 , where h = 4 πλ −1 sin θ ; 2 θ is the scattering angle and λ is the X‐ray wavelength. The order j of the polynomial is selected to give the best fit to the measured curve over the entire interval of angles for which data are available. The corrected curve is also a polynomial in h 2 of order j , and the coefficients of this polynomial can be easily evaluated. Tests of the method on a theoretical scattering curve and two experimental curves are described.