Information processing in spectroscopy

Abstract

In all spectroscopic methods, there exists an integral equation relating the observed spectrum and the intensity distribution observed by the spectroscopic instrument. An improved spectrum can be reconstructed by solving this integral equation. A process of eigenvalue analysis based on the theory of Hilbert and Schmidt was developed and applied to solve the equation. Formulation of this method and some computer simulations are presented on the results from a Fabry-Perot interferometer, a diffraction grating, and a two-beam interferometer. We also apply this method to spectroscopic techniques and considerations of resolution.

Retrieval of Spectra from Interferograms with a Small Optical Path Difference Using a Genetic Algorithm

“…Expansion of the kernel in eigenfunctions gives a more stable solution with better resolution and reduced noise level [16], but to do this we need an analytical description of the instrumental function for the interferometer, and it is not applicable to all types of interferometers. A nonparametric algorithm, determining the spectral estimation by the iterative method of regularization in the Cauchy-Gauss model, gives a spectral resolution exceeding the resolution for both the conventional and some alternative methods, but may retrieve spurious lines [11].…”

“…Secondly, the infl uence of noise on the individual spectral segments is reduced over the entire interferogram [9]. Due to the smaller size of the instrumental function matrix, the error in spectral estimation by solution of an integral equation, reduced to an ill-posed system of equations [16], decreases and consequently the spectral resolution increases [14]. Lowering the dimension of the spectra/solutions space lets us use a genetic algorithm (GA) to search for the solution.…”