Numerical calculation of Fresnel diffraction is widely used in optical applications where wave propagation is needed. Most cases for simulating Fresnel diffraction only consider sampling of complex amplitude fields, which lacks comprehensiveness when different diffraction fields are of interest. In this study, from the perspective of phase space optics, we provide systematical analysis on the sampling of all Fresnel diffraction fields, including the complex amplitude, intensity, amplitude, and phase. The space-bandwidth product of each field is illustrated with the aid of a phase space diagram, which is further demonstrated from a physical point of view. Such comprehensive sampling analysis could provide practical suggestions to the numerical calculations of various diffraction fields according to the requirements. Numerical experiments with discrete Fresnel diffraction are implemented to verify feasibility of the analyses.

中文翻译：

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基于相空间表示的菲涅耳衍射场采样分析

菲涅耳衍射的数值计算广泛用于需要波传播的光学应用中。大多数模拟菲涅耳衍射的情况只考虑复振幅场的采样，当关注不同的衍射场时缺乏全面性。在这项研究中，我们从相空间光学的角度，对所有菲涅耳衍射场的采样进行了系统的分析，包括复振幅、强度、振幅和相位。借助相空间图来说明每个场的空间带宽积，并从物理角度进一步说明。这种全面的采样分析可以根据需要为各种衍射场的数值计算提供实用的建议。