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An analysis of errors in the Fourier coefficients of the α 1 line profile
Author(s) -
Delhez R.,
Mittemeijer E. J.
Publication year - 1975
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/s0021889875011478
Subject(s) - fourier transform , computation , intensity (physics) , fourier analysis , fourier series , line (geometry) , harmonic , function (biology) , mathematics , term (time) , physics , mathematical analysis , statistics , computational physics , optics , algorithm , geometry , quantum mechanics , evolutionary biology , biology
The errors in the Fourier coefficients of the α 1 component obtained by α 2 elimination are investigated analytically. The effects of counting statistics, of an incorrect intensity ratio of the α 1 and α 2 components and of an incorrect doublet separation are calculated. The mean‐square error in the Fourier coefficient caused by counting statistics is a periodic function of the harmonic number, while errors in the intensity ratio and in the doublet separation primarily affect the first Fourier coefficients. The results are confirmed by computer simulations and by computations with experimental line profiles. The α 2 elimination methods assume a perfect shape identity of the α 1 and α 2 components, but this assumption is not completely justified. Deviations might be interpreted as local errors in the doublet separation and the intensity ratio.