为了提高衍射远场显微成像的分辨率, 采用一种振幅透过率随半径呈幂函数分布的光瞳滤波器进行了理论分析和数值模拟。通过在光路中加入幂函数分布的振幅型光瞳滤波器, 利用标量衍射理论推导出夫琅禾费衍射分布的计算公式; 通过MATLAB软件给出衍射图样, 对比衍射分布的主瓣宽度。结果表明,当幂次数为3时, 模拟仿真的衍射分布斯特雷尔比为0.16, 最大旁瓣强度比为0.1, 分辨参量为0.76, 分辨率提高倍数为1.3;随着振幅透过率幂次数的增加, 主瓣宽度依次减小; 同时也伴随着主瓣强度降低和旁瓣强度增大的缺点。这一研究对于远场光学显微镜实现超分辨成像是有帮助的。

In order to improve the resolution of far-field diffraction microscopy, a pupil filter whose amplitude transmittance had the distribution of power function with radius was proposed. Theoretical analysis and numerical simulation were carried out. By using scalar diffraction theory, the formula of Fraunhofer diffraction distribution was derived when an amplitude pupil filter with the distribution of power function was added in optical path. Diffraction pattern was obtained through MATLAB software, and the main lobe width of diffraction distribution was compared. The results show that when the power number is 3, Strehl ratio of diffraction distribution is 0.16, the maximum sidelobe intensity ratio is 0.1, the resolution parameter is 0.76, and the enhancement factor of resolution is 1.3. With the increase of power number of amplitude transmittance, the main lobe width decreases. At the same time, the main lobe intensity decreases and the side lobe intensity increases. This study is helpful for the realization of super-resolution imaging in the far field optical microscopes.