Abstract
Series solutions are presented for the problem of the numerical design of generalized aplanatic lenses zoned, or stepped in thickness, and extremized in the sense of having maximum aperture or minimum volume for fixed values of the other lens parameters, including the zone angular apertures or f/numbers, some of which also may be required to be minimal or nearly minimal in some sense. The solutions are developed by the method of limits or Cauchy-Kovalevsky process which in turn leads to the establishment of an existence and convergence theory for the problem. Applications to both classical optics and contemporary microwave and acoustic lens antenna problems are illustrated.
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