Sampling analysis for Fresnel diffraction fields based on phase space representation

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.