We develop the theoretical background of a holographic method in which the hologram is sampled simultaneously in space and in time by a charge-coupled device (CCD) sensor. With the use of temporal heterodyning (rather than spatial heterodyning, which is employed in conventional holography), in-line, single-sideband holograms of fields having an arbitrary degree of spatial coherence are recorded in an exposure time that can theoretically be as short as four frames of the CCD. The method is applied to microholography and is shown to avoid the main drawbacks of conventional holographic microscopy, namely, the need for high-spatial-bandwidth detectors and for a high degree of spatial coherence, which unavoidably leads to speckle noise. The possibility of a posteriori aberration compensation is demonstrated, and experimental results are presented.
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