Abstract

Most of the lighting designs are based on the far-field characteristics of light sources. It is important to know whether the measurement distance is far enough to simulate the light source as a point source. In this paper, we deduce the far-field conditions for surface light sources with continuous luminous area. The relative far-field distance for several typical flat and curved surface light sources, such as the round, rectangular, annular, hemispherical, and semi-cylindrical sources are calculated. Results show that the classical five times rule is not applicable to surface light sources with hemispherical, arc-shaped semi-cylindrical, and narrow annular luminous areas.

© 2013 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. 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]
  3. I. Moreno, C. Y. Tsai, D. Bermudez, and C. C. Sun, “Simple function for intensity distribution from LEDs,” Proc. SPIE 6670, 66700H (2007).
    [CrossRef]
  4. A. Ryer, Light Measurement Handbook (International Light, 1998).
  5. BSI, “Light and lighting-measurement and presentation of photometric data of lamps and luminaries,” BS EN 13032-1:2004 (British Standards Institution, 2005).
  6. CIE 121-1996, “Photometry and goniophotometry of luminaires,” CIE Technical Committee TC2-10 (1996).
  7. SAC, “General requirements for the photometry and goniophotometry of luminaries,” GB/T 9468-2008 (Standard Press of China, 2008).
  8. CIE 127-2007, “Measurement of LEDs,” CIE Technical Committee TC2-45 (2007).
  9. I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 7058, 70580R (2008).
    [CrossRef]
  10. C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. Chien, “Analysis of the far-field region of LEDs,” Opt. Express 17, 13918–13927 (2009).
    [CrossRef]
  11. L. Svilainis and V. Dumbrava, “LED far field pattern approximation performance study,” in Proceedings of the ITI 2007 29th International Conference on Information Technology Interfaces (ITI, 2007), pp. 645–649.
  12. H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16, 21641–21646 (2008).
    [CrossRef]
  13. S. Tryka, “Spherical object in radiation field from a point source,” Opt. Express 12, 512–517 (2004).
    [CrossRef]
  14. V. A. Zverevand and I. Y. Suborova, “Converting the radiation of a flat source into a light tube of cylindrical shape,” J. Opt. Technol. 75, 401–405 (2008).
    [CrossRef]
  15. I. Moreno, C. C. Sun, and R. Ivanov, “Far-field condition for light-emitting diode arrays,” Appl. Opt. 48, 1190–1197 (2009).
    [CrossRef]
  16. I. Moreno, “LED intensity distribution” in International Optical Design Conference (2006), OSA Technical Digest Series (Optical Society of America, 2006), paper TuD6.

2009

2008

2007

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

2006

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

2004

Bergmans, J. W. M.

Bermudez, D.

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

Chien, W. T.

Chien, Y.

Dumbrava, V.

L. Svilainis and V. Dumbrava, “LED far field pattern approximation performance study,” in Proceedings of the ITI 2007 29th International Conference on Information Technology Interfaces (ITI, 2007), pp. 645–649.

Hovila, J.

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]

Hsieh, C. C.

Ikonen, E.

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]

Ivanov, R.

Kärhä, P.

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]

Linnartz, J.-P. M. G.

Manninen, P.

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]

Moreno, I.

C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. Chien, “Analysis of the far-field region of LEDs,” Opt. Express 17, 13918–13927 (2009).
[CrossRef]

I. Moreno, C. C. Sun, and R. Ivanov, “Far-field condition for light-emitting diode arrays,” Appl. Opt. 48, 1190–1197 (2009).
[CrossRef]

I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 7058, 70580R (2008).
[CrossRef]

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

I. Moreno, “LED intensity distribution” in International Optical Design Conference (2006), OSA Technical Digest Series (Optical Society of America, 2006), paper TuD6.

Rietman, R.

Ryer, A.

A. Ryer, Light Measurement Handbook (International Light, 1998).

Schenk, T. C. W.

Suborova, I. Y.

Sun, C. C.

I. Moreno, C. C. Sun, and R. Ivanov, “Far-field condition for light-emitting diode arrays,” Appl. Opt. 48, 1190–1197 (2009).
[CrossRef]

C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. Chien, “Analysis of the far-field region of LEDs,” Opt. Express 17, 13918–13927 (2009).
[CrossRef]

I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 7058, 70580R (2008).
[CrossRef]

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

Svilainis, L.

L. Svilainis and V. Dumbrava, “LED far field pattern approximation performance study,” in Proceedings of the ITI 2007 29th International Conference on Information Technology Interfaces (ITI, 2007), pp. 645–649.

Tryka, S.

Tsai, C. Y.

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

Yang, H.

Young, R.

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

Zverevand, V. A.

Appl. Opt.

J. Opt. Technol.

Opt. Express

Proc. SPIE

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

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

I. Moreno and C. C. Sun, “LED array: where does far-field begin?,” Proc. SPIE 7058, 70580R (2008).
[CrossRef]

Other

I. Moreno, “LED intensity distribution” in International Optical Design Conference (2006), OSA Technical Digest Series (Optical Society of America, 2006), paper TuD6.

A. Ryer, Light Measurement Handbook (International Light, 1998).

BSI, “Light and lighting-measurement and presentation of photometric data of lamps and luminaries,” BS EN 13032-1:2004 (British Standards Institution, 2005).

CIE 121-1996, “Photometry and goniophotometry of luminaires,” CIE Technical Committee TC2-10 (1996).

SAC, “General requirements for the photometry and goniophotometry of luminaries,” GB/T 9468-2008 (Standard Press of China, 2008).

CIE 127-2007, “Measurement of LEDs,” CIE Technical Committee TC2-45 (2007).

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]

L. Svilainis and V. Dumbrava, “LED far field pattern approximation performance study,” in Proceedings of the ITI 2007 29th International Conference on Information Technology Interfaces (ITI, 2007), pp. 645–649.

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Figures (11)

Fig. 1.
Fig. 1.

Geometry for measuring surface light source.

Fig. 2.
Fig. 2.

Schematic diagram of round light source with radius R for far-field distance calculation.

Fig. 3.
Fig. 3.

Schematic diagram of rectangular light source with length a and width b for far-field distance calculation.

Fig. 4.
Fig. 4.

RFFD as a function of rectangular length–width ratio p for a rectangular light source.

Fig. 5.
Fig. 5.

Schematic diagram of circular ring-shaped light source for far-field distance calculation. R1 and R2 are outer and inner radii, respectively.

Fig. 6.
Fig. 6.

RFFD as a function of inner–outer ratio q for a circular ring-shaped light source.

Fig. 7.
Fig. 7.

Schematic diagram of rectangular ring-shaped light source for far-field distance calculation. a, b, a, and b are length and width for outer and inner rectangles, respectively.

Fig. 8.
Fig. 8.

RFFD as a function of inner–outer rectangular length ratio p for different length–width ratio q for a rectangular ring-shaped light source.

Fig. 9.
Fig. 9.

Schematic diagram of hemispherical light source with radius R for far-field distance calculation.

Fig. 10.
Fig. 10.

Schematic diagram of semi-cylindrical light source for far-field distance calculation. R and b are radius and height, respectively.

Fig. 11.
Fig. 11.

RFFD as a function of height–radius ratio k for a semi-cylindrical light source.

Equations (29)

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ΔΦd=LodsAdcosγ·cosα|r⃗|2dAd,
I(d)=ΣdI(d)ds=ΣΔΦdΩdds=L0Σd2cosγcosα|r⃗|2ds=L0Σcosγcos3αds.
I=L0Σcosγds.
Δ=II(d)I.
I(d)=L0d4Σ1|r⃗|4ds.
I=SLo.
I(d)=L0d4Σr(r2+d2)2dθdr=d2d2+R2πR2L0=d2d2+R2I.
Δ=14FR2+1.
I(a,b,d)=L0d4Σr(r2+d2)2dθdr=L0d4·4[0θ00a2cosθr(r2+d2)2drdθ+θ0π20b2sinθr(r2+d2)2drdθ]=2L0d2g(a,b,d),
θo=arctan(b/a),
g(a,b,d)=aa2+4d2arctan(ba2+4d2)+bb2+4d2arccot(b2+4d2a).
Δ=12FR2(1+p2)pg(p,1,FR1+p2).
I=π(R12R22)L0.
I(d)=I1(d)I2(d)=πd4(R12R22)(d2+R12)(d2+R22)L0.
Δ=4FR2q2+4FR2+q2(4FR2+1)(4FR2+q2),
I(d)=I1(d)I2(d)=2d2[g(a,b,d)g(a,b,d)]L0,
Δ=12FR2(1+p2)ppq2[g(p,1,FR1+p2)g(pq,q,FR1+p2)].
I(d)=L0Σcosγcos3αds=4L0R20arccosRdarcsinRdπ2(dsinθcosϕR)·(dRsinθcosϕ)3(R2+d22Rdsinθcosϕ)2sinθdθdϕ.
cosγ=dsinθcosϕRR2+d22Rdsinθcosϕ,
cosα=dRsinθcosϕR2+d22Rdsinθcosϕ.
I=L0Σcosγds=L0·40π20π2R2sin2θcosϕdθdϕ=πR2L0.
Δ=14π0arccos12FRarcsin12FRπ2(2FRsinθcosϕ1)·(2FRsinθcosϕ)3(1+4FR24FRsinθcosϕ)2sinθdθdϕ.
I(d)=L0ΣRcosγcos3αdθdx=4L0R0arccosRddθ0b2(dcosθR)(dRcosθ)3(R2+d2+x22Rdcosθ)2dx=4L0R0arccosRd[arctanb2g(d,θ)2g3(d,θ)+b4g2(d,θ)(b24+g2(d,θ))]·f(d,θ)dθ,
cosγ=dcosθR|r⃗|,
cosα=dRcosθ|r⃗|,
f(d,θ)=(dcosθR)(dRcosθ)3,
g(d,θ)=R2+d22Rdcosθ.
I=L0·40π20b2Rcosθdθdx=2RbL0.
FR=d/(2R)2+b2.

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