Topography of the merit function landscape in optical system design

Topography of the merit function landscape in optical system design

van Driel, E.
Bociort, F.
Serebriakov, A.

Applied Sciences

Optics Research Groep

2004-02-18

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.

global optimization
saddle point
Morse index
network
optical system design

http://resolver.tudelft.nl/uuid:440be13a-ffb8-4e24-aa39-1d52ad2a0d4b

SPIE

0277-786X

Proceedings of SPIE, 2004 vol. 5249

Institutional Repository

conference paper

(c)2004 Van Driel, E., Bociort, F., Serebriakov, A.