为了在系统结构简单的前提下实现凸面光栅成像光谱仪的大相对孔径、高分辨率成像、轻小型化以及系统的易加工装调, 优化设计了一种基于变间距凸面光栅的消像差凸面光栅成像光谱系统, 该系统为双光学元件全反射式同心结构, 克服了已有消像差结构的复杂性与应用局限性。提出了基于光栅的像差理论进行消像差的设计方法, 构建了系统的几何像差理论模型, 并结合罗兰圆条件分析了系统在子午与弧矢方向上的聚焦条件, 建立了凸面光栅刻线间距与系统像散关系的数学模型; 通过全局化的优化算法实现了对凸面光栅成像光谱仪的消像散设计。设计结果表明: 该消像散的凸面光栅成像光谱系统在300~800 nm实现了相对孔径为F/2.7时极限光谱分辨力优于1.9 nm的高像质成像,可实现约201个高光谱通道, 而且系统在全波段内的光学传递函数值优于0.7, 对轻小型、高光谱的消像差凸面光栅成像光谱仪的研究具有重要意义。

An imaging spectrometer with a varied line-space convex grating was designed and optimized in this study to realize a large relative aperture, high-resolution imaging, and light miniaturization, thus ensuring easy processing, assembly, and adjustment of the optical system based on a simple system structure. With a double-element system in a reflection concentric structure, the complexity and application limitations of the existing aberration-correction configurations were overcome. An aberration-correction design method was proposed based on the aberration theory of gratings, and a theoretical model of the geometric aberration of the system was briefly derived. The focal conditions of the system in both the meridional and sagittal directions were then analyzed in combination with the Rowland circles of the concentric configuration.This analysis established a mathematical model of the relationship between the astigmatism and line spacing of the convex grating. Finally, an anastigmatic design of the imaging spectrometer with a convex grating was realized using a global optimization algorithm. Design results show that the system can achieve high-quality imaging in the spectral range of 300~800 nm with a large relative aperture of F/2.7 and a resolution of 1.9 nm.In addition, approximately 201 hyperspectral channels are covered. The modulation transfer function for the whole spectral band is greater than 0.7, which meets the design requirements of the system. This study contributes significantly to the research of hyperspectral imaging spectrometers with aberration-correction convex gratings in terms of light weight and compactification.