RECOVERY OF DISCRETE SPECTRA RADIATED BY SUBSTANCE IN DEEP VACUUM USING INTEGRAL APPROXIMATION ALGORITHM

Abstract

Subject of Research. The topical spectroscopy inverse problem is considered: the recovery of a discrete (line) spectrum from the measured continuous spectrum and the spectrometer response (instrument, hardware, spread) function in the presence of noise. Method. The problem is reduced to solving a system of linear-nonlinear equations with respect to the intensities of lines entering linearly and the frequencies of lines entering nonlinearly in the spectrum. To solve the system of linear-nonlinear equations, an integral approximation algorithm is developed that combines the solution of a linear integral equation and a system of linear algebraic equations without solving non-linear equations. Main Results. The proposed solution makes it possible to determine the number of lines in the spectrum and their parameters and is confirmed by the solution of numerical examples. Practical Relevance. The proposed algorithm provides the increase of spectrometer resolution (resolve close lines and isolate weak lines from noise) by applying mathematical-computer processing of the discrete spectrum.

Keywords

• spectroscopy inverse problem
• discrete (line) spectrum
• deep vacuum
• system of linear nonlinear equations
• intensities (amplitudes) and frequencies of lines
• integral approximation algorithm