Using saddle points for challenging optical design tasks

Livshits, Irina; Hóu, Zhé; Grol, P. van; Shao, Yijia; Turnhout, Maarten van; Urbach, Paul; Bociort, Florian

doi:10.1117/12.2061975

Cited by 4 publications

(5 citation statements)

References 11 publications

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“…Combining SPC with conventional design methods, as shown in Fig. 6, can lead to good complex designs starting from simpler ones [15].…”

Section: Discussionmentioning

confidence: 99%

“…Excepting simple problems, no known global optimization method can guarantee finding all (good) solutions in a reasonable time, and SPC is no exception. However, high-quality designs have already been obtained with the special [12,13] and with the general versions [15] of SPC. SPC will be finally validated if many high-quality designs will be obtained in this way.…”

Section: Discussionmentioning

confidence: 99%

“…In this section we consider a design landscape that is simple enough to be studied in detail and show how different local minimums can be reached rapidly with SPC, when local optimization converges to one of them. We study a wide-angle pinhole lens design, suitable for application in security cameras, which has an aperture stop with a small diameter placed in front of the system (discussed in a preliminary form, unrefereed, in [15]). All lenses are in contact, one lens is cemented, and three different glass materials are used [see Fig.…”

Section: Switching Between Local Minimumsmentioning

confidence: 99%

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One-dimensional searches for finding new lens design solutions efficiently

2016

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A special structure is present in the lens design landscape that makes it different from a general global optimization problem: many local minimums are closely related to minimums of simpler problems and can therefore be found by decomposing the search for them in simple steps. We show here that in the design landscape of a wide-angle pinhole lens and in closely related optimization landscapes, all good local minimums found by other methods can be obtained easily with a succession of one-dimensional searches starting from simpler systems. By replacing high-dimensional searches with a succession of one-dimensional searches, the design efficiency can be increased significantly. By combining this method with conventional design methods, the wide-angle pinhole lens can be designed starting from a single lens.

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“…Combining SPC with conventional design methods, as shown in Fig. 6, can lead to good complex designs starting from simpler ones [15].…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Switching Between Local Minimumsmentioning

confidence: 99%

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One-dimensional searches for finding new lens design solutions efficiently

2016

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“…The lens model used in this paper is a modified version of a wide-angle pinhole lens with a full FOV of 90 • [21]. The system is smaller than 15 mm in length and the pinhole has a diameter of 1 mm.…”

Section: Modelmentioning

confidence: 99%

Wide-angle spectral imaging using a Fabry-Pérot interferometer

Strauch

Livshits²,

Bociort

et al. 2015

J. Eur. Opt. Soc.-Rapid Publ.

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We show that wide-angle spectral imaging can be achieved with compact and cost-effective devices using Fabry-Pérot interferometers. Designs with a full field of view of 90 • , in which the Fabry-Pérot interferometer is mounted either in front of an imaging lens system or behind a telecentric lens system, are presented and analysed. We show the dependency of the spectral resolution on the numerical aperture of the lens system and demonstrate its value as a design criterion.

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“…In order to see whether this ability of SPC to find many new system shapes can also be observed in problems that are very different from the special case mentioned above, we have first examined the landscape of a wide-angle pinhole lens with a full field of 110 degrees 8 . With other methods (see below) we find three stable solutions (i.e.…”

Section: Decomposing the High-dimensional Search For New Local Minimamentioning

confidence: 99%

Reducible complexity in lens design

Hóu

Bociort

2015

SPIE Proceedings

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A major challenge in lens design is the presence of many local minima in the optimization landscape. However, unlike other global optimization problems, the lens design landscape has an additional structure, that can facilitate the design process: many local minima are closely related to minima of simpler problems. For discussing this property, in addition to local minima other critical points in the landscape must also be considered. Usually, in a global optimization problem with M variables one has to perform M-dimensional searches in order to find minima that are different from the known ones. We discuss here simple examples where, due to the special structure that is present, all types of local minima found by other methods can be obtained by a succession of one-dimensional searches. Replacing M-dimensional searches by a set of one-dimensional ones has very significant practical advantages. If the ability to reach solutions by decomposing the search in simple steps will survive generalization to more complex systems, new design tools using this property could have a significant impact on lens design.

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Using saddle points for challenging optical design tasks

Cited by 4 publications

References 11 publications

One-dimensional searches for finding new lens design solutions efficiently

One-dimensional searches for finding new lens design solutions efficiently

Wide-angle spectral imaging using a Fabry-Pérot interferometer

Reducible complexity in lens design

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