采用矩阵分解和用有限个复高斯函数之和逼近硬边光阑窗口函数相结合的方法,从柯林斯衍射积分公式出发,对高斯光束通过空间滤波器的传输特性进行了分析,得到了相应的解析式。通过对解析式的数值模拟,得出了直观的结果,并进行了误差分析。数值计算结果表明,最佳滤波小孔尺寸的选择和计算误差均与光束的截断参数有关。在此基础上,进一步研究了空间滤波器具有像传递功能时,高斯光束和平顶高斯光束(N=12)通过空间滤波器的传输特性,得出了截断参数与滤波后光强分布的关系,并证实了此方法也可用于计算其他类型光束通过空间滤波器的传输。

Based on the method of matrix decomposition and expanding the rectangular function into a sum of complex Gaussian functions and the Collins diffraction integral formulae, the propagation characteristics of a Gaussian beams passing through spatial filter are studied. As a result, corresponding analytical formulae are obtained respectively. By using the numerical method, the analytical formulae are numerically simulated and the results can be got from the simulated figure. Numerical calculations have shown the dependence of the optimum pinhole size on the truncation parameters of the beams. As further extension , numerical calculations are performed for Gaussian beams and flattened Gaussian beams (N=12) propagating in spatial filter of B=0. The relation of truncation parameter and intensity distribution of Gaussian beams passing through filter is obtained.