Scanning holographic microscopy is a two-pupil synthesis method allowing the capture of single-sideband inline holograms of noncoherent (e.g., fluorescent) three-dimensional specimens in a single two-dimensional scan. The flexibility offered by the two-pupil method in synthesizing unusual point-spread functions is discussed. We illustrate and compare three examples of holographic recording, using computer simulations. The first example is the classical hologram in which each object point is encoded as a spherical wave. The second example uses pupils with spherical phase distributions having opposite curvatures, leading to reconstructed images with a resolution limit that is half that of the objective. In the third example, axicon pupils are used to obtain axially sectioned images.
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