Abstract
Aberration in imaging systems due to the presence of spherical surfaces is usually treated by the expansion of the aberration function in terms of a complete set of polynomials that are orthogonal over the interior of a circle of unit radius. This method involves a set of complicated programs, and the interpretation of the components in the expansion in terms of physical quantities is not possible. To avoid such complications, Fourier transform techniques are used. This method is applied to determine the diffraction pattern of a circular acoustical reflector. It is shown that the amplitude distribution function using this technique and the language of J. W. Goodman's Introduction to Fourier Optics is consistent with experimental results obtained in the laboratory. In particular, the effects of varying the radius of the spherical surface, index of refraction, and wavelength in the reduction of spherical aberration are obvious in the resulting equation. [This work supported by ARPA and monitored by ONR.]
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