为了对望远光学系统实现横向超分辨成像, 设计了一种高斯特列尔比的二维多项式函数形式的位相型光瞳滤波器, 分析了其对光学系统焦点附近光强分布的有益影响。理论分析表明, 加入滤波器之后, 与无滤波器时相比系统横向光学分辨率提升了1.33倍, 同时斯特列尔比为无滤波器时的0.75倍。给出了该种滤波器与典型的三区型、四区型和一维多项式位相型光瞳滤波器的对比, 从对比结果可知, 二维多项式型滤波器的斯特列尔比为几种滤波器中的最优, 且其横向分辨倍率仅次于四区型滤波器, 但四区型滤波器的斯特列尔比过低, 不适合应用于望远系统。研究了入射光视场角对应用该种滤波器的望远光学系统成像效果的影响, 视场角不大于±4°时, 具有较佳的超分辨效果。

In order to realize the transverse super-resolution imaging with a telescope optical system, a two-dimensional polynomial function phase pupil filter with a high strehl ratio was designed, and its improvement for the light distribution around the focal point of the optical imaging system was demonstrated. The result of the theory analysis shows that, when the filter is added into the system, the system transverse optical resolution is increased 1.33 times, and the Strehl ratio is 0.75 time as much as that of the system without this pupil filter. The performance of two-dimensional polynomial filter was compared with the other typical phase pupil filters, including the three-zone, the four-zone and the one-dimensional polynomial phase filter. The comparison results show that the Strehl ratio of the two-dimensional polynomial filter is the highest in these filters, and the transverse super-resolution ratio of this filter is next only to that of the four-zone filter. But the Strehl ratio of the four-zone filter is too low to be applied into the telescope. The influence of the incident field angle on the imaging results of the telescope optical system was also be studied, and it was found that the super-resolution effect of the system is better when the field-of-view is no more than ±4°.