二维互素阵列设计及在量子成像中的应用

Quantum imaging can be seen as an active array radar system which is working at optical frequency. In the traditional design of array system, the distance between two elements is less than the half wavelength in order to avoid aliasing. At the optical frequency this requirement will cause many difficulties, epically for the fabrication of large aperture array. Co-prime array consists of two sparse sub-array, which are generated by sub-sampling of the original dense array. The co-differential array of these two co-prime arrays is equivalent to the original array. With this feature, the co-prime array can reach the M*N degree of freedom with M+N elements. In this project, we extend the co-prime array to the cause of two-dimensional, and introduce it to the area of quantum imaging. The project begins with the equivalent definition of co-prime of integer matrices and the construction of these matrices. In the constraint of degree of freedom, the elements of array and the prosperity of the co-differential array generated by the Lattices are optimized. In the framework of compressed sensing, the phase modulation of element is also optimized with the goal function that the recovery condition of easements are best. The numerical simulation of the whole quantum imaging system based on the two-dimensional co-prime array will be realized. The physical two-dimensional optical co-prime array will be developed, and the relevant optical system will be set up to validate the theoretical results of this project. Our research will improve the theory of quantum imaging and support its practical application.

量子成像系统可以看作是工作在光学频段的主动式阵列雷达系统。经典的阵列系统设计中，为了避免周期性的栅瓣，要求相邻阵元之间的间距小于信号波长的一半。在光学频段，该限制将成为技术瓶颈，尤其是在大孔径阵列的制造中，硬件实现变得尤为困难。互素阵由两个降采样的稀疏子阵组成，其互差分阵列可以等效为均匀密阵列，从而由M+N个阵元数，实现MN的自由度。本课题将互素阵推广到二维，并用应用于量子成像。项目从互素整数矩阵的等价定义及构造方法出发，在自由度约束下，研究阵元数最少、互差分阵性质最优的Lattice生成方法；以（压缩感知框架下）测量光场重构性质最优为目标，优化阵元相位调制方式；开展基于二维互素阵列的量子成像全链路数值仿真，制备二维互素光学阵列，搭建物理实验系统，对项目研究成果进行验证。课题的研究成果可为量子成像理论的进一步完善和应用的推广提供支持。

量子成像系统是一种新的计算成像体制，虽然基本原理以及实际成像试验方面均有一定的研究基础，但在光源的设计、以及成像算法方面，仍有优化的空间。二维互素采样可以通过两个适当构造的降采样稀疏子阵，等效为均匀密阵列，因此在量子成像光源设计上有巨大的应用潜力。另一方面，压缩采样、稀疏重构等算法在量子成像中，如何进一步优化使用，也需要深入研究。本项目就二维互素阵列设计及在量子成像中应用开展了研究，还在双线性成像模型、超分辨率高光谱成像技术等应用方面进行了拓展。具体来说，本项目研究了互素整数矩阵构造以及基于Lattice 生成理论的二维互素阵列优化方法，由此构造的互素阵较可以再带来自由度的提升；提出了二维阵列变密度自适应采样方法，可以显著降低图像重构所需的测量数据；开展了二维互素阵列光源计算量子成像全链路仿真，根据多项指标的对比，充分验证了其对成像性能的提升；指出了新体制计算成像的双线性模型，推导了双线性成像模型下的最小测量数定理；研究了基于压缩采样的超分辨高光谱成像方法，可以在不减小探测器像元大小的条件下通过编码孔径提高图像分辨率；开展了及外场量子成像试验光场特性分析研究，指出了实际量子成像光场不满足经典压缩感知的条件，在此基础上提出了成像算法改进研究。项目的研究成果一定程度上完善了以计算量子成像、超分辨高光谱成像为代表的新体制计算成像理论，部分成果得到了国防创新特区项目、装备预研项目等课题的后续研究资助，为推动其在新体制军事遥感成像中技术发展的实际应用提供了支撑。