为了研制长焦距大视场离轴三反空间光学系统, 描述了自由曲面光学数理模型, 设计了基于自由曲面的离轴三反光学系统。针对焦距为4 500 mm, 成像视场角为11°, 系统总长与焦距的比值为1/3的光学系统, 对比分析了传统离轴三反光学系统和次镜为自由曲面的离轴三反光学系统的关键性能。在提出的光学系统中次镜采用自由曲面设计, 提升了光学系统的像差平衡能力; 最终选用相对孔径为1/9.5的设计方案, 使光学系统全视场平均波像差优于0.030λ(λ=632.8 nm), 平均传递函数优于0.434(71.4 lp/mm), 接近衍射极限; 在同等条件下系统设计传递函数比传统离轴三反系统提高5%以上。优化设计后光学系统自由曲面次镜与理论球面偏差为1.1λ, 采用定制的标准球面镜结合基于数字样板的非零位检测方法可完成面形实时高精度检测, 解决了大口径凸自由曲面检测的难题。结果表明, 采用基于自由曲面次镜的空间光学系统, 具有体积小、技术可实现性强、波像差和传递函数等关键性能优越等优点。

A freeform off-axis three-mirror system based on a freeform mirror was designed for the long focal length and wide-field off-axis three-mirror system in a space telescope. To obtain a system with a focal length of 4 500 mm, field of view of 11° and the ratio of the total length of system and the focal length in 1/3, the design and performance between traditional off-axis three-mirror system and freeform off-axis three-mirror system were compared. In the designed optical system, the freeform mirror was introduced to the secondary mirror to enhance system optimization and improve the balance capacity for optical aberration. After the comparison and optimization, the relative aperture of 1/9.5 was chosen.In the system, the average of wavefront error of all field of view is better than 0.030λ(λ=632.8 nm), and the average of the Modulation Transform Function(MTF) of all field of view is greater than 0.434(71.4 lp/mm) that is close to the diffraction limitation. Furthermore, the MTF has im-proved more than 5% compared to that of traditional TMA system and the departure of the secondary freeform mirror and theoretical spherical surface is only 1.1λ(λ=632.8 nm). The highly precision testing can be accomplished only by a standard sphere combined with the non-null testing method based on digital mask, which solves the problem of large-aperture convex freeform mirror testing and is helpful for the manufacturing of freeform secondary mirror. The off-axis three-mirror system based on freeform secondary mirror shows its advantages in smaller cubage, better realizability in engineering, better wavefront error and higher MTF.