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Extended pseudo‐Voigt function for approximating the Voigt profile
Author(s) -
Ida T.,
Ando M.,
Toraya H.
Publication year - 2000
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/s0021889800010219
Subject(s) - voigt profile , gaussian , computation , mathematics , function (biology) , mathematical analysis , polynomial , full width at half maximum , gaussian function , order (exchange) , physics , optics , algorithm , quantum mechanics , spectral line , evolutionary biology , biology , finance , economics
The formula of the pseudo‐Voigt function expressed by a weighted sum of Gaussian and Lorentzian functions is extended by adding two other types of peak functions in order to improve the accuracy when approximating the Voigt profile. The full width at half‐maximum (FWHM) values and mixing parameters of the Gaussian, the Lorentzian and the other two component functions in the extended formula can be approximated by polynomials of a parameter ρ = Γ L /(Γ G + Γ L ), where Γ G and Γ L are the FWHM values of the deconvoluted Gaussian and Lorentzian functions, respectively. The maximum deviation of the extended pseudo‐Voigt function from the Voigt profile is within 0.12% relative to the peak height when sixth‐order polynomial expansions are used. The systematic errors of the integrated intensity Γ G and Γ L , estimated by fitting the extended formula to Voigt profiles, are typically less than 1/10 of the errors arising from the application of the original formula of the pseudo‐Voigt approximation proposed by Thompson et al. [ J. Appl. Cryst. (1987), 20 , 79–83], while the time required for computation of the extended formula is only about 2.5 relative to the computation time required for the original formula.