Journal of Applied Spectroscopy, Vol. 86, No. 4, September, 2019 (Russian Original Vol. 86, No. 4, July–August, 2019) ALGORITHM FOR SECOND-ORDER DIFFRACTION CORRECTION IN A CONCAVE DIFFRACTION GRATING SPECTROMETER S. I. Bruchkouskaya, * G. S. Litvinovich, I. I. Bruchkousky, UDC 535.421;681.785.554 and L. V. Katkovsky A feature of diffraction grating spectrometers in the visible and near IR range is that the second-order diffraction spectrum overlaps the first-order diffraction spectrum. This leads to distortions of the recorded spectrum in its long- wavelength region. We propose a method for correction of the second-order diffraction, based on representing the spectrum as the sum of Gaussians with parameters that are experimentally determined for individual wavelengths, followed by numerical interpolation. We also use parametrization of the second-order line shape. We describe the details of the experiment required, and test the performance of the method using an SSP-600N spectrometer as an example. Keywords: overlap of diffraction orders, second-order diffraction, diffraction correction, spectral correction, correction algorithm, post-processing, diffraction grating spectrometer. Introduction. A wide range of problems in real-time monitoring of the Earth ′ s surface are solved using compact spectrometers. In particular, we can use spectral analysis of the underlying surface to monitor emergency situations, the status of forest and agricultural areas, and processes in ecology and geology [1]. The major advantages of spectrometers with a concave diffraction grating as the dispersive element are the minimal number of elements in the optical system and the possibility of recording a broad range of wavelengths, as well as the compact size. However, concave diffraction grating spectrometers have an important disadvantage when working in a broad wavelength range: overlap of spectra formed in different orders of diffraction. This leads to distortion of the recorded spectra and problems in their subsequent interpretation and processing. The problem of overlapping orders of diffraction can be partially solved using a correcting plate, which is an interference filter mounted either directly on the detector [2] or with a small air gap, and attenuating multiple diffraction orders. Integrating such a plate into the spectrometer is a nontrivial task, and does not completely solve the problem. The quality of the spectrum deteriorates, since the filter creates additional wavy distortions. In international practice, the problem of overlapping second orders of diffraction is generally solved using cutoff filters, which are mounted in front of the spectrometer [3]. However, such solutions increase the weight and size of the instrument and lead to an increase in the time required to record the spectrum, which is critical in some Earth remote sensing (ERS) problems. There is a method for theoretically calculating the higher-order diffraction spectra [4] which does not take into account the individual features of the spectrometer. Consequently, its results need to be tested for use in practice. Often correction methods are used in which the second-order diffraction spectrum is calculated taking into account the dependence of the second-order to first-order intensity ratio. In order to determine this dependence, the parameters have been measured for narrow-band [2, 5] or broadband [6, 7] radiation sources. Note that in such cases, broadening and shape of second-order lines are not considered. In this paper, we propose an analytical method for second-order diffraction correction, taking into account both the shape and the intensity of the second-order lines. The performance of the method has been demonstrated using an SSP-600N spectrometer as an example. 0021-9037/19/8604-0671 ©2019 Springer Science+Business Media, LLC 671 A. N. Sevchenko Institute of Applied Physical Problems, Belarusian State University, 7 Kurchatov Str., Minsk, 220108, Belarus; email: ms.bruchkovskaya@yandex.ru. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 86, No. 4, pp. 620–626, July–August 2019. Original article submitted March 27, 2019. _____________________ * To whom correspondence should be addressed. DOI 10.1007/s10812-019-00877-3