Performance assessment and enhancement of high-resolution space telescopes under the effect of micro-vibrations

To accurately characterize the imaging performance of opto-mechanical systems under micro-vibrations, this study first establishes an integrated "disturbance-optics-structure" analysis model, then proposes three analysis methods, time-domain analysis, frequency-domain analysis, and Lyapunov analysis, to characterize the transient characteristics and statistical characteristics through the peak-to-peak value(<i>P-P_LOS</i>) and RMS value(<i>RMS_LOS</i>) of the line-of-sight(LOS) error, respectively. The analysis results show that under the given micro-vibration disturbance, the <i>P-P_LOS</i> of a certain coaxial two-mirror telescope is 0.346'', and the <i>RMS_LOS</i> calculated by the three analysis methods are 0.03797'', 0.03786'', and 0.03789'', respectively, with a relative error of less than 1%, verifying their effectiveness. By identifying critical frequencies through PSD and cumulative RMS curves, two optimization approaches are proposed: structural optimization and vibration isolation, reducing the <i>P-P_LOS</i> and <i>RMS_LOS</i> values by 14.5% / 23.4% and 22.0% / 28.0%, respectively. The research establishes a quantitative assessment framework for LOS error of the space telescopes under random vibrations and provides theoretical guidance for performance enhancement.