When a hologram is desired from an object which does not exist physically but is known in mathematical terms, one can compute the hologram. An automatic plotter will make a drawing at a large scale which is then reduced photographically. Since the drawing can contain only black and white areas, we have developed a theory for binary holograms. They are equivalent in terms of image reconstruction with ordinary holograms. This has been proven theoretically and verified experimentally.

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Among the conceivable uses of Fresnel Zone Plates (FZP) are image formation, synthesis of holograms, coherence measurements, spectrometry, optical analog computation, and optical testing. Sometimes it is desirable to change the scale of the FZP continuously, for example to give a zoom lens effect when the FZP is used for image formation. Here we describe four ways of creating a FZP pattern as a moiré effect by superposing pairs of suitable masks. The relative position of the two masks determines the FZP scale. The theory presented here is sufficiently general to allow the synthesis of patterns other than the FZP by means of a variable moiré effect.

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The setup used in many optical data processing schemes is a coherent optical image forming system. The most important lement in this setup is the complex spatial filter. It can perform a large variety of linear operations upon the object or input. In general, it is difficult to produce complex filters, since both amplitude transmission and phase delay may vary across the filter plane in a complicated manner. Our own filters which are very similar to binary holograms, consist of many little transparent rectangles on opaque background. They can easily be drawn on a large scale by a computer-guided plotter, and then photographically reduced in size. We show that our filters, despite containing only amplitude values zero and one, can perform any data processing operation which could be performed by any complex filter. After explaining the principle, we present three groups of applications. First, we describe new versions of some classical methods: schlieren observation and phase contrast. Next, we report on spatial which perform differential operations upon the object in order to enhance gradients or corners. Finally, we use our binary filters for signal detection.