Abstract

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

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References

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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.

2006 (1)

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]

2002 (1)

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]

2001 (2)

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.

J. F. Van Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," in Proc. SPIE 4445, 119-129 (2001).

1999 (2)

K. F. Man, Genetic Algorithms (Addison-Wesley, 1999), Chaps. 1-7.
[CrossRef]

K. F. Man, K. S. Tang, and S. Kwong, Genetic Algorithms: Concepts and Designs (Springer-Verlag, 1999).
[CrossRef]

1998 (1)

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]

1997 (2)

M. Gen and R. W. Cheng, Genetic Algorithms and Engineering Design (Addison-Wesley, 1997), Chaps. 1-3.

F. T. S. Yu and X. Y. Yang, Introduction to Optical Engineering (Cambridge University, 1997), Chaps. 1-3.

1993 (1)

A. L. Lehninger, D. L. Nelson, and M. M. Cox, Principles of Biochemistry, 2nd ed. (Worth, 1993).

1990 (1)

A. E. H. Emery and D. L. Rimoin, Principles and Practice of Medical Genetics, 2nd ed. (Churchill, Liveringstone, 1990).

1989 (1)

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989), Chaps. 1-4.

Bush, R. C.

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.

Chen, W. G.

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]

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.

Chen, W.-G.

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]

Cheng, R. W.

M. Gen and R. W. Cheng, Genetic Algorithms and Engineering Design (Addison-Wesley, 1997), Chaps. 1-3.

Cox, M. M.

A. L. Lehninger, D. L. Nelson, and M. M. Cox, Principles of Biochemistry, 2nd ed. (Worth, 1993).

Davis, A.

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.

Emery, A. E. H.

A. E. H. Emery and D. L. Rimoin, Principles and Practice of Medical Genetics, 2nd ed. (Churchill, Liveringstone, 1990).

Foley, M. F.

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.

Gen, M.

M. Gen and R. W. Cheng, Genetic Algorithms and Engineering Design (Addison-Wesley, 1997), Chaps. 1-3.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989), Chaps. 1-4.

Harvey, J. C.

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.

Horng, J. B.

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]

Kwong, S.

K. F. Man, K. S. Tang, and S. Kwong, Genetic Algorithms: Concepts and Designs (Springer-Verlag, 1999).
[CrossRef]

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]

Lai, F.-Z.

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.

Lee, S. J.

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.

Lehninger, A. L.

A. L. Lehninger, D. L. Nelson, and M. M. Cox, Principles of Biochemistry, 2nd ed. (Worth, 1993).

Liu, Z. F.

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]

Man, K. F.

K. F. Man, Genetic Algorithms (Addison-Wesley, 1999), Chaps. 1-7.
[CrossRef]

K. F. Man, K. S. Tang, and S. Kwong, Genetic Algorithms: Concepts and Designs (Springer-Verlag, 1999).
[CrossRef]

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]

Nelson, D. L.

A. L. Lehninger, D. L. Nelson, and M. M. Cox, Principles of Biochemistry, 2nd ed. (Worth, 1993).

Rimoin, D. L.

A. E. H. Emery and D. L. Rimoin, Principles and Practice of Medical Genetics, 2nd ed. (Churchill, Liveringstone, 1990).

Tang, K. S.

K. F. Man, K. S. Tang, and S. Kwong, Genetic Algorithms: Concepts and Designs (Springer-Verlag, 1999).
[CrossRef]

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]

Uang, C. M.

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]

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]

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.

Van Derlofske, J. F.

J. F. Van Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," in Proc. SPIE 4445, 119-129 (2001).

Yang, X. Y.

F. T. S. Yu and X. Y. Yang, Introduction to Optical Engineering (Cambridge University, 1997), Chaps. 1-3.

Yu, F. T. S.

F. T. S. Yu and X. Y. Yang, Introduction to Optical Engineering (Cambridge University, 1997), Chaps. 1-3.

IEEE Trans. Indust. Electron. (1)

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]

Opt. Eng. (1)

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]

Proc. SPIE (1)

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]

Other (13)

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.

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.

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.

F. T. S. Yu and X. Y. Yang, Introduction to Optical Engineering (Cambridge University, 1997), Chaps. 1-3.

Reflexite Display Optics, 1300 Mt. Read Boulevard, Rochester, NY 14606, http://www.display-optics.com/.

J. F. Van Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," in Proc. SPIE 4445, 119-129 (2001).

TracePro Reference Manual, Lambda Research Corporation, 80 Taylor Street, P. O. Box 1400, Littleton, Mass., http://www.lambdares.com/.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989), Chaps. 1-4.

M. Gen and R. W. Cheng, Genetic Algorithms and Engineering Design (Addison-Wesley, 1997), Chaps. 1-3.

K. F. Man, Genetic Algorithms (Addison-Wesley, 1999), Chaps. 1-7.
[CrossRef]

A. E. H. Emery and D. L. Rimoin, Principles and Practice of Medical Genetics, 2nd ed. (Churchill, Liveringstone, 1990).

A. L. Lehninger, D. L. Nelson, and M. M. Cox, Principles of Biochemistry, 2nd ed. (Worth, 1993).

K. F. Man, K. S. Tang, and S. Kwong, Genetic Algorithms: Concepts and Designs (Springer-Verlag, 1999).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Cross section of a conventional Fresnel lens with 330 grooves.

Fig. 2
Fig. 2

Simulated reading light system.

Fig. 3
Fig. 3

(a) Cone-frustum-shaped reflector and LED light source. (b) Arrangement of five LEDs in the light source set.

Fig. 4
Fig. 4

Reading surface with 5 equal-area rings, 120 equal-area sectors.

Fig. 5
Fig. 5

(a) General structure of a chromosome in the proposed HGA. (b) Special structure of a chromosome in the proposed HGA, for example, N seg = 66 .

Fig. 6
Fig. 6

Flow diagram of the proposed approach.

Fig. 7
Fig. 7

Silhouette of a light ray tracing of a simulated reading light system with FL con .

Fig. 8
Fig. 8

Silhouette of a light ray tracing of a simulated reading light system with FL 33 .

Fig. 9
Fig. 9

Irradiance map of a simulated reading light system with FL con .

Fig. 10
Fig. 10

Irradiance map of a simulated reading light system with FL 33 .

Fig. 11
Fig. 11

Uniformity of distribution in quantity for a simulated reading light system with FL con .

Fig. 12
Fig. 12

Uniformity of distribution in quantity for a simulated reading light system with FL 33 .

Fig. 13
Fig. 13

Cross section of FL 33 .

Fig. 14
Fig. 14

Convergence statuses of the proposed HGAs using FL 10 , FL 15 , FL 33 , and FL 66 .

Fig. 15
Fig. 15

Convergence statuses of the conventional GA using FL con and the proposed HGA using FL 33 .

Tables (2)

Tables Icon

Table 1 Distribution of 330 Groove Angles on 66 Segments for N seg = 66

Tables Icon

Table 2 Parameters Used in the Proposed Approach

Equations (9)

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R t = r = 1 N r s = 1 N s R r s ,
R a = R t Nr × Ns .
I = G r = 1 N r s = 1 N s L r s ,
G = ( R t R C ) × G w ,
L r s = { ( 1 R a R r s ) × L w for   R r s R a , ( 1 R r s R a ) × L w otherwise,
C i = C i ( 1 : k 1 ) + C j ( k 1 : k 2 ) + C i ( k 2 : N seg ) ,
C j = C j ( 1 : k 1 ) + C i ( k 1 : k 2 ) + C j ( k 2 : N seg ) ,
C i = C j ( 1 : k 1 ) + C i ( k 1 : k 2 ) + C j ( k 2 : N seg ) ,
C j = C i ( 1: k 1 ) + C j ( k 1 : k 2 ) + C i ( k 2 : N seg ) .

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