Wavelength Selection for Simultaneous Spectroscopic Analysis. Experimental and Theoretical Study

Abstract

Simultaneous multicomponent analysis is usually carried out by multivariate calibration models (such as principal component regression) that utilize the full spectrum. We demonstrate, by both experimental and theoretical considerations, that better results can be obtained by a proper selection of the spectral range to be included in calculations. We develop the theory that models the analytical uncertainty in multicomponent analysis and show the conditions where wavelength selection is essential (for example, when considerable spectral overlapping exists). An error indicator function is developed to predict the analytical performance under given experimental conditions, using a certain spectral range. This function is applied for allocation of the most informative spectral ranges to be utilized in multicomponent analysis. Selection of spectral ranges by this method is shown to ensure optimal results that considerably improve analytical performance in some cases. The similarity between the results obtained by this function and actual experimental results prove the validity of the proposed error indicator for wavelength selection. In addition to the experimental examples, extensive computer simulations have been carried out in order to study the validity of the theory over a wide range of the relevant parameters.Multicomponent spectral analysis is now gaining popularity. Numerous spectral data can be collected by modern instruments (such as photodiode arrays and CCD detectors), and several mathematical approaches have been designed to deal with these over-determined systems. [1][2][3][4][5][6] Early applications used complete spectra for determination of all components in a mixture. Ross and Pardue showed, however, that accuracy can be improved by a careful selection of wavelength ranges, which results in a collinearity or spectral overlap reduction. 7 The decision of how many data points and which wavelengths should be included in the analytical process is not trivial and is usually an empirical choice. 8 Various criteria have already been developed to allow for automatic wavelength selection. 8-25 Among the proposed meth-ods, the determinant and the condition number of calibration matrix are the most preferred criteria for prediction of the best wavelength combination. [8][9][10][11][12] Nevertheless, these two criteria are principally designed for exactly determined systems, although some modifications have been made to deal with overdetermined systems. [Most applications use RMSEP to characterize the performance of principal component regression (PCR) procedure, carried out under optimized conditions as obtained by the above criteria.] The major disadvantage of the current criteria is that all components are examined together with the same matrix, while in most cases, the optimal conditions for determination of each component is different and should be optimized separately. Recently, two stochastic search heuristics, namely, simulated annealing and genetic algorithms, have been suggested for wavelength selectio...

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