Design of Imaging Spectrometers Based on Freeform Surfaces

Imaging spectrometers are advanced optical instruments that combine spectral analysis with imaging capabilities,playing a crucial role in diverse fields such as environmental monitoring,biomedicine and materials science. The ability to capture both spectral and spatial information allows for the identification, quantification, and localization of substances, providing essential data for scientific investigation and practical applications. With the continuous advancement of technology,the demand for spectrometers with high spectral resolution and high imaging quality has increased substantially. Among the various optical designs,the Czerny-Turner（C-T）configuration is widely adopted due to its well-established dispersion performance and mature manufacturing process. However,the conventional C-T structure, which utilizes spherical mirrors,suffers from inherent limitations in aberration correction across the full wavelength range,ultimately affecting the overall performance of the spectrometer. To address these limitations,various solutions have been proposed,including the integration of cylindrical lenses,divergent optical paths,hyperbolic mirrors,and the incorporation of freeform surfaces. Among these,freeform surfaces have emerged as a particularly promising option due to their flexibility and the simplicity of their optical paths,making them increasingly attractive for spectrometer design in recent years. Despite their significant potential, the effectiveness of freeform optical systems is highly dependent on the initial structure,rendering the design process critical. Several methods have been explored for the design of freeform surfaces,such as progressive optimization methods,vector aberration theory-based approaches, and direct design methods. However, these approaches often encounter challenges, including high empirical requirements,limited theoretical understanding,and computational complexity. We introduce a novel method for designing freeform surface in high-resolution imaging spectrometers,with a particular focus on the Czerny-Turner configuration. The approach is based on the design principles of multi-off-axis parabolic freeform surfaces. By employing Zernike polynomial fitting,it effectively facilitates the seamless integration of off-axis parabolic sub-surfaces,culminating in the construction of a continuous freeform surface. The proposed method significantly simplifies the design process and provides a more computationally efficient solution compared to traditional methods. The Zernike polynomial fitting method is employed to create the initial surface shape,which is subsequently optimized using Zemax optical design software. This optimization effectively corrects aberrations over the entire wavelength range and field of view. Simulation results demonstrate that,within a field of view defined by a 6 mm high slit,the Root Mean Square（RMS）radius of the imaging spot is less than 5 μm,which is smaller than the typical CCD pixel size used in scientific research systems of imaging spectrometers. This achievement ensures high-quality imaging across the full field of view. Furthermore,under the conditions of 500 mm focal length and a 1 200 lp/mm grating,the system's spectral resolution reaches 0.015 nm,surpassing the performance of commercially available spectrometers of similar type. These results indicate the effectiveness of the proposed method in achieving both high imaging quality and high spectral resolution in a compact design. The novelty of this research lies in the combination of Zernike polynomial fitting and aberration-free surface fusion for freeform surface design. This method not only enhances the imaging quality but also provides a new design strategy for freeform surfaces in other optical systems. It offers a promising solution to the challenges of aberration correction and spectral resolution enhancement in existing imaging spectrometer systems,paving the way for more advanced and efficient spectrometer designs. In summary, this study provides a practical and effective design method for high-resolution imaging spectrometers based on freeform mirrors. The method achieves a balance between design simplicity, computational efficiency,and high optical performance,making it a significant contribution to the field of optical design while providing insights into the application of freeform surfaces in various optical systems.