Deformable Mirror(DM) is a key device in adaptive optics system for wavefront correction, and its performance directly determines the wavefront correction capability of the system. By studying DM and their control algorithm, the wavefront correction capability of adaptive optics system can be continuously improved. On one hand, the accuracy and response speed of DM can be enhanced to better correct various complex wavefront distortions. On the other hand, the control algorithm can be improved to increase the efficiency and accuracy of the correction. These studies will directly affect the imaging quality and performance of adaptive optics system. Therefore, investigating the DM and their control algorithm is of great significance for improving the wavefront correction capability, expanding application fields, and enhancing imaging quality and performance of adaptive optics system.

The article aims to summarize the research progress on DM and their control algorithm both domestically and internationally, as well as analyze the correction accuracy of different control algorithm for wavefront distortion, establishing the groundwork for the advancement of adaptive optics. Firstly, several typical DMs are used as examples to model the DM and provide detailed introductions to the structures and working principles of separate actuator DM, splicer DM, thin film DM, dual piezoelectric DM, Micro Electromechanical System (MEMS) DM and voice coil DM. Then, several control algorithms such as the Prandtl-Ishlinskii (PI) hysteresis model-based control algorithm, decoupled control algorithm, and sparse sampling control algorithm are analyzed.

Summarized the work done by Xi'an Technological University in this field, and finally pointed out the future technological breakthroughs and improvement directions in this field.

The research progress on DM and their control algorithm lays the foundation for the development of adaptive optics, enabling its application in more fields and further improving the performance of adaptive optics system. This will help improve imaging quality and drive the development of adaptive optics technology.