Generating saddle points in the merit function landscape of optical systems

Generating saddle points in the merit function landscape of optical systems

Bociort, F.
Van Turnhout, M.

Applied Sciences

Optics Research Groep

2005-09-30

Finding multiple local minima in the merit function landscape of optical system optimization is a difficult task, especially for complex designs that have a large number of variables. We discuss here a method that enables a rapid generation of new local minima for optical systems of arbitrary complexity. We have recently shown that saddle points known in mathematics as Morse index 1 saddle points can be useful for global optical system optimization. In this work we show that by inserting a thin meniscus lens (or two mirror surfaces) into an optical design with N surfaces that is a local minimum, we obtain a system with N+2 surfaces that is a Morse index 1 saddle point. A simple method to compute the required meniscus curvatures will be discussed. Then, letting the optimization roll down on both sides of the saddle leads to two different local minima. Often, one of them has interesting special properties.

saddle point
optimization
optical system design
lithography

http://resolver.tudelft.nl/uuid:05dfafdc-cd7c-4b17-a92f-8420e5bb78a0

SPIE

0277-786X

Proceedings of SPIE, 2005 vol. 5962

Institutional Repository

conference paper

(c)2005 Bociort, F., Van Turnhout, M.