An LED array with 2N-1 lines and N rows is designed, which consists of red, blue, and far-red LEDs. The red and blue LEDs with N lines and N rows are uniformly and intervally arranged. The central distance between adjacent red and blue LEDs is d. The far-red LEDs are filled in-between every two lines of red and blue LEDs, which results in an array of far-red LEDs with N-1 lines and N rows. The central distance of adjacent far-red LEDs is also d. By using the imperfect Lambertian model, the irradiance distribution of the LED array with N being even and odd is derived in the reference plane, respectively. Also, solving equation of the optimal distance d is presented. Numerical results show that irradiance distributions of the three mixed-color, red, blue, and far-red lights of the LED array are uniform in the reference plane. Ratios of R/B and R/Fr are both relatively uniform in the reference plane. The ratio of R/B in the case of N being even is more uniform than that in the case of N being odd. However, the ratio of R/Fr is opposite.
1. Bula, R. J., R. C. Morrow, T. W. Tibbits, and D. J. Barta, "Light-emitting diodes as a radiation source for plants," Hort Sci., Vol. 26, 203-205, 1991.
2. Chen, J.-Y., J.-Y. Yeh, L.-W. Chen, Y.-G. Li, and C.-C. Wang, "Design and modeling for enhancement of light extraction in light-emitting diodes with archimedean lattice photonic crystals," Progress In Electromagnetics Research B, Vol. 11, 265-279, 2009. doi:10.2528/PIERB08112704
3. Whang, A. J. W., Y. Y. Chen, and Y. T. Teng, "Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays," J. Disp. Technol., Vol. 5, 94-103, 2009. doi:10.1109/JDT.2008.2001865
4. Yang, H., 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 T. Signal Proces., Vol. 57, 1044-1057, 2009. doi:10.1109/TSP.2008.2009269
5. Tan, J., K. Yang, M. Xia, and Y. Yang, "Analysis of uniform illumination system with imperfect Lambertian LEDs," Opt. Appl., Vol. 41, 507-517, 2011.
6. Su, Z., D. Xue, and Z. Ji, "Designing LED array for uniform illumination distribution by simulated annealing algorithm," Opt. Express, Vol. 20, 843-855, 2012. doi:10.1364/OE.20.00A843
7. Moreno, I., M. Avendano-Alejo, and R. I. Tzonchev, "Designing light-emitting diode arrarys for uniform near-field irradiance," Appl. Opt., Vol. 45, 2265-2272, 2006. doi:10.1364/AO.45.002265
8. Zhou, G., J. Zhen, Y. Zhou, X. Chu, and Y. Ni, "Optimal design of LED assembled light source used in the production of greenhouse plant," J. Optoelectron. Laser, Vol. 19, 1319-1323, 2008.
9. Heraut-Bron, V., C. Robin, C. Varlet-Grancher, D. Afif, and A. Guckert, "Light quality (red: far-red ratio): does it affect photosynthetic activity, net CO2 assimilation, and morphology of young white clover leaves?," Cana. J. Botany, Vol. 7, 1425-1431, 1999. doi:10.1139/cjb-77-10-1425
10. Wood, D., Optoelectronic Semiconductor Devices, Prentice Hall, London, 1994.