Abstract

In practice, any cluster of light-emitting diodes (LEDs) can be modeled or measured as a directional point source if the detector is far enough away from the cluster. We propose a far-zone condition for measuring or modeling propagation of light from an LED array. An equation gives the far-field distance as a function of the LED radiation pattern, array geometry, and number of LEDs. The far field is shorter for high packaging density clusters, and the far field considerably increases with increasing beam directionality of LEDs. In contrast with the classical rule of thumb (5 times the source size), the near zone of an array with highly directional LEDs can extend to more than 60 times the array size. We also analyze the effect of introducing random variations of light flux among LEDs of the array, which shows that far-field variability is low in high packaging density arrays.

© 2009 Optical Society of America

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References

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  1. R. Young, “Measuring light emission from LEDs,” Proc. SPIE 6355, 63550H (2006).
    [CrossRef]
  2. G. Sauter and J. Schuette, “Measurement of the optical properties of LED clusters and arrays,” CIE Technical Committee TC2-50, Germany (to be published).
  3. IESNA, Photometric Testing of Indoor Fluorescent Luminaires, IES LM-41-1985 (Illuminating Engineering Society of North America, 1985).
  4. IEEE 100 The Authoritative Dictionary of IEEE Standards Terms, 7th ed. (IEEE, 2000).
  5. A. Ryer, “Light measurement handbook,” http://www.intl-light.com/handbook/ (1998).
  6. I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 705870580R (2008).
    [CrossRef]
  7. E. F. Zalewski, “Radiometry and photometry,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. II.
  8. P. Manninen, J. Hovalita, P. Karha, and E. Ikonen, “Method for analyzing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18, 223-229 (2007).
    [CrossRef]
  9. In a forthcoming paper we address the issue of far field for a single LED.
  10. I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16, 1808-1819 (2008).
    [CrossRef] [PubMed]
  11. L. Svilainis, “LED directivity measurement in situ,” Measurement 41, 647-654 (2008).
    [CrossRef]
  12. M. Burmen, F. Pernus, and B. Likar, “Automated optical quality inspection of light emitting diodes,” Meas. Sci. Technol. 17, 1372-1378 (2006).
    [CrossRef]
  13. M. Bürmen, F. Pernuš, and B. Likar, “LED light sources: a survey of quality-affecting factors and methods for their assessment,” Meas. Sci. Technol. 19, 122002 (2008).
    [CrossRef]
  14. S. H. Jang and M. W. Shin, “Thermal analysis of LED arrays for automotive headlamp with a novel cooling system,” IEEE Trans. Device Mater. Reliab. 8, 561-564 (2008).
    [CrossRef]
  15. “Cree XLamp LED binning and labeling,” Application Note CLD-AP12.007, http://www.cree.com/Products/xlamp7090_xre.asp.

2008 (5)

I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 705870580R (2008).
[CrossRef]

I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16, 1808-1819 (2008).
[CrossRef] [PubMed]

L. Svilainis, “LED directivity measurement in situ,” Measurement 41, 647-654 (2008).
[CrossRef]

M. Bürmen, F. Pernuš, and B. Likar, “LED light sources: a survey of quality-affecting factors and methods for their assessment,” Meas. Sci. Technol. 19, 122002 (2008).
[CrossRef]

S. H. Jang and M. W. Shin, “Thermal analysis of LED arrays for automotive headlamp with a novel cooling system,” IEEE Trans. Device Mater. Reliab. 8, 561-564 (2008).
[CrossRef]

2007 (1)

P. Manninen, J. Hovalita, P. Karha, and E. Ikonen, “Method for analyzing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18, 223-229 (2007).
[CrossRef]

2006 (2)

M. Burmen, F. Pernus, and B. Likar, “Automated optical quality inspection of light emitting diodes,” Meas. Sci. Technol. 17, 1372-1378 (2006).
[CrossRef]

R. Young, “Measuring light emission from LEDs,” Proc. SPIE 6355, 63550H (2006).
[CrossRef]

Burmen, M.

M. Burmen, F. Pernus, and B. Likar, “Automated optical quality inspection of light emitting diodes,” Meas. Sci. Technol. 17, 1372-1378 (2006).
[CrossRef]

Bürmen, M.

M. Bürmen, F. Pernuš, and B. Likar, “LED light sources: a survey of quality-affecting factors and methods for their assessment,” Meas. Sci. Technol. 19, 122002 (2008).
[CrossRef]

Hovalita, J.

P. Manninen, J. Hovalita, P. Karha, and E. Ikonen, “Method for analyzing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18, 223-229 (2007).
[CrossRef]

Ikonen, E.

P. Manninen, J. Hovalita, P. Karha, and E. Ikonen, “Method for analyzing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18, 223-229 (2007).
[CrossRef]

Jang, S. H.

S. H. Jang and M. W. Shin, “Thermal analysis of LED arrays for automotive headlamp with a novel cooling system,” IEEE Trans. Device Mater. Reliab. 8, 561-564 (2008).
[CrossRef]

Karha, P.

P. Manninen, J. Hovalita, P. Karha, and E. Ikonen, “Method for analyzing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18, 223-229 (2007).
[CrossRef]

Likar, B.

M. Bürmen, F. Pernuš, and B. Likar, “LED light sources: a survey of quality-affecting factors and methods for their assessment,” Meas. Sci. Technol. 19, 122002 (2008).
[CrossRef]

M. Burmen, F. Pernus, and B. Likar, “Automated optical quality inspection of light emitting diodes,” Meas. Sci. Technol. 17, 1372-1378 (2006).
[CrossRef]

Manninen, P.

P. Manninen, J. Hovalita, P. Karha, and E. Ikonen, “Method for analyzing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18, 223-229 (2007).
[CrossRef]

Moreno, I.

I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 705870580R (2008).
[CrossRef]

I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16, 1808-1819 (2008).
[CrossRef] [PubMed]

Pernus, F.

M. Burmen, F. Pernus, and B. Likar, “Automated optical quality inspection of light emitting diodes,” Meas. Sci. Technol. 17, 1372-1378 (2006).
[CrossRef]

Pernuš, F.

M. Bürmen, F. Pernuš, and B. Likar, “LED light sources: a survey of quality-affecting factors and methods for their assessment,” Meas. Sci. Technol. 19, 122002 (2008).
[CrossRef]

Ryer, A.

A. Ryer, “Light measurement handbook,” http://www.intl-light.com/handbook/ (1998).

Shin, M. W.

S. H. Jang and M. W. Shin, “Thermal analysis of LED arrays for automotive headlamp with a novel cooling system,” IEEE Trans. Device Mater. Reliab. 8, 561-564 (2008).
[CrossRef]

Sun, C. C.

I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 705870580R (2008).
[CrossRef]

I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16, 1808-1819 (2008).
[CrossRef] [PubMed]

Svilainis, L.

L. Svilainis, “LED directivity measurement in situ,” Measurement 41, 647-654 (2008).
[CrossRef]

Young, R.

R. Young, “Measuring light emission from LEDs,” Proc. SPIE 6355, 63550H (2006).
[CrossRef]

Zalewski, E. F.

E. F. Zalewski, “Radiometry and photometry,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. II.

IEEE Trans. Device Mater. Reliab. (1)

S. H. Jang and M. W. Shin, “Thermal analysis of LED arrays for automotive headlamp with a novel cooling system,” IEEE Trans. Device Mater. Reliab. 8, 561-564 (2008).
[CrossRef]

Meas. Sci. Technol. (3)

M. Burmen, F. Pernus, and B. Likar, “Automated optical quality inspection of light emitting diodes,” Meas. Sci. Technol. 17, 1372-1378 (2006).
[CrossRef]

M. Bürmen, F. Pernuš, and B. Likar, “LED light sources: a survey of quality-affecting factors and methods for their assessment,” Meas. Sci. Technol. 19, 122002 (2008).
[CrossRef]

P. Manninen, J. Hovalita, P. Karha, and E. Ikonen, “Method for analyzing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18, 223-229 (2007).
[CrossRef]

Measurement (1)

L. Svilainis, “LED directivity measurement in situ,” Measurement 41, 647-654 (2008).
[CrossRef]

Opt. Express (1)

Proc. SPIE (2)

I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 705870580R (2008).
[CrossRef]

R. Young, “Measuring light emission from LEDs,” Proc. SPIE 6355, 63550H (2006).
[CrossRef]

Other (7)

G. Sauter and J. Schuette, “Measurement of the optical properties of LED clusters and arrays,” CIE Technical Committee TC2-50, Germany (to be published).

IESNA, Photometric Testing of Indoor Fluorescent Luminaires, IES LM-41-1985 (Illuminating Engineering Society of North America, 1985).

IEEE 100 The Authoritative Dictionary of IEEE Standards Terms, 7th ed. (IEEE, 2000).

A. Ryer, “Light measurement handbook,” http://www.intl-light.com/handbook/ (1998).

E. F. Zalewski, “Radiometry and photometry,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. II.

In a forthcoming paper we address the issue of far field for a single LED.

“Cree XLamp LED binning and labeling,” Application Note CLD-AP12.007, http://www.cree.com/Products/xlamp7090_xre.asp.

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Figures (10)

Fig. 1
Fig. 1

There are two working conditions for the optical modeling and experimental characterization of an LED array: near field and far field.

Fig. 2
Fig. 2

(a) Geometry used in the on-axis definition of the far field condition for an LED cluster, i.e., Eq. (1). (b) The polar coordinates ( r , θ , ϕ ) that describe the direction of optical radiation emanating from the LED array.

Fig. 3
Fig. 3

(a) Far-field condition as a function of the view angle θ (for ϕ = 0 ) in a square 2 × 2 array for the radiation patterns shown in (b). The far-zone condition is normalized to the array size D, i.e., r min / D . The dashed line indicates the far- field condition for a uniform circular Lambertian source with diameter D.

Fig. 4
Fig. 4

Geometry for definition of flux transfer from a flat source to a detector. Here n s and n d are unitary vectors that are normal to the source and detector surfaces, respectively.

Fig. 5
Fig. 5

Geometry for coordinates used in Eqs. (7, 8, 9).

Fig. 6
Fig. 6

Far-field condition as a function of the number of LEDs in a square array. The condition is plotted for LEDs with Lambertian, batwing, and side emission radiation patterns. A low packaging density 2 × 2 array to a 10 × 10 LED array are shown. Lines are for indication only.

Fig. 7
Fig. 7

Far-field condition as a function of the number of LEDs in a triangular array. Arrays with 3, 7, 22, 45, 76, and 115 LEDs are shown. The condition is plotted for LEDs with Lambertian, batwing, and side emission radiation patterns. Lines are for indication only.

Fig. 8
Fig. 8

Far-field condition for several LED radiation patterns. Selected values for square arrays with 2 × 2 and 10 × 10 LEDs are shown.

Fig. 9
Fig. 9

Far-field condition of a square array with directional LEDs for several half-angles β 1 / 2 . Lines are for indication only.

Fig. 10
Fig. 10

Far-field condition for square arrays with random variations of light flux among LEDs of every array. LED fluxes of each array are randomly created. (a) LEDs have a directional radiation pattern with β 1 / 2 = 10 ° . (b) LEDs are Cree XLamp XR-E white LEDs (group code M2).

Equations (14)

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i N I ( α i ( r ) ) i cos 3 [ α i ( r ) ] i N I ( 0 ) i = ( 1 Δ ) ,
α i ( r ) = arctan [ x i 2 + y i 2 r ] .
Δ Φ d = L cos α s cos α d | r d r s | 2 d A s d A d ,
Δ Φ d ( r ) = A d L ( r s , r ) cos α s cos α d | r r s | 2 d A s ,
I ( r , θ , ϕ ) = { L ( x , y , θ , ϕ ) [ 1 ( x cos ϕ + y sin ϕ ) sin θ r ] [ 1 2 ( x cos ϕ + y sin ϕ ) sin θ r + x 2 + y 2 r 2 ] 2 d x d y } cos θ .
I ( θ , ϕ ) = [ L ( x , y , θ , ϕ ) d x d y ] cos θ .
I ( r , θ , ϕ ) = i N [ 1 ( x i cos ϕ + y i sin ϕ ) sin θ r ] [ 1 2 ( x i cos ϕ + y i sin ϕ ) sin θ r + x i 2 + y i 2 r 2 ] 3 / 2 I ( α i , β i ) i ,
cos α i = [ 1 2 ( x i cos ϕ + y i sin ϕ ) sin θ r + x i 2 + y i 2 r 2 ] 1 / 2     cos θ ,
cos β i = ( cos ϕ sin θ x i r ) [ sin 2 θ 2 ( x i cos ϕ + y i sin ϕ ) sin θ r + x i 2 + y i 2 r 2 ] 1 / 2 .
I ( θ , ϕ ) = i N I ( θ , ϕ ) i .
1 M + 1 m = 0 M I ( θ m , ϕ m ) I max [ I ( r , θ m , ϕ m ) I ( θ m , ϕ m ) 1 ] 2 = Δ RMS .
m = 0 M I ( θ m ) 0 [ I ( r , θ m ) N I ( θ m ) 0 1 ] 2 = ( M + 1 ) Δ RMS 2 ,
I ( r , θ m ) = i N I ( α i ) 0 [ 1 x i sin θ m r ] [ 1 2 x i sin θ m r + x i 2 + y i 2 r 2 ] 3 / 2 ,
α i = arccos { [ 1 2 x i sin θ m r + x i 2 + y i 2 r 2 ] 1 / 2 cos θ m } .

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