Discrete Spectrum Reconstruction Using Integral Approximation Algorithm. Issue 7 (July 2017)

• Record Type: Journal Article
• Authors: Sizikov, Valery; Sidorov, Denis
• Is Part Of: Applied spectroscopy. Volume 71:Issue 7(2017)
• Page Start: 1640
• Page End: 1651
• Publication Date: 2017-07
• Subjects: Inverse problem of spectroscopy -- discrete spectrum -- system of linear and nonlinear equations -- integral equations -- regularization -- resolution enhancement -- integral approximation algorithm -- lines intensities and frequencies; Spectrum analysis -- Periodicals; 543.505
• DOI: 10.1177/0003702817694181
• Languages: English
• ISSNs: 0003-7028

Abstract

An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of linear–nonlinear equations (SLNE) with respect to intensities and frequencies of the discrete spectral lines. The SLNE is linear with respect to lines' intensities and nonlinear with respect to the lines' frequencies. The integral approximation algorithm is proposed for the solution of this SLNE. The algorithm combines solution of linear integral equations with solution of a system of linear algebraic equations and avoids nonlinear equations. Numerical examples of the application of the technique, both to synthetic and experimental spectra, demonstrate the efficacy of the proposed approach in enabling an effective enhancement of the spectrometer's resolution.