Correction of wavefront rotation between interferometer and shack-hartmann sensor using bending modes

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 degrees and 0.085 degrees 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.