Off-axis three-mirror freeform systems design based on improved W-W differential equations

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.