Spectral reduction algorithm for echelle grating spectrometer based on least-squares image coordinate correction

Ouyang Yuxuan; Fu Xiao; Duan Fajie; Wang Kuan; Wu Jingxin

doi:10.12086/oee.2024.240134

Article navigation > Opto-Electronic Engineering > 2024 Vol. 51 > No. 7 > 240134

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Ouyang Y X, Fu X, Duan F J, et al. Spectral reduction algorithm for echelle grating spectrometer based on least-squares image coordinate correction[J]. Opto-Electron Eng, 2024, 51(7): 240134. doi: 10.12086/oee.2024.240134

Citation:

Ouyang Y X, Fu X, Duan F J, et al. Spectral reduction algorithm for echelle grating spectrometer based on least-squares image coordinate correction[J]. Opto-Electron Eng, 2024, 51(7): 240134. doi: 10.12086/oee.2024.240134

Spectral reduction algorithm for echelle grating spectrometer based on least-squares image coordinate correction

1.
The State Key Lab of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
2.
China Aerospace Hunan Power Machinery Research Institute, Zhuzhou, Hunan 412002, China

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^*Corresponding author: fuxiao215@tju.edu.cn

Received Date 07 June 2024

Revised Date 01 August 2024

Accepted Date 02 August 2024

Published Date 20 August 2024

Abstract

Abstract

The echelle grating spectrometer has cross-dispersion characteristics, and two-dimensional spectral map reduction is the key link to determine its wavelength measurement accuracy, but the changes of spot coordinates caused by environmental changes, processing and mounting have a serious impact on the accuracy of spectral map reduction. In this paper, a spectrum reduction algorithm based on least-squares image coordinate correction is proposed for the middle-step spectrometer. Firstly, the center-of-mass coordinates of the multi-wavelength spot of the calibrated mercury lamp light source are extracted, and the coefficient matrix is constructed by using the theoretical and actual image point coordinates. The translation, scaling, and rotating coefficients of the two-dimensional image plane are obtained by the least-squares estimation method, and then a polynomial fitting is adopted to reduce the influence of residuals, to achieve the correction of the image coordinates of the spot at different wavelengths, and then achieve the accurate resolution of wavelength, and realize the wavelength accurate solving. The experimental results show that the algorithm can effectively improve the spectral image reduction accuracy of the middle-step spectrometer, and the deviation of the corrected coordinates from the ideal coordinates is less than 0.6 image element under the condition of simulating larger mounting errors, which proves that the algorithm has high accuracy.
- spectroscopy /
- spectrometer /
- two-dimensional spectrogram /
- centroid extraction /
- spectrogram reduction

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References

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Overview

Overview

Echelle grating spectrometer uses a cross-dispersive optical structure for spectroscopy, forming a two-dimensional spectral image on the image plane. The reduction accuracy of the two-dimensional spectral image is to determine the accuracy of its wavelength measurement, but environmental changes, processing and mounting and other reasons will lead to the error between the actual spot coordinates and the theoretical spot coordinates, and the change of the spot coordinates will have a serious impact on the reduction accuracy of the spectral image. In this paper, a spectrum reduction algorithm for an echelle grating spectrometer based on least squares image coordinate correction is proposed. Firstly, the theoretical spot coordinates of the mercury lamp are recorded by simulation software, and then measurements are made using a calibrated mercury lamp light source, and the background noise reduction and morphological processing of the two-dimensional spectral map are carried out to obtain the center-of-mass coordinates of the actual spot of the wavelength of the mercury lamp, and then the coefficient matrix is constructed by utilizing the theoretical and actual image point coordinates, and then the coefficient matrix is solved from the obtained two-dimensional spectrum by the method of least squares. The coefficient matrix is solved by the least squares method to obtain the fitting coefficients of translation, scaling and rotation of the two-dimensional image plane, and then the polynomial fitting is used to reduce the influence of the residuals, realizing the image coordinate correction of the spot at different wavelengths, and then realize the accurate wavelength solution.

The experimental results show that the algorithm can effectively improve the spectral image reduction accuracy of the echelle grating spectrometer, and the center of mass extraction error is controlled at 0.6 image elements, and under the simulation of large mounting errors and environmental errors, the corrected coordinates of the measurements of the common elements deviate from their ideal coordinates by less than 0.6 image elements, which proves that the algorithm has high accuracy and provides a basis for the measurement of broad-band atomic emission spectra.