OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 42, Iss. 20 — Jul. 10, 2003
  • pp: 4156–4165

Multiplexed computer-generated holograms with polygonal-aperture layouts optimized by genetic algorithm

Jean-Numa Gillet and Yunlong Sheng  »View Author Affiliations

Applied Optics, Vol. 42, Issue 20, pp. 4156-4165 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (1919 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Using a novel genetic algorithm (GA) with a Lamarckian search we optimize the polygonal layout of a new type of multiplexed computer-generated hologram (MCGH) with polygonal apertures. A period of the MCGH is divided into cells, and the cell is further divided into polygonal apertures according to a polygonal layout, which is to be optimized. Among an ensemble of 1.21 × 1024 possible polygonal layouts, we take a population of 102 solutions, which are coded as chromosomes of bits, and find the optimal solution with our GA. We introduce rank-based selection with cumulative normal distribution fitness, double crossover, exponentially decreasing mutation probability and Lamarckian downhill search with a small number of offspring chromosomes into our GA, which shows a rapid convergence to the global minimum of the cost function. In a second step of optimization the phase distributions over the subholograms in the MCGH are determined with our iterative subhologram design algorithm. Our MCGH designs show large-size reconstructed images with high diffraction efficiency and low reconstruction error.

© 2003 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.1970) Diffraction and gratings : Diffractive optics
(060.4230) Fiber optics and optical communications : Multiplexing
(090.1760) Holography : Computer holography
(090.1970) Holography : Diffractive optics
(090.4220) Holography : Multiplex holography

Original Manuscript: December 5, 2002
Revised Manuscript: April 1, 2003
Published: July 10, 2003

Jean-Numa Gillet and Yunlong Sheng, "Multiplexed computer-generated holograms with polygonal-aperture layouts optimized by genetic algorithm," Appl. Opt. 42, 4156-4165 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J.-N. Gillet, Y. Sheng, “Multiplexed computer-generated holograms with irregular-shaped polygonal apertures and discrete phase levels,” J. Opt. Soc. Am. A 19, 2403–2413 (2002). [CrossRef]
  2. J.-N. Gillet, Y. Sheng, “Multiplexed computer-generated hologram with polygonal apertures,” Appl. Opt. 41, 298–307 (2002). [CrossRef] [PubMed]
  3. J.-N. Gillet, “Éléments optiques diffractifs conçus avec des ouvertures trapézoïdales et polygonales et de nouveaux algorithmes d’optimisation,” Ph.D. dissertation (Université Laval, Québec, PQ, Canada, 2001), Chap. 3, pp. 63–93.
  4. J. N. Mait, D. W. Prather, X. Gao, A. Scherer, O. Dial, “Characterization of a binary subwavelength diffractive lens,” in Diffractive Optics and Micro-Optics, Vol. 41 of Trends in Optics and Photonics Series OSA (Optical Society of America, Washington, D.C., 2000), pp. 108–109.
  5. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  6. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980). [CrossRef]
  7. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990). [CrossRef]
  8. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988). [CrossRef]
  9. W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, Vol. 41 of Topics in Applied Research, B. R. Frieden, ed. (Springer-Verlag, Berlin, 1980), pp. 291–366.
  10. J.-N. Gillet, Y. Sheng, “Iterative simulated quenching for designing irregular-spot-array generators,” Appl. Opt. 39, 3456–3465 (2000). [CrossRef]
  11. J.-N. Gillet, Y. Sheng, “Irregular spot array generator with trapezoidal apertures of varying heights,” Opt. Commun. 166, 1–7 (1999). [CrossRef]
  12. J.-N. Gillet, “Éléments optiques diffractifs conçus avec des ouvertures trapézoïdales et polygonales et de nouveaux algorithmes d’optimisation,” Ph.D. dissertation (Université Laval, Québec, PQ, Canada, 2001), Chap. 1 and 2, pp. 6–62.
  13. M. A. McCord, M. J. Rooks, “Electron beam lithography,” in SPIE Handbook of Microlithography, Micromachining and Microfabrication, Vol. 1: Microlithography, P. Rai-Choudhury, ed., SPIE Press Monograph39 and IEE Materials and Devices Series12 (SPIE Press, Bellingham, WA, 1997), Chap. 2, pp. 139–250.
  14. J. Komrska, “Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures,” J. Opt. Soc. Am. 72, 1382–1384 (1982). [CrossRef]
  15. R. Straubel, Über die Berechnung der Fraunhoferschen Beregungserscheinungen durch Randintegrale mit Besondere Berücksichtigung der Theorie der Beugung in Heliometer (Frommansche, Jena, Germany, 1888).
  16. O. K. Ersoy, J. Y. Zhuang, J. Brede, “Iterative interlacing approach for synthesis of computer-generated holograms,” Appl. Opt. 31, 6894–6901 (1992). [CrossRef] [PubMed]
  17. M. P. Chang, O. K. Ersoy, “Iterative interlacing error diffusion for synthesis of computer-generated holograms,” Appl. Opt. 32, 3122–3128 (1993). [CrossRef] [PubMed]
  18. J. H. Holland, “Genetic algorithms,” Scientific American, July1992, pp. 66–72.
  19. J. H. Holland, Adaptation in Natural and Artificial System (Univ. of Michigan Press, Ann Arbor, Mich., 1975).
  20. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison–Wesley, Reading, Mass., 1989).
  21. E. E. Agoston, R. Hinterding, Z. Michalewicz, “Parameter control in evolutionary algorithms,” IEEE Trans. Comput. 3, 124–141 (1999). [CrossRef]
  22. W. S. Klug, M. R. Cummings, Concepts of Genetics, 6th ed. (Prentice Hall, Upper Saddle River, N.J., 2000).
  23. M. Gen, R. Cheng, Genetic Algorithms and Engineering Design (Wiley, New York, 1997).
  24. R. L. Haupt, S. E. Haupt, Practical Genetic Algorithms (Wiley, New York, 1998).
  25. P. J. B. Hancock, “An empirical comparison of selection methods in evolutionary algorithms,” in Evolutionary Computing, Lecture Notes in Computer Science 865, T. C. Fogarty, ed. (Springer-Verlag, Berlin, 1994), pp. 80–94. [CrossRef]
  26. E. G. Johnson, A. D. Kathman, D. H. Hochmuth, A. Cook, D. R. Brown, B. Delaney, “Advantages of genetic algorithm optimization methods in diffractive optic design,” in Diffractive and Miniaturized Optics, S.-H. Lee, ed., CR49 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1993), pp. 54–74.
  27. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, Berlin, 1992). [CrossRef]
  28. C. Y. Lu, H. Z. Liao, C. K. Lee, J. S. Wang, “Energy control by linking individual patterns to self-repeating diffractive optical elements,” Appl. Opt. 36, 4702–4712 (1997). [CrossRef] [PubMed]
  29. C. Darwin, The Origin of Species, 6th ed., 1872 (The New American Library of World Literature, New York, 1958; with a special Introduction by J. Huxley).
  30. J.-B.-P.-A. Lamarck, Philosophie Zoologique, 1809 (GF-Flammarion, Paris, 1994; with Presentation and Notes by A. Pichot).
  31. G. Zhou, Y. Chen, Z. Wang, H. Song, “Genetic local search algorithm for optimization design of diffractive optical elements,” Appl. Opt. 38, 4281–4290 (1999). [CrossRef]
  32. P. Charbonneau, “Genetic algorithms in astronomy and astrophysics,” The Astrophysical Journal Supplement Series 101, 309–334 (1995). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited