Analysis of Overlapping Bands by an Analytic Geometric Approach: The Potential of Band-Stripping and the Complementary Matching Method in Extraction of Band Components from Overlapping Bands

As a novel method for extracting individual band components from heavily overlapping bands, we propose a band stripping/complementary matching method that is based on first-derivative–second-derivative (D1–D2) plots of an experimental spectrum, coupled with a new concept called a complementary band. By using the concept of complement of a set, the ith band can be indirectly expressed by using a complementary band created by subtracting all the bands, exclusive of the ith estimated band, from an experimental spectrum. The degree of coincidence of both shapes between an estimated band and its complementary band provides a very suitable measure for the quality of fit for each individual band. The analysis method consists of two stages. The first stage is concerned with the geometric approach, which estimates a set of values for the parameters of a component band in the overlapping bands, and repeats band decomposition of the remaining bands in the same manner after removing the estimated band from the overlapping bands. The second stage is to minimize the difference between the profiles of the estimated band and its complementary band by a least-squares optimization and then determine the optimum values of the band parameters with the best-fit band shape. The algorithm and procedures of this method are illustrated by use of a synthetic spectrum consisting of a number of component bands, a background component, and random noise. The quality of fit is so satisfactory in terms of the coincidence between the individual estimated band and the corresponding complementary one that visual observation permits us to determine the optimum estimates of the band parameters and avoid potential problems of curve fitting.