Chen Sike, Wei Yangjie, Sun YiWei, Li BaoTing, Zhao Ji
Appl Opt. 2023 May 20;62(15):3892-3903. doi: 10.1364/AO.483753.
Design of an off-axis system using the Wassermann-Wolf (W-W) differential equations can effectively eliminate the spherical aberration and coma problem; however, it is complicated and time consuming to calculate the discrete point coordinates on the freeform mirror surfaces due to multiple numbers of reference system transformation in the design process. This paper presents an improved W-W-differential-equations-based design method for off-axis three-mirror freeform systems. First, to reduce the number of coordinate transformations, a geometric relationship between different optical rays in an off-axis system is established using the distance between the central points of adjacent mirrors. Second, a three-dimensional rotation matrix is used to associate the optical paths passing through adjacent mirrors in different reference coordinate systems, and new simplified W-W differential equations based on the ray vectors are constructed. The experimental results show that our method can easily and effectively design off-axis three-mirror freeform systems with different parameters and structures, and the designed systems have good imaging quality.
使用瓦塞尔曼-沃尔夫（W-W）微分方程设计离轴系统可以有效消除球差和彗差问题；然而，由于设计过程中参考系变换次数较多，计算自由曲面镜面上的离散点坐标既复杂又耗时。本文提出了一种基于W-W微分方程的改进设计方法，用于离轴三镜自由曲面系统。首先，为了减少坐标变换次数，利用相邻镜中心点之间的距离建立离轴系统中不同光线之间的几何关系。其次，使用三维旋转矩阵关联不同参考坐标系中通过相邻镜的光路，并构建基于光线矢量的新简化W-W微分方程。实验结果表明，我们的方法能够轻松有效地设计具有不同参数和结构的离轴三镜自由曲面系统，且所设计的系统具有良好的成像质量。
