Holography is reformulated by using the framework of phase-space optics. The Leith-Upatnieks off-axis reference hologram is compared with precursors, namely, single-sideband holography. The phase-space representation of complex amplitudes focuses on similarities between different holographic recording schemes and is particularly useful for investigating the degree of freedom and the space-bandwidth product of optical signals and systems. This allows one to include computer-generated holography and recent developments in digital holography in the discussion.
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