Abstract

Improvements have been made in previous least-squares regression analyses of infrared spectra for the quantitative estimation of concentrations of multicomponent mixtures. Spec- tral baselines are fitted by least-squares methods, and overlap- ping spectral features are accounted for in the fitting procedure. Selection of peaks above a threshold value reduces computation time and data storage requirements. Four weighted least- squares methods incorporating different baseline assumptions were investigated using FT-IR spectra of the three pure xylene isomers and their mixtures. By fitting only regions of the spectra that follow Beer's Law, accurate results can be obtained using three of the fitting methods even when baselines are not cor- rected to zero. Accurate results can also be obtained using one of the fits even in the presence of Beer's Law deviations. This is a consequence of pooling the weighted results for each spectral peak such that the greatest weighting is automatically given to those peaks that adhere to Beer's Law. It has been shown with the xylene spectra that semiquantitative results can be obtained even when all the major components are not known or when expected components are not present. This improvement over previous methods greatly expands the utility of quantitative least-squares analyses.

Application of the Least-Squares Method*

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J. Opt. Soc. Am. 46(3) 223-226 (1956)

Computer Analysis of Resonance Profiles by the Method of Least Squares

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