Convergence and Multiple Solutions in Computerized Lens Design.
WHITE SANDS MISSILE RANGE N MEX INSTRUMENTATION DIRECTORATE
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The two purposes of the research are to give a better mathematical description of lens design problems near a solution and to make a contribution to the problem of global optimization in lens design. Orthogonal transformations derived by solving eigenvalue problems in two vector spaces, the space of lens construction variables and the space of image defects, have been used to simplify the problem so that the effects of nonlinearity could be more easily studied. The most important nonlinear effects have been deduced and implications of these effects for two important algorithms, Damped Least Squares and Greys orthonormalization method, have been worked out. The nonlinear structure of the lens design problem is such that Damped Least Squares is subject to serious stagnation phenomena. Greys method is superior in this respect. A different approach to handling nonlinearity has been developed, and an algorithm which embodies this approach is described. Author