Structural design of cemented triplets by genetic algorithm

We present an implementation of a genetic algorithm in the structural design of cemented triplets according to a prespecified set of Gaussian characteristics and primary aberration targets. The approach is directed toward obtaining a suite of promising solutions allowing some floating of the primary aberration targets. This method obviates the need for any heuristic preselection of glasses for the three elements of the triplet. Searches for optimal solutions are conducted in the total configu- ration space of the degrees of freedom, consisting of continuous vari- ables like shape factor and power distributions, and discrete variables like available glass types. The role of genetic diversity in the evolving population on convergence of the optimization runs has been investi- gated, and, accordingly suitable modifications are incorporated in the basic genetic algorithm to eliminate undue stagnation and premature convergence problems. Some illustrative examples are given. © 2004

[1]  C. B. Lucasius,et al.  Optical design with the aid of a genetic algorithm. , 1996, Bio Systems.

[2]  Kimiaki Yamamoto,et al.  An experiment in genetic optimization in lens design , 1997 .

[3]  Donald C. O'Shea,et al.  Global view of optical design space , 1991 .

[5]  L Hazra,et al.  Structural design of multicomponent lens systems. , 1984, Applied optics.

[6]  Robert Rennie Shannon,et al.  The Art and Science of Optical Design , 1997 .

[7]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[8]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[9]  Donald P. Umstadter,et al.  High-harmonic generation in plasmas by relativistic Thomson scattering , 2002 .

[10]  Saswatee Banerjee,et al.  Thin lens design of Cooke triplet lenses: application of a global optimization technique , 1998, Optics & Photonics.

[11]  N. Lessing,et al.  Selection of Optical Glasses in Apochromats , 1957 .

[12]  S Banerjee,et al.  Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets. , 2001, Applied optics.

[13]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[14]  J. Colotti,et al.  EMC DESIGN FUNDAMENTALS , 2006, 2006 IEEE Long Island Systems, Applications and Technology Conference.

[15]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[16]  Saswatee Banerjee,et al.  Structural design of doublet lenses with prespecified aberration targets , 1997 .

[17]  David Shafer,et al.  Global Optimization in Optical Design , 1994 .

[18]  Michael J. Kidger,et al.  Existence of local minima in lens design , 1991, Other Conferences.

[19]  Masaki Isshiki.  Global optimization with escape function , 1998, Other Conferences.

[20]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[21]  M. Herzberger,et al.  The Design of Superachromatic Lenses , 1963 .

[22]  T. H. Jamieson.  Optimization techniques in lens design , 1971 .

[23]  Saswatee Banerjee,et al.  Experiments with GSA techniques in structural design of doublet lenses , 1998, Other Conferences.

[24]  M. Iqbal Khan.  Cemented Triplets: A Method for Rapid Design , 1984 .

[25]  Saswatee Banerjee,et al.  Genetic algorithm in the structural design of Cooke triplet lenses , 1999, Optical Systems Design.

[26]  H. Hopkins,et al.  Wave theory of aberrations , 1950 .

[27]  Isao Ono,et al.  Global and multi-objective optimization for lens design by real-coded genetic algorithms , 1998, Other Conferences.

[28]  Saswatee Banerjee,et al.  Simulated annealing with constrained random walk for structural design of doublet lenses , 1998 .

[29]  T. P. Cotter,et al.  An Attempt To Develop An "Intelligent" Lens Design Program , 1986, Other Conferences.

[30]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[31]  L. Hazra,et al.  Structural design of broken contact doublets with prespecified aberration targets using genetic algorithm , 2002 .

[32]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[33]  H. Zimmermann.  Towards global optimization 2: L.C.W. DIXON and G.P. SZEGÖ (eds.) North-Holland, Amsterdam, 1978, viii + 364 pages, US $ 44.50, Dfl. 100,-. , 1979 .

[34]  M. Isshiki,et al.  Lens Design: Global Optimization with Escape Function , 1995 .