运用自由曲面设计一款大视场离轴三反光学系统, 该系统焦距为2 000 mm, F数为12, 视场角为35°×1°, 主镜和三镜采用XY多项式自由曲面设计, 且主镜设计为凸面, 使子午视场达到35°, 进一步拓宽了成像视场.基于优化后的XY多项式系数, 利用Matlab软件仿真出主镜和三镜的XY自由曲面面型.设计结果表明, 全视场内该系统的光学传递函数在63 lp/mm处优于0.4, 弥散斑直径小于一个像元尺寸, 最大相对畸变小于3%, 波像差均优于λ/14, 系统能量集中度高, 成像质量接近衍射极限.可见自由曲面在提升离轴反射式光学系统的成像视场和成像质量方面具有很大优势, 该系统克服了传统离轴反射式光学系统子午方向视场角小的缺点, 适合大幅宽推扫成像.

Freeform surface is applied to design a large field of view off-axis three-mirror optical system. The focal length of the system is 2 000 mm, the F-number is 12, and the field angle is 35°×1°. In the system, XY polynomial freeform surfaces are applied as the primary mirror and the tertiary mirror surfaces, and the primary mirror is designed as a convex surface, so that the meridional field of view reaches 35°, further widening the imaging field of view. Based on the optimized XY polynomial coefficients, Matlab software is used to simulate the XY freeform surfaces of the primary mirror and the tertiary mirrors. The design results show that the optical transfer function of the system in the full field of view is better than 0.4 at 63 lp/mm, the diameter of the diffusion spot is less than one pixel size, the maximum relative distortion is less than 3%, and the wavefront error value is better than λ/14. The system has high energy concentration and the imaging quality is close to the diffraction limit. It can be seen that the freeform surface has great advantages in improving the imaging field of view and imaging quality of the off-axis reflection optical system. The system overcomes the shortcoming of the small field of view in the radial direction of the conventional off-axis reflective optical system, and it is suitable for wide swath imaging.