菲涅尔衍射可看作一个线性空间平移不变系统,因此可以在频谱域中,利用角谱算法来数值计算菲涅尔衍射积分.首先详细阐明了角谱算法的具体实施过程,澄清了理想采样条件、卷绕误差产生的原因和影响范围以及计算窗口尺寸的选取依据等相关问题.然后采用角谱算法数值计算了高斯光束照明余弦光栅的菲涅尔衍射场.数值解与解析解的对比表明,当满足理想采样条件并正确选取计算窗口尺寸时,角谱算法可以达到非常高的计算精度.最后数值仿真了单透镜相干成像实验,进一步展示了角谱算法的应用过程.
Fresnel diffraction can be regarded as a linear space-invariant system, so the Fresnel diffraction integral can be calculated numerically in the spectral domain using the angular spectrum. First, the implementation of the angular spectrum algorithm is explained in detail, including the ideal sampling conditions, the origins and influence range of the wraparound error, and the selection of the calculation window size. Then the Fresnel diffraction field of a Gaussian beam illuminated cosine grating is numerically calculated using the angular spectrum algorithm. A comparison between the numerical solution and the analytical solution shows that the angular spectrum algorithm can achieve very high accuracy when the ideal sampling conditions are met and the calculation window size is correctly selected. Finally, a single-lens coherent imaging is numerically simulated to further demonstrate the implementation of the angular spectrum algorithm.
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