Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces

Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces

Marinescu, O.
Bociort, F.
Braat, J.

Applied Sciences

Optics Research Groep

2004-10-14

When Extreme Ultraviolet mirror systems having several high-order aspheric surfaces are optimized, the configurations often enter into highly unstable regions of the parameter space. Small changes of system parameters lead then to large changes in ray paths, and therefore optimization algorithms crash because certain sssumptions upon which they are based become invalid. We describe a technique that keeps the configuration away from the unstable regions. The central component of our technique is a finite-aberration quantity, the so-called quasi-onvariant, which has been originally introduced by H. A. Buchdahl. The quasi-invariant is computed for several rays in the system, and its average change per surface is determined for all surfaces. Small values of these average changes indicate stability. The stabilization technique consists of two steps: First, we obtain a stable initial configuration for subsequent optimization by choosing the system parameters such that the quasi-invariant change per surface is minimal. Then, if the average changes per surfaces of the quasi-invariant remain small during optimization, the configuration is kept in the safe region of the parameter space. This technique is applicable for arbitrary rotationally symmetric optical systems. Examples from the design of aspheric mirror systems for EUV lithography will be given.

mirror systems
aspheres
EUV lithography
optimization
relaxation

http://resolver.tudelft.nl/uuid:c253f0fa-a879-422b-8027-b3de1f91775a

SPIE

0277-786X

Proceedings of SPIE, 2004 vol. 5523

Institutional Repository

conference paper

(c)2004 Marinescu, O., Bociort, F., Braat, J.