中文摘要：

基于菲涅尔衍射积分和将硬边孔径函数展开成有限项复高斯级数方法推导出了计算透镜衍射光强分布的解析表达式．所得的解析表达式克服了直接计算衍射积分的困难．应用这个表达式研究了截断参数（透镜的半径与高斯光束束腰半径的比值）对透镜衍射场分布的影响．数值结果显示，由于透镜的孔径对高斯光束的截断使得焦点向着透镜迁移，截断参数愈大，焦移量愈大，成像光斑愈大．

英文摘要：

Based on the Fresnel diffraction integral and the complex Gaussian expansion for the hard-edge aperture function, a simple and analytical expression for calculating the diffraction field distribution of an apertured lens is presented. This analytical expression can overcome the difficulty in computing the diffraction integral directly. It is found from the analytical expression that the truncation parameter, which is defined as the ratio between the waist of the Gaussian beam and the radius of the lens, has an important effect on the diffraction field distribution of the lens. The numerical results show that as the truncation parameter increases the actual focus shifts towards the lens and the spot size becomes larger gradually.