Liu Jung-Ping
Department of Photonics, Feng Chia University, Taichung, Taiwan.
J Opt Soc Am A Opt Image Sci Vis. 2012 Sep 1;29(9):1956-64. doi: 10.1364/JOSAA.29.001956.
The well-sampling conditions for the digital calculations of the scalar diffraction, including the Huygens convolution method (HCM), the angular spectrum method (ASM), and the Fresnel diffraction integral (FDI), were discussed. We found the aliasing always occurs unless proper zero-padding--that is, to pad zero-value pixels around the initial field--is applied prior to the simulation of the diffraction. From the aspect of well-sampling, the ASM is applicable to a short propagation distance, while the HCM is applicable to a long propagation distance. However, we found that the free-space point spread function in the HCM is low-pass filtered when the propagation distance is long. As a result, it is recommended to always use the ASM in conjunction with sufficient zero-padding for the digital calculation of the diffraction field. The FDI can be directly applied to a long-distance propagation without the necessity of the zero-padding, provided only the intensity is of interest. If the phase of the diffraction field is important, the zero-padding is necessary and the propagation distance is severely restricted.
讨论了标量衍射数字计算的良好采样条件，包括惠更斯卷积方法（HCM）、角谱方法（ASM）和菲涅耳衍射积分（FDI）。我们发现，除非在衍射模拟之前应用适当的零填充——即在初始场周围填充零值像素，否则总是会出现混叠现象。从良好采样的角度来看，ASM适用于较短的传播距离，而HCM适用于较长的传播距离。然而，我们发现当传播距离较长时，HCM中的自由空间点扩散函数会被低通滤波。因此，建议在衍射场的数字计算中始终将ASM与足够的零填充结合使用。如果只关注强度，FDI可以直接应用于长距离传播而无需零填充。如果衍射场的相位很重要，则需要零填充且传播距离会受到严格限制。
