With the rapid advancement of remote sensing technology, the spatial and spectral resolution of optical imaging systems has improved significantly, with ground resolution advancing from tens of kilometers in the early stages of development to today’s sub-meter levels. While low-resolution and low-detection precision space optical imaging systems are relatively insensitive to environmental disturbances, the increase in space imaging resolution has revealed that optical imaging systems are highly sensitive to their operational environment. Uncontrolled disturbances can lead to a significant decline in imaging quality, with micro-vibration being a key contributing factor. In this paper, we investigate the degradation of image quality caused by micro-vibrations in space optical systems. Micro-vibrations are minute vibrations generated by moving parts of a satellite, such as flywheels and refrigerators, during in-orbit operation. These vibrations are amplified through structural transmission, causing the overall movement of the space optical payload and the micro-movements of optical elements. The acceleration amplitude of these vibrations is about 10^-3g, and their frequency ranges from 10^-2 to 10³ Hz. While traditional research on the effects of micro-vibration has focused on theoretical and experimental studies of specific optical systems, there remains a need for generalized quantitative analysis methods.

In this paper, we propose a quantitative analysis method for evaluating the degradation of imaging quality caused by micro-vibrations in space optical imaging systems. A quantitative image quality degradation model is developed using the modulation transfer function (MTF) as the evaluation standard. This method is based on Fourier series expansion principles, modeling optical surface micro-vibrations as a linear combination of sinusoidal components. Each sinusoidal component is analyzed independently. The vibration influence boundary (VIB) and optical structure influence boundary (OSIB) are defined based on the distribution of exposure duration within the vibration cycle. The light tracing principle is employed to derive the intersection point between light rays and quadratic surfaces, obtaining the point spread function (PSF) of the vibrating optical system. Fast Fourier transform (FFT) is then used for spectral analysis, producing MTF curves for the two influence boundaries. These curves facilitate the quantitative analysis of the disturbed optical system, providing insights into the relationships among MTF values, exposure duration, vibration periods, and spatial frequencies, and enabling the identification of sensitive frequency bands.

In the simulations verifying the extremum properties of the two influence boundaries, exposure durations of 10.000 ms and 15.125 ms are analyzed. The results demonstrate a consist relationship between the initial exposure offset and the influence boundaries, confirming that both VIB and OSIB exhibit extremum properties under specific conditions (Fig. 9). The quantitative analysis model is validated through simulations, involving various vibration directions, forms, and exposure duration parameters. Translational vibrations along the x-axis cause MTF reductions in both the x and y directions, with greater influence observed on the x-axis itself (Fig. 10). For optically symmetric systems, rotational vibration has a more pronounced effect in directions orthogonal to the axis of rotation (Fig. 11). The analysis also reveals that the relationship between the influence boundary MTF values and exposure duration is non-linear. Sensitive frequency band analysis is conducted using the proposed model and reveals the relationship among MTF values, vibration frequency, and spatial frequency under conditions of 15 ms exposure duration, 70?100 Hz vibration frequency, and 0?100 lp/mm spatial frequency (Fig. 12). Using the DFS-SQP optimization algorithm, the sensitive frequency center is determined to be approximately 74.8 Hz. Analysis of sensitive exposure duration shows the relationship among MTF values, exposure duration, and spatial frequency under conditions of 80 Hz vibration frequency, 3.125?34.375 ms exposure duration, and 0?100 lp/mm spatial frequency (Fig. 13).

Analysis and simulation confirm that VIB and OSIB exhibit extremum properties. Translational vibrations along a given axis have a greater influence on the MTF in that direction compared to rotational vibration. The sensitive vibration frequency for relational movements of the main optical surface in the x-direction is identified at approximately 74.8 Hz. The minimum MTF value of 0.2310 is observed at the OSIB in the y-direction. Structural designs should avoid matching the natural frequency of the main optical surface with the central sensitive frequency. The MTF values at Nyquist frequencies of the two boundaries are influenced by exposure duration. Selecting exposure durations that avoid coinciding with the minimum points of the MTF curve is critical.