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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 30 — Oct. 20, 2006
  • pp: 7832–7840

Hierarchical-genetic-algorithm-based design of a large scale Fresnel lens for a reading light system with multiple LED sources

Wen-Gong Chen and Chii-Maw Uang  »View Author Affiliations

Applied Optics, Vol. 45, Issue 30, pp. 7832-7840 (2006)

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A conventional Fresnel lens is suitable to be used in the reading light system due to its features of directing and collecting light rays, as well as its properties of being essentially flat, plastic, lightweight, and cost efficient. However, it is not suitable for a reading light system with multiple light sources. To a reading light system with multiple light sources, a Fresnel lens with suitably designed groove angles can be used to improve the performance of that system in both illuminance and uniformity. Nevertheless, suitable groove angles are rather difficult to find if a Fresnel lens consists of a lot of groove angles and each angle covers a wide range of degrees. We develop a hierarchical genetic algorithm (HGA) to search for a set of optimal groove angles to design a Fresnel lens for a reading light system with multiple light sources from an enormous searching space. In addition, the groove angles of the Fresnel lens are directly derived from a conventional Fresnel lens database. The design goal is to maximize the illuminance and simultaneously maintain the uniformity of light rays incident to a specified reading surface. As a result, we can demonstrate that a HGA really works better than a genetic algorithm and the optimally designed Fresnel lens, indeed, offers a better light-guiding performance than a conventional Fresnel lens for a multiple-LED reading light system.

© 2006 Optical Society of America

OCIS Codes
(200.4560) Optics in computing : Optical data processing
(220.3620) Optical design and fabrication : Lens system design

ToC Category:
Optical Design and Fabrication

Original Manuscript: March 13, 2006
Revised Manuscript: May 26, 2006
Manuscript Accepted: June 4, 2006

Wen-Gong Chen and Chii-Maw Uang, "Hierarchical-genetic-algorithm-based design of a large scale Fresnel lens for a reading light system with multiple LED sources," Appl. Opt. 45, 7832-7840 (2006)

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  1. A. Davis, R. C. Bush, J. C. Harvey, and M. F. Foley, "Fresnel lenses in rear projection displays," Society for Information Display 2001 Digest (2001), Vol. XXXII, pp. 934-937.
  2. F. T. S. Yu and X. Y. Yang, Introduction to Optical Engineering (Cambridge University, 1997), Chaps. 1-3.
  3. Reflexite Display Optics, 1300 Mt. Read Boulevard, Rochester, NY 14606, http://www.display-optics.com/.
  4. J. F. Van Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," in Proc. SPIE 4445, 119-129 (2001).
  5. W. G. Chen and C. M. Uang, "A better reading light system with light-emitting diodes using optimized Fresnel lens," Opt. Eng. 45, 063001 (2006). [CrossRef]
  6. TracePro Reference Manual, Lambda Research Corporation, 80 Taylor Street, P. O. Box 1400, Littleton, Mass., http://www.lambdares.com/.
  7. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989), Chaps. 1-4.
  8. M. Gen and R. W. Cheng, Genetic Algorithms and Engineering Design (Addison-Wesley, 1997), Chaps. 1-3.
  9. K. F. Man, Genetic Algorithms (Addison-Wesley, 1999), Chaps. 1-7. [CrossRef]
  10. A. E. H. Emery and D. L. Rimoin, Principles and Practice of Medical Genetics, 2nd ed. (Churchill, Liveringstone, 1990).
  11. A. L. Lehninger, D. L. Nelson, and M. M. Cox, Principles of Biochemistry, 2nd ed. (Worth, 1993).
  12. K. F. Man, K. S. Tang, and S. Kwong, Genetic Algorithms: Concepts and Designs (Springer-Verlag, 1999). [CrossRef]
  13. K. S. Tang, K. F. Man, S. Kwong, and Z. F. Liu, "Minimal fuzzy memberships and rule using hierarchical genetic algorithms," IEEE Trans. Indust. Electron. 45, 162-169 (1998). [CrossRef]
  14. C. M. Uang, W.-G. Chen, and J. B. Horng, "Genetic algorithm-based tri-state neural networks," in Proc. SPIE 4935, 128-134 (2002). [CrossRef]
  15. C. M. Uang, and F.-Z. Lai, "GA-based fuzzy clustering applied to irregular shape," in Conference on Avionic Technology and Application, presented at the Conference on Avionic Technology and Application, Kaohsiung, Taiwan, October 2003, paper A3.
  16. W. G. Chen and S. J. Lee, "Fuzzy classification using hierarchical genetic algorithm with multiple rule gene tables," presented at the National Computer Symposium, Taipei, Taiwan, December 2001, paper B001.

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