Wigner distribution function and digital holography

We investigate the principles of digital holography based on the Wigner distribution function (WDF). We apply the WDF to the analysis of generic optical setups which are used to record and reconstruct image Fresnel holograms. We use the graphical representation of the Wigner chart to derive various important properties, including the required space-bandwidth product of the digital hologram, CCD sampling and numerical reconstruction and the optimum required object size to optimize the system efficiency. This allows us to offer a simple comparison of the various recording schemes. The analysis also allows us to graphically compare the numerical reconstruction methods and the restrictions it may impose on the CCD parameters. We show how this insightful analysis leads us to a new method of digital holography which we call 'dual-shift' DH.