光束通过硬边光阑光学系统变换的改进算法

 使用傅里叶级数与有限个复高斯函数之和的乘积作为硬边光阑的窗口函数的近似式，提出了含硬边光阑近轴ABCD光学系统对光束变换的改进算法。以高斯光束的变换为例，推导出了一个表示为初等函数之和的近似解析传输公式。给出了数值计算结果，并与直接积分Collins公式和使用Wen方法的结果作了比较。研究表明，改进算法能兼顾计算精度和机时，并能用于远场和近场。而使用Wen方法时，在近场（小于0.12倍菲涅尔距离）有明显误差。

Improved algorithm for beam transformation through hard-aperture optics

The product of Fourier series and a finite sum of complex Gaussian functions is used to approximate the window function of a hard-edged aperture, an improved algorithm for the beam propagation through a paraxial ABCD optical system with hard-edged aperture is proposed. The transformation of Gaussian beams is taken as an example, an approximate analytical propagation expression in terms of a sum of elementary functions is derived. Numerical calculation results are given and compared with those by the direct integral of the Collins formula and by using Wen's method. It is shown that the improved algorithm provides a good trade-off between the computational accuracy and computer time, and is applicable to the far field and near field, whereas there are noticeable discrepancies in the near field(less than 0.12 times the Fresnel distance) by Wen's method.