中文摘要：

通过将圆孔光阑函数展开为有限复高斯函数和的方法，利用惠更斯一菲涅尔衍射积分推导出了椭圆对称奇异空心光束通过具有圆孔光阑的近轴ABCD光学系统的传输近似解析公式，并对椭圆对称奇异空心光束在自由空间中通过不同孔径下的硬边光阑的传输特性进行了数值模拟研究。结果表明：自由空间中的近轴光学系统无论在近场还是远场，椭圆对称奇异空心光束的衍射光强分布都与光阑大小有很大的关系。该研究方法对椭圆对称奇异空心光束通过具有圆孔光阑的传输和变换的研究非常有益。

英文摘要：

Based on the Huygens-Fresnel diffraction integral and the expansion of the circular aperture function into a finite sum of Gaussian functions, the approximate analytical expression of an elliptical symmetry anomalous hollow beams passing through a circular aperture paraxial ABCD optical system was derived. Based on the approximate analytical expression, the propagation properties in free space were numerically illustrated. The results indicate that in the paraxial optical system of the free space, no matter in the near field or the distant field, elliptical symmetry anomalous hollow beams diffracted light intensity distribution are strongly affected by different aperture size. This method provides a convenient tool for studying the propagation and transformation properties of elliptical symmetry anomalous hollow beams passing through a circular aperture paraxial ABCD optical system.