Abstract The classical Schwarzschild imaging spectrometer consists of a plane grating and three spherical mirrors. It suffers from a slow optical speed and a small field of view (FOV). Furthermore, astigmatism aberration is present in the conventional configuration due to the dispersion of the plane grating. In this study, a group design method was developed to design a Schwarzschild imaging spectrometer with freeform surfaces. The group design method corrects the astigmatism aberrations in the collimating system and focusing system separately and gives a higher-performing initial structure. To achieve fast optical speed and a larger FOV, freeform surfaces are used to correct the large off-axis aberration. Based on this method, a Schwarzschild imaging spectrometer with a fast optical speed (F/2) and large FOV (32 mm slit) using freeform surfaces is proposed. The initial structure design, optimization procedure, and tolerance analysis are described in detail. The design results indicate that good optical performance and manufacturability of the system are obtained.

中文翻译：

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自由曲面施瓦西成像光谱仪的光学设计

摘要 经典的施瓦西成像光谱仪由一个平面光栅和三个球面镜组成。它的光学速度慢且视场 (FOV) 小。此外，由于平面光栅的色散，在常规配置中存在像散像差。在这项研究中，开发了一种组设计方法来设计具有自由曲面的 Schwarzschild 成像光谱仪。组设计方法分别校正准直系统和聚焦系统中的散光像差，并给出更高性能的初始结构。为了获得更快的光学速度和更大的 FOV，自由曲面用于校正大的离轴像差。基于这种方法，提出了一种使用自由曲面的具有快速光学速度 (F/2) 和大 FOV（32 毫米狭缝）的 Schwarzschild 成像光谱仪。详细描述了初始结构设计、优化程序和公差分析。设计结果表明，该系统获得了良好的光学性能和可制造性。