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Obtaining new local minima in lens design by constructing saddle points

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Author: Turnhout, M. van · Grol, P. van · Bociort, F. · Urbach, H.P.
Type:article
Date:2015
Publisher: Optical Society of America (OSA)
Source:Optics Express, 5, 23
Identifier: 523319
Keywords: Electronics · Mathematical methods · Geometric optical design · Lens system design · High Tech Systems & Materials · Industrial Innovation · Nano Technology · OPT - Optics · TS - Technical Sciences

Abstract

We show that in the lens design landscape saddle points exist that are closely related to local minima of simpler problems. On the basis of this new theoretical insight we develop a systematic and efficient saddlepoint method that uses a-priori knowledge for obtaining new local minima. In contrast with earlier saddle-point methods, the present method can create both positive and negative lenses. As an example, by successively using the method a good-quality local minimum is obtained from a poor-quality one. The method could also be applicable in other global optimization problems that satisfy the requirements discussed in this paper.