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

Abstract

We propose a method for retrieval of an optical line spectrum limited to a narrow spectral range using a short interferogram, based on the use of a multi-stage genetic algorithm. We have run simulations for the example of spectra with lines having wavenumbers lying in the 100 cm -1 range, and the maximum optical path difference for the interferograms was 1200 μm. We show that the spectral resolution can be improved by a factor of 3-4 compared with Fourier transform estimation.Introduction. Interference spectral instruments have high luminosity, low signal-to-noise ratio as a result of multiplexing, and a broad working spectral range. Retrieval of the spectrum in conventional Fourier transform spectroscopy is based on the Wiener-Khinchin theorem, relating the power spectral density for a stationary random process to its autocorrelation function (interference pattern or interferogram) by means of a Fourier transform [1]. In this case, the theoretical spectral resolution is inversely proportional to the maximum optical path difference, and therefore it is low in compact instruments.It is diffi cult to substantially improve the resolution of compact instruments strictly with hardware. Fast continuous scanning, used in popular laboratory Fourier transform spectrometers, requires a high-precision drive and constant operating parameters of the instrument for high-quality retrieval of the spectrum, which is complicated to achieve in a small instrument [2]. Experimental systems using scanning of the optical path difference in a more compact size (for example, using a Wollaston prism [3] or in a standing-wave interferometer [4]) do not provide a substantial increase (by a factor of 3-5) in the spectral resolution and generally form a poorer quality interferogram. Recording a stationary interferogram based on a multi-element photodetector makes it possible to dispense with the scanning mechanism and thus to reduce the size of the instrument [5-7]. However, due to the small number of pixels in the detector, an increase in the length of the interferogram causes narrowing of the spectral range for retrieval. Parallel recording of sections of the interferogram on a two-dimensional photodetector and "splicing" them into one interferogram with a large effective length requires, in addition to complicated post-processing, an increase in the dimensions of the optical part of the instrument while maintaining light beam homogeneity [8]. Recording the interferograms from different spectral intervals on different regions of the same two-dimensional array decreases the infl uence of noise at individual frequencies on the rest of the spectrum, but the spectral resolution for each of the intervals remains poor since the interferogram is short [9].Alternatives to the Fourier transform method for spectral estimation in some cases (more often for quasi-line spectra) let us improve the spectral resolution without increasing the maximum path difference. For example, knowing the mathematical model for the signal a priori in autoregression metho...