A Fourier-series representation of a Fresnel zone plate is set up and used, with a paraxial approximation, to predict features of the image-forming and Fourier-transforming properties of the plate. These properties are compared and contrasted with those of a lens, and examples of a Fraunhofer diffraction pattern from a plate and a lens are illustrated.
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Harburn et al. (1975) studied this question.
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