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Non‐linear least squares refinement with constraints. Evaluation through curve fitting on emulated XPS‐like spectra and application to the analysis of carbon fibres
Author(s) -
Ceipidor Ugo Biader,
Cataldi Tommaso R. I.,
Desimoni Elio,
Salvi Anna Maria
Publication year - 1994
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1180080305
Subject(s) - gaussian , spectral line , least squares function approximation , range (aeronautics) , curve fitting , noise (video) , mathematics , a priori and a posteriori , position (finance) , poisson distribution , algorithm , mathematical analysis , computational physics , statistics , computer science , physics , materials science , artificial intelligence , philosophy , image (mathematics) , epistemology , finance , quantum mechanics , astronomy , estimator , economics , composite material
A non‐linear least squares iterative refinement has been implemented which shows high performance on a multiple‐peak spectrum including baseline or background. Constraints as well as links within a range are introduced to drive the mathematical optimization: each peak parameter (i.e. height, position, Gaussian/Lorentzian mixing ratio and HWHM on both left and right sides) has assigned to it an allowed range of variation and can be strained to be correlated with other parameters belonging either to the same peak (symmetrical peaks) or to other peaks (doublets, triplets, etc.). Peak shapes typical of XP spectra are used and applications in the field of XPS are discussed. Through emulated curves with Poisson distributed noise, the accuracy and precision of back‐calculated (refined) parameters have been estimated. Moreover, a confidence level calculated from X 2 and degrees of freedom has been suggested to check the overall fitting of experimental curves where the signal‐to‐noise ratio is a priori unknown. An application to real C ls XP spectra is described as an example and a list of suggestions is given to match operator requirements. Finally, features of NLLSRC are discussed with respect to other approaches.