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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 1 — Jan. 5, 2009
  • pp: 314–328

Instabilities and fractal basins of attraction in optical system optimization

M. van Turnhout and F. Bociort  »View Author Affiliations


Optics Express, Vol. 17, Issue 1, pp. 314-328 (2009)
http://dx.doi.org/10.1364/OE.17.000314


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Abstract

Many optical design programs use various forms of the damped least-squares method for local optimization. In this paper, we show that damped least-squares algorithms, with maximized computational speed, can create sensitivity with respect to changes in initial conditions. In such cases, starting points, which are very close to each other, lead to different local minima after optimization. Computations of the fractal capacity dimension show that sets of these starting points, which lead to the same minimum (the basins of attraction for that minimum), have a fractal structure. Introducing more damping makes the optimization process stable.

© 2009 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(220.2740) Optical design and fabrication : Geometric optical design
(220.3620) Optical design and fabrication : Lens system design
(080.1753) Geometric optics : Computation methods

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: November 4, 2008
Revised Manuscript: December 22, 2008
Manuscript Accepted: December 23, 2008
Published: January 2, 2009

Citation
M. van Turnhout and F. Bociort, "Instabilities and fractal basins of attraction in optical system optimization," Opt. Express 17, 314-328 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-1-314


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References

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