We propose a numerical optimization method designing LED array for achieving a good uniform illumination distribution on target plane. Simulated annealing algorithm is employed to optimize LED array arrangement. Using the method, we optimized three LED arrays with various luminous intensity profiles. In order to exhibit the design freedom of the method, we use some LEDs with different intensity value in the first and third array, respectively. By optimizing, the three arrays all produced highly uniform illumination distribution with the uniformity of 0.12, 0.23 and 0.13, respectively. It indicates our method can design various luminous intensity distribution LED arrays and design array consisting of LEDs with different intensity value. In addition, the method is simple and can optimize the LED array automatically by computer program. To the best of our knowledge, it is first time to use numerical optimization method to design the optimal LED array arrangement for uniform irradiance.

© 2012 OSA

1. Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express16(17), 12958–12966 (2008). [CrossRef] [PubMed]
2. K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009). [CrossRef]
3. B. Kim, H. Kim, and S. Kang, “Reverse functional design of discontinuous refractive optics using an extended light source for flat illuminance distributions and high color uniformity,” Opt. Express19(3), 1794–1807 (2011). [CrossRef] [PubMed]
4. Z. X. Feng, Y. Luo, and Y. J. Han, “Design of LED freeform optical system for road lighting with high luminance/illuminance ratio,” Opt. Express18(21), 22020–22031 (2010). [CrossRef] [PubMed]
5. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt.45(10), 2265–2272 (2006). [CrossRef] [PubMed]
6. I. Moreno, J. Muñoz, and R. Ivanov, “Uniform illumination of distant targets using a spherical light-emitting diode array,” Opt. Eng.46(3), 033001 (2007). [CrossRef]
7. H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform illumination rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009). [CrossRef]
8. A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illuminance systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009). [CrossRef]
9. Z. Qin, K. Wang, F. Chen, X. Luo, and S. Liu, “Analysis of condition for uniform lighting generated by array of light emitting diodes with large view angle,” Opt. Express18(16), 17460–17476 (2010). [CrossRef] [PubMed]
10. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys.21(6), 1087–1092 (1953). [CrossRef]
11. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science220(4598), 671–680 (1983). [CrossRef] [PubMed]
12. V. Cerny, “Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm,” J. Optim. Theory Appl.45(1), 41–51 (1985). [CrossRef]
13. Z. Zhenrong, H. Xiang, and L. Xu, “Freeform surface lens for LED uniform illumination,” Appl. Opt.48(35), 6627–6634 (2009). [CrossRef] [PubMed]
14. I. Moreno, “Illumination uniformity assessment based on human vision,” Opt. Lett.35(23), 4030–4032 (2010). [CrossRef] [PubMed]
15. K. Wang, D. Wu, Z. Qin, F. Chen, X. B. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express19(S4Suppl 4), A830–A840 (2011). [CrossRef] [PubMed]
16. P. J. van Laarhoven and E. H. Aarts, “Simulated annealing,” in Simulated Annealing:Theory and Applications.(Kluwer Academic Publishers, Dordrecht,1987)
17. L. Wang, H. Y. Zhang, and X. P. Zheng, “Inter-domain routing based on simulated annealing algorithm in optical mesh networks,” Opt. Express12(14), 3095–3107 (2004). [CrossRef] [PubMed]
18. http://lambdares.com/software_products/tracepro/ .
19. W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express15(12), 7572–7577 (2007). [CrossRef] [PubMed]

Appl. Opt.

• I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt.45(10), 2265–2272 (2006). [CrossRef] [PubMed]
• Z. Zhenrong, H. Xiang, and L. Xu, “Freeform surface lens for LED uniform illumination,” Appl. Opt.48(35), 6627–6634 (2009). [CrossRef] [PubMed]

IEEE Trans. Signal Process.

• H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform illumination rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009). [CrossRef]

J. Chem. Phys.

• N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys.21(6), 1087–1092 (1953). [CrossRef]

J. Disp. Technol.

• A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illuminance systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009). [CrossRef]

J. Opt. A, Pure Appl. Opt.

• K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009). [CrossRef]

J. Optim. Theory Appl.

• V. Cerny, “Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm,” J. Optim. Theory Appl.45(1), 41–51 (1985). [CrossRef]

Opt. Eng.

• I. Moreno, J. Muñoz, and R. Ivanov, “Uniform illumination of distant targets using a spherical light-emitting diode array,” Opt. Eng.46(3), 033001 (2007). [CrossRef]

Opt. Express

• B. Kim, H. Kim, and S. Kang, “Reverse functional design of discontinuous refractive optics using an extended light source for flat illuminance distributions and high color uniformity,” Opt. Express19(3), 1794–1807 (2011). [CrossRef] [PubMed]
• Z. X. Feng, Y. Luo, and Y. J. Han, “Design of LED freeform optical system for road lighting with high luminance/illuminance ratio,” Opt. Express18(21), 22020–22031 (2010). [CrossRef] [PubMed]
• Z. Qin, K. Wang, F. Chen, X. Luo, and S. Liu, “Analysis of condition for uniform lighting generated by array of light emitting diodes with large view angle,” Opt. Express18(16), 17460–17476 (2010). [CrossRef] [PubMed]
• Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express16(17), 12958–12966 (2008). [CrossRef] [PubMed]
• K. Wang, D. Wu, Z. Qin, F. Chen, X. B. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express19(S4Suppl 4), A830–A840 (2011). [CrossRef] [PubMed]
• L. Wang, H. Y. Zhang, and X. P. Zheng, “Inter-domain routing based on simulated annealing algorithm in optical mesh networks,” Opt. Express12(14), 3095–3107 (2004). [CrossRef] [PubMed]
• W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express15(12), 7572–7577 (2007). [CrossRef] [PubMed]

Opt. Lett.

• I. Moreno, “Illumination uniformity assessment based on human vision,” Opt. Lett.35(23), 4030–4032 (2010). [CrossRef] [PubMed]

Science

• S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science220(4598), 671–680 (1983). [CrossRef] [PubMed]

Other

• http://lambdares.com/software_products/tracepro/ .
• P. J. van Laarhoven and E. H. Aarts, “Simulated annealing,” in Simulated Annealing:Theory and Applications.(Kluwer Academic Publishers, Dordrecht,1987)

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