## 1 Introduction  
To achieve high-resolution aerial imaging, aerial cameras need longer focal length optical lenses, which will result in a smaller field of view (FOV) and narrower imaging width, thus reducing the efficiency of practical applications. To solve this problem, aerial mapping cameras can adopt a scanning imaging mode [1; 2; 3; 4]. However, this imaging mode can cause scanning image-motion problems. Considering the characteristics of the airborne platform, the image motions of aerial cameras mainly include the aircraft attitude image motion, vibration image motion, forward image motion, and scanning image motion. The large motion of the image will significantly impact the imaging quality of the system, leading to issues such as image trailing, blurred contours, and overlapping details, and ultimately resulting in a significant decrease in image resolution [5; 6]. The phenomenon of carrier attitude image motion refers to the image motion that occurs as a consequence of a change in carrier attitude at the time of the camera exposure. The size of the image motion is contingent upon the carrier flight status and the camera exposure time, and it can be compensated for by a two-dimensional stable platform. Vibrational image motion is the image motion caused by the vibration of the airborne platform itself, transmitted to the camera system. Compared with other image motions, this image motion belongsto a high-frequency image motion. By choosing a vibration damping system that does not exhibit angular displacement, with an appropriate stiffness and damping ratio, the angular displacement that has a significant impact on imaging can be converted to a linear displacement that has a minimal impact on imaging, thus reducing or even eliminating the vibration image motion. However, the working mechanism of the camera's scanning imaging determines that large image motions in both the flight and scanning directions are inevitable. In order to minimize the impact of these motions on imaging quality to an acceptable level, it is necessary to analyze and compensate for the imaging motions of the camera, thereby reducing their effect on imaging and ensuring the camera's imaging capability. Currently, Raytheon's Global Hawk camera, Recon Optical, Inc.'s CA-295, Goodrich's DB-110, L3 Harris Technologies' LOROP, and VisionMap Company's VisionMap A3 are the mainstream airborne cameras with advanced performance. Among them, CA-295, DB-110, and LOROP utilize a multi-axis stabilized platform and optical system to achieve image-motion compensation. The Global Hawk camera adopts the composite control technology of visual axis with continuous scanning of the primary mirror and synchronous movement of the built-in mirror to realize image-motion compensation. The VisionMap A3 employs multi-dimensional motions of the secondary mirror to realize comprehensive image-motion compensation. This highly integrated design concept of optical imaging and image-motion compensation has the effect of simplifying the complexity of the optical imaging system, which in turn facilitates the compact and lightweight design of the imaging system. However, due to the particularity of the earth observation field, there is little published literature on this kind of technology. On this basis, this paper provides an in-depth study of image-motion compensation technology based on the multi-dimensional motion of the secondary mirror, and it realizes high-precision image-motion compensation and pointing measurement through multi-dimensional fast motion of the secondary mirror [7; 8]. This technology addresses the challenge of image blurring and distortion caused by the motion of the aircraft during aerial reconnaissance and mapping activities. By compensating for these image motions, the technology ensures that the captured images are of high quality, enabling accurate and reliable mapping and reconnaissance data to be obtained.