A new computer algorithm has been developed for selecting the optimal set of wavelengths for spectroscopic quantitative analysis of mixture samples. The method is based on the criterion of the minimum mean square error between concentrations of the mixture components and their estimates. The branch and bound algorithm finds the optimal set from all possible combinations of wavelengths. This algorithm saves computation time significantly, compared with the enumerative method. The mathematical formulation of the lower bound of the mean square errors for the combinations in a given subset is derived as a recurrence inequality. Experimental results of wavelength selection for infrared absorption spectra of xylene-isomer mixtures are shown to demonstrate the effectiveness of the algorithm in terms of computation complexity and accuracy in quantitative analysis for the fixed measurement time.
K. Sasaki, S. Kawata, and S. Minami, "Optimal Wavelength Selection for Quantitative Analysis," Appl. Spectrosc. 40, 185-190 (1986)