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Reconstruction of continuous spectra by the regularization method using model spectra

Optics and Spectroscopy, ISSN: 1562-6911, Vol: 117, Issue: 6, Page: 1010-1017
2014
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Article Description

The inverse problem of spectroscopy—reconstruction of continuous spectra by solving the Fredholm integral equation of the first kind (an ill-posed problem)—is considered. The equation is solved by the Tikhonov regularization method using the method of computational experiments, according to which, along with initial example P, where experimental spectrum u is specified and true spectrum z is sought for, “similar” model example spectrum Q (or several examples) with specified z and modeled u is processed with allowance for additional information on true spectrum z in example P. This approach makes it possible to choose regularization parameter α and estimate the error in reconstructing spectrum z in example P. Some numerical illustrations are presented. Different response functions of spectrometers are considered: slotlike, triangular, diffraction, Gaussian, dispersion, and exponential; identical widths a(λ) at a level of 0.5 and identical integral widths W(λ) are used.

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