Abstract
Designing a lens is equivalent to solving a set of simultaneous, nonlinear, algebraic equations with prescribed boundaries. Having thus stated the problem, one has said everything—or nothing—since general solutions are unknown. A popular approach is to introduce and attempt to minimize a merit function whose magnitude depends upon the residual aberrations. It must be easy to compute and closely related to lens performance. An approximate form of the characteristic function may lead to a suitable merit function. However, minimizing it is still the central difficulty. One possibility is the method of “steepest descent” or any of its numerous progeny. The second is a linearization method, and the third employs interpolation. Numerical examples of the first two will be given. Finally there are both good and bad ways to control the boundary conditions. These consist of a set of inequalities regulating such things as edge thicknesses, distances between elements, lens-to-film distance, and choice of available glasses.
© 1962 Optical Society of America
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