For tapered circular aperture with illumination of the form [b + (1 —ξ)v]/(b + 1) expressions for the on-axis electric-field intensity, power density, and directivity reduction are developed. Those expressions are presented in terms of the degenerate hypergeometric function. When v is an integer, the use of recurrence relationship permits simple expressions in closed form to be obtained. For special values of v and b, a set of curves is presented. Also, the application of the expressions developed for any other nonuniform illumination involving circular symmetry are briefly presented.
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