In some active optics system, the influence function, which is the surface deformation ability of an actuator, is measured by directly detecting the mirror surface using an interferometer and the surface correction of the primary mirror is done using the Shack-Hartmann (S-H) sensor. However, if the wavefronts of the interferometer and the S-H sensor have an obvious rotation, a large error will be introduced to the correction force calculations. In this paper, bending modes are used to detect this wavefront rotation. Bending modes are a series of orthonormal stiffness-increasing modes calculated using the influence functions. Two methods, optimum search and top-line (a line passes through the surface center and the top of surface deformation peaks) detection, are developed and tested in simulation using the experimental data of a 620-mm active optics system. The detection errors of the two methods are 0.286° and 0.085° in the simulation, respectively. The rotation detection method is then tested on this 620-mm system. The simulation and experimental results show that top-line detection is a suitable method for the detection of wavefront rotation.

中文翻译：

---

使用弯曲模式校正干涉仪和Shack-Hartmann传感器之间的波前旋转

在某些有源光学系统中，影响函数（即执行器的表面变形能力）是通过使用干涉仪直接检测镜表面来测量的，而主镜的表面校正是使用Shack-Hartmann（SH）传感器进行的。但是，如果干涉仪和SH传感器的波前有明显的旋转，则校正力的计算将引入较大的误差。在本文中，弯曲模式用于检测波前旋转。弯曲模式是使用影响函数计算的一系列正交刚度增加模式。两种方法，最佳搜索和顶线（一条线穿过表面中心和表面变形峰的顶部），使用620毫米有源光学系统的实验数据开发并在仿真中进行了测试。两种方法的检测误差在仿真中分别为0.286°和0.085°。然后在此620毫米系统上测试旋转检测方法。仿真和实验结果表明，顶线检测是一种合适的波前旋转检测方法。