Self-subtraction improves consistency in spectral curve fitting

• Published in: Journal of quantitative spectroscopy & radiative transfer Vol. 277; p. 107991
• Main Authors: Kojić, Dušan, Tsenkova, Roumiana, Yasui, Masato
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2022
• Subjects: Bandwidth estimation; Curve fitting; Resolution enhancement; Second derivative; Voigt profile; Resolution enhancement; Second derivative; Voigt profile; Curve fitting; Bandwidth estimation
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/j.jqsrt.2021.107991

•A purely functional algorithm for resolving positions and widths of overlapped bands is presented on the basis of self-subtracted spectra.•Significant improvements, demonstrated both theoretically and practically, over the popular second derivative transform are achieved.•The method eliminates any bias related to the choice of a basis function because it outputs the least-squares fit to the data.•Higher consistency with retained accuracy follow naturally from a systematic analysis of XRF spectra, across a variety of Voigt profile line shapes. [Display omitted] Common practice in curve fitting of overlapped spectral features often imparts overextending the number of optimized parameters, resulting in increased model complexity and exacerbated sensitivity to initial conditions, that ultimately leads to inflated uncertainty in values of optimized parameters. We introduce a lightweight operator that unifies two important steps of model initialization: (1) resolution of overlapped bands that exceeds the benefits of the widely used second derivative transform, and (2) bandwidth estimation for overlapped features, to achieve a reliable data-driven contraction of optimization complexity and outperform similar methods in terms of speed, flexibility and ease of interpretation. Since only the spectrum at hand is used, the curve fitting process is steamlined by avoiding multivariate models and/or assumptions about the profile line shape included in the choice of a digital filter or a basis function. All statements are reinforced with illustrative theoretical models and x-ray fluorescence spectra obtained from a publicly available database.