Dynamic surface error response analysis of large-aperture space mirror

The optical surface error is one of the crucial factors to guarantee the image quality of space telescopes. The growing of aperture and pursuing of lightweight structure result in a relatively lightweight and flexible telescope mirror, whose surface figure is vulnerable to micro-vibration disturbances. Unfortunately, there are a variety of disturbances in space, such as control moment gyroscopes, momentum wheels, and cryocoolers. In order to investigate the dynamic optical surface error result from disturbances, a method based on mode superposition theory and Zernike polynomials (ZPs) fitting is proposed. On the basis of normal mode theory, the responses of an opto-mechanical structure under forced excitations can be approximated by the sum of a series of single normal modes of the system. Meanwhile, for each mode shape of an optical surface, it can be fitted as a linear combination of ZPs, which are typically used to describe optical surface errors and represent the aberrations of optical systems. Therefore, the dynamic Zernike coefficients can be computed by the superposition of the Zernike coefficients of each single mode shape. From the combination of normal mode theory and ZPs fitting technique, the relationship between the dynamic responses of optical surface error and micro-vibration disturbances is established. So, the influence of micro-vibration on the aberrations of optical system can be predicted straightforwardly. Finally, an example is given to show the effectiveness of the proposed method.