Spectrometers are widely used optical analysis instruments designed based on the principle of optical dispersion. They are extensively applied in industrial production, chemical analysis, biomedical research, and astronomical studies[[1], [2], [3], [4]]. Among various spectrometer structures, the C–T type spectrometer, due to its simple structure and ease of alignment, offers resolution directly dependent on the grating line density and focal length, making it the most suitable structure for detecting weak spectral signals such as Raman and LIBS spectra [5,6]. Traditional large C–T spectrometers, with their bulky volume, high cost, and high power consumption, are mainly used in research institutions and universities where cost is not a major concern [7]. In recent years, with the development of industrial inspection, hydrological surveys, military reconnaissance, biomedical research, and space exploration, there is growing demand for spectrometers that are portable, aberration–free, and highly accurate. The fixed grating crossed C–T spectrometer, featuring a compact optical path, high stability, high measurement accuracy, wide range, fast speed, and ease of use, effectively enhances the accuracy and reliability of spectral analysis. Therefore, it has been widely applied in scientific research and industrial applications.

The structure of the crossed C–T spectrometer is shown in Fig. 1. It consists of an entrance slit, a spherical collimating mirror, a planar diffraction grating, a spherical converging mirror, and a detector. For crossed C–T spectrometers, a compact layout of the optical path is achieved by precisely regulating the off–axis angle of the light beam. However, aberrations such as coma, field curvature, and astigmatism introduced by the off–axis optical path are aggravated as the angle increases [8,9]. These aberrations severely affect the imaging quality and the spectral resolution, thus becoming key challenges in the design optimization process.

In the field of aberration reduction for spectrometers, researchers have devoted extensive efforts to exploration [10,11].Among them, coma and astigmatism, as the main forms of off–axis aberrations, have received widespread attention. In 1964, Shafer et al. were the first to propose a method for correcting coma at a specific wavelength and successfully demonstrated the effectiveness of this method in reducing coma over a wide spectral range [8]. For the reduction of astigmatism, Rosendahl and Shafer respectively proposed solutions of adding compensating lenses and using toroidal mirrors [12]. Dalton innovatively proposed a method of using convex diffraction gratings to achieve divergent illumination for astigmatism correction [13]. With the ongoing advancement of spectrometer technology, substantial efforts have been devoted to astigmatism correction. Lee et al. [14] introduced a tilted cylindrical lens positioned in front of the detector to perform preliminary astigmatism compensation. Zhong et al. [15] extended Rosendahl's approach by employing a compensating lens to mitigate astigmatic aberrations. Xue et al. [16] proposed the use of a wedged cylindrical lens to reduce astigmatism across a broad spectral range. Although the aforementioned methods have achieved remarkable progress in the correction of coma and astigmatism, they still exhibit certain limitations when addressing astigmatism across the entire wavelength band. Additionally, at present, there is a dearth of systematic and comprehensive analysis and design of aberrations for crossed C–T spectrometers, resulting in a disparity in attaining the goal of comprehensive aberration reduction.

To improve the wavelength accuracy of spectrometers and ensure the accuracy, reliability, and reproducibility of spectral measurement results, numerous studies have been conducted on wavelength calibration algorithms[[17], [18], [19], [20]]. These algorithms are diverse and encompass a wide range of peak detection methods, including direct peak positioning, peak detection based on the principle of symmetrical zero area, gaussian function fitting, and centroid methods. The primary goal of these methods is to achieve accurate determination of peak positions.

In practical applications, polynomial fitting has been widely adopted for the calibration of spectrometers due to its broad applicability and computational efficiency[[21], [22], [23]]. Theoretically, by calculating the relative positions of any two wavelengths on the detector, the corresponding wavelengths for each detector position can be derived. This approach provides a fundamental basis for achieving precise wavelength measurements in spectrometers.

In this study, a method for reducing off–axis aberrations in portable crossed C–T spectrometers was proposed. The method corrects coma at the central wavelength using the Shafer equation, optimizes the grating position to correct field curvature, and eliminates astigmatism by adjusting the tilt and wedge angles of the cylindrical lens. Additionally, a wavelength calibration method based on sine–constrained least squares fitting was developed. This method establishes a relationship between wavelength and CCD pixel position, creating an analytical calibration model for the crossed C–T optical system. Experimental results showed that the proposed calibration method achieved a wavelength calibration accuracy of 0.01 nm (resolution better than 3212), outperforming traditional polynomial fitting methods. The developed experimental instrument demonstrates improved imaging quality and enhanced calibration precision.