An efficient representation of radiation from a circular aperture with tapered amplitude and quadratic phase

An efficient series representation is derived for I/sub pab/, a quadratic phase integral commonly encountered in aperture-antenna theory. The accuracy and efficiency of the series formula relative to ordinary numerical integration are discussed. This formula may be useful in solving such problems as quadratic-phase error effects on beamwidth, field in the Fresnel-region, on-axis defocus characteristics of a paraboloidal reflector, or shadow-region field behind a disk.<
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