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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 Collins diffraction integral formula, the transmission characteristics of the Gaussian beam passing through the spatial filter are analyzed and the corresponding analytical solutions are obtained by using matrix decomposition and the method of approximating the hard-edge aperture window function by the sum of finite complex Gaussian functions formula. Through the analytical numerical simulation, the direct result is obtained and the error analysis is carried out. The numerical results show that the selection of optimal filter aperture size and the calculation error are related to the beam truncation parameters. On this basis, the relationship between the cutoff parameters and the filtered light intensity distribution is obtained through the transmission characteristics of the Gaussian beam and the flat-topped Gaussian beam (N = 12) through the spatial filter when the spatial filter has the image transmission function. And confirmed that this method can also be used to calculate the transmission of other types of beams through the spatial filter.