A simple analytical formula is derived for the Fourier transform of an arbitrary quasiplane uniform polygon. The form of the expression is such that prominent features of the Fraunhofer diffraction pattern are readily interpreted; a typical diffractometer photograph and the corresponding computed density plot are presented. The shape of the central bright spot is determined by a momental ellipse of the projected aperture, and contour plots have shown that the innermost minima for a variety of apertures tend to occur close to spatial frequencies 1.22/4g and never less than 1/4g, where g is the appropriate radius of gyration of the brightness distribution. In the appendices algorithms are developed for rapid computation of the transform over a rectangular network of points, and for finding the coordinates of the momental ellipse.
© 1979 Optical Society of AmericaFull Article | PDF Article
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