Calculation of the Real Spectral Line Shape by Solving the Ill-Posed Inverse Problem

Abstract

The solving of the ill- posed inverse problem for spectral line shapes or problem of reduction to the ideal spectral device is discussed in this paper. Two different methods were used to determine the real spectral line profile and to separate the instrument function: i) solving the ill-posed inverse problem by means of the Tikhonov’s regularization method; and ii) the mathematical modelling by means of a non-linear multiparameter chi-square fit. The solution of the inverse problem by the Tikhonov’s regularization method was implemented using program written in Delphi. The results of the test and statistical modelling of this program were presented. The mathematical modelling for the estimation the true profile and fitting the modelled line to an experimental profile by a non-linear multi-parameter chi-square procedure was used for the validation and comparison