Realization of Fourier Images without Using a Lens by Sampling the Optical Object

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Abstract
The realization of the Fourier image of a two-dimensional object without using a lens is described. The two-dimensional Fourier transform is generated optically by means of a periodic array of pin-holes (the sampling filter). The object is illuminated by a monochromatic, coherent plane wave and sampled by the pin-hole array. Multiple Fourier images of the object appear in certain planes behind the sampling filter. The simple theory of this phenomenon, together with experimental results, is given.

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