基于矢量像差理论，提出了以Zernike 多项式为表征函数的自由曲面光学系统像差分析方法，推导了在未消像散和彗差的光学系统中引入自由曲面后系统像差解析表达式，利用光学设计软件对远离光阑位置的自由曲面所导致的像差节点分布特性进行了仿真验证。仿真结果与理论推导一致，证明该方法可以用来解析自由曲面光学系统像差。最后，应用该方法设计了含有自由曲面的大视场离轴三反光学系统。系统焦距850 mm，F 数6.5，系统在成像视场20°×2°范围内的畸变小于0.25％，成像质量满足使用要求。

Based on the vector aberration theory, an analysis method of aberration field distribution induced by Zernike polynomial freeform surface is proposed. The analysis expression of aberration by inducing freeform surfaces into the optical system with residual astigmatism and coma is deduced. The aberration nodal distribution leaded by freeform surface which is away from the stop position is simulated by optical design software. The simulation result is agreed with the analysis result which proves the method can be utilized to analyze the freeform optical system aberration. Lastly, a three mirror optical system with large field of view including freeform surface is designed by utilizing this method. The effective focal length is 850 mm, F number is 6.5, the field of view is 20°× 2°. The result shows that the system distortion is lower than 0.25％ through the field of view. The system can achieve the requirement of earth observation.