Abstract

Light-emitting diodes (LEDs) will play a major role in future indoor illumination systems. In general, the generalized Lambertian pattern is widely used as the radiation pattern of a single LED. In this letter, we show that the illuminance distribution due to this Lambertian pattern, when projected onto a horizontal surface such as a floor, can be well approximated by a Gaussian function.

© 2008 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Modeling the radiation pattern of LEDs

Ivan Moreno and Ching-Cherng Sun
Opt. Express 16(3) 1808-1819 (2008)

Exploring the effect of diffuse reflection on indoor localization systems based on RSSI-VLC

Nazmi A. Mohammed and Mohammed Abd Elkarim
Opt. Express 23(16) 20297-20313 (2015)

Evolutionary algorithm based uniform received power and illumination rendering for indoor visible light communication

Jupeng Ding, Zhitong Huang, and Yuefeng Ji
J. Opt. Soc. Am. A 29(6) 971-979 (2012)

References

  • View by:
  • |
  • |
  • |

  1. Lumileds, “LUXEON Power LEDs”, http://www.lumileds.com/products/luxeon/.
  2. J. M. Kahn and J. R. Barry, “Wireless Infrared Communications” Proc. IEEE,  85, 265–298 (1997).
    [Crossref]
  3. I. Moreno, C.-Y. Tsai, D. Bermũdez, and C.-C. Sun, “Simple function for intensity distribution from LEDs”, Proc. SPIE,  6670, 66700H-66700H-7 (2007).
    [Crossref]
  4. I. Moreno and U. Contreras, “Color distribution from multicolor LED arrays”, Opt. Express 15, 3607–3618 (2007).
    [Crossref] [PubMed]
  5. L. Svilainis and V. Dumbrava, “LED Far Field Pattern Approximation Performance Study”, in Prof. Int. Conf. on Information Technology Interfaces (2007), pp. 645–649.
    [Crossref]
  6. Lumileds, “LUXEON LED Radiation Patterns:Light Distribution Patterns,” http://www.lumileds.com/technology/radiationpatterns.cfm.
  7. R. Otte, L. P. de Jong, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999), Chap. 3.
  8. Lumileds, “LUXEON for Flashlight Applications,” http://www.lumileds.com/pdfs/DR02.PDF.
  9. Faren Srl, “FHS Lens Series,” http://www.fraen.com/pdf/FHS Lens Series Datasheet.pdf.
  10. Marubeni, “Fully Sealable APOLLO Lens for LUXEON,” http://www.led-spot.com/data/APOLLO.pdf.
  11. 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,” to appear in IEEE Trans. Signal Processing, 2009.
  12. P. R. Boyce, Human Factors in Lighting, Second Edition (Taylar & Francis Inc, 2003).
    [Crossref]
  13. V. Jungnickel, V. Pohl, S. Nönnig, and C. V. Helmolt, “A Physical Model of theWireless Infrared Communication Channel,” IEEE J. Select. Areas Commun. 20, 631–640 (2002).
    [Crossref]

2007 (2)

I. Moreno, C.-Y. Tsai, D. Bermũdez, and C.-C. Sun, “Simple function for intensity distribution from LEDs”, Proc. SPIE,  6670, 66700H-66700H-7 (2007).
[Crossref]

I. Moreno and U. Contreras, “Color distribution from multicolor LED arrays”, Opt. Express 15, 3607–3618 (2007).
[Crossref] [PubMed]

2002 (1)

V. Jungnickel, V. Pohl, S. Nönnig, and C. V. Helmolt, “A Physical Model of theWireless Infrared Communication Channel,” IEEE J. Select. Areas Commun. 20, 631–640 (2002).
[Crossref]

1997 (1)

J. M. Kahn and J. R. Barry, “Wireless Infrared Communications” Proc. IEEE,  85, 265–298 (1997).
[Crossref]

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless Infrared Communications” Proc. IEEE,  85, 265–298 (1997).
[Crossref]

Bergmans, J. W. M.

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,” to appear in IEEE Trans. Signal Processing, 2009.

Bermudez, D.

I. Moreno, C.-Y. Tsai, D. Bermũdez, and C.-C. Sun, “Simple function for intensity distribution from LEDs”, Proc. SPIE,  6670, 66700H-66700H-7 (2007).
[Crossref]

Boyce, P. R.

P. R. Boyce, Human Factors in Lighting, Second Edition (Taylar & Francis Inc, 2003).
[Crossref]

Contreras, U.

de Jong, L. P.

R. Otte, L. P. de Jong, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999), Chap. 3.

Dumbrava, V.

L. Svilainis and V. Dumbrava, “LED Far Field Pattern Approximation Performance Study”, in Prof. Int. Conf. on Information Technology Interfaces (2007), pp. 645–649.
[Crossref]

Faren Srl,

Faren Srl, “FHS Lens Series,” http://www.fraen.com/pdf/FHS Lens Series Datasheet.pdf.

Helmolt, C. V.

V. Jungnickel, V. Pohl, S. Nönnig, and C. V. Helmolt, “A Physical Model of theWireless Infrared Communication Channel,” IEEE J. Select. Areas Commun. 20, 631–640 (2002).
[Crossref]

Jungnickel, V.

V. Jungnickel, V. Pohl, S. Nönnig, and C. V. Helmolt, “A Physical Model of theWireless Infrared Communication Channel,” IEEE J. Select. Areas Commun. 20, 631–640 (2002).
[Crossref]

Kahn, J. M.

J. M. Kahn and J. R. Barry, “Wireless Infrared Communications” Proc. IEEE,  85, 265–298 (1997).
[Crossref]

Linnartz, J. P. M. G.

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,” to appear in IEEE Trans. Signal Processing, 2009.

Lumileds,

Lumileds, “LUXEON Power LEDs”, http://www.lumileds.com/products/luxeon/.

Lumileds, “LUXEON LED Radiation Patterns:Light Distribution Patterns,” http://www.lumileds.com/technology/radiationpatterns.cfm.

Marubeni,

Marubeni, “Fully Sealable APOLLO Lens for LUXEON,” http://www.led-spot.com/data/APOLLO.pdf.

Moreno, I.

I. Moreno and U. Contreras, “Color distribution from multicolor LED arrays”, Opt. Express 15, 3607–3618 (2007).
[Crossref] [PubMed]

I. Moreno, C.-Y. Tsai, D. Bermũdez, and C.-C. Sun, “Simple function for intensity distribution from LEDs”, Proc. SPIE,  6670, 66700H-66700H-7 (2007).
[Crossref]

Nönnig, S.

V. Jungnickel, V. Pohl, S. Nönnig, and C. V. Helmolt, “A Physical Model of theWireless Infrared Communication Channel,” IEEE J. Select. Areas Commun. 20, 631–640 (2002).
[Crossref]

Otte, R.

R. Otte, L. P. de Jong, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999), Chap. 3.

Pohl, V.

V. Jungnickel, V. Pohl, S. Nönnig, and C. V. Helmolt, “A Physical Model of theWireless Infrared Communication Channel,” IEEE J. Select. Areas Commun. 20, 631–640 (2002).
[Crossref]

Rietman, R.

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,” to appear in IEEE Trans. Signal Processing, 2009.

Schenk, T. C. W.

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,” to appear in IEEE Trans. Signal Processing, 2009.

Sun, C.-C.

I. Moreno, C.-Y. Tsai, D. Bermũdez, and C.-C. Sun, “Simple function for intensity distribution from LEDs”, Proc. SPIE,  6670, 66700H-66700H-7 (2007).
[Crossref]

Svilainis, L.

L. Svilainis and V. Dumbrava, “LED Far Field Pattern Approximation Performance Study”, in Prof. Int. Conf. on Information Technology Interfaces (2007), pp. 645–649.
[Crossref]

Tsai, C.-Y.

I. Moreno, C.-Y. Tsai, D. Bermũdez, and C.-C. Sun, “Simple function for intensity distribution from LEDs”, Proc. SPIE,  6670, 66700H-66700H-7 (2007).
[Crossref]

van Roermund, A. H. M.

R. Otte, L. P. de Jong, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999), Chap. 3.

Yang, H.

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,” to appear in IEEE Trans. Signal Processing, 2009.

IEEE J. Select. Areas Commun. (1)

V. Jungnickel, V. Pohl, S. Nönnig, and C. V. Helmolt, “A Physical Model of theWireless Infrared Communication Channel,” IEEE J. Select. Areas Commun. 20, 631–640 (2002).
[Crossref]

Opt. Express (1)

Proc. IEEE (1)

J. M. Kahn and J. R. Barry, “Wireless Infrared Communications” Proc. IEEE,  85, 265–298 (1997).
[Crossref]

Proc. SPIE (1)

I. Moreno, C.-Y. Tsai, D. Bermũdez, and C.-C. Sun, “Simple function for intensity distribution from LEDs”, Proc. SPIE,  6670, 66700H-66700H-7 (2007).
[Crossref]

Other (9)

Lumileds, “LUXEON Power LEDs”, http://www.lumileds.com/products/luxeon/.

L. Svilainis and V. Dumbrava, “LED Far Field Pattern Approximation Performance Study”, in Prof. Int. Conf. on Information Technology Interfaces (2007), pp. 645–649.
[Crossref]

Lumileds, “LUXEON LED Radiation Patterns:Light Distribution Patterns,” http://www.lumileds.com/technology/radiationpatterns.cfm.

R. Otte, L. P. de Jong, and A. H. M. van Roermund, Low-Power Wireless Infrared Communications (Kluwer Academic Publishers, 1999), Chap. 3.

Lumileds, “LUXEON for Flashlight Applications,” http://www.lumileds.com/pdfs/DR02.PDF.

Faren Srl, “FHS Lens Series,” http://www.fraen.com/pdf/FHS Lens Series Datasheet.pdf.

Marubeni, “Fully Sealable APOLLO Lens for LUXEON,” http://www.led-spot.com/data/APOLLO.pdf.

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,” to appear in IEEE Trans. Signal Processing, 2009.

P. R. Boyce, Human Factors in Lighting, Second Edition (Taylar & Francis Inc, 2003).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

LOS path geometry between an LED and a flat surface.

Fig. 2.
Fig. 2.

The illuminance distribution at h=3 meter due to a single LED.

Fig. 3.
Fig. 3.

The numerical values of the Fourier transforms, FL(u,v), Fg(u,v) and g(u,v), as function of u, at h=3 meter, and v=0.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

f L ( d ) = m + 1 2 π f 0 cos m ( θ ) cos ( θ ) r 2 = ( m + 1 ) f 0 2 π h 2 ( 1 + d 2 h 2 ) m + 3 2 ,
F L ( u , v ) = { ( 2 ) m 2 f 0 h m + 1 ( m 1 ) ! ! ( ξ ) m 2 [ 1 ξ exp ( 2 π ξ u 2 + v 2 ) ] ξ = h 2 , if m is even ( 2 ) ( m + 1 ) 2 f 0 h m + 1 ( m 1 ) ! ! ( ξ ) ( m + 1 ) 2 [ K 0 ( 2 π ξ u 2 + v 2 ) ] ξ = h 2 , if m is odd
f L ( d ) = ( m + 1 ) f 0 2 π h 2 ( m + 3 2 ) ( 1 + d 2 h 2 ) m + 5 2 2 d h 2 = ( m + 3 ) d d 2 + h 2 f L ( d ) .
f L ( d ) ( m + 3 ) d h 2 f L ( d ) d · f L ( d ) ,
Δ f L ( d ) = m + 3 h 2 d 3 d 2 + h 2 f L ( d ) .
f g ( d ) = 2 d σ 2 f g ( d ) .
f g ( d ) = ( m + 1 ) f 0 2 π h 2 exp { m + 3 2 · d 2 h 2 } .
m + 3 2 ln ( 1 + d 2 h 2 ) = m + 3 2 d 2 h 2 + m + 3 2 ( 1 2 d 4 h 4 1 3 d 6 h 6 + B ( d 8 h 8 ) ) .
f ̂ g ( d ) = ( m + 1 ) f 0 2 π h 2 exp { m 2 · d 2 h 2 } ,

Metrics