中文摘要：

大型光学天文望远镜中存在由于不同坐标系转换造成的物方视场旋转和望远镜内部光路中折轴平面反射镜之间的相对转动造成的像方视场旋转。为了提高空间分辨率和获得稳定的图像，需要对视场旋转进行补偿（消旋）。采用K 镜作为消旋器件，并通过矩阵方法分析其消旋原理及消旋条件，由此把K 镜分为两种结构：对称式和非对称式。与棱镜类似，K 镜对系统光轴和成像有影响。在设计时，K 镜的口径、体积和角度需要考虑加工装调和望远镜整体光路的要求，在满足要求后，可进行一定的优化。用Zemax 可实现对K 镜的光学设计，最后用空间几何关系来计算装调误差，并利用MATLAB 和Zemax得到误差分析结果。

英文摘要：

Two kinds of field rotation occur in large optical telescopes, one is caused by the coordinate transformation between horizontal coordinate system and equatorial coordinate system, the other is caused by the mutual rotation among fold mirrors in telescope. In order to get high spatial resolution and stationary image, field rotation compensation is required. Now K mirror, as a derotator, is widely applied. Using matrix can explain the principal of K mirror and achieve the requirements for derotation, which leads to two sorts of K mirror： the symmetric and asymmetric. Similar to prisms, K mirror can affect the optical axis and imaging.Considered the requirements of machining, assembly and the total optical path, the aperture, volume and base angles of K mirror have been analyzed and optimized in this paper. An example of the symmetric K mirror is designed by Zemax. The tolerance of assembly and alignment have been explained by 3D-geometric relationship and calculated by Zemax and MATLAB.