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Error Propagation of Quantitative Analysis Based on Ratio Spectra

Error propagation of the quantitative analysis of binary and ternary mixtures based on the ratio spectra and the mean-centred ratio spectra has been studied. Gaussian doublets and triplets were used as models of the mixture pure-component spectra. The mixture spectra were disturbed by random constant and proportional noises and unknown background. The perturbations of the calibration matrix were modelled by systematic errors caused by the wavelength shifts. The least-squares estimation of the concentration vector and the estimation errors were obtained theoretically and numerically. The condition number of the matrix of the pure-component ratio spectra was theoretically evaluated for binary mixtures. The advantages and disadvantages of the ratio spectra methods are discussed.