CONTINUOUS SPECTRA RESTORATION BY AN ADAPTIVE WAY OF COMPUTING EXPERIMENTS WITH REGULARIZATION

Abstract

The article deals with inverse spectroscopy problem - restoration of continuous spectra by mathematical treatment of measured spectra, distorted by the spectrometer instrument function and noises. The problem is reduced to solution of the first-kind Fredholm integral equation. This problem is illegal; therefore, the Tikhonov regularization method is used for stable numerical solving of the equation. Furthermore, the adaptive way of computing experiments is used, according to which, one treats the model spectrum Q with prescribed true spectrum z and simulated measured spectrum u with regard to additional (a priori) information about the true spectrum P. This makes it possible to choose the regularization parameter a. The proposed technique can be used to enhance the spectrometer resolving power. Numerical illustrations are given.

Keywords

• continuous spectrum
• inverse spectroscopy problem
• integral equation
• Tikhonov regularization method
• way of computing experiments
• spectrometer resolving power enhancement