Abstract

An array of spatially distributed light-emitting diodes (LEDs) can produce an illumination pattern that approaches an image by individually modulating each LED. In this letter, I analyze the first-order design of such systems in order to achieve the best match between the illumination distribution and a desired image. In particular, simple formulas are given for the optimal number of LEDs, working distance, array size, and LED beam pattern. The analysis developed here may be applied to the design of LED systems such as architecture lighting, energy-efficient lighting, backlight local dimming for displays, and structured illumination microscopy with micro-LED arrays.

© 2012 Optical Society of America

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References

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  1. E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
    [CrossRef]
  2. D. Caicedo, A. Pandharipande, and G. Leus, Lighting Res. Technol. 43, 217 (2011).
    [CrossRef]
  3. A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
    [CrossRef]
  4. D. Cho, W. S. Oh, and G. W. Moon, J. Disp. Technol. 7, 29 (2011).
    [CrossRef]
  5. F. Li, X. Feng, I. Sezan, and S. Daly, J. Soc. Inf. Display 15, 989 (2007).
    [CrossRef]
  6. N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
    [CrossRef]
  7. I. Moreno, Proc. SPIE 7058, 705811 (2008).
    [CrossRef]
  8. In this letter, the rms difference is a convenient similarity index because of its generality, thus allowing the reported equations to be applied to a wide variety of illumination systems. Indeed, the Δrms could be the best index for applications like structured illumination microscopy, lithography, and energy-efficient illumination.
  9. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, Appl. Opt. 45, 2265 (2006).
    [CrossRef]
  10. I. Moreno and C. C. Sun, Opt. Express 16, 1808 (2008).
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  11. K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, Opt. Express 19, A830 (2011).
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  12. I. Moreno, Opt. Lett. 35, 4030 (2010).
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  14. R. Deepa and S. Arvind, Opt. Express 19, A639 (2011).
    [CrossRef]

2011 (6)

D. Caicedo, A. Pandharipande, and G. Leus, Lighting Res. Technol. 43, 217 (2011).
[CrossRef]

A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
[CrossRef]

D. Cho, W. S. Oh, and G. W. Moon, J. Disp. Technol. 7, 29 (2011).
[CrossRef]

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, Opt. Express 19, A830 (2011).
[CrossRef]

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

R. Deepa and S. Arvind, Opt. Express 19, A639 (2011).
[CrossRef]

2010 (2)

I. Moreno, Opt. Lett. 35, 4030 (2010).
[CrossRef]

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

2008 (2)

2007 (1)

F. Li, X. Feng, I. Sezan, and S. Daly, J. Soc. Inf. Display 15, 989 (2007).
[CrossRef]

2006 (1)

2005 (1)

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Arvind, S.

Avendaño-Alejo, M.

Burrone, J.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Caicedo, D.

D. Caicedo, A. Pandharipande, and G. Leus, Lighting Res. Technol. 43, 217 (2011).
[CrossRef]

A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
[CrossRef]

Chen, F.

Cho, D.

D. Cho, W. S. Oh, and G. W. Moon, J. Disp. Technol. 7, 29 (2011).
[CrossRef]

Daly, S.

F. Li, X. Feng, I. Sezan, and S. Daly, J. Soc. Inf. Display 15, 989 (2007).
[CrossRef]

Dawson, M. D.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Deepa, R.

Degenaar, P.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Dong, J.-T.

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

Drakakis, E. M.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Feng, X.

F. Li, X. Feng, I. Sezan, and S. Daly, J. Soc. Inf. Display 15, 989 (2007).
[CrossRef]

Gong, Z.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Grossman, N.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Grubb, M. S.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Kennedy, G. T.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Kim, J. K.

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Leus, G.

D. Caicedo, A. Pandharipande, and G. Leus, Lighting Res. Technol. 43, 217 (2011).
[CrossRef]

Li, F.

F. Li, X. Feng, I. Sezan, and S. Daly, J. Soc. Inf. Display 15, 989 (2007).
[CrossRef]

Li, Q.

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

Liu, S.

Lu, R.-S.

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

Luo, X.

McGovern, B.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Moon, G. W.

D. Cho, W. S. Oh, and G. W. Moon, J. Disp. Technol. 7, 29 (2011).
[CrossRef]

Moreno, I.

Neil, M. A. A.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Nikolic, K.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Oh, W. S.

D. Cho, W. S. Oh, and G. W. Moon, J. Disp. Technol. 7, 29 (2011).
[CrossRef]

Palmini, R. B.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Pandharipande, A.

A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
[CrossRef]

D. Caicedo, A. Pandharipande, and G. Leus, Lighting Res. Technol. 43, 217 (2011).
[CrossRef]

Poher, V.

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

Qin, Z.

Schubert, E. F.

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Sezan, I.

F. Li, X. Feng, I. Sezan, and S. Daly, J. Soc. Inf. Display 15, 989 (2007).
[CrossRef]

Shi, Y.-Q.

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

Sun, C. C.

Tzonchev, R. I.

Wang, K.

Wu, D.

Xia, R.-X.

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

Xu, Y.

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

Appl. Opt. (1)

Energy Build. (1)

A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
[CrossRef]

J. Disp. Technol. (1)

D. Cho, W. S. Oh, and G. W. Moon, J. Disp. Technol. 7, 29 (2011).
[CrossRef]

J. Neural Eng. (1)

N. Grossman, V. Poher, M. S. Grubb, G. T. Kennedy, K. Nikolic, B. McGovern, R. B. Palmini, Z. Gong, E. M. Drakakis, M. A. A. Neil, M. D. Dawson, J. Burrone, and P. Degenaar, J. Neural Eng. 7, 016004 (2010).
[CrossRef]

J. Soc. Inf. Display (1)

F. Li, X. Feng, I. Sezan, and S. Daly, J. Soc. Inf. Display 15, 989 (2007).
[CrossRef]

Lighting Res. Technol. (1)

D. Caicedo, A. Pandharipande, and G. Leus, Lighting Res. Technol. 43, 217 (2011).
[CrossRef]

Opt. Eng. (1)

J.-T. Dong, R.-S. Lu, Y.-Q. Shi, R.-X. Xia, Q. Li, and Y. Xu, Opt. Eng. 50, 043001 (2011).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

I. Moreno, Proc. SPIE 7058, 705811 (2008).
[CrossRef]

Science (1)

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Other (1)

In this letter, the rms difference is a convenient similarity index because of its generality, thus allowing the reported equations to be applied to a wide variety of illumination systems. Indeed, the Δrms could be the best index for applications like structured illumination microscopy, lithography, and energy-efficient illumination.

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Figures (5)

Fig. 1.
Fig. 1.

LED array producing an image-like illumination by modulating the intensity of each LED. Here s is the working distance, D×D is the array size, and N×N is the number of LEDs. Batman logo is a trademark of DC Comics and is used with permission.

Fig. 2.
Fig. 2.

Concept of optimal working distance. If distance s is too long, the light pattern is blurred; and if it is too short, the pattern becomes a hot-spot distribution. Note that LEDs are modulated with the optimal intensities that require each of these three working distances. Batman logo is a trademark of DC Comics and is used with permission.

Fig. 3.
Fig. 3.

Methodology used to find the optimal relationship between the illumination distance, LED array size, and number of LEDs. In this letter I consider only square grids (Fig. 1).

Fig. 4.
Fig. 4.

Optimal illumination distance in function of the separation between two adjacent LEDs. Shown here are the linear fitting [Eq. (2)], and numerical results using three different target images. Each numerical point is obtained using the method described in Fig. 3 for Lambertian LEDs. Batman logo is a trademark of DC Comics and is used with permission.

Fig. 5.
Fig. 5.

Radiation pattern of an LED with the cosine-power model [10]. Here Θ is the half-width at half-maximum (HWHM) angle.

Equations (6)

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

Δrms=1k1i,jk(PijIijIave)2,
so=34(DN1),
No=round(3D4s)+1,
so=4m+54(DN1).
No=round(4m+54Ds)+1.
Θo=arccos{2[4D2[4s(N1)]25D2]}.

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