基于自由曲面的多子镜稀疏孔径空间望远镜成像及优化理论研究

The development of the space remote technique is in urgent need of high resolution space telescope. Conventional large aperture telescope fails to meet the requirements because of the limitation of materials and weights. The sparse aperture optical system has become one of the techniques to overcome the challenge, yet it still has the problem of lower image quality due to information loss. In this project, we apply the freeform primary mirror for sparse aperture space telescope. The freeform has the advantages of correcting the aberrations as well as making the system miniaturize and lightweight. The field will become larger and the modulation transfer function will improve, thus the imaging resolution is increased. However, the flexible property of the freeform has led to the failure of the existing design theory and optimization method of the sub-mirrors, which poses huge challenges to the application of the freeform to the sparse aperture system. In the light of this, theoretical mode of the freeform multiple-mirror primary mirror is well researched. The sub-mirrors array of the freeform primary is optimized, and the optical image and image restoration algorithm are investigated. Then we establish the imaging and optimization theory based on the freeform primary mirror and set up the principle prototype. This project will build theoretical and experimental foundation for the application of the sparse aperture system to the space remote field. The bottleneck troubling the development of the large aperture and high resolution space telescope will be solved and the application of the freeform in the space remote system will be greatly expanded.

航天遥感迫切需要高分辨空间望远镜，然而受材料、重量等因素制约，常规大口径望远镜无法满足实际需求，因此稀疏孔径光学系统成为解决此限制的方案之一。但稀疏孔径光学系统存在信息丢失，成像质量低等问题。本项目提出在稀疏孔径空间望远镜中采用自由曲面主镜，利用自由曲面超强校正像差的能力使系统实现小型化、轻量化和大视场，同时改善系统调制传递函数，提高成像分辨率。但由于自由曲面元件面形自由无约束，已有的稀疏孔径光学成像设计理论及子孔径优化方法失效，使自由曲面元件应用于稀疏孔径望远镜中面临巨大难题。针对此，本项目主要研究稀疏孔径自由曲面多子镜主镜理论模型、自由曲面主镜子孔径阵列优化、光学成像特性及图像复原算法等，以期建立基于自由曲面的稀疏孔径望远镜成像及优化理论，并搭建原理样机，为稀疏孔径系统应用于航天遥感提供理论与实验基础。项目有助于解决困扰大口径高分辨空间望远镜发展的瓶颈，并拓展自由曲面在航天遥感的应用。

航天遥感迫切需要高分辨空间望远镜，然而受材料、重量、发射等因素的制约，常规大口径望远镜无法满足实际需求，因此稀疏孔径光学系统成为解决此限制的方案之一。但稀疏孔径光学系统存在信息丢失，成像质量低等问题。本项目提出在稀疏孔径空间望远镜中采用自由曲面主镜，构建自由曲面稀疏孔径望远系统，利用自由曲面超强校正像差以及能使系统实现小型化、轻量化和增大视场的能力，改善系统调制传递函数，提高成像分辨率。但由于自由曲面元件面型自由无约束，已有的稀疏孔径光学成像设计理论及子孔径优化方法失效，使自由曲面元件应用于稀疏孔径望远镜中面临巨大难题。针对此，本项目主要建立稀疏孔径自由曲面多子镜主镜理论模型、进行自由曲面主镜子孔径阵列优化、构建光学成像特性及图像复原算法等，获得基于自由曲面的稀疏孔径望远镜成像及优化理论。在上述理论研究基础上，设计了一款包围口径为250mm，F数为5.8，焦距为1450mm，全视场角为0.5deg，子镜直径为80mm（填充因子为30.7%）三子镜稀疏孔径望远镜，该望远镜在全视场范围内成像质量达到衍射极限。采用双泽尼克多项式描述在不同视场角下稀疏孔径望远镜的光瞳函数，通过傅立叶变换获得不同视场稀疏孔径光学系统的点扩散函数PSF和调制传递函数MTF。采用泽尼克多项式描述主镜和子镜的波前像差，根据子镜相对于主镜中心的位置以及子镜的尺寸大小，构建子镜相对于主镜的泽尼克多项式系数转换矩阵，从而计算各个子镜的泽尼克多项式系数。通过设计加工和装调，搭建了基于自由曲面的主镜三子镜稀疏孔径望远镜原理样机，并开展成像实验研究和图像复原。实验结果表明: 与具有相同口径的球面稀疏孔径相比较，自由曲面稀疏孔径望远镜具有更大的成像范围和更高的成像对比度。项目研究有助于解决困扰大口径高分辨空间望远镜发展的瓶颈，并拓展自由曲面在航天遥感的应用。

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