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Using saddle points for challenging optical design tasks

Author: Livshits, I. · Hou, Z. · Grol, P. van · Shao, Y. · Turnhout, M. van · Urbach, H.P. · Bociort, F.
Publisher: SPIE
Source:Mahajan, V.N.Johnson, R.B.Mahajan, V.N.Thibault, S., 9192
Identifier: 523280
ISBN: 9781628412192
Article number: 919204
Keywords: Electronics · Saddle points · wide-angle lens · Design · Optical design · Optical instrument lenses · Automatic design · Lens designs · Local minimums · Optical merit functions · Saddle point · Special properties · Traditional techniques · Wide-angle lens · Lenses · High Tech Systems & Materials · Industrial Innovation · Physics & Electronics · OPT - Optics · TS - Technical Sciences


The present research is part of an effort to develop tools that make the lens design process more systematic. In typical optical design tasks, the presence of many local minima in the optical merit function landscape makes design non-trivial. With the method of Saddle Point Construction (SPC) which was developed recently ([F. Bociort and M. van Turnhout, Opt. Engineering 48, 063001 (2009)]) new local minima are obtained efficiently from known ones by adding and removing lenses in a systematic way. To illustrate how SPC and special properties of the lens design landscape can be used, we will present the step-by-step design of a wide-angle pinhole lens and the automatic design of a 9-lens system which, after further development with traditional techniques, is capable of good performance. We also give an example that shows how to visualize the saddle point that can be constructed at any surface of any design of an imaging system that is a local minimum.