###### Abstract  
Satellite vibration is an important factor that can seriously reduce the image quality of remote sensing imaging. In this paper, the influence of the random vibration of the payload on the frame-by-frame imaging quality of the area-array CMOS camera is studied. Firstly, the mode of the camera's dynamic frame-by-frame imaging is established; secondly, the curvature mapping function between the ground and camera focal planes is derived based on the invariance of the field of view (FOV). The frequency domain-filtered template of random vibration is constructed. Then, the distortion and degradation images, of single-frame images at different attitude angles, are inversed; finally, the influence of attitude angle, exposure time, and the error of velocity, caused by random vibrations on dynamic frame-by-frame imaging, are analyzed. The simulation results show that the degree of image edge distortion gets larger when the attitude angle increases from \(0^{\circ}\) to \(50^{\circ}\). At the same time, the MTF decreases rapidly with the increase of the error of velocity and the attitude angle. Meanwhile, when the output-image SSIM decreases by 0.1, the MSE increases by 18.5. The experimental results show that the field of view (FOV) of dynamic imaging should be reasonably set, and the error of velocity should be effectively reduced to obtain high-quality remote sensing images. remote sensing; satellite vibration; frequency domain analysis; image distortion +
Footnote †: journal: _Photonics  
of the modulation transfer function (MTF) was extended to the full frequency range by [PERSON] et al. [13]. Since the total MTF was reduced by spatial vibration, a frequency domain filtering system, which included various vibration types, had been mentioned by [PERSON] [14] and [PERSON] et al. [15] to simulate the image degradation phenomenon caused by the multi-source vibration of the payload. In recent years, many new modes of dynamic imaging have been proposed in order to improve the imaging width and resolution. A circular-scanning imaging model was established by [PERSON] et al. [16]. By setting a reasonable scanning speed, the overlapping output of multi-frame images was completed to maximize the imaging coverage of the camera. [PERSON] et al. [17] further described the optical rotation phenomenon between the object and the image, in the circular scanning imaging model, by establishing different coordinate systems, so the imaging model of the circular scanning sensor tended to be mature. [PERSON] [18] et al. proposed a scanning mirror system, which consisted of an objective lens, relay lens, and three-stage imaging lens, to simulate the relationship between objects and images in a two-dimensional scanning motion. It provided a theoretical basis for the structural design of the scanning mirror. Meanwhile, [PERSON] et al. [19] established an experimental dynamic scanning imaging system with fast steering mirrors, which was used to monitor hot targets and scout hot areas in real time. With the increase of the scanning attitude angle, the output image was seriously distorted. [PERSON] et al. [20] confirmed that imaging distortion could be corrected by measuring the four polarization directions of polarization imaging. In the scanning imaging system, using a camera's front mirror, [PERSON] [21] further expounded on the design scheme from two aspects: structure and the control circuit. In this system, the encoder read the payload attitude information when the mirror of the camera periodically scanned. With the development of dynamic optical imaging technology, the vibration analysis of traditional imaging can't meet the actual requirements. Therefore, it is necessary to further study the law of image degradation, caused by vibration, in the new dynamic imaging mode. During the frame-by-frame imaging process, the internal disturbance source of the payload randomly vibrates irregularly. When random vibration is coupled with the disturbance characteristics of the dynamic frame-by-frame imaging model, new problems will appear.