大视场稀疏孔径望远镜的成像理论及方法研究

The quest for finer image resolution in ground observation and space exploration is growing, and it is imperative to develop the large-aperture telescope. However, considering the traditional single- and large-aperture telescope is constrained by factors such as the manufacturing method and the launching capability of the vehicle, the multi-mirror sparse aperture imaging technique based on the interference principle is thereby adopted as an alternative. The previous multi-mirror sparse aperture telescopes have problems such as the lack of theory of selecting the sub-mirror structure, the mismatching of the parameters between the optical and image receiving systems, and the small field of view. Based on the distribution characteristics of the spatial frequency and high resolution requirements of the imaging target, this project is tend to derive the optimal non-redundant structure of the sub-mirror array using the optimization algorithm reversely. The fill factor of the sparse aperture imaging system can be determined by calculating the Nyquist frequency of the smallest pixel size of the image receiving device. Experiments are performed to validate the calculation results. In addition, On the premise of ensuring the reasonable tube size and image quality of the sparse aperture telescope, an aspheric corrector group is designed in front of the imaging plane to enlarge the field of view of the telescope. The research of this project has solved the problems of the choice of the sub-mirror structure and the demand of the field of view. The research results will provide valuable theory of optical imaging and research methods for the application of multi-mirror sparse aperture telescope in aerospace.

对地观测和空间探索对图像分辨率的要求越来越高，迫切需要发展大口径望远镜系统。然而传统单一大口径望远镜系统受制造、发射等诸多因素限制，基于干涉成像原理的多子镜稀疏孔径成像技术是解决上述问题的方案之一。目前多子镜稀疏孔径望远镜设计缺乏相应的子镜结构选择理论，且存在光学系统与图像接收系统参数不匹配以及视场角小等问题。本项目从成像目标物的空间频率分布特征和高分辨率要求出发，利用最优化算法反向推导子镜阵列的最佳非冗余结构。由光学系统图像接收器的最小像元尺寸计算得到稀疏孔径成像系统对应的填充因子值，并通过实验验证计算方法的合理性。在此基础上，通过设计像面前的非球面校正镜组，在保证望远镜合理尺寸及成像质量的前提下，增大稀疏孔径望远镜的视场角。本项目的研究主要解决稀疏孔径望远镜子镜结构选择与视场需求方面的难题，将为多子镜稀疏孔径望远镜在航天领域的应用提供具有价值的光学成像理论以及研究方法。

近年来，对地遥感探测和空间观测对图像分辨率的要求越来越高，需要发展大口径的光学系统，然而在研制单一大口径望远镜系统的过程中，受加工、检测及发射等诸多因素的制约，人们开始寻求新的方法解决上述问题，稀疏孔径空间望远镜是方案之一。本项目通过理论分析与研究，构建稀疏孔径子镜阵列结构和调制传递函数的目标函数，通过最优算法反向推导出适合于具有特定空间频率特征目标物的稀疏孔径阵列结构；提出了基于Zernike系数转换的波前像差检测方法，推导了子孔径与包围孔径的Zernike系数转换矩阵，根据该转换矩阵以及包围孔径的波前像差计算得到每个子孔径的波前像差数据。结果表明：随着填充因子的增加，用于表征子孔径波前像差的Zernike多项式的高阶项系数逐渐趋于零。根据稀疏孔径望远镜的角分辨率指标，理论推导出稀疏孔径望远镜的填充因子，据此设计一同轴稀疏孔径望远镜，并采用蒙特卡洛方法对望远镜进行了公差分析；提出一种基于离轴两反结构的稀疏孔径望远镜，主镜为球面Golay3稀疏孔径结构，次镜为自由曲面，由X-Y多项式表征。通过优化，系统的填充因子达到了58.4%，视场角增大至2.5deg。基于节点像差理论，设计了一主镜为自由曲面的同轴稀疏孔径望远镜，主镜为由Zernike多项式表征的自由曲面。系统的填充因子达到了40.3%。通过在稀疏孔径系统中采用自由曲面，有效增大稀疏孔径望远镜的填充因子，提高了系统的能量收集效率和成像质量。