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The standard representation of an aspheric optical surface is a power series added to a base conic. This dissertation considers alternate ways of describing an aspheric surface, and the effect of such alternate descriptions on the design of optical systems. In rare cases one may represent an aspheric by an expression in closed form that allows the system to yield imagery that is in some sense perfect. A new family of such systems, having perfect axial imagery, is described. In most cases one must represent an aspheric by a series of basis functions added to a base conic. Nonpolynomial basis functions are discussed and used to design several different lenses. They are shown to give better image quality than the same number, or a larger number, of polynomial series terms. When used as optimization variables, the nonstandard basis functions are shown to converge to a solution in fewer iterations, in some cases, than when power series variables were used. The increase in convergence rate is at least paritially offset by the fact that the nonstandard functions take longer to evaluate than polynomials. Optical testing of aspheric surfaces having nonpolynomial descriptions is discussed to the extent necessary to show the feasibility, in principle, of testing and manufacturing some of the design examples presented in the dissertation. When the idea of designing aspheric surfaces with nonstandard functions as variables is accepted, one needs to know which of the many possible such variables to use in a given application. Some methods of searching for the most appropriate variables are described. A hypothesis is presented on which types of optical systems will benefit from nonstandard aspheric representations, and which will be adequately designed with polynomial representations.

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QC 351 A7 no. 64 / Generalized bending is a one -parameter family of changes to two curvatures and related thicknesses of a previously defined optical system consisting of spherical and plane refracting surfaces. This family of changes leaves first-order properties invariant at all other surfaces in the system. Thus, third-order aberrations at the other surfaces are also unchanged. The third-order aberrations may then be expressed as functions of independent generalized bends at different locations; therefore, simultaneous correction of several aberrations is possible. Comparison of ray fan plots for real rays through an optical system shows marked differences for various degrees and locations of generalized bending. Surfaces at which a generalized bend would make significant changes to aberrations of the original lens are easily identified. This use of generalized bending would be helpful in advanced stages of a design routine.

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