为了克服传统三反射系统设计中初始结构求解复杂、使用非球面时收敛缓慢的问题, 提出了基于Wassermann-Wolf微分方程的离轴三反光学系统设计方法。根据反射定律和正弦条件, 推导了一组用于求解同轴三反初始结构的Wassermann-Wolf微分方程。通过多项式拟合Wassermann-Wolf曲面, 获得了像质良好的同轴三反初始结构。实现了长焦距(1200 mm)、大视场(18°×4°)、大相对孔径(F数为4)的离轴三反光学系统设计。系统各个视场的调制传递函数在50 lp/mm处均大于0.5。结果表明, Wassermann-Wolf微分方程设计方法简单有效、收敛快, 可以为三反射光学系统提供很好的设计起点。此外, 系统的主镜为二次曲面, 次镜和三镜为非球面, 3个反射镜均无偏心和倾斜, 有效降低了制造成本和装调难度。

To solve the problems in conventional design of three-mirror system such as complicated initial structure solution and slow convergence when using aspheric surfaces, a design for off-axis three-mirror optical system based on Wassermann-Wolf differential equations is proposed. According to the law of reflection and sine condition, the Wassermann-Wolf differential equations for solving coaxial three-mirror initial structure are derived. The coaxial three-mirror initial structure with good image quality is obtained by fitting Wassermann-Wolf surfaces with polynomial. An off-axis three-mirror optical system is achieved with long effective focal length (1200 mm), wide field of view(18°×4°), and large relative aperture (F number is 4). The modulation transfer function is over 0.5 at 50 lp/mm in every field of the system. Result of the design indicates that this method based on Wassermann-Wolf differential equations is simple, effective, fast in convergence, and it provides a good starting point for the design of three-mirror optical system. Besides, the primary mirror is of conic surface, and both the second and tertiary mirrors are aspheric. The three reflectors are neither eccentric nor tilted, so the fabrication cost as well as the alignment difficulty are effectively reduced.