Abstract

We propose a design for a high-efficiency backlight module that does not require a brightness enhancement film (BEF). With the high-efficiency backlight module it is possible to achieve almost the same half-luminance angle as a conventional edge-lit backlight module can achieve. The backlight system is comprised of a crisscross light guide plate (LGP) and one diffuser sheet. The crisscross LGP is composed of a LGP and optically patterned film (OPF). The backlight module allows light to be extracted through the direct guiding mode and top guiding mode, respectively. We controlled arrangement of the microstructures to increase the optical efficiency and the uniformity by two modes. Compared to the conventional edge-lit backlight module, there is a two-fold improvement in both the total optical efficiency and on-axis luminance with the high-efficiency backlight module.

© 2014 Optical Society of America

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References

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  1. W. Zhang, H. Wang, L. Ji, and C. Liu, “Design and simulation of the LGP structure for LED backlight,” Proc. SPIE 7655, 765537 (2010).
    [CrossRef]
  2. T. Dekker, T. Bergman, and G. Vissenberg, “From backlight to Luminaire,” SID Int. Symp. Dig. Tech. Pap. 43, 248–251 (2012).
  3. K. Käläntär, S. Matsumoto, and T. Onishi, “Functional light guide plate characterized by optical micro-deflector and micro-reflector for LCD backlight,” IEICE Trans. Electron. E84-C, 1637–1646 (2001).
  4. M. Anandan, “Progress of LED backlights for LCDs,” J. Soc. Inf. Disp. 16, 287–310 (2008).
    [CrossRef]
  5. S. Kobayashi, S. Mikoshiba, and S. Lim, LCD Backlights (Wiley, 2009).
  6. K. Käläntär, “Modified functional light guide plate for backlighting transmissive LCDs,” J. Soc. Inf. Disp. 11, 641–645 (2003).
    [CrossRef]
  7. J. H. Lee, J. B. Yoon, J. Y. Choi, and J. B. Yoon, “A novel LCD backlight unit using a light guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID Int. Symp. Dig. Tech. Pap. 38, 465–468 (2007).
  8. O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
    [CrossRef]
  9. J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
    [CrossRef]
  10. D. Grabovičkić, P. Benítez, J. C. Miñano, and J. Chaves, “LED backlight designs with the flow-line method,” Opt. Express 20, A62–A68 (2012).
    [CrossRef]
  11. K. Fujisawa, I. Onishi, and Y. Fujiwara, “Edge-light backlight unit using optically patterned film,” Jpn. J. Appl. Phys. 46, 194–199 (2007).
    [CrossRef]
  12. A. Nagasawa and K. Fujisawa, “An ultra-slim backlight system using optical- patterned film,” SID Int. Symp. Dig. Tech. Pap. 36, 570–573 (2005).
    [CrossRef]
  13. American National Standards Institute (ANSI) IT7.215-1992, http://www.ansi.org .
  14. Chi Mei Optoelectronics Corp., http://www.datasheet.in/datasheet-html/N/1/0/N101L6-L0B_CMIMEI.pdf.html .
  15. 3M-Vikuiti™ ESR Film, http://www.pronatindustries.com/eng/catalogue.php?instance_id=2&actions=list&id=556 .
  16. KEIWA Inc., http://www.keiwa.co.jp/e/product/pdf_Folder/Opalus_E_200904.pdf .
  17. TSUJIDEN CO. LTD., http://www.tsujiden.co.jp/eng/product/product_info_diffusion.html .
  18. J. W. Pan and C. W. Fan, “High luminance hybrid light guide plate for backlight module application,” Opt. Express 19, 20079–20087 (2011).
    [CrossRef]
  19. D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
    [CrossRef]
  20. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, (Academic, 2004).
  21. A. Nagasawa, T. Eguchi, Y. Sanai, and K. Fujisawa, “Ultra-slim and bendable system with a unified component for liquid crystal display applications,” Opt. Rev. 15, 38–43 (2008).
    [CrossRef]
  22. P. A. Davies, “Edge-ray principle of nonimaging optics,” J. Opt. Soc. Am. A 11, 1256–1259 (1994).
    [CrossRef]

2012 (2)

T. Dekker, T. Bergman, and G. Vissenberg, “From backlight to Luminaire,” SID Int. Symp. Dig. Tech. Pap. 43, 248–251 (2012).

D. Grabovičkić, P. Benítez, J. C. Miñano, and J. Chaves, “LED backlight designs with the flow-line method,” Opt. Express 20, A62–A68 (2012).
[CrossRef]

2011 (1)

2010 (1)

W. Zhang, H. Wang, L. Ji, and C. Liu, “Design and simulation of the LGP structure for LED backlight,” Proc. SPIE 7655, 765537 (2010).
[CrossRef]

2008 (2)

A. Nagasawa, T. Eguchi, Y. Sanai, and K. Fujisawa, “Ultra-slim and bendable system with a unified component for liquid crystal display applications,” Opt. Rev. 15, 38–43 (2008).
[CrossRef]

M. Anandan, “Progress of LED backlights for LCDs,” J. Soc. Inf. Disp. 16, 287–310 (2008).
[CrossRef]

2007 (2)

J. H. Lee, J. B. Yoon, J. Y. Choi, and J. B. Yoon, “A novel LCD backlight unit using a light guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID Int. Symp. Dig. Tech. Pap. 38, 465–468 (2007).

K. Fujisawa, I. Onishi, and Y. Fujiwara, “Edge-light backlight unit using optically patterned film,” Jpn. J. Appl. Phys. 46, 194–199 (2007).
[CrossRef]

2006 (1)

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

2005 (3)

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

A. Nagasawa and K. Fujisawa, “An ultra-slim backlight system using optical- patterned film,” SID Int. Symp. Dig. Tech. Pap. 36, 570–573 (2005).
[CrossRef]

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
[CrossRef]

2003 (1)

K. Käläntär, “Modified functional light guide plate for backlighting transmissive LCDs,” J. Soc. Inf. Disp. 11, 641–645 (2003).
[CrossRef]

2001 (1)

K. Käläntär, S. Matsumoto, and T. Onishi, “Functional light guide plate characterized by optical micro-deflector and micro-reflector for LCD backlight,” IEICE Trans. Electron. E84-C, 1637–1646 (2001).

1994 (1)

Alvarez, R.

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

Anandan, M.

M. Anandan, “Progress of LED backlights for LCDs,” J. Soc. Inf. Disp. 16, 287–310 (2008).
[CrossRef]

Benitez, P.

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

Benítez, P.

Bergman, T.

T. Dekker, T. Bergman, and G. Vissenberg, “From backlight to Luminaire,” SID Int. Symp. Dig. Tech. Pap. 43, 248–251 (2012).

Chaves, J.

D. Grabovičkić, P. Benítez, J. C. Miñano, and J. Chaves, “LED backlight designs with the flow-line method,” Opt. Express 20, A62–A68 (2012).
[CrossRef]

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

Choi, J. Y.

J. H. Lee, J. B. Yoon, J. Y. Choi, and J. B. Yoon, “A novel LCD backlight unit using a light guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID Int. Symp. Dig. Tech. Pap. 38, 465–468 (2007).

Davies, P. A.

Dekker, T.

T. Dekker, T. Bergman, and G. Vissenberg, “From backlight to Luminaire,” SID Int. Symp. Dig. Tech. Pap. 43, 248–251 (2012).

Dross, O.

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

Eguchi, T.

A. Nagasawa, T. Eguchi, Y. Sanai, and K. Fujisawa, “Ultra-slim and bendable system with a unified component for liquid crystal display applications,” Opt. Rev. 15, 38–43 (2008).
[CrossRef]

Falicoff, W.

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

Fan, C. W.

Fan, S.

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
[CrossRef]

Feng, D.

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
[CrossRef]

Fujisawa, K.

A. Nagasawa, T. Eguchi, Y. Sanai, and K. Fujisawa, “Ultra-slim and bendable system with a unified component for liquid crystal display applications,” Opt. Rev. 15, 38–43 (2008).
[CrossRef]

K. Fujisawa, I. Onishi, and Y. Fujiwara, “Edge-light backlight unit using optically patterned film,” Jpn. J. Appl. Phys. 46, 194–199 (2007).
[CrossRef]

A. Nagasawa and K. Fujisawa, “An ultra-slim backlight system using optical- patterned film,” SID Int. Symp. Dig. Tech. Pap. 36, 570–573 (2005).
[CrossRef]

Fujiwara, Y.

K. Fujisawa, I. Onishi, and Y. Fujiwara, “Edge-light backlight unit using optically patterned film,” Jpn. J. Appl. Phys. 46, 194–199 (2007).
[CrossRef]

Grabovickic, D.

Hernandez, M.

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

Ji, L.

W. Zhang, H. Wang, L. Ji, and C. Liu, “Design and simulation of the LGP structure for LED backlight,” Proc. SPIE 7655, 765537 (2010).
[CrossRef]

Jin, G.

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
[CrossRef]

Käläntär, K.

K. Käläntär, “Modified functional light guide plate for backlighting transmissive LCDs,” J. Soc. Inf. Disp. 11, 641–645 (2003).
[CrossRef]

K. Käläntär, S. Matsumoto, and T. Onishi, “Functional light guide plate characterized by optical micro-deflector and micro-reflector for LCD backlight,” IEICE Trans. Electron. E84-C, 1637–1646 (2001).

Kobayashi, S.

S. Kobayashi, S. Mikoshiba, and S. Lim, LCD Backlights (Wiley, 2009).

Lee, J. H.

J. H. Lee, J. B. Yoon, J. Y. Choi, and J. B. Yoon, “A novel LCD backlight unit using a light guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID Int. Symp. Dig. Tech. Pap. 38, 465–468 (2007).

Lim, S.

S. Kobayashi, S. Mikoshiba, and S. Lim, LCD Backlights (Wiley, 2009).

Liu, C.

W. Zhang, H. Wang, L. Ji, and C. Liu, “Design and simulation of the LGP structure for LED backlight,” Proc. SPIE 7655, 765537 (2010).
[CrossRef]

Matsumoto, S.

K. Käläntär, S. Matsumoto, and T. Onishi, “Functional light guide plate characterized by optical micro-deflector and micro-reflector for LCD backlight,” IEICE Trans. Electron. E84-C, 1637–1646 (2001).

Mikoshiba, S.

S. Kobayashi, S. Mikoshiba, and S. Lim, LCD Backlights (Wiley, 2009).

Miñano, J. C.

D. Grabovičkić, P. Benítez, J. C. Miñano, and J. Chaves, “LED backlight designs with the flow-line method,” Opt. Express 20, A62–A68 (2012).
[CrossRef]

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, (Academic, 2004).

Nagasawa, A.

A. Nagasawa, T. Eguchi, Y. Sanai, and K. Fujisawa, “Ultra-slim and bendable system with a unified component for liquid crystal display applications,” Opt. Rev. 15, 38–43 (2008).
[CrossRef]

A. Nagasawa and K. Fujisawa, “An ultra-slim backlight system using optical- patterned film,” SID Int. Symp. Dig. Tech. Pap. 36, 570–573 (2005).
[CrossRef]

Onishi, I.

K. Fujisawa, I. Onishi, and Y. Fujiwara, “Edge-light backlight unit using optically patterned film,” Jpn. J. Appl. Phys. 46, 194–199 (2007).
[CrossRef]

Onishi, T.

K. Käläntär, S. Matsumoto, and T. Onishi, “Functional light guide plate characterized by optical micro-deflector and micro-reflector for LCD backlight,” IEICE Trans. Electron. E84-C, 1637–1646 (2001).

Pan, J. W.

Parkyn, W. A.

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

Sanai, Y.

A. Nagasawa, T. Eguchi, Y. Sanai, and K. Fujisawa, “Ultra-slim and bendable system with a unified component for liquid crystal display applications,” Opt. Rev. 15, 38–43 (2008).
[CrossRef]

Santamaria, A.

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

Vissenberg, G.

T. Dekker, T. Bergman, and G. Vissenberg, “From backlight to Luminaire,” SID Int. Symp. Dig. Tech. Pap. 43, 248–251 (2012).

Wang, H.

W. Zhang, H. Wang, L. Ji, and C. Liu, “Design and simulation of the LGP structure for LED backlight,” Proc. SPIE 7655, 765537 (2010).
[CrossRef]

Winston, R.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, (Academic, 2004).

Yan, Y.

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
[CrossRef]

Yang, X.

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
[CrossRef]

Yoon, J. B.

J. H. Lee, J. B. Yoon, J. Y. Choi, and J. B. Yoon, “A novel LCD backlight unit using a light guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID Int. Symp. Dig. Tech. Pap. 38, 465–468 (2007).

J. H. Lee, J. B. Yoon, J. Y. Choi, and J. B. Yoon, “A novel LCD backlight unit using a light guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID Int. Symp. Dig. Tech. Pap. 38, 465–468 (2007).

Zhang, W.

W. Zhang, H. Wang, L. Ji, and C. Liu, “Design and simulation of the LGP structure for LED backlight,” Proc. SPIE 7655, 765537 (2010).
[CrossRef]

IEICE Trans. Electron. (1)

K. Käläntär, S. Matsumoto, and T. Onishi, “Functional light guide plate characterized by optical micro-deflector and micro-reflector for LCD backlight,” IEICE Trans. Electron. E84-C, 1637–1646 (2001).

J. Opt. A (1)

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light guide plates for liquid crystal display backlight,” J. Opt. A 7, 111–117 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Soc. Inf. Disp. (2)

M. Anandan, “Progress of LED backlights for LCDs,” J. Soc. Inf. Disp. 16, 287–310 (2008).
[CrossRef]

K. Käläntär, “Modified functional light guide plate for backlighting transmissive LCDs,” J. Soc. Inf. Disp. 11, 641–645 (2003).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Fujisawa, I. Onishi, and Y. Fujiwara, “Edge-light backlight unit using optically patterned film,” Jpn. J. Appl. Phys. 46, 194–199 (2007).
[CrossRef]

Opt. Express (2)

Opt. Rev. (1)

A. Nagasawa, T. Eguchi, Y. Sanai, and K. Fujisawa, “Ultra-slim and bendable system with a unified component for liquid crystal display applications,” Opt. Rev. 15, 38–43 (2008).
[CrossRef]

Proc. SPIE (3)

O. Dross, W. A. Parkyn, J. Chaves, W. Falicoff, J. C. Miñano, P. Benitez, and R. Alvarez, “A superior architecture of brightness enhancement for display backlighting,” Proc. SPIE 6338, 63380G (2006).
[CrossRef]

J. C. Miñano, P. Benitez, J. Chaves, M. Hernandez, O. Dross, and A. Santamaria, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE 5942, 594202 (2005).
[CrossRef]

W. Zhang, H. Wang, L. Ji, and C. Liu, “Design and simulation of the LGP structure for LED backlight,” Proc. SPIE 7655, 765537 (2010).
[CrossRef]

SID Int. Symp. Dig. Tech. Pap. (3)

T. Dekker, T. Bergman, and G. Vissenberg, “From backlight to Luminaire,” SID Int. Symp. Dig. Tech. Pap. 43, 248–251 (2012).

J. H. Lee, J. B. Yoon, J. Y. Choi, and J. B. Yoon, “A novel LCD backlight unit using a light guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID Int. Symp. Dig. Tech. Pap. 38, 465–468 (2007).

A. Nagasawa and K. Fujisawa, “An ultra-slim backlight system using optical- patterned film,” SID Int. Symp. Dig. Tech. Pap. 36, 570–573 (2005).
[CrossRef]

Other (7)

American National Standards Institute (ANSI) IT7.215-1992, http://www.ansi.org .

Chi Mei Optoelectronics Corp., http://www.datasheet.in/datasheet-html/N/1/0/N101L6-L0B_CMIMEI.pdf.html .

3M-Vikuiti™ ESR Film, http://www.pronatindustries.com/eng/catalogue.php?instance_id=2&actions=list&id=556 .

KEIWA Inc., http://www.keiwa.co.jp/e/product/pdf_Folder/Opalus_E_200904.pdf .

TSUJIDEN CO. LTD., http://www.tsujiden.co.jp/eng/product/product_info_diffusion.html .

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, (Academic, 2004).

S. Kobayashi, S. Mikoshiba, and S. Lim, LCD Backlights (Wiley, 2009).

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Figures (12)

Fig. 1.
Fig. 1.

Principles of the crisscross LGP: (a) architecture of the conventional edge-lit backlight module, (b) architecture of the high-efficiency backlight module, and (c) extracted light of the two modes.

Fig. 2.
Fig. 2.

Collimation principles for the crisscross light guide plate: (a) horizontal cross-sectional view of the crisscross light guide plate and (b) calculation of the slanted angle.

Fig. 3.
Fig. 3.

Efficiency and uniformity of the high-efficiency backlight module: (a) illumination chart for the direct passing mode, (b) illumination chart for the two modes, (c) distribution of the top prism and bottom prism microstructures, and (d) efficiency and uniformity of the high-efficiency backlight module.

Fig. 4.
Fig. 4.

Definition of the density of the trapezoid microstructures and the influence of the density on the optical efficiency and normalized on-axis luminance: (a) illumination chart for density; (b) relationship between the trapezoidal microstructures, optical efficiency, and normalized on-axis luminance.

Fig. 5.
Fig. 5.

Measured data and simulated data.

Fig. 6.
Fig. 6.

Receiver settings and loss analysis in the two backlight modules: (a) receiver settings for the conventional edge-lit backlight module, (b) receiver settings for the high-efficiency backlight module, and (c) loss analysis for the conventional edge-lit backlight module and the high-efficiency backlight module.

Fig. 7.
Fig. 7.

3D intensity chart for the conventional edge-lit backlight module.

Fig. 8.
Fig. 8.

3D intensity chart for the high-efficiency backlight module.

Fig. 9.
Fig. 9.

Optical efficiency of the conventional edge-lit backlight module and the high-efficiency backlight module.

Fig. 10.
Fig. 10.

Angular distributions for the conventional edge-lit backlight module and the high-efficiency backlight module.

Fig. 11.
Fig. 11.

Tolerance analysis for the contraposition problem: (a) shifted placement of microstructures and (b) relationship between uniformity and placement of the microstructures.

Fig. 12.
Fig. 12.

Relationship between the round angles of the microstructures, normalized optical efficiency and normalized on-axis luminance.

Tables (2)

Tables Icon

Table 1. Simulated Conditions for Each Layer

Tables Icon

Table 2. Exact Sizes of Three Kinds of Microstructures

Equations (13)

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

β=180°(90°φ)θ,
α=90°β=θφ.
W2=2W1,
W2W12tanθ=W12cot(θφ),
θ+θφ=2θφ=90°.
nPMMAsinφ=nAIRsin(90°),
φ=sin1(1nPMMA)42°,
θ=90°+42°2=66°.
B=0xL×W(x)dx,
α|W(x)=Wbottom=BA|W(x)=Wbottom.
α|W(x)=Wtop=BA|W(x)=Wtop.
ρ=NW.
γ(%)=[(αβη)α]×100%.

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