光学合成孔径技术是一种利用多个小孔径系统组合构成大孔径光学系统，从而实现高分辨率空间成像的技术。该技术能够通过增长基线来提高成像分辨率，从而有效降低空间望远镜的设计难度和发射负荷，同时消除地球大气环境的干扰，有望在未来空间科学研究任务中扮演重要角色。然而，该技术也面临着诸多挑战，其中之一就是空间环境中的振动对光学系统的影响。由于光学系统结构精密复杂，对载荷稳定性要求极高，而航天器载荷上的各种控制组件会产生不同类型和频率的振动，导致光学系统子孔径位置发生变化，造成相位误差，降低成像质量。因此，研究天基平台光学合成孔径成像过程中的振动效应并对误差进行优化校正是十分重要的。本文主要从以下几个方面展开了研究内容：

1.    构建一种多孔径共相误差耦合模型。基于信息光学理论，考虑并引入随时间变化的振动函数，推导建立了新的多孔径共相误差耦合模型。通过与现有模型的对比，验证了本文模型的有效性，为振动影响的仿真分析研究奠定基础。

2.    提出两种考虑时间维度的评价指标：时间累积斯特里尔比（TISR）和全频特性衰减率（FFCA）。相较于现有评价指标，这两种指标能够在空间域和频率域两个层面，评估振动影响下的光学合成孔径系统成像性能。采用双孔径和四孔径阵列结构，通过调整振动函数参数，模拟了空间环境下振动信号对光学系统成像性能的影响过程，揭示出光学系统成像质量随时间累积而呈现出衰退、波动和收敛的动态变化，为评估光学合成孔径系统在复杂振动环境下的性能提供了重要的参考。

3.    提出一种振动误差校正算法。该算法通过改进随机下降算法的阈值和收敛方式，能够实现快速迭代，解算出未知误差的最优解并进行反向校正，提升光学系统的成像性能。相较于现有算法，该算法能够在20个迭代循环之内完成解算，在迭代计算速度方面有较大优势。通过数值仿真分析，提出的校正算法能够有效减缓FFCA的下降幅度，使FFCA波形更加平滑且整体稳定在0.95以上，提升了光学系统的成像性能。

本文提出的理论模型、评价指标、分析方式和校正算法对于光学合成孔径成像研究具有积极的意义，为光学合成孔径系统的设计和性能分析提供了一定的研究基础和理论支撑。
 

The optical synthetic aperture technology is a technique that combines multiple small aperture systems to form a large aperture optical system, which enables high-resolution spatial imaging. This technology can improve imaging resolution by increasing the baseline, effectively reducing the design difficulty and launch load of space telescopes, while eliminating interference from the Earth's atmosphere. It is expected to play an important role in future space science research missions. However, this technology also faces many challenges, one of which is the impact of vibrations in the space environment on the optical system. Due to the precision and complexity of the optical system structure, high requirements for load stability are necessary. Various control components on the spacecraft payload produce different types and frequencies of vibrations, causing changes in the position of the optical system sub-apertures and resulting in phase errors, which decrease the imaging quality. Therefore, it is crucial to investigate the vibration effects in the optical synthetic aperture imaging process of space-based platforms and to optimize and correct errors. This article mainly focuses on the following aspects of research content:

1. A multi-aperture co-phase error coupling model is established. Based on the information optics theory, a new multi-aperture co-phase error coupling model is derived and established by considering and introducing a vibration function that varies with time. Through comparison with existing models, the effectiveness of the proposed model is verified, laying the foundation for the simulation and analysis of vibration effects.

2. Two evaluation indexes considering time dimension are proposed: Time Integrated Strehl Ratio (TISR) and Full Frequency Characteristic Attenuation (FFCA). Compared to existing evaluation metrics, these two metrics can assess the imaging performance of optical synthetic aperture systems under vibration effects in both spatial and frequency domains. Using a dual-aperture and a quad-aperture array structure, the impact of vibration signals on the imaging performance of optical systems in spatial environments is simulated by adjusting the vibration function parameters. The dynamic changes in the image quality of the optical system, including degradation, fluctuation, and convergence, are revealed over time accumulation, providing important reference for evaluating the performance of optical synthetic aperture systems in complex vibration environments. 

3. A vibration error correction algorithm is proposed. By improving the threshold and convergence method of the stochastic gradient descent algorithm, the algorithm can achieve fast iteration, solve the optimal solution of unknown errors, and perform reverse correction, so as to improve the imaging performance of the optical system. Compared with existing algorithms, this algorithm can complete the calculation within 20 iterations, and has a significant advantage in iteration calculation speed. Through numerical simulation analysis, the proposed correction algorithm can effectively reduce the magnitude of FFCA decline, make the FFCA waveform smoother, and stabilize above 0.95 overall, improving the imaging performance of the optical system.

The theoretical models, evaluation metrics, analysis methods, and correction algorithms proposed in this article have positive implications for optical synthetic aperture imaging research, offering a theoretical basis and research foundation for the performance analysis and design of optical synthetic aperture systems.