OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 3 — Feb. 4, 2008
  • pp: 1808–1819

Modeling the radiation pattern of LEDs

Ivan Moreno and Ching-Cherng Sun  »View Author Affiliations

Optics Express, Vol. 16, Issue 3, pp. 1808-1819 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (920 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Light-emitting diodes (LEDs) come in many varieties and with a wide range of radiation patterns. We propose a general, simple but accurate analytic representation for the radiation pattern of the light emitted from an LED. To accurately render both the angular intensity distribution and the irradiance spatial pattern, a simple phenomenological model takes into account the emitting surfaces (chip, chip array, or phosphor surface), and the light redirected by both the reflecting cup and the encapsulating lens. Mathematically, the pattern is described as the sum of a maximum of two or three Gaussian or cosine-power functions. The resulting equation is widely applicable for any kind of LED of practical interest. We accurately model a wide variety of radiation patterns from several world-class manufacturers.

© 2008 Optical Society of America

OCIS Codes
(120.5630) Instrumentation, measurement, and metrology : Radiometry
(150.2950) Machine vision : Illumination
(220.4830) Optical design and fabrication : Systems design
(230.3670) Optical devices : Light-emitting diodes
(350.4600) Other areas of optics : Optical engineering

ToC Category:
Optical Devices

Original Manuscript: December 3, 2007
Revised Manuscript: January 20, 2008
Manuscript Accepted: January 21, 2008
Published: January 25, 2008

Ivan Moreno and Ching-Cherng Sun, "Modeling the radiation pattern of LEDs," Opt. Express 16, 1808-1819 (2008)

Sort:  Year  |  Journal  |  Reset  


  1. E. F. Schubert, J. K. Kim, "Solid-state light sources getting smart," Science 308, 1274-1278 (2005). [CrossRef] [PubMed]
  2. Y. Narukawa, "White-light LEDs," Opt. Photon. News 15, 24-29 (2004).
  3. A. Zukauskas, M. S. Schur, R. Gaska, Introduction to Solid State Lighting (Wiley-Interscience, NY, 2002).
  4. M. S. Kaminski, K. J. Garcia, M. A. Stevenson, M. Frate, and R. J. Koshel, "Advanced Topics in Source Modeling," Proc. SPIE 4775, 46 (2002). [CrossRef]
  5. H. Zerfhau-Dreihöfer, U. Haack, T. Weber, and D. Wendt, "Light source modeling for automotive lighting devices," Proc. SPIE 4775, 58 (2002). [CrossRef]
  6. M. Jongewaard, "Guide to selecting the appropriate type of light source model," Proc. SPIE 4775, 86-98 (2002). [CrossRef]
  7. W. J. Cassarly, "LED modelling: pros and cons of common methods," Photon. Tech Briefs IIa-2a (April 2002), special supplement to NASA Tech Briefs.
  8. P. Benitez and J. C. Miñano, "The future of illumination design," Opt. Photonics News 18, 20-25 (2007). [CrossRef]
  9. M. W. Siegel and R. D. Stock, "General near-zone light source model and its application to computer-automated reflector design," Opt. Eng. 35, 2661-2679 (1996). [CrossRef]
  10. R. D. Stock and M. W. Siegel, "Orientation invariant light source parameters," Opt. Eng. 35, 2651 (1996). [CrossRef]
  11. I. Ashdown, "Near-field photometry: a new approach," J. Illum. Eng. Soc. 22, 163-180 (1993).
  12. I. Moreno, "Spatial distribution of LED radiation," Proc. SPIE 6342, 634216 (2006). [CrossRef]
  13. P. Manninen, J. Hovila, P. Kärhä, and E. Ikonen, "Method for analysing luminous intensity of light-emitting diodes," Meas. Sci. Technol. 18, 223-229 (2007). [CrossRef]
  14. 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]
  15. W. T. Chien, C. C. Sun, and I. Moreno, "Precise optical model of multi-chip white LEDs," Opt. Express 15, 7572-7577 (2007). [CrossRef] [PubMed]
  16. Application brief AB20-5, "Secondary Optics Design Considerations for SuperFlux LEDs" Philips Lumileds.
  17. E. F. Schubert, J. K. Kim, H. Luo, and J. Q. Xi, "Solid-state lighting—a benevolent technology," Rep. Prog. Phys. 69, 3069-3099 (2006). [CrossRef]
  18. C. C. Sun, C. Y. Lin, T. X. Lee, and T. H. Yang, "Enhancement of light extraction of GaN-based light-emitting diodes with a microstructure array," Opt. Eng. 43, 1700-1701 (2004). [CrossRef]
  19. A. Estrada-Hernandez, L. P. Gonzalez-Galvan, H. Zarate-Hernandez, R. Cardoso, and E. Rosas, "Luminous flux and correlated color temperature determination for LED sources," SPIE 6422, 64220O (2007). [CrossRef]
  20. R. Young, "Measuring light emission from LEDs," SPIE 6355, 63550H (2006). [CrossRef]
  21. C. Daniel and F. S. Wood, Fitting equations to data: computer analysis of multifactor data (2nd ed.), (Wiley, New York, 1999).
  22. L. Fu, R. Leutz, and H. Ries, "Physical modeling of filament light sources," J. Appl. Phys. 100, 103528 (2006). [CrossRef]
  23. J. Arasa, S. Royo, C. Pizarro, and J. Martinez, "Flux spatial emission obtained from technical specifications for a general filament light source," Appl. Opt. 38, 7009-7017 (1999). [CrossRef]
  24. D. R. Jenkins and H. Monch, "Source Imaging Goniometer Method of Light Source Characterization for Accurate Projection System Design," SID Symposium Digest 31, 862-865 (2000). [CrossRef]
  25. S. Preuss, D. Potthoff, T. Preuss, and K. Lischka, "LED encapsulation- a new approach of rear light design," SPIE 6198, 61980I (2006). [CrossRef]
  26. S. C. Allen and A. J. Steckl, "ELiXIR—Solid-State Luminaire With Enhanced Light Extraction by Internal Reflection," J. Display Technol. 3, 155-159 (2007). [CrossRef]
  27. I. Moreno and U. Contreras, "Color distribution of multicolor LED arrays," Opt. Express 15, 3607-3618 (2007). [CrossRef] [PubMed]
  28. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, "Designing light-emitting diode arrays for uniform near-field irradiance," Appl. Opt. 45, 2265-2272 (2006). [CrossRef] [PubMed]
  29. S. Tryka, "Radiative flux from a planar multiple point source within a cylindrical enclosure reaching a coaxial circular plane," Opt. Express 15, 3777-3790 (2007) [CrossRef] [PubMed]
  30. S. Tryka, "Spherical object in radiation field from a point source," Opt. Express 12, 512-517 (2004). [CrossRef] [PubMed]
  31. J. L. Balenzategui and A. Marti, "Design of hemispherical cavities for LED-based illumination devices," Appl. Phys. B 82, 75-80 (2006). [CrossRef]
  32. A. L. Dubovikov, S. S. Repin, and S. N. Natarovskii, "Features of the use of LEDs in artificial-vision systems," J. Opt. Technol. 72, 40-42 (2005). [CrossRef]
  33. T. Matsumoto, N. Inoue, and M. Suzuki, "Optimum arrangement of LEDs in base station of optical wireless LANs," SPIE 6134, 613403 (2006). [CrossRef]
  34. C. G. Lee, C. S. Park, J. H. Kim, and D. H. Kim, "Experimental verification of optical wireless communication link using high-brightness illumination light-emitting diodes," Opt. Eng. 46, 125005 (2007). [CrossRef]
  35. J. M. Kahn and J. R. Barry, "Wireless infrared communications," Proc. IEEE 85, 265-298 (1997). [CrossRef]
  36. D. W. K. Wong and G. Chen, "Illumination design of a white-light-emitting diode wireless transmission system," Opt. Eng. 46, 085002 (2007). [CrossRef]
  37. M. Akanegawa, Y. Tanaka, and M. Nakagawa, "Basic study on traffic information system using LED traffic lights," IEEE Transactions on Intelligent Transportation Systems 2, 197-203 (2001). [CrossRef]
  38. I. Moreno, J. Muñoz, and R. Ivanov, "Uniform illumination of distant targets using a spherical light-emitting diode array," Opt. Eng. 46, 033001 (2007). [CrossRef]
  39. I. Moreno, "Color tunable hybrid lamp: LED-incandescent and LED-fluorescent," SPIE 6422, 64220N (2007). [CrossRef]
  40. Y. Tu, S. Jin, Y. Wang, and L. Dou, "Color uniformity and data simulation in High-Power RGB LED modules using different LED-chips arrays," SPIE 6828, 682816 (2007). [CrossRef]
  41. C. Deller, G. Smith, and J. Franklin, "Colour mixing LEDs with short microsphere doped acrylic rods," Opt. Express 12, 3327-3333 (2004). [CrossRef] [PubMed]
  42. C. A. Deller, J. B. Franklin, and G. B. Smith, "Lighting simulations using smoothed LED profiles compared with measured profiles," SPIE 6337, 63370X (2006). [CrossRef]
  43. M. A. Volkova, S. V. Zlatina, S. N. Natarovskii, O. N. Nemkova, T. F. Selezneva, N. B. Skobeleva, D. N. Frolov, L. M. Kogan, and B. P. Papchenko, "Prospects of using LEDs in the illuminating systems of microscopes," J. Opt. Technol. 72, 186-190 (2005). [CrossRef]
  44. C. Ye, Y. Liu, and F. Yu, "New illumination patterns in microscopes" SPIE 6033, 60330L (2005). [CrossRef]
  45. J. Xu, Z. Xiao, and T. Lin, "The design of microscope field illumination system based on LED" SPIE 6841, 68410U (2007). [CrossRef]
  46. C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, "Brightness management in a direct LED backlight for LCD TVs," J. Soc. Inf. Disp. In press (2007).
  47. G. Harbers, S. J. Bierhuizen, and M. R. Krames, "Performance of high power light emitting diodes in display illumination applications" J. Display Technol. 3, 98-109 (2007). [CrossRef]
  48. J. W. Whang and Y. T. Teng, "Uniform illumination system with desired emitting angle," SID Conf. Rec. Int. Display Res. Conf., 100-103 (2006).
  49. Y. Uchida and T. Taguchi, "Lighting theory and luminous characteristics of white light-emitting diodes," Opt. Eng. 44, 124003 (2005). [CrossRef]
  50. L. Svilainis and V. Dumbrava, "LED Far Field Pattern Approximation Performance Study," Information Technology Interfaces, 2007. ITI 2007. 29th International Conference on, 645-649 (2007).
  51. M. Bennahmias, E. Arik, K. Yu, D. Voloshenko, K. Chua, R. Pradhan, T. Forrester, and T. Jannson, "Modeling of non-Lambertian sources in lighting applications," SPIE 6669, 66691A (2007). [CrossRef]
  52. A. L. Fischer, "LEDs and displays: Analytical method for computing color patterns in LEDs," Photonics Spectra 41, 87-88 (June 2007).
  53. K. Man and I. Ashdown, "Accurate colorimetric feedback for RGB LED clusters," SPIE 6337, 633702 (2006). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1. Fig. 2. Fig. 3.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited