Abstract

A lighting cavity is a reflecting box with light sources inside. Its exit side is covered with a diffuser plate to mix and distribute light, which addresses a key issue of luminaires, display backlights, and other illumination systems. We derive a simple but precise formula for the optical efficiency of diffuser plates attached to a light cavity. We overcome the complexity of the scattering theory and the difficulty of the multiple calculations involved, by carrying out the calculation with a single ray of light that statistically represents all the scattered rays. We constructed and tested several optical cavities using light-emitting diodes, bulk-scattering diffusers, white scatter sheets, and silver coatings. All measurements are in good agreement with predictions from our optical model.

© 2010 OSA

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References

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  1. J. J. Vos, “On the cause of disability glare and its dependence on glare angle, age and ocular pigmentation,” Clin. Exp. Optom. 86(6), 363–370 (2003).
    [CrossRef] [PubMed]
  2. T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
    [CrossRef]
  3. J. A. Wheatley, G. J. Benoit, J. E. Anderson, R. W. Biernath, D. G. Freier, T. R. Hoffend, C. D. Hoyle, T. T. Liu, J. D. Lu, M. A. Meis, V. V. Savvateev, C. R. Schardt, M. E. Sousa, M. F. Weber, and T. J. Nevitt, “Efficient LED light distribution cavities using low loss, angle-selective interference transflectors,” Opt. Express 17(13), 10612–10622 (2009).
    [CrossRef] [PubMed]
  4. A. Travis, T. Large, N. Emerton, and S. Bathiche, “Collimated light from a waveguide for a display backlight,” Opt. Express 17(22), 19714–19719 (2009).
    [CrossRef] [PubMed]
  5. I. Moreno, “Creating a desired lighting pattern with an LED array,” Proc. SPIE 7058, 705811 (2008).
    [CrossRef]
  6. C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16(4), 519 (2008).
    [CrossRef]
  7. M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
    [CrossRef]
  8. H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
    [CrossRef]
  9. M. Gebauer, P. Benoit, P. Knoll, and M. Neiger, “P-9: Ray Tracing Tool for Developing LCD-Backlights” SID Symposium Digest of Technical Papers–May 2000–Volume 31, Issue 1, pp. 558-561
  10. C. H. Tien and C. H. Hung, “An iterative model of diffuse illumination from bidirectional photometric data,” Opt. Express 17(2), 723–732 (2009).
    [CrossRef] [PubMed]
  11. D. Voigt, I. A. Hagendoorn, and E. W. M. van der Ham, “Compact large-area uniform colour-selectable calibration light source,” Metrologia 46(4), S243–S247 (2009).
    [CrossRef]
  12. M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. J. Sant, and J. C. Dainty, “Light transmission from a randomly rough dielectric diffuser: theoretical and experimental results,” Opt. Lett. 15(22), 1261–1263 (1990).
    [CrossRef] [PubMed]
  13. P. Manninen, P. Kärhä, and E. Ikonen, “Determining the irradiance signal from an asymmetric source with directional detectors: application to calibrations of radiometers with diffusers,” Appl. Opt. 47(26), 4714–4722 (2008).
    [CrossRef] [PubMed]
  14. P. Manninen, “Characterization of diffusers and light-emitting diodes using radiometric measurements and mathematical modeling,” Doctoral Dissertation Thesis, Helsinki University of Technology, Finland (2008).
  15. B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
    [CrossRef]
  16. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
    [CrossRef] [PubMed]
  17. Labsphere, Inc., A Guide to Integrating Sphere Theory and Applications, at http://www.labsphere.com/
  18. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983).
  19. D. Terr, “Weighted Mean” From MathWorld-A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/WeightedMean.html
  20. C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17(16), 13918–13927 (2009).
    [CrossRef] [PubMed]
  21. I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16(3), 1808–1819 (2008).
    [CrossRef] [PubMed]
  22. I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
    [CrossRef]

2010

H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
[CrossRef]

2009

2008

I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16(3), 1808–1819 (2008).
[CrossRef] [PubMed]

P. Manninen, P. Kärhä, and E. Ikonen, “Determining the irradiance signal from an asymmetric source with directional detectors: application to calibrations of radiometers with diffusers,” Appl. Opt. 47(26), 4714–4722 (2008).
[CrossRef] [PubMed]

I. Moreno, “Creating a desired lighting pattern with an LED array,” Proc. SPIE 7058, 705811 (2008).
[CrossRef]

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16(4), 519 (2008).
[CrossRef]

2007

M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
[CrossRef]

2006

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
[CrossRef] [PubMed]

2003

J. J. Vos, “On the cause of disability glare and its dependence on glare angle, age and ocular pigmentation,” Clin. Exp. Optom. 86(6), 363–370 (2003).
[CrossRef] [PubMed]

1998

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

1993

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
[CrossRef]

1990

Aizawa, D.

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

Anderson, J. E.

Avendaño-Alejo, M.

Bathiche, S.

Benoit, G. J.

Biernath, R. W.

Caneau, C.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
[CrossRef]

Chen, H. F.

H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
[CrossRef]

Chevalier, B.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Chien, W. T.

C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17(16), 13918–13927 (2009).
[CrossRef] [PubMed]

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16(4), 519 (2008).
[CrossRef]

Chung, S. H.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16(4), 519 (2008).
[CrossRef]

Dainty, J. C.

Emerton, N.

Freier, D. G.

Gmitter, T. J.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
[CrossRef]

Ha, T. H.

H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
[CrossRef]

Hagendoorn, I. A.

D. Voigt, I. A. Hagendoorn, and E. W. M. van der Ham, “Compact large-area uniform colour-selectable calibration light source,” Metrologia 46(4), S243–S247 (2009).
[CrossRef]

Han, B. H.

H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
[CrossRef]

Heidrich, W.

M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
[CrossRef]

Hoffend, T. R.

Hoyle, C. D.

Hsieh, C. C.

Hsieh, C. T.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16(4), 519 (2008).
[CrossRef]

Hung, C. H.

Hutchins, M. G.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Ikonen, E.

Irikura, T.

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

Iwamoto, M.

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

Kärhä, P.

Kasahara, T.

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

Kim, H. R.

H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
[CrossRef]

Large, T.

Liu, T. T.

Lo, Y. C.

Lu, J. D.

Maccari, A.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Manninen, P.

Meis, M. A.

Moreno, I.

Moriyama, T.

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

Nevitt, T. J.

Nieto-Vesperinas, M.

Olive, F.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Oversloot, H.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Platzer, W.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Polato, P.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Roos, A.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Rosenfeld, J. L. J.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Sánchez-Gil, J. A.

Sant, A. J.

Savvateev, V. V.

Schardt, C. R.

Scherer, A.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
[CrossRef]

Schnitzer, I.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
[CrossRef]

Seetzen, H.

M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
[CrossRef]

Sousa, M. E.

Squire, T.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Sun, C. C.

Sung, J. H.

H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
[CrossRef]

Tien, C. H.

Toda, M.

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

Travis, A.

Trentacoste, M.

M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
[CrossRef]

Tzonchev, R. I.

van der Ham, E. W. M.

D. Voigt, I. A. Hagendoorn, and E. W. M. van der Ham, “Compact large-area uniform colour-selectable calibration light source,” Metrologia 46(4), S243–S247 (2009).
[CrossRef]

Voigt, D.

D. Voigt, I. A. Hagendoorn, and E. W. M. van der Ham, “Compact large-area uniform colour-selectable calibration light source,” Metrologia 46(4), S243–S247 (2009).
[CrossRef]

Vos, J. J.

J. J. Vos, “On the cause of disability glare and its dependence on glare angle, age and ocular pigmentation,” Clin. Exp. Optom. 86(6), 363–370 (2003).
[CrossRef] [PubMed]

Ward, G.

M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
[CrossRef]

Weber, M. F.

Wheatley, J. A.

Whitehead, L.

M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
[CrossRef]

Yablonovitch, E.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
[CrossRef]

Yang, T. H.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16(4), 519 (2008).
[CrossRef]

Yoshimura, K.

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174 (1993).
[CrossRef]

Clin. Exp. Optom.

J. J. Vos, “On the cause of disability glare and its dependence on glare angle, age and ocular pigmentation,” Clin. Exp. Optom. 86(6), 363–370 (2003).
[CrossRef] [PubMed]

J. Light Vis. Env.

T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30(2), 95–103 (2006).
[CrossRef]

J. Soc. Inf. Disp.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16(4), 519 (2008).
[CrossRef]

H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18(1), 57 (2010).
[CrossRef]

J. Vis. Commun. Image Represent.

M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18(5), 439–451 (2007).
[CrossRef]

Metrologia

D. Voigt, I. A. Hagendoorn, and E. W. M. van der Ham, “Compact large-area uniform colour-selectable calibration light source,” Metrologia 46(4), S243–S247 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

I. Moreno, “Creating a desired lighting pattern with an LED array,” Proc. SPIE 7058, 705811 (2008).
[CrossRef]

Sol. Energy Mater. Sol. Cells

B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54(1-4), 197–202 (1998).
[CrossRef]

Other

Labsphere, Inc., A Guide to Integrating Sphere Theory and Applications, at http://www.labsphere.com/

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983).

D. Terr, “Weighted Mean” From MathWorld-A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/WeightedMean.html

P. Manninen, “Characterization of diffusers and light-emitting diodes using radiometric measurements and mathematical modeling,” Doctoral Dissertation Thesis, Helsinki University of Technology, Finland (2008).

M. Gebauer, P. Benoit, P. Knoll, and M. Neiger, “P-9: Ray Tracing Tool for Developing LCD-Backlights” SID Symposium Digest of Technical Papers–May 2000–Volume 31, Issue 1, pp. 558-561

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Figures (12)

Fig. 1
Fig. 1

(a) A simple lighting cavity, with and without diffuser. (b) An example of LED luminaire with and without a covering diffuser sheet. (c) A direct LED backlight (of a television display) without diffuser.

Fig. 2
Fig. 2

(a) Optical cavity with 1 and 2 diffusers. (b) Diffuser plate. R0 and T0 are the single-shot power reflection and transmission efficiency at normal incidence, respectively. Here Φin is the input light flux at normal incidence, ΦT is the total transmitted light flux to the right of diffuser, ΦR is the total reflected light flux to the left of diffuser. ϕn and ϕm are the light fluxes associated to each ray of light reflected and transmitted, respectively.

Fig. 3
Fig. 3

(a) Defining the optical efficiency of the diffuser incorporated into the cavity. (b) Multiple reflections of the equivalent ray of light inside the chamber incorporated with one single diffuser. Here the T is the one-shot transmission efficiency of the diffuser plate; the R is the one-shot reflection efficiency of the diffuser; and Rb is the one-shot reflection efficiency of the inner surfaces.

Fig. 11
Fig. 11

Single-shot transmittance (left) and reflectance (right) of diffusers D55, D60 and D70 in function of the angle of incidence.

Fig. 4
Fig. 4

Multiple reflections in a cavity with two diffusers. (a) Multiple reflections of the equivalent ray of light between the two diffusers. (b) Multiple reflections of the equivalent ray of light inside the chamber incorporated with two diffusers. T12 is the one-shot overall transmission of the 2 diffusers, i.e. the summation of transmissions shown in (a).

Fig. 5
Fig. 5

Cross section of inner walls and diffuser for experimental measurements. (a) Shows the cross-section of the silver scatter sheet. (b) Shows the cross-section of the white scatter sheet. (c) Bulk-scattering diffuser plate.

Fig. 6
Fig. 6

Experiment setup with an integrating sphere for measuring the optical efficiencies of diffuser, side walls, and LCCD. (a) Shows the set up for measuring the effective one-shot transmission coefficient T. (b) Shows the set up for the effective one-shot reflection coefficient R. The angle of incidence of all measurements is at 45 degrees when using silver coatings, and it is 30 degrees when using white scatter sheets. (c) Experiment setup for measuring DALC efficiency, η.

Fig. 7
Fig. 7

Comparison between theory and experiment. In graphs “Cal” is the value given by Eqs. (1) and (4), and “Exp” indicates the experimental measurement. The graphs show the efficiency η of bulk scattering diffusers attached to a lighting cavity. Some cavities are assembled with one diffuser (1D) and others with two diffusers (2D). The inner walls of cavities in graph (a) are white scatter sheets, and the inner walls of cavities in plot (b) are silver scatter sheets.

Fig. 8
Fig. 8

Efficiency of DALC with one diffuser in function of the effective reflectivity of inner walls.

Fig. 9
Fig. 9

Effect of LED pitch P, and height of cavity walls H. This figure shows the calculated values (●) by using Eqs. (1) and (4), and experimentally measured values (▲,■). These graphs are for LCCDs assembled with silver scatter sheets.

Fig. 10
Fig. 10

Cone of light flux, emitted by an LED, transmitted through a diffuser plate.

Fig. 12
Fig. 12

Angular radiation pattern of the inner walls for different angles of incidence. (a) Shows the silver coating, and (b) white scatter plate.

Equations (12)

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η = T + T R b R + T R b 2 R 2 + · · · = T 1 R b R ,
T 12 = T 1 T 2 ( 1 + R 1 R 2 + R 1 2 R 2 2 + · · · ) = T 1 T 2 1 R 1 R 2 ,
R 12 = R 2 + T 2 2 R 1 ( 1 + R 1 R 2 + R 1 2 R 2 2 + · · · ) = R 2 + T 2 2 R 1 1 R 1 R 2 ,
η = T 12 1 R b R 12 .
θ e f f = i w i θ i i w i ,
θ e f f = w ( θ ) θ d θ w ( θ ) d θ ,
d Φ T = I ( θ , ϕ ) T ( θ ) d Ω = I ( θ , ϕ ) T ( θ ) sin θ d θ d ϕ ,
d Φ R = I ( θ , ϕ ) R ( θ ) d Ω = I ( θ , ϕ ) R ( θ ) sin θ d θ d ϕ .
θ e f f T = 0 2 π 0 π 2 I ( θ , ϕ ) T ( θ ) θ sin θ d θ d ϕ 0 2 π 0 π 2 I ( θ , ϕ ) T ( θ ) sin θ d θ d ϕ .
θ e f f R = 0 2 π 0 π 2 I ( θ , ϕ ) R ( θ ) θ sin θ d θ d ϕ 0 2 π 0 π 2 I ( θ , ϕ ) R ( θ ) sin θ d θ d ϕ .
θ e f f = θ e f f T + θ e f f R 2 .
θ e f f = 1 2 [ n I ( θ n ) T ( θ n ) θ n sin θ n n I ( θ n ) T ( θ n ) sin θ n + n I ( θ n ) R ( θ n ) θ n sin θ n n I ( θ n ) R ( θ n ) sin θ n ] .

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