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Hansen's recently described one-parameter distribution for the circular aperture and Taylor's earlier one-parameter line source distribution produce radiation patterns that are members of a broader two-parameter family originally described by Bickmore and Spellmire. As Hansan points out, his distribution is a compromise between various conflicting desirable characteristics. Among other things, determination of the true optimum pattern for a given application requires careful consideration of the relative importance of the peak sidelobe specification and the level of the more remote sidelobes.
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W. White (1977) studied this question.
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