In imaging spectrometers for greenhouse gas detection, a large field of view (FOV) enables comprehensive monitoring across wide geographical or atmospheric volumes, supporting detailed spatiotemporal analysis of greenhouse gas concentrations and emission patterns. This broad coverage helps accurately identify greenhouse gas sources, providing essential data to locate and address emission points. A larger FOV enhances coverage, reduces revisit cycles, and improves the temporal resolution of the instrument. However, as the FOV increases, smile distortion and chromatic distortion become more prominent, which negatively affects spectral resolution, introduces misalignment in images, and complicates data processing tasks such as spectral radiometric calibration. Current methods for spectral line curvature correction focus primarily on two areas: calibration and optical design. While electronic calibration has shown effectiveness in mitigating smile distortion, it cannot resolve the underlying issues of spectral line curvature that influence detector efficiency and complicate pixel alignment, adding complexity to image processing. Optical design correction methods, although effective, often encounter difficulties in assembling and manufacturing optical components, especially when required to support a large FOV or instantaneous FOV systems. In this paper, we propose a novel design approach that leverages an algorithm to automatically generate prism-grating-prism (PGP) dispersion module parameters that meet performance requirements, achieving a large-field, high-resolution system with minimized smile distortion.

To develop a large-field, high-resolution spectrometer system with minimized smile distortion, we propose using a P+G+P dispersion model that combines prisms and grating. Based on the specific characteristics of smile distortion and the dispersion properties of this model, a theoretical derivation is conducted to build the P+G+P dispersion model. A parameter-solving method for correcting smile distortion within the P+G+P dispersion model is also developed. Finally, the proposed algorithm is applied to design a large-field, high-resolution spectrometer system utilizing the P+G+P dispersion model for smile distortion correction.

Based on the proposed solution for correcting smile distortion in large-field, high-resolution spectrometer systems using the PGP dispersion model, a PGP dispersion model is derived by analyzing the characteristics of smile distortion and dispersion. This includes a process to determine parameters specifically for correcting smile distortion. To validate the effectiveness of the approach, a large-field, high-resolution P+G+P spectrometer system is designed with a spectral range of 747?777 nm, a spectral resolution of 0.04 nm, and a slit length of 60 mm, making it suitable for detecting the O₂-A band in greenhouse gas monitoring (Table 1). For this system, the collimator group uses an off-axis three-mirror anastigmatic structure with aspheric mirrors, while the imaging group combines spherical and aspherical lenses in a transmission structure. The design results show that the system achieves a dispersed spectrum width of 15 mm across a 30 nm spectral range, with an average spectral resolution of 0.0386 nm, exceeding the design requirement of 0.04 nm (Fig.12). At a Nyquist frequency of 25 lp/mm, the modulation transfer function (MTF) across the full spectral range is greater than 0.6 (Fig. 10), while the root mean square (RMS) spot size remains below 12 μm (Fig. 11). The corrected smile distortion at the maximum FOV is less than 1 pixel (20 μm) (Fig. 13), and the keystone distortion is approximately 0.5 pixel (20 μm) (Fig. 14).

The design proposed in this study offers several advantages, including easier realization of a large FOV, reduced spectral line curvature, and streamlined fabrication processes. The proposed design approach for large-field, high-resolution systems with smile distortion correction is universally applicable to P+G+P dispersion model spectrometers. In this paper, we establish a complete design process and methodology for large-field, high-resolution P+G+P spectrometers with spectral line curvature correction, enabling faster identification of optimal system parameters across various specifications. This significantly shortens the design cycle and improves design efficiency. The large-field, high-resolution P+G+P spectrometer designed here effectively corrects the severe spectral line curvature typically associated with large-field systems, without adding complexity. Compared to traditional large-field P+G+P spectrometers, the FOV is increased by 250%. The final design achieves a dispersed spectrum width of 15 mm over a 30 nm spectral range, with an average spectral resolution of 0.0386 nm. At the maximum FOV, smile distortion is maintained below 1 pixel, ensuring excellent imaging quality.