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Proceedings Paper

Systematics of the design shapes in the optical merit function landscape
Author(s): F. Bociort; P. van Grol
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Paper Abstract

In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where the merit function gradient vanishes) can be very useful starting points. We study here a problem that is simple enough to be analyzed in detail, the design landscape of triplets with variable curvatures. We show here how representatives of all triplet design shapes observed in global optimization runs can be obtained in a simple and systematic way by locally optimizing for each design shape one starting point obtained with the new method. Good approximations of these special starting points are also computed analytically with two theoretical models. We have found a one-to-one correspondence between the possible triplet design shapes and the critical points resulting from a model based on third-order spherical aberration within the framework of thin-lens theory. The same number and properties of critical points are predicted by a second model, which is even simpler and mathematically more general.

Paper Details

Date Published: 14 May 2010
PDF: 14 pages
Proc. SPIE 7717, Optical Modelling and Design, 77170F (14 May 2010); doi: 10.1117/12.853924
Show Author Affiliations
F. Bociort, Delft Univ. of Technology (Netherlands)
P. van Grol, Delft Univ. of Technology (Netherlands)

Published in SPIE Proceedings Vol. 7717:
Optical Modelling and Design
Frank Wyrowski; John T. Sheridan; Jani Tervo; Youri Meuret, Editor(s)

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