Objective  Space-based target detection is the main way to observe space debris. In recent years, with the gradual increase of space debris, it is difficult for small field of view space cameras to meet the observation needs, and the use of large field of view space cameras is increasing. During the observation of space debris, due to the orbital motion of the satellite itself and the motion of the two-dimensional turntable, the image rotation will occur in the imaging of the large field of view space camera, especially when observing dim targets, the camera's exposure time will increase, and the generated image rotation will also increase. It seriously affects the accuracy of recognition and reduces the efficiency of large field of view space camera. Therefore, image rotation compensation must be carried out for large field of view space camera.

  Methods  In order to determine the performance index of image rotation compensation, the imaging coordinate system of the system is established (Fig.1), and the image rotation of the system is calculated by the homogeneous coordinate change method. According to the performance index of image rotation compensation, a new type of image rotation compensation mechanism based on the inner and outer rings of symmetrical right straight circular flexure hinge is proposed (Fig.3). Then, the flexibility and accuracy formula of the flexible element of the image rotation compensation mechanism is deduced according to the second theorem of Cassegrain, and the relationship between the flexibility and the structure size is analyzed. Then, the image rotation compensation structure is optimized by genetic algorithm. Finally, the static and modal analysis of the image rotation compensation mechanism is carried out by simulation (Fig.11, 12, 14), and it is verified by experiments.

  Results and Discussions   By analyzing and calculating the ± 2′ image rotation of a large field of view space camera, an image rotation compensation mechanism composed of eight completely symmetrical flexible elements is designed for the image rotation change. By analyzing it, the relationship between the flexibility and accuracy of the flexible element and the size of the flexible element is obtained (Fig.7-8). Through genetic algorithm, the final design size of the flexible element is t=0.5 mm, r=5.5 mm, w=18 mm, l=9 mm. The simulation analysis results show that the maximum displacement component in the plane is 77.5 μm. The error with theoretical calculation model is 1.79%, far less than 5%, which meets the design requirements of the system; The maximum stress is 65 MPa, which is far less than the allowable stress of 330 MPa, which meets the design requirements of the system. The image rotation compensation mechanism has high stability and safety. Through experimental verification, the experimental value and theoretical error of the image rotation compensation mechanism are also less than 5%, and the image rotation compensation mechanism has good linearity in the working range (Fig.14). The results of modal analysis (Tab.3) show that all modes of the system meet the design requirements.

  Conclusions  For the image rotation generated by the large field of view space camera during imaging, the image rotation angle generated by the camera is calculated by the homogeneous coordinate transformation method to be ± 2′, and then a set of image rotation compensation mechanism based on the flexible element is designed by this technical index, the mathematical model of the image rotation compensation mechanism is established, and the flexibility matrix and precision matrix of the flexible element of the image rotation compensation mechanism are derived; Then, according to the derived formula and the stress and fundamental frequency of the system, the image rotation compensation mechanism is optimized by genetic algorithm. Finally, the image rotation compensation mechanism is determined to be composed of the inner and outer rings connected by 8 straight beam fillet flexible elements. When the total force is 115 N, the camera is compensated with ± 2′ image rotation, and the maximum displacement of the inner ring is 77.5 μm. Then the first six natural frequencies of the system are verified by the finite element simulation, which meet the system design requirements, and the system is verified by experiments. According to the experimental results, the system has good linearity, and the error between the experimental results and the simulation results is less than 5%, which verifies the reliability of the system.