Networks, local minima and saddle points in optical system optimization

 

"If a physicist could at the same time be a poet, he might convey to others the pleasure, the satisfaction, almost the reverence, which the subject inspires. The aesthetic side of the subject is, I confess, by no means the least attractive to me. Especially is its fascination felt in the branch which deals with light...These beauties of form and color, so constantly recurring in the varied phenomena of refraction, diffraction, and interference, are, however, only incidentals; and, though a never-failing source of aesthetic delight, must be resolutely ignored if we would perceive the still higher beauties which appeal to the mind, not directly through the senses, but through the reasoning faculty; for what can surpass in beauty the wonderful adaptation of Nature's means to her ends, and the never-failing rule of law and order which governs even the most apparently irregular and complicated of her manifestations? These laws it is the object of the scientific investigator to discover and apply. In such successful investigation consists at once his keenest delight as well as his highest reward."

A. A. Michelson, "Light Waves and Their Uses", The University of Chicago Press, 1902



Papers 

(those marked with * are the most readable for non-experts)

  1. F. Bociort, E. van Driel and A. Serebriakov, Network structure of the set of local minima in optical system optimization, Proc. SPIE 5174, 26-34 (2003) pdf version
  2. E. van Driel, F. Bociort and A. Serebriakov, Topography of the merit function landscape in optical system design, Proc. SPIE 5249, 353-363 (2004) pdf version
  3. F. Bociort, E. van Driel and A. Serebriakov, Networks of local minima in optical system optimization, Optics Letters 29, 189-191 (2004) pdf version
  4. F. Bociort, A. Serebriakov, and M. van Turnhout, Saddle points in the merit function landscape of systems of thin lenses in contact , Proc. SPIE 5523, 174-184 (2004) pdf version , lens files related to this paper
  5. F. Bociort and M. van Turnhout, Generating saddle points in the merit function landscape of optical systems , Proc. SPIE 5962, 0S1-8 (2005) (Note: This unrefereed paper is updated and expanded in Ref. 14) pdf version
  6. O. Marinescu and F. Bociort, Saddle points in the merit function landscape of lithographic objectives, Proc. SPIE 5962, 0T1-8 (2005) pdf version
  7. F. Bociort and M. van Turnhout, Looking for order in the optical design landscape, Proc. SPIE 6288, 628806(9 pages), (2006) pdf version
  8. O. Marinescu and F. Bociort, Designing lithographic objectives by constructing saddle points, Proc. SPIE 6342,6342L(7 pages) (2006) pdf version
  9. F. Bociort, M. van Turnhout and O. Marinescu,  Practical guide to saddle-point construction in lens design, Proc. SPIE 6667, 666708(13pages )(2007) pdf file, lens files with examples
  10. O. Marinescu and F. Bociort, Network search method in the design of EUV lithographic objectives,  Applied Optics 46, 8385-8393 (2007), pdf file
  11. O. Marinescu and F. Bociort, Saddle-point construction in the design of lithographic objectives, part 1: method, Optical Engineering 47, 093002 (2008), pdf 
  12. O. Marinescu and F. Bociort, Saddle-point construction in the design of lithographic objectives, part 2: application, Optical Engineering 47, 093003 (2008), pdf 
  13.  * F.  Bociort and M. van Turnhout, Saddle points reveal essential properties of the merit-function landscape, SPIE Newsroom (2008), link to page, pdf
  14. F.  Bociort and M. van Turnhout, Finding new local minima in lens design landscapes by constructing saddle points , Optical Engineering 48, 063001 (2009), pdf
  15. P. van Grol, F. Bociort and M. van Turnhout, Finding order in the design landscape of simple optical systems, Proc. SPIE 7428, 742808 (2009), pdf

 

 About our research

  1. Section The Saddle Point Method of Bociort in H. Gross, H. Zuegge, M. Peschka, F. Blechinger, Handbook of Optical Systems, Vol. 3, Wiley-VCH, pp362-365,370 (2007) , pdf version

  2.  * Article in Terrific Technology 2007, p 15-17, pdf version

  3. *  M. Evenblij, Design: an evolutionary process, Florian Bociort, in R. Didde, M. Evenblij, P. Vermaas and N. Roozenburg, A room with a view, Delft design, TU Delft, p80-82 (2008), pdf


Image gallery

Cooke Triplet Network htm document , Animation in PowerPoint document (select "Slide Show, View Show" in Power Point")

Change of system shape along some arbitrary closed loop in the network of the
Double Gauss run
The position in the network of the system shown in black on the right is given on the left by the last added point.
The green system on the right is the previous one in the loop and it is overlapped over the current system in order
 to make the changes from node to node visible. In the title, the system number and merit function are shown;
 "m" denotes a local minimum and "s" denotes a saddle point. 

dbgauss_loop.gif (41777 bytes)

Saddle-point construction

       Unlike other global optimization methods, saddle-point construction (SPC) uses a specific behavior of the  merit function landscape when the number of variables is increased in a certain way: local minima become saddle points. (See animation.)
        In lens design, SPC is a new method to insert lenses into an existing design. Designers frequently insert lenses into their designs and, in the traditional way, one new system shape results after optimization. However, when a lens is inserted with SPC, two distinct system shapes result and for further design one can choose the better one. With SPC, by inserting and then, if necessary, by extracting lenses, new system shapes can be obtained very rapidly, even for complex systems with many variables.  The practical implementation is very easy and the method can be fully integrated with all other traditional design tools.
      In principle, SPC should also be applicable in other optimization problems, which satisfy certain mathematical conditions, e.g. in thin-film optimization.

 This research is supported at present by the Project DWI.6817 of the Dutch Technology Foundation STW                                                           This page is maintained by Florian Bociort

For other work on Control of complexity in optical design problems, see our page Fractals and chaos in optical system optimization