Spatial filters for replicating images

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Abstract
The conditions for self-imaging, longitudinal periodicity are relaxed to demand image replication only along the optical axis. Lateral periodicity in the square of the radius, in the spatial-frequency domain, is necessary and sufficient for image replication along the optical axis. This formulation allows one to employ any zone plate as a spatial filter that creates self-replicating images of a given object, under either coherent or incoherent illumination.