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Eigen‐System Analysis of X‐ray Diffraction Profile Deconvolution Methods Explains Ill‐Conditioning
Author(s) -
Armstrong N.,
Kalceff W.
Publication year - 1998
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/s0021889897019638
Subject(s) - deconvolution , spurious relationship , diffraction , function (biology) , noise (video) , algorithm , upper and lower bounds , statistical physics , optics , computational physics , physics , mathematics , mathematical analysis , computer science , statistics , artificial intelligence , image (mathematics) , biology , evolutionary biology
Several deconvolution methods common in X‐ray diffraction profile studies have been examined using an eigen‐system analysis in which an error‐bound function is used to represent the maximum difference between the solution and true specimen profiles. This approach quantifies the sources of misfitting and ill‐conditioning that appear in the solution profile and expresses them as a function of the control parameter for a particular method. A simulation of an instrument‐broadened profile overlaid with random noise and background signals was used to evaluate the error‐bound function for the iterative and constrained deconvolution methods, and the properties of the error‐bound function were related to the features of the solution profile for each method. This analysis quantifies the terms that contribute to the ill‐conditioning of the solution profile. It shows that, even for optimum values of the control parameters, positivity is not preserved and spurious oscillations are present in the solution profile.