Optics and Spectroscopy

, Volume 117, Issue 6, pp 1010–1017 | Cite as

Reconstruction of continuous spectra by the regularization method using model spectra

Geometric and Applied Optics


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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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.St. Petersburg State University of Information Technologies, Mechanics, and OpticsSt. PetersburgRussia

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