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| Improved Segmental Polynomial Fitting Algorithm for Two-Dimensional Spectral Restoration |
| GAI Qiao-na, LOU Xiao-ping, LÜ Sheng-yu-jie, MU Tao-tao* |
School of Instrument Science and Opto-Electronics Engineering, Beijing Information Science and Technology University, Beijing 100192，China
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Abstract The middle Echelle grating spectrometer has the advantages of wide spectral range and high Spectral resolution. To separate the spectra that are aliased due to the high diffraction order of the middle Echelle grating, the dispersion system of the middle Echelle grating spectrometer uses two elements that conduct cross dispersion in mutually perpendicular directions, and finally forms a two-dimensional spectral image on the detector. To obtain the intuitive spectral information of the substances detected by the spectrometer, it is necessary to convert the two-dimensional spectral image into the one-dimensional spectral image corresponding to the light intensity and wavelength through the spectral image reduction algorithm. The quality of the spectral image reduction algorithm directly determines the material analysis accuracy and efficiency of the middle Echelle grating spectrometer. An improved piecewise polynomial fitting two-dimensional spectrogram restoration algorithm is proposed based on existing spectrogram restoration algorithms. The middle Echelle grating spectrometer based on the algorithm in this paper uses a transmission prism, which is different from the traditional method of ray tracing to obtain fitting data points. The pixel coordinate data corresponding to the wavelength is obtained through the dispersion law of the middle Echelle grating and prism. Then the detector image surface is divided into multiple areas according to pixel coordinates on the horizontal axis; Due to the certain correlation between the X coordinate and the diffraction level m, the principle of the algorithm is to establish a fitting relationship between the X coordinate and m, which can be used to obtain the diffraction level of the light ray from the X coordinate of the detector's image plane. By combining the relationship between the Y coordinate of the image plane and the wavelength, the relationship between the coordinate and the wavelength can be obtained. Perform polynomial fitting on each region to obtain the relationship between each region's wavelength and pixel coordinates and establish a model for restoring the entire region spectrum. Experimental verification shows that the calculation error of the established spectrogram reduction model is 0.000 1 nm. In summary, the algorithm designed in the paper has simple operations, can quickly achieve spectral restoration, and improves the accuracy of spectral restoration.
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Received: 2023-06-19
Accepted: 2023-12-12
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Corresponding Authors:
MU Tao-tao
E-mail: mfjmtt@163.com
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