## 1 Introduction  
Along with the rapid development of Earth observational technology, both the resolution and the pointing accuracy of optical satellites are getting higher. Cameras are becoming more sensitive to microvibrations associated with the active part of the satellite in orbit [1]. To provide altitude control torque or to maintain stability, flywheels are commonly used as altitude control actuators in high-performance spacecrafts [2]. However, it inevitably produces perturbations under working conditions, resulting in decreased pointing accuracy of the satellite and degraded imaging performance [3, 4]. Microvibrations are difficult to measure because they have small amplitudes. Judging the effect of perturbations through optical imaging testing seems to be a feasible program [5, 6]. However, the harsh application environment and long lead time of space cameras greatly restrict the application of this scheme. Therefore, combining simulations and more reasonable test schemes is of great importance, not only for the evaluation of optical images but also for the application of vibration control measures [7, 8].  
The effect of microvibrations on optical satellites is complicated, as it includes structure, control, and optics [9; 10]. So far, an effective means is to integrate the structure, control, and optical system as a whole calculation model; this reflects the relationship between microvibrations and the camera, from perturbation sources through the loading path to imaging quality [11; 12]. The whole calculation model can be checked and verified by ground testing [13]. Validation tests on ground are key in microvibration research. Up to now, two kinds of test methods for optical satellites have been mainly adopted. One is an optical imaging test, which simulates the condition of the camera in orbit to show the influence of microvibrations [14; 15]. The result is not only intuitive but also consistent with the camera's in orbit performance. The other method is by using a high-precision acceleration sensor to measure the mechanical response characteristics of key components. This scheme is mainly used to test the efficiency of microvibration isolation [16].  
This paper focuses on the influence of flywheel microvibrations on an optical satellite. Pixel offset can be obtained by simulation and experiments based on a high-precision acceleration sensor. The flow of the analysis and experiment is shown in Figure 1. The displacement and angular displacement of each optical component are calculated in the frequency domain, and the data are transformed into time domain using inverse discrete Fourier transform (IDFT). Pixel offset of the whole optical system can be calculated by integrating the displacement and angular displacement of each optical component with its optical amplification factor, computed by a linear optical model. The simulation scheme can not only predict the pixel offset of the whole camera, but also analyze the effect of perturbation influences on each optical component, which can provide guidance for later experiments [17]. The experiment scheme based on high-precision acceleration sensors can reflect the amplification of microvibrations along a loading path as well as measure pixel offset of the whole optical system by integrating an optical amplification factor.  
Figure 1: A flow chart showing the combination of the simulation and the experiment.  
The paper is organized as follows. In Section 2, the development of a linear optical model is discussed to calculate the optical amplification factor of each optical component. Section 3 analyzes pixel offset of the whole optical system through simulation. The influence ratio of each optical component on pixel offset is calculated. Section 4 discusses the comparison between two test results and the simulation, and this is followed by a list of conclusions in Section 5.