The echelle spectrometer, with its high spectral resolution, is increasingly applied in various fields and has become one of the primary spectroscopic analysis instruments. Spectrum reconstruction technology is at the core of data processing in echelle spectrometers. It achieves rapid reconstruction from two-dimensional (2D) images to one-dimensional (1D) spectra by establishing a correspondence between the wavelength and imaging position. The accuracy of the spectrum reconstruction directly determines the performance of the echelle spectrometer, making it a key and challenging aspect of instrument development. Spectrum reconstruction algorithms have evolved from ray tracing, modeling (deviation method and mathematical modeling), and calibration methods. The evolution of algorithms is an ongoing process of continuous optimization and improvement. Each spectrum reconstruction algorithm has its advantages and disadvantages. However, a consistent mainstream approach is to achieve high accuracy and speed. Factors such as environmental conditions and application requirements must also be considered. Therefore, it is crucial to develop a spectrum reconstruction algorithm that combines these various advantages.

This study proposes a convenient and widely applicable spectrum reconstruction algorithm, adopting a nontraditional approach that initially focuses on improving the modeling speed, followed by further enhancement of accuracy. The main research method involves leveraging the advantage of rapid modeling using the deviation method to establish an initial model quickly. Subsequently, the initial model is subjected to holographic surface fitting with the theoretical model traced using ray-tracing software to obtain a standard model. Calibration is thereafter incorporated into the modeling process, allowing the standard model to fit an actual model comprising elemental lamp spectrum data. Through this process, the final model is obtained, and a spectrum reconstruction model is established. Following this, denoising is applied to the 2D spectra of the elemental lamps, completing the wavelength extraction. Finally, five elemental lamps are selected as test light sources to validate the accuracy of the proposed algorithm.

Holographic surface fitting is performed between the initial and theoretical models (Fig.7). After holographic surface fitting, a standard model is obtained (Fig.8). The error within the holographic surface of the standard model is within 2 pixel (Table 3). In the two-stage modeling process, the standard model is fitted with the actual model to obtain the final model. The error within the holographic surface of the final model after fitting is within 3 pixel (Fig.10). In the image denoising process, a denoising algorithm is developed based on the characteristics of the original 2D spectrum, accomplishing the denoising task and removing the majority of the noise (Fig.13). Finally, by selecting five types of elemental lamps as test light sources (Table 4) and 42 characteristic wavelengths as test data (Table 5), experimental results exhibit an extraction error of 0.01 nm for the average wavelength within the selected wavelength range. The entire image surface deviation is validated by the spectrum reconstruction model (Table 6). Within the wavelength range of 200?800 nm, the image surface deviation is within 2 pixel (Fig.16). The spectrum reconstruction algorithm presented in this paper demonstrates excellent accuracy.

This study proposes a spectrum reconstruction algorithm for echelle spectrometers based on holographic surface fitting. The algorithm demonstrates notable advantages in both modeling speed and model accuracy. As concerns calibration during the modeling process, this algorithm overcomes the impact of environmental changes and instrument movements, thereby saving resources and time. This study shifts its focus to the modeling process, initially prioritizing modeling speed, and later pursuing model accuracy. The advantage of rapid modeling using the deviation method is leveraged to establish an initial model. Thereafter, the spectrum reconstruction model is constructed using holographic surface fitting, cleverly incorporating calibration into the modeling process. After model establishment, denoising is applied to the 2D original images, and wavelength extraction is completed. Finally, the accuracy of the model is validated using five types of elemental lamps. The experimental results indicate that within the entire wavelength range (200?800 nm), the average wavelength extraction error is within 0.01 nm, and the pixel deviation for extracting characteristic wavelengths within the holographic surface is 2 pixel, which does not lead to significant misinterpretations. The algorithm can correctly output 1D spectra of the characteristic wavelengths and intensities. These experimental results fully demonstrate the capability of the algorithm to meet precision requirements. Moreover, the algorithm is straightforward, versatile, and applicable, making it more conducive to widespread use in practical production. These aspects are significant for enhancing the performance and practicality of echelle spectrometers.