光学望远镜成像系统的分辨率主要受观测波长及系统口径影响，当观测波长一定时，系统角分辨率大小主要取决于光学成像系统口径。稀疏孔径成像技术是增大望远镜系统等效口径，提高系统分辨能力的有效途径，其难点在于子孔径间共相误差的检测校正。本文提出了基于随机并行梯度下降算法(Stochastic parallel gradient descent algorithm，SPGD)的稀疏孔径成像共相误差校正技术，可有效避免传统方法中对共相误差的探测，简化共相误差校正过程。

首先，本文从单孔径成像系统的基本原理出发，推导了单色光及复色光情况下稀疏孔径成像系统的点扩散函数PSF及调制传递函数MTF的数学表达式，通过对比分析单孔径和稀疏孔径系统的点扩散函数和调制传递函数，揭示了稀疏孔径成像系统提高空间角分辨率和空间频率对比度传递能力的机理。介绍了稀疏孔径系统的三种典型阵列结构：环型(Ring)、戈莱型(Golay)、Y型，并对相关阵列结构的MTF分布进行了数值仿真分析，论述了阵列结构的三种性能评价方式。

其次，阐述了稀疏孔径成像系统存在的两种共相误差：活塞误差、倾斜误差，解释了两种共相误差的产生原因，推导了稀疏孔径系统存在活塞误差和倾斜误差时点扩散函数和调制传递函数的数学表达形式，并仿真了共相误差存在下点扩散函数和调制传递函数的分布，分析了不同共相误差对稀疏孔径系统成像质量的影响。

然后，阐述了随机并行梯度下降算法的基本原理及算法流程，介绍了三种图像清晰度评价方式作为SPGD算法的性能评价函数，分析了三种性能评价函数在单色光及复色光情况下随共相误差增加的变化情况。本文在此基础上提出了一种基于随机并行优化算法的共相误差校正方法，并且建立了数值仿真研究平台，对单色光及复色光情况下，基于随机并行梯度下降算法的双孔径成像系统共相误差校正效果进行了研究。分析了随机并行优化算法中的关键参数——增益系数和扰动幅值对随机并行梯度下降算法收敛性能的影响，给出了一种自适应更新增益系数的方法平衡了算法的收敛速度和稳定性。

最后，基于双孔径实验平台搭建了基于随机并行梯度下降算法的共相误差闭环校正系统，在单色光及复色光情况下分别基于点目标和面目标，利用SPGD算法对稀疏孔径系统中的共相误差进行了校正，实验结果验证了相关理论分析及仿真结果的有效性。

The spatial angle resolution of optical telescope imaging system is mainly affected by the observation wavelength and the system’s aperture. When the wavelength is constant, the spatial angle resolution depends on the diameter of aperture of optical telescope imaging system. The optical multi-aperture imaging system is an effective way to increase the aperture and the resolution of the optical imaging system, the difficulty of which is lied in detecting and correcting of co-phase error. This paper presents a method based on stochastic parallel gradient decent algorithm (SPGD) to correct the co-phase error. Compared with the current method, SPGD method can avoid detecting the co-phase error and simplify the process of the co-phase error’s correction.

First, this paper deduced the mathematical expression of PSF and MTF of the multi-aperture imaging system based on the basic principle of the single aperture imaging system, revealed the reason why the multi-aperture imaging system can raise the spatial angle resolution of the imaging system by comparing with the single aperture’s PSF and the multi-aperture’s PSF, introduced three kinds of multi-aperture array structures——Ring type, Golay-3 type ,Y type and simulated the MTF of them, discussed three performance evaluation methods of the multi-aperture array structures.

Second, introduced two kinds co-phase error of the multi-aperture imaging system——piston error and tilt error and explained the cause of them, given the mathematical expression of PSF and MTF of the multi-aperture imaging system with piston error and tilt error and simulated of the PSF and the MTF, analysed the influence of co-phase error on the imaging quality of the multi-aperture imaging system.

Third, introduced the basic principle and procedure of the stochastic parallel gradient decent algorithm, presented three evaluation methods of the image’s definition, analysed the influence of the co-phase error on the performance evaluation methods under monochromatic light and multi wavelength and proposed a co-phase error correction method based on stochastic parallel gradient decent algorithm. In the case of single wavelength and multi wavelength, simulated the process of the correction of the co-phase error based on stochastic parallel gradient decent algorithm. Introduced the influence of the gain coefficient and disturbance amplitude on the stochastic parallel gradient decent algorithm and given a method adaptive updated the gain coefficient to balance the convergence speed and the stability of the algorithm.

Finally, based on the double aperture imaging platform, the closed loop correction system was built. This system based on SPGD algorithm corrected the co-phase error of the double aperture imaging system in the case of single wavelength and multi wavelength. The experimental results proved the correctness of the analysis of the theoretical and the simulation results.