###### Abstract  
The optical system that combines imaging and image motion compensation is conducive to the miniaturization of aerial mapping cameras, but the movement of optical element for image motion compensation will cause a decrease in image quality. To solve this problem, reducing the sensitivity of moving optical element is one of the effective ways to ensure the imaging quality of aerial mapping cameras. Therefore, this paper proposes an optimization method for the low tilt sensitivity of the secondary mirror based on the Nodal aberration theory. In this method, the analytical expressions of the tilt sensitivity of the secondary mirror in different tilt directions are given in the form of zernike polynomial coefficients, and the influence of the field of view on the sensitivity is expressed in the mathematical model. The desensitization optimization function and desensitization optimization method are proposed. The catadioptric optical system with a focal length of 350 mm is used for desensitization optimization. The results show that the desensitization function proposed in this paper is linearly related to the decrease of sensitivity within a certain range, and the standard deviation of the system after desensitization is 0.020, which is 59% of the system without desensitization. Compared with the traditional method, the method in this paper widens the range of angle reduction sensitivity and has a better desensitization effect. The research results show that the optimization method for low tilt sensitivity of the secondary mirror based on the Nodal aberration theory proposed in this paper reduces the tilt sensitivity of the secondary mirror, revealing that the reduction of the sensitivity depends on the reduction of the aberration coefficient related to the misalignment in the field of view, which is critical for the development of an optical system for aerial mapping cameras that combines imaging and image motion compensation. a 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 202 2022 2022 202 2022 2022 2022 2022 20 abroad. [PERSON] used the two-mirror system and the lens as two independent parts in the research of the catadioptric optical system based on the fast secondary mirror. The decentering of the secondary mirror was used to realize the image motion compensation of the system, but the influence of the lens was ignored [2]. The image motion compensation is performed by controlling the movement of the secondary mirror of the refractive optical system in the aerial mapping camera visionmap-A3, the ground-based large-aperture FAST-TRAC astronomical telescope, and the SIRTF infrared astronomical telescope [3; 4; 5], but the analysis of optical systems is barely mentioned. Image motion compensation in adaptive optics mainly relies on the detection of the wavefront by the sensor, and the control voltage for the wavefront corrector is calculated by the wavefront controller, and the wavefront corrector is driven to correct the aberration [6]. When the image motion compensation of the optical system does not depend on the precise control of the sensor, the movement of the optical element will degrade the imaging quality, so it is necessary to design an optical system that realizes image motion compensation through the movement of optical element. Many experts have conducted a series of studies on decreasing tolerance sensitivity. The two processes of optical system optimization and tolerance allocation are separated in the traditional optical design process. The optical design optimization process does not account for the degradation of imaging quality caused by processing (decenter, tilt, surface irregularity, etc.) and assembly (decenter, tilt of components) errors, which leads to the need to redesign the optics when the tolerance requirements are not met. It takes time.