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

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References

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  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. Berm˜udez 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. Nonnig and C. V. Helmolt, "A Physical Model of theWireless Infrared Communication Channel," IEEE J. Select. Areas Commun. 20, 631-640 (2002).
    [CrossRef]

2007 (1)

2002 (1)

V. Jungnickel, V. Pohl, S. Nonnig 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]

Contreras, U.

Helmolt, C. V.

V. Jungnickel, V. Pohl, S. Nonnig 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. Nonnig 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]

Moreno, I.

Nonnig, S.

V. Jungnickel, V. Pohl, S. Nonnig and C. V. Helmolt, "A Physical Model of theWireless Infrared Communication Channel," IEEE J. Select. Areas Commun. 20, 631-640 (2002).
[CrossRef]

Pohl, V.

V. Jungnickel, V. Pohl, S. Nonnig and C. V. Helmolt, "A Physical Model of theWireless Infrared Communication Channel," IEEE J. Select. Areas Commun. 20, 631-640 (2002).
[CrossRef]

IEEE J. Select. Areas Commun. (1)

V. Jungnickel, V. Pohl, S. Nonnig 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]

Other (10)

I. Moreno, C.-Y. Tsai, D. Berm˜udez and C.-C. Sun, "Simple function for intensity distribution from LEDs," Proc. SPIE 6670, 66700H-66700H-7 (2007).
[CrossRef]

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]

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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)

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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 } ,

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