Lens design and local minima

Details Lens design and local minima Lens design and local minima

Feb 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apopt..20..384b&link_type=abstract

Applied Optics, vol. 20, Feb. 1, 1981, p. 384-387. Research supported by the U.S. Department of Energy.

Mathematics

7

Error Functions, Least Squares Method, Lens Design, Minima, Computer Programs, Imaging Techniques, Light Beams, Matrices (Mathematics), Optimization

Scientific paper

The widespread belief that local minima exist in the least squares lens-design error function is not confirmed by the Los Alamos Scientific Laboratory (LASL) optimization program. LASL finds the optimum-minimum region, which is characterized by small parameter gradients of similar size, small performance improvement per iteration, and many designs that give similar performance. Local minima and unique prescriptions have not been found in many-parameter problems. The reason for these absences is that image errors caused by a change in one parameter can be compensated by changes in the remaining parameters. False local minima have been found, and four cases are discussed.

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