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Lissage d'un profil de raie de diffraction pour analyse de Fourier
Author(s) -
Bourniquel B.,
Feron J.
Publication year - 1985
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/s0021889885010226
Subject(s) - fourier transform , initialization , function (biology) , constant (computer programming) , fourier analysis , gaussian , mathematics , fourier series , mathematical analysis , algorithm , computer science , physics , evolutionary biology , quantum mechanics , biology , programming language
The fast Fourier transform algorithm commonly used for line profile analysis requires a list of values of the diffracted intensity with constant sin θ step; raw data are usually obtained at constant 2 θ step; to interpolate between the measured values an analytic expression of the profile function is very useful. Statistical estimation is used to fit an analytic function to data; the only assumption made is the continuity of this function and no critical initialization is needed. Three different expressions are used: a Fourier sum for the peak and two polynomials of a suitable variable for the tails; the algorithm provides continuity for the function and its first derivative. Simulated examples using a Lorentzian and a Gaussian function are given and several criteria of goodness of fit are examined. The program runs on a PDP 11/03 Digital computer with only 45 kbytes available memory.