Finding new local minima in lens design landscapes by constructing saddle points

Florian Bociort; Maarten van Turnhout

doi:10.1117/1.3156022

1 June 2009 Finding new local minima in lens design landscapes by constructing saddle points

Florian Bociort, Maarten van Turnhout

Author Affiliations +

Optical Engineering, Vol. 48, Issue 6, 063001 (June 2009). https://doi.org/10.1117/1.3156022

Abstract

Finding good new local minima in the merit function landscape of optical system optimization is a difficult task, especially for complex design problems where many minima are present. Saddle-point construction (SPC) is a method that can facilitate this task. We prove that, if the dimensionality of the optimization problem is increased in a way that satisfies certain mathematical conditions (the existence of two independent transformations that leave the merit function unchanged), then a local minimum is transformed into a saddle point. With SPC, lenses are inserted in an existing design in such a way that subsequent optimizations on both sides of the saddle point result in two different system shapes, giving the designer two choices for further design. We present a simple and efficient version of the SPC method. In spite of theoretical novelty, the practical implementation of the method is very simple. We discuss three simple examples that illustrate the essence of the method, which can be used in essentially the same way for arbitrary systems.

©(2009) Society of Photo-Optical Instrumentation Engineers (SPIE)

Citation Download Citation

Florian Bociort and Maarten van Turnhout "Finding new local minima in lens design landscapes by constructing saddle points," Optical Engineering 48(6), 063001 (1 June 2009). https://doi.org/10.1117/1.3156022

Published: 1 June 2009

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