Abstract

A closed-form solution to a two-dimensional Fourier transform of a toothed wheel or sunburst is presented. The solution was obtained by decomposing the sunburst aperture into triangles and applying the superposition principle to sum the Fourier transforms of the subapertures. This technique is applicable to analyzing and designing other complicated apertures. Computer plots are presented that show the spatial transforms along the radial and angular directions. For small radial distances, the transform resembles that of a circle, whereas for large radial distances, it has preferred angular directions that are perpendicular to every edge of the aperture. The power spectrum or the magnitude squared of the transform is a close approximation of the Fraunhofer diffraction pattern of the aperture. Contour shaping of this type is an effective means of apodizing diffraction of unwanted sources of small angular subtense but becomes ineffective when the angular subtense of the unwanted sources are large.

© 1974 Optical Society of America

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