Topography of the merit function landscape in optical system design

Eco van Driel; Florian Bociort; Alexander Serebriakov

doi:10.1117/12.512973

18 February 2004 Topography of the merit function landscape in optical system design

Eco van Driel, Florian Bociort, Alexander Serebriakov

Author Affiliations +

Proceedings Volume 5249, Optical Design and Engineering; (2004) https://doi.org/10.1117/12.512973
Event: Optical Systems Design, 2003, St. Etienne, France

Abstract

We have shown recently that, when certain quite general conditions are satisfied, the set of local minima in the optical merit function space forms a network where they are all connected through optimization paths generated from saddle points having a Morse index of 1. A new global optimization method, that makes use of this linking network to systematically detect all minima, is presented. The central component of this new method, the algorithm for saddle point detection, is described in detail and we show that the initialization of this algorithm has a significant impact on the performance. For a simple global optimization search (Cooke triplet) several representation forms of the network of the corresponding set of local minima are presented. These representations, which can be visualized in two dimensions, are independent of the dimensionality of the design space so that they can provide insight into the topography of merit function landscapes of arbitrary dimensionality.

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Eco van Driel, Florian Bociort, and Alexander Serebriakov "Topography of the merit function landscape in optical system design", Proc. SPIE 5249, Optical Design and Engineering, (18 February 2004); https://doi.org/10.1117/12.512973

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