Optimal design of an irregular Fresnel lens for multiple light sources using a three-layered Hierarchical Genetic Algorithm

Wen-Gong Chen; Chii-Maw Uang; Chen-Hai Jou

doi:10.1364/OE.15.009918

Optimal design of an irregular Fresnel lens for multiple light sources using a three-layered Hierarchical Genetic Algorithm

Wen-Gong Chen, Chii-Maw Uang, and Chen-Hai Jou

Optics Express
Vol. 15,
Issue 16,
pp. 9918-9935
(2007)
•https://doi.org/10.1364/OE.15.009918

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Wen-Gong Chen, Chii-Maw Uang, and Chen-Hai Jou, "Optimal design of an irregular Fresnel lens for multiple light sources using a three-layered Hierarchical Genetic Algorithm," Opt. Express 15, 9918-9935 (2007)

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Related Topics
Table of Contents Category
- Optical Design and Fabrication
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Lens system design (220.3620)
- Optical data processing (200.4560)
- Ophthalmic optics and devices (330.4460)

About this Article
History
- Original Manuscript: May 9, 2007
- Revised Manuscript: June 24, 2007
- Manuscript Accepted: July 6, 2007
- Published: July 23, 2007
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 2, Iss. 9

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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.

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References

View by:
Article Order
|
Year
|
Author
|
Publication

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
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]
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]
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]
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]
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).
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).
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]
Lambda Research Corporation, MA, USA, TRACEPRO Reference Manual, Available: http://www.lambdares.com/.
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 (1)

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 (4)

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]

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]

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]

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]

2005 (1)

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 (2)

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]

Benitez, P.

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]

Blen, J.

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]

Bush, R. C.

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

Chaves, J.

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]

Chen, W. G.

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]

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).

Cheng, R. W.

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

Chien, W.-T.

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]

Davis, A.

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

Dross, O.

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]

Falicoff, W.

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]

Foley, M. F.

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

Gen, M.

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

Goldberg, D. E.

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

Harvey, J. C.

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

Hemandez, M.

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]

Huang, S.

Huang, S. M

Lee, T. X.

Lee, T.-X.

Lee, Y. L.

Lee, Y.-L.

Ma, S. H.

Ma, S.-H.

Minano, J. C.

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]

Mohendano, R.

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]

Moreno, I.

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]

Munoz, F.

Parkyn, B.

Sun, C. C.

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]

Uang, C. M.

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]

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).

Yang, X. Y.

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

Yu, T. S.

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

Appl. Opt. (1)

Opt. Eng. (3)

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. (1)

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. (2)

Proc. SPIE (1)

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 (6)

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)

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Fig. 15.
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Fig. 16.
Fig. 17.

Fig. 1. The fixed-length segment division mechanism

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Fig. 2. The corresponding genes of the i^th gene in the first control layer for the FLSDM.

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Fig. 3. The varied-length segment division mechanism.

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Fig. 4. The corresponding genes of the i^th gene in the first control layer for the VLSDM.

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Fig. 5. A cycled loading mechanism.

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Fig. 6. A general structure of a chromosome in HGA3L for the case of FLSDM and N_{sub_seg} =3.

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Fig. 7. Part of a chromosome of a special example with FLSDM, N_seg=33, and N _{sub_seg}=3.

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Fig. 8. The flow diagram of the proposed HGA3L.

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Fig. 9. A simulated reading light system.

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Fig. 10. A cone-frustum shaped reflector and an LED light source.

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Fig. 11. A reading surface with 5 equal-area rings, 120 equal-area sectors

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Fig. 12. Performances and convergence statuses of PA_{HGA3L_33_FLSD} and PA_{HGA2L_33}.

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Fig. 13. An irradiance map of a reading light system through FLHGA3L_33_FLSD.

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Fig. 14. An irradiance map of a reading light system through FL_{HGA2L_33}.

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Fig. 15. (a). The cross section of FL_{HGA3L_33_FLSD}.

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Fig. 15. (b). The cross section of PA_{HGA2L_33}

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Fig. 16. Performances and convergence statuses of PA_{HGA3L_33_FLSD} and PA_{HGA3L_33_VLSD} compared to PA_{HGA2L_33}.

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Fig. 17. An irradiance map through FL_{HGA3L_33_VLSD} up to 2400 generations.

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Tables (4)

Table 1. Distribution of 330 groove angles on 33 segments

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Table 2. Parameters used in HGA3L

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Table 3. Distribution of light rays on the reading surface through FL_{HGA3L_33_FLSD}.

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Table 4. Distribution of light rays on the reading surface through FL_{HGA2L_33}.

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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 \times (k_{1} - 1) - 1)} + C_{j (x + Nsub_seg \times (k 1 - 1) : x + Nsub_seg \times (k 2 - 1) - 1)} + C_{i (x + Nsub_seg \times (k 2 - 1) : y),}

C_{j (x : y)}^{'} = C_{j (x : x + Nsub_seg \times (k_{1} - 1) - 1)} + C_{j (x + N sub_seg \times (k 1 - 1) : x + Nsub_seg \times (k 2 - 1) - 1)} + C_{j (x + Nsub_seg \times (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 \times (k_{1} - 1) - 1)} + C_{i (x + N sub_seg \times (k 1 - 1) : x + Nsub_seg \times (k 2 - 1) - 1)} + C_{j (x + Nsub_seg \times (k 2 - 1) : y)},

C_{j (x : y)}^{'} = C_{i (x : x + Nsub_seg \times (k_{1} - 1) - 1)} + C_{j (x + Nsub_seg \times (k 1 - 1) : x + Nsub_seg \times (k 2 - 1) - 1)} + C_{i (x + Nsub_seg \times (k 2 - 1) : y)} .

R_{d} = \sum_{r = 1}^{N_{r}} \sum_{s = 1}^{N_{s}} R_{rs},

R_{a} = \frac{R_{d}}{N_{r} \times N_{s}} .

I = G - L,

G = (R_{d} - R_{c}) \times G_{w},

L= \sum_{r = 1}^{N_{r}} \sum_{s = 1}^{N_{s}} L_{rs},

L_{rs} = {\begin{matrix} (1 - \frac{R_{a}}{R_{rs}}) \times L_{w} & for R_{rs} \geq R_{a} \\ (1 - \frac{R_{rs}}{R_{a}}) \times L_{w} & otherwise \end{matrix},

Segment	Groove angles
1	0.12,0.33,0.53,0.73,0.94,1.14,1.34,1.55,1.75,1.97
2	3.17,3.37,3.57,3.78,3.98, 2.16,2.36,2.56,2.76,2.97
3	4.18,4.38,4.58,4.78,4.99,5.19,5.39,5.59,5.79,5.99
…	…
31	44.84,44.93,45.02,45.10,45.19,45.28,45.37,45.54,45.63,45.71
32	45.80,45.88,45.97,46.05,46.14, 46.22,46.30,46.39,46.47,46.55
33	46.64,46.72,46.80,46.88,46.96,47.04,47.13,47.21,47.29,47.37

Parameters	Value
Population size, N_p	30
Mutation Rates, M_r	0.05
Number of light rays emitted from an LED, N	1000
Number of segments, N_seg	33
Size (number of grooves) of a fixed-length segment, FS_seg	10
Number of equal-area rings of the reading surface, N_r	5
Number of equal-area sectors of a ring, N_s	24
Gain weight of performance index, G_w	10
Loss weight of performance index, L_w	40
Size (number of segments) of composing or decomposing, S_c or S_d	3
Number of sub-segments in a segment, N_sub-seg	3
Number of total groove angles of Fresnel lens database, N_ga	330
Number of total grooves of a designed Fresnel lens, N_tg	330

Segment	Groove angles
1	0.12,0.33,0.53,0.73,0.94,1.14,1.34,1.55,1.75,1.97
2	3.17,3.37,3.57,3.78,3.98, 2.16,2.36,2.56,2.76,2.97
3	4.18,4.38,4.58,4.78,4.99,5.19,5.39,5.59,5.79,5.99
…	…
31	44.84,44.93,45.02,45.10,45.19,45.28,45.37,45.54,45.63,45.71
32	45.80,45.88,45.97,46.05,46.14, 46.22,46.30,46.39,46.47,46.55
33	46.64,46.72,46.80,46.88,46.96,47.04,47.13,47.21,47.29,47.37

Parameters	Value
Population size, N_p	30
Mutation Rates, M_r	0.05
Number of light rays emitted from an LED, N	1000
Number of segments, N_seg	33
Size (number of grooves) of a fixed-length segment, FS_seg	10
Number of equal-area rings of the reading surface, N_r	5
Number of equal-area sectors of a ring, N_s	24
Gain weight of performance index, G_w	10
Loss weight of performance index, L_w	40
Size (number of segments) of composing or decomposing, S_c or S_d	3
Number of sub-segments in a segment, N_sub-seg	3
Number of total groove angles of Fresnel lens database, N_ga	330
Number of total grooves of a designed Fresnel lens, N_tg	330

rs	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	sub	per
0	13	10	7	11	16	7	11	8	12	6	6	7	6	11	10	6	10	17	9	5	6	9	7	11	221	0.0466
1	12	15	11	24	10	9	13	15	13	15	8	10	12	14	8	12	19	20	13	8	13	13	10	13	310	0.0654
2	39	31	28	27	21	28	24	32	26	23	20	18	25	31	25	27	21	25	33	19	32	19	21	23	618	0.1304
3	50	55	42	40	55	46	42	44	45	53	38	35	45	47	46	56	47	44	43	47	48	46	46	44	11 04	0.2330
4	113	98	103	84	102	112	10 7	101	92	93	98	96	116	103	118	105	101	122	110	101	94	110	108	98	24 85	0.5245
total																									47 38	0.9999

s	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	sub	per
0	7	6	5	9	7	8	5	6	6	8	8	7	8	9	12	9	7	11	5	8	7	6	4	9	177	0.0382
1	19	15	8	19	11	7	15	12	8	10	9	13	9	18	3	7	16	13	18	6	15	7	19	15	292	0.0630
2	31	23	22	29	22	26	27	21	18	26	22	17	21	23	27	20	23	19	18	23	32	26	18	25	559	0.1207
3	59	42	55	51	37	56	49	50	65	43	33	41	51	34	40	62	42	38	54	28	59	47	31	43	1110	0.2397
4	93	99	99	79	109	93	108	107	95	107	108	111	116	95	120	112	89	101	99	114	106	124	112	97	2493	0.5383
total																									4631	0.9999

Abstract

References

2007 (1)

2006 (4)

2005 (1)

2004 (2)

Benitez, P.

Blen, J.

Bush, R. C.

Chaves, J.

Chen, W. G.

Cheng, R. W.

Chien, W.-T.

Davis, A.

Dross, O.

Falicoff, W.

Foley, M. F.

Gen, M.

Goldberg, D. E.

Harvey, J. C.

Hemandez, M.

Huang, S.

Huang, S. M

Lee, T. X.

Lee, T.-X.

Lee, Y. L.

Lee, Y.-L.

Ma, S. H.

Ma, S.-H.

Minano, J. C.

Mohendano, R.

Moreno, I.

Munoz, F.

Parkyn, B.

Sun, C. C.

Uang, C. M.

Yang, X. Y.

Yu, T. S.

Appl. Opt. (1)

Opt. Eng. (3)

Opt. Express. (1)

Opt. Lett. (2)

Proc. SPIE (1)

Other (6)

Cited By

Figures (18)

Tables (4)

Equations (14)

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