Finding new local minima in lens design landscapes by constructing saddle points

Bociort, Florian

doi:10.1117/1.3156022

Cited by 14 publications

(16 citation statements)

References 17 publications

(28 reference statements)

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“…5) in the range explored are small compared to the variation given by the front central curvature (on Fig. 4(c)), as it is common to find in conventional multi-parameter optimization of the spherical optics [14].…”

Section: Phase I Optimizationmentioning

confidence: 97%

SMS-based optimization strategy for ultra-compact SWIR telephoto lens design

Wang¹,

Benı́tez²,

Miñano³

et al. 2012

Opt. Express

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Abstract:A new optical design strategy for rotational aspheres using very few parameters is presented. It consists of using the SMS method to design the aspheres embedded in a system with additional simpler surfaces (such as spheres, parabolas or other conics) and optimizing the free-parameters. Although the SMS surfaces are designed using only meridian rays, skew rays have proven to be well controlled within the optimization. In the end, the SMS surfaces are expanded using Forbes series and then a second optimization process is carried out with these SMS surfaces as a starting point. The method has been applied to a telephoto lens design in the SWIR band, achieving ultra-compact designs with an excellent performance.

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Section: Phase I Optimizationmentioning

confidence: 97%

SMS-based optimization strategy for ultra-compact SWIR telephoto lens design

Wang¹,

Benı́tez²,

Miñano³

et al. 2012

Opt. Express

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show abstract

“…If the meniscus is inserted in contact with an existing surface of the starting minimum (the reference surface) and has the same glass as the one at the reference surface, we have proven mathematically that if the three consecutive surfaces in Fig. 1b have the same curvature, then the resulting system is a saddle point (SPC-special case) 4 . In the resulting system it is possible to find analytically two directions in the variable space (see Eqs.…”

Section: Saddle-point Constructionmentioning

confidence: 99%

“…9-11 in Ref. 4) such that, when the merit function is plotted along them, we obtain the well-known shape of a saddle surface: a maximum along one of the two directions and a minimum along the other one (Fig. 2).…”

Section: Saddle-point Constructionmentioning

confidence: 99%

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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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“…The algorithm looks at every known local minimum for index-1 saddle-points around it, and for each detected saddle-point it finds a new minimum on the other side of the "saddle". While SPD is a "blind" and relatively slow search, the algorithm of saddle-point construction (SPC) takes into account special properties of the lens design landscape that allow a fast prediction of the position of saddle points 4,5 . SPC is a tool for changing the system shape in a computationally efficient way that works for optical systems of arbitrary complexity and is presently implemented in the commercial lens design program SYNOPSYS under the name Saddle-point-build (SPB).…”

Section: Introductionmentioning

confidence: 99%

Finding starting points analytically for optical system optimization

Bociort

Grol

2012

SPIE Proceedings

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Understanding the structure of the design space in optical system optimization is difficult, because common human intuition fails when it encounters the challenge of high dimensionality, resulting from the many optimization parameters of lens systems. However, a deep mathematical idea, that critical points structure the properties of the space around them, is fruitful in lens design as well. Here we discuss simple systems, triplets with curvatures as variables, for which the design space is still simple enough to be studied in detail, but complex enough to be non-trivial. A one-to-one correspondence between the possible design shapes and the critical points resulting from a simplified model based on third-order spherical aberration within the framework of thin-lens theory could lead in the future to a new way to determine good starting points for subsequent local optimization.

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Finding new local minima in lens design landscapes by constructing saddle points

Cited by 14 publications

References 17 publications

SMS-based optimization strategy for ultra-compact SWIR telephoto lens design

SMS-based optimization strategy for ultra-compact SWIR telephoto lens design

Reducible complexity in lens design

Finding starting points analytically for optical system optimization

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