Abstract

A two-layered Hierarchical Genetic Algorithm (HGA) was proposed in a previous paper to solve the design problem of a large scale Fresnel lens used in a multiple-source lighting system. The research objective of this paper is to extend the previous work by utilizing a three-layered HGA. The goal of the suggested approach is to decrease the reliance on deciding the number of groove segments for the designed Fresnel lenses, as well as to increase the variety of groove angles in a segment to improve the performance of the designed Fresnel lens. The proposed algorithm will be applied on a simulated reading light system, and the simulation results demonstrate that the proposed approach not only makes the design of a large scale Fresnel lens more feasible but also works better than the previous one in both illuminance and uniformity for a simulated reading light system.

© 2007 Optical Society of America

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References

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  1. T. S. Yu and X. Y. Yang, Introduction to Optical Engineering, Chap. 1-3, 1997.
  2. Reflexite Display Optics, NY , USA. Available: http://www.display-optics.com/.
  3. A. Davis, R. C. Bush, J. C. Harvey and M. F. Foley, "Fresnel lenses in rear projection displays," SID 2001 Digest, Volume XXXII, pp. 934-937, June 2001
  4. C. C. Sun, T.-X. Lee, S.-H. Ma, Y.-L. Lee, and S. Huang, "Precise optical modeling for LED lighting verified by cross correlation in the midfield region," Opt. Lett. 31, 2193-2195 (2006).
    [CrossRef] [PubMed]
  5. W.-T. Chien, C. C. Sun, and I. Moreno, "Precise optical modeling of multi-chip white LEDs," Opt. Express. 15, 7572-7577 (2007).
    [CrossRef] [PubMed]
  6. C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M Huang, "Precise optical modeling for LED lighting verified by cross correlation in the midfield region," Opt. Lett. 31, 2193-2195 (2006).
    [CrossRef] [PubMed]
  7. F. Munoz, P. Benitez, O. Dross, J. C. Minano, and B. Parkyn, "Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes," Opt. Eng. 43,1522-1530 (2004).
    [CrossRef]
  8. P. Benitez, J. C. Minano, J. Blen, R. Mohendano, J. Chaves, O. Dross, M. Hemandez, and W. Falicoff, "Simultaneous multiple surface optical design," Opt. Eng. 43, 1489-1502 (2004).
    [CrossRef]
  9. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, (Addison Wesley, 1989).
  10. M. Gen and R. W. Cheng, Genetic Algorithms and Engineering Design, (Addison Wesley, 1997).
  11. W. G. Chen and C. M. Uang, "The design of a reading light system with RGB white light LED by Fresnel lens and evolutionary algorithms," Proc. SPIE 5560,370-379 (2005).
  12. W. G. Chen and C. M. Uang, "Better Reading Light System with light-emitting diodes using optimized Fresnel lens," Opt. Eng. 45, 063001-1-7 (2006).
    [CrossRef]
  13. Lambda Research Corporation, MA, USA, TRACEPRO Reference Manual, Available: http://www.lambdares.com/.
  14. W. G. Chen and C. M. 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).
    [CrossRef] [PubMed]

2007

W.-T. Chien, C. C. Sun, and I. Moreno, "Precise optical modeling of multi-chip white LEDs," Opt. Express. 15, 7572-7577 (2007).
[CrossRef] [PubMed]

2006

2005

W. G. Chen and C. M. Uang, "The design of a reading light system with RGB white light LED by Fresnel lens and evolutionary algorithms," Proc. SPIE 5560,370-379 (2005).

2004

F. Munoz, P. Benitez, O. Dross, J. C. Minano, and B. Parkyn, "Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes," Opt. Eng. 43,1522-1530 (2004).
[CrossRef]

P. Benitez, J. C. Minano, J. Blen, R. Mohendano, J. Chaves, O. Dross, M. Hemandez, and W. Falicoff, "Simultaneous multiple surface optical design," Opt. Eng. 43, 1489-1502 (2004).
[CrossRef]

Appl. Opt.

Opt. Eng.

F. Munoz, P. Benitez, O. Dross, J. C. Minano, and B. Parkyn, "Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes," Opt. Eng. 43,1522-1530 (2004).
[CrossRef]

P. Benitez, J. C. Minano, J. Blen, R. Mohendano, J. Chaves, O. Dross, M. Hemandez, and W. Falicoff, "Simultaneous multiple surface optical design," Opt. Eng. 43, 1489-1502 (2004).
[CrossRef]

W. G. Chen and C. M. Uang, "Better Reading Light System with light-emitting diodes using optimized Fresnel lens," Opt. Eng. 45, 063001-1-7 (2006).
[CrossRef]

Opt. Express.

W.-T. Chien, C. C. Sun, and I. Moreno, "Precise optical modeling of multi-chip white LEDs," Opt. Express. 15, 7572-7577 (2007).
[CrossRef] [PubMed]

Opt. Lett.

Proc. SPIE

W. G. Chen and C. M. Uang, "The design of a reading light system with RGB white light LED by Fresnel lens and evolutionary algorithms," Proc. SPIE 5560,370-379 (2005).

Other

Lambda Research Corporation, MA, USA, TRACEPRO Reference Manual, Available: http://www.lambdares.com/.

T. S. Yu and X. Y. Yang, Introduction to Optical Engineering, Chap. 1-3, 1997.

Reflexite Display Optics, NY , USA. Available: http://www.display-optics.com/.

A. Davis, R. C. Bush, J. C. Harvey and M. F. Foley, "Fresnel lenses in rear projection displays," SID 2001 Digest, Volume XXXII, pp. 934-937, June 2001

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

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

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Figures (18)

Fig. 1.
Fig. 1.

The fixed-length segment division mechanism

Fig. 2.
Fig. 2.

The corresponding genes of the ith gene in the first control layer for the FLSDM.

Fig. 3.
Fig. 3.

The varied-length segment division mechanism.

Fig. 4.
Fig. 4.

The corresponding genes of the ith gene in the first control layer for the VLSDM.

Fig. 5.
Fig. 5.

A cycled loading mechanism.

Fig. 6.
Fig. 6.

A general structure of a chromosome in HGA3L for the case of FLSDM and Nsub_seg =3.

Fig. 7.
Fig. 7.

Part of a chromosome of a special example with FLSDM, Nseg=33, and N sub_seg=3.

Fig. 8.
Fig. 8.

The flow diagram of the proposed HGA3L.

Fig. 9.
Fig. 9.

A simulated reading light system.

Fig. 10.
Fig. 10.

A cone-frustum shaped reflector and an LED light source.

Fig. 11.
Fig. 11.

A reading surface with 5 equal-area rings, 120 equal-area sectors

Fig. 12.
Fig. 12.

Performances and convergence statuses of PAHGA3L_33_FLSD and PAHGA2L_33.

Fig. 13.
Fig. 13.

An irradiance map of a reading light system through FLHGA3L_33_FLSD.

Fig. 14.
Fig. 14.

An irradiance map of a reading light system through FLHGA2L_33.

Fig. 15.
Fig. 15.

(a). The cross section of FLHGA3L_33_FLSD.

Fig. 15.
Fig. 15.

(b). The cross section of PAHGA2L_33

Fig. 16.
Fig. 16.

Performances and convergence statuses of PAHGA3L_33_FLSD and PAHGA3L_33_VLSD compared to PAHGA2L_33.

Fig. 17.
Fig. 17.

An irradiance map through FLHGA3L_33_VLSD up to 2400 generations.

Tables (4)

Tables Icon

Table 1. Distribution of 330 groove angles on 33 segments

Tables Icon

Table 2. Parameters used in HGA3L

Tables Icon

Table 3. Distribution of light rays on the reading surface through FLHGA3L_33_FLSD.

Tables Icon

Table 4. Distribution of light rays on the reading surface through FLHGA2L_33.

Equations (14)

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C i ( 1 : Nseq ) = C i ( 1 : k 1 1 ) + C j ( k 1 : k 2 1 ) + C i ( k 2 : Nseg ) ,
C j ( 1 : Nseg ) = C j ( 1 : k 1 1 ) + C i ( k 1 : k 2 1 ) + C j ( k 2 : Nseg ) .
C i ( x : y ) = C i ( x : x + Nsub _ seg × ( k 1 1 ) 1 ) + C j ( x + Nsub _ seg × ( k 1 1 ) : x + Nsub _ seg × ( k 2 1 ) 1 ) + C i ( x + Nsub _ seg × ( k 2 1 ) : y ) ,
C j ( x : y ) = C j ( x : x + Nsub _ seg × ( k 1 1 ) 1 ) + C j ( x + N sub _ seg × ( k 1 1 ) : x + Nsub _ seg × ( k 2 1 ) 1 ) + C j ( x + Nsub _ seg × ( k 2 1 ) : y )
C i ( 1 : Nseq ) = C j ( 1 : k 1 1 ) + C i ( k 1 : k 2 1 ) + C j ( k 2 : Nseg ) ,
C j ( 1 : Nseg ) = C i ( 1 : k 1 1 ) + C j ( k 1 : k 2 1 ) + C i ( k 2 : Nseg ) ,
C i ( x : y ) = C j ( x : x + Nsub _ seg × ( k 1 1 ) 1 ) + C i ( x + N sub _ seg × ( k 1 1 ) : x + Nsub _ seg × ( k 2 1 ) 1 ) + C j ( x + Nsub _ seg × ( k 2 1 ) : y ) ,
C j ( x : y ) = C i ( x : x + Nsub _ seg × ( k 1 1 ) 1 ) + C j ( x + Nsub _ seg × ( k 1 1 ) : x + Nsub _ seg × ( k 2 1 ) 1 ) + C i ( x + Nsub _ seg × ( k 2 1 ) : y ) .
R d = r = 1 N r s = 1 N s R rs ,
R a = R d N r × N s .
I = G L ,
G = ( R d R c ) × G w ,
L= r = 1 N r s = 1 N s L rs ,
L rs = { ( 1 R a R rs ) × L w for R rs R a ( 1 R rs R a ) × L w otherwise ,

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