To image distant and dim objects, this paper designs a sparse aperture optical system with a small F number and a large filling factor. The design process is divided into three steps. To start with, the curvature radius and spacing of the primary and secondary mirrors are calculated under the guidance of the paraxial imaging theory. Then, based on the primary aberration theory, the conic coefficients of the primary and secondary mirrors are also calculated. Finally, the node aberration theory is used to increase the field of view and eliminate the residual aberrations. Through theoretical derivation and computer-aided methods, a Golay3 sparse aperture optical system with primary mirror used Zernike polynomial is designed. The full field of view is 0.3° and the F number is 5.

为了成像远处和暗淡的物体，本文设计了一个F值较小且填充系数较大的稀疏孔径光学系统。设计过程分为三个步骤。首先，在近轴成像理论的指导下计算主镜和副镜的曲率半径和间距。然后，基于主像差理论，还计算了主，副镜的圆锥系数。最后，节点像差理论用于增加视野并消除残留像差。通过理论推导和计算机辅助方法，设计了使用Zernike多项式的具有主镜的Golay3稀疏孔径光学系统。全视野为0.3°，F值为5。