The superposition of several periodic or quasiperiodic patterns produces moiré effects. In particular, the combination of three grid structures adds great flexibility to the use of moiré phenomena. Information about the fringe structure, given by vector addition in Fourier space, allows investigation of formations, interpretation, and expectation problems concerning moiré-pattern parameters. Any frequency and orientation of the pattern is possible, using three-line gratings. On the other hand, three quasiperiodic gratings with variations of frequency and/or orientation result in a zone-plate shape of the moiré pattern regardless of grating distortions. Both elliptical and hyperbolic zone plates occur. Several illustrations demonstrate these phenomena and indicate some potential applications.
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