NONLINEAR LEAST-SQUARES REFINEMENT WITH CONSTRAINTS - EVALUATION THROUGH CURVE-FITTING ON EMULATED XPS-LIKE SPECTRA AND APPLICATION TO THE ANALYSIS OF CARBON-FIBERS

A non-linear least squares iterative refinement has been implemented w hich shows high performance on a multiple-peak spectrum including base line or background. Constraints as well as links within a range are in troduced to drive the mathematical optimization: each peak parameter ( i.e. height, position, Gaussian/Lorentzian mixing ratio and HWHM on bo th left and right sides) has assigned to it an allowed range of variat ion and can be strained to be correlated with other parameters belongi ng either to the same peak (symmetrical peaks) or to other peaks (doub lets, triplets, etc.). Peak shapes typical of XP spectra are used and applications in the field of XPS are discussed. Through emulated curve s with Poisson distributed noise, the accuracy and precision of back-c alculated (refined) parameters have been estimated. Moreover, a confid ence level calculated from chi2 and degrees of freedom has been sugges ted to check the overall fitting of experimental curves where the sign al-to-noise ratio is a priori unknown. An application to real C Is XP spectra is described as an example and a list of suggestions is given to match operator requirements. Finally, features of NLLSRC are discus sed with respect to other approaches.