Separation of Complex Spectra into Individual Bands by the Generalized Alentsev Method

Abstract

The need to separate complex absorption or luminescence spectra into their individual components arises in many cases such as luminescence analysis of complex mixtures or investigations of luminescence centers in crystal phosphors known to contain many types of luminescence center. Whenever the spectral bands belonging to centers or molecules of different types overlap one another we are dealing with some form of a complex spectrum. Usually, a spectrum of this kind is separated into individual bands on the assumption that the bands have Gaussian profiles and the problem usually discussed is that of the simplest method for finding the half-widths and the positions of the maxima of such bands. This is typical of the approach used, for example, in [1, 2].

The paper deals with the theory of the Alentsev method for separation of complex spectra into individual bands. The method is generalized to the many-band case. An estimate is given of the precision of the results obtained and the conditions of validity of the method are discussed. Numerical examples are considered in detail and the recommended sequence of operations is given.