Abstract

An LED optical element is proposed as an alternative to cold-cathode fluorescent lamps. The optical element generates two symmetric uniformly illuminated line segments on the diffuse reflector. The illuminated segments then act as secondary linear light sources. The calculation of the optical element is reduced to the integration of the system of two explicit ordinary differential equations. The results of the simulation of an illumination system module consisting of a set of optical elements generating a set of line segments on the surface of the diffuse reflector are presented. The elements are located directly on the surface of the reflector. The simulation results demonstrate the uniform illumination of a rectangular area at a distance of 30–40 mm from the light source plane. The lighting efficiency of the designed system exceeds 83%.

© 2013 Optical Society of America

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References

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  1. C.-F. Lin, Y.-B. Fang, and P.-H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol.7(1), 3–9 (2011).
    [CrossRef]
  2. M. Doshi, R. Zane, and F. J. Azcondo, “Low frequency architecture for multi-lamp CCFL systems with capacitive ignition,” J. Disp. Technol.5(5), 152–161 (2009).
    [CrossRef]
  3. R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “LED backlight module by lightguide-diffusive component,” J. Disp. Technol.8(2), 79–86 (2012).
    [CrossRef]
  4. Labsphere, “Labsphere: Spectralon Targets,” http://www.labsphere.com/products/reflectance-standards-and-targets/spectralon-reflectance-standards/default.aspx .
  5. A. Bhandari, B. Hamre, Ø. Frette, L. Zhao, J. J. Stamnes, and M. Kildemo, “Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light,” Appl. Opt.50(16), 2431–2442 (2011).
    [CrossRef] [PubMed]
  6. V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).
  7. L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, and A. Y. Tzaregorodtzev, “Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment,” Optik (Stuttg.)101, 37–41 (1995).
  8. M. A. Moiseev and L. L. Doskolovich, “Design of TIR optics generating the prescribed irradiance distribution in the circle region,” J. Opt. Soc. Am. A29(9), 1758–1763 (2012).
    [CrossRef] [PubMed]
  9. Future Lighting Solutions, “Future Lighting Solutions: Remote Phosphor,” http://www.futurelightingsolutions.com/en/technologies/Pages/remote_phosphor.aspx .
  10. H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar Lighting System Using Array of Blue Leds to Excite Yellow Remote Phosphor Film,” J. Disp. Technol.7(1), 44–51 (2011).
    [CrossRef]
  11. A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
    [CrossRef]
  12. L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
    [CrossRef]
  13. L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt.52(12), 2521–2526 (2013).
    [CrossRef] [PubMed]

2013 (1)

2012 (2)

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “LED backlight module by lightguide-diffusive component,” J. Disp. Technol.8(2), 79–86 (2012).
[CrossRef]

M. A. Moiseev and L. L. Doskolovich, “Design of TIR optics generating the prescribed irradiance distribution in the circle region,” J. Opt. Soc. Am. A29(9), 1758–1763 (2012).
[CrossRef] [PubMed]

2011 (3)

H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar Lighting System Using Array of Blue Leds to Excite Yellow Remote Phosphor Film,” J. Disp. Technol.7(1), 44–51 (2011).
[CrossRef]

A. Bhandari, B. Hamre, Ø. Frette, L. Zhao, J. J. Stamnes, and M. Kildemo, “Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light,” Appl. Opt.50(16), 2431–2442 (2011).
[CrossRef] [PubMed]

C.-F. Lin, Y.-B. Fang, and P.-H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol.7(1), 3–9 (2011).
[CrossRef]

2009 (2)

M. Doshi, R. Zane, and F. J. Azcondo, “Low frequency architecture for multi-lamp CCFL systems with capacitive ignition,” J. Disp. Technol.5(5), 152–161 (2009).
[CrossRef]

A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

2005 (1)

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
[CrossRef]

1995 (1)

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, and A. Y. Tzaregorodtzev, “Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment,” Optik (Stuttg.)101, 37–41 (1995).

Azcondo, F. J.

M. Doshi, R. Zane, and F. J. Azcondo, “Low frequency architecture for multi-lamp CCFL systems with capacitive ignition,” J. Disp. Technol.5(5), 152–161 (2009).
[CrossRef]

Bernard, S.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
[CrossRef]

Bezus, E. A.

Bhandari, A.

Chang, R.-S.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “LED backlight module by lightguide-diffusive component,” J. Disp. Technol.8(2), 79–86 (2012).
[CrossRef]

Chen, Y.-Y.

A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

Dmitriev, A. Y.

Doshi, M.

M. Doshi, R. Zane, and F. J. Azcondo, “Low frequency architecture for multi-lamp CCFL systems with capacitive ignition,” J. Disp. Technol.5(5), 152–161 (2009).
[CrossRef]

Doskolovich, L. L.

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt.52(12), 2521–2526 (2013).
[CrossRef] [PubMed]

M. A. Moiseev and L. L. Doskolovich, “Design of TIR optics generating the prescribed irradiance distribution in the circle region,” J. Opt. Soc. Am. A29(9), 1758–1763 (2012).
[CrossRef] [PubMed]

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
[CrossRef]

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, and A. Y. Tzaregorodtzev, “Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment,” Optik (Stuttg.)101, 37–41 (1995).

Fang, Y.-B.

C.-F. Lin, Y.-B. Fang, and P.-H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol.7(1), 3–9 (2011).
[CrossRef]

Frette, Ø.

Hamre, B.

Huang, H.-T.

H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar Lighting System Using Array of Blue Leds to Excite Yellow Remote Phosphor Film,” J. Disp. Technol.7(1), 44–51 (2011).
[CrossRef]

Huang, Y.-P.

H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar Lighting System Using Array of Blue Leds to Excite Yellow Remote Phosphor Film,” J. Disp. Technol.7(1), 44–51 (2011).
[CrossRef]

Kazanskiy, N. L.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
[CrossRef]

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, and A. Y. Tzaregorodtzev, “Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment,” Optik (Stuttg.)101, 37–41 (1995).

Kharitonov, S. I.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
[CrossRef]

Kildemo, M.

Li, T.-Y.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “LED backlight module by lightguide-diffusive component,” J. Disp. Technol.8(2), 79–86 (2012).
[CrossRef]

Liao, H.-L.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “LED backlight module by lightguide-diffusive component,” J. Disp. Technol.8(2), 79–86 (2012).
[CrossRef]

Lin, C.-F.

C.-F. Lin, Y.-B. Fang, and P.-H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol.7(1), 3–9 (2011).
[CrossRef]

Moiseev, M. A.

Perlo, P.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
[CrossRef]

Soifer, V. A.

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, and A. Y. Tzaregorodtzev, “Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment,” Optik (Stuttg.)101, 37–41 (1995).

Stamnes, J. J.

Teng, Y.-T.

A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

Tsai, C.-C.

H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar Lighting System Using Array of Blue Leds to Excite Yellow Remote Phosphor Film,” J. Disp. Technol.7(1), 44–51 (2011).
[CrossRef]

Tsai, J.-Z.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “LED backlight module by lightguide-diffusive component,” J. Disp. Technol.8(2), 79–86 (2012).
[CrossRef]

Tzaregorodtzev, A. Y.

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, and A. Y. Tzaregorodtzev, “Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment,” Optik (Stuttg.)101, 37–41 (1995).

Whang, A. J.-W.

A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

Yang, P.-H.

C.-F. Lin, Y.-B. Fang, and P.-H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol.7(1), 3–9 (2011).
[CrossRef]

Zane, R.

M. Doshi, R. Zane, and F. J. Azcondo, “Low frequency architecture for multi-lamp CCFL systems with capacitive ignition,” J. Disp. Technol.5(5), 152–161 (2009).
[CrossRef]

Zhao, L.

Appl. Opt. (2)

J. Disp. Technol. (5)

H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar Lighting System Using Array of Blue Leds to Excite Yellow Remote Phosphor Film,” J. Disp. Technol.7(1), 44–51 (2011).
[CrossRef]

A. J.-W. Whang, Y.-Y. Chen, and Y.-T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

C.-F. Lin, Y.-B. Fang, and P.-H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol.7(1), 3–9 (2011).
[CrossRef]

M. Doshi, R. Zane, and F. J. Azcondo, “Low frequency architecture for multi-lamp CCFL systems with capacitive ignition,” J. Disp. Technol.5(5), 152–161 (2009).
[CrossRef]

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “LED backlight module by lightguide-diffusive component,” J. Disp. Technol.8(2), 79–86 (2012).
[CrossRef]

J. Mod. Opt. (1)

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt.52, 1529–1536 (2005).
[CrossRef]

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

Optik (Stuttg.) (1)

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, and A. Y. Tzaregorodtzev, “Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment,” Optik (Stuttg.)101, 37–41 (1995).

Other (3)

Future Lighting Solutions, “Future Lighting Solutions: Remote Phosphor,” http://www.futurelightingsolutions.com/en/technologies/Pages/remote_phosphor.aspx .

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Labsphere, “Labsphere: Spectralon Targets,” http://www.labsphere.com/products/reflectance-standards-and-targets/spectralon-reflectance-standards/default.aspx .

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Figures (5)

Fig. 1
Fig. 1

Configuration of a backlight system with fluorescent lamps (a); configuration of an LED-based backlight system module (b).

Fig. 2
Fig. 2

Optical element for focusing into a line segment on the Ox axis.

Fig. 3
Fig. 3

Cross section (a) and wireframe model (b) of the optical element for the uniform illumination of two symmetrical line segments on the Ox axis.

Fig. 4
Fig. 4

(a) Irradiance distribution generated by the designed optical element for the uniform illumination of two line segments in the plane z = 0; (b) Irradiance distribution generated by two linear arrays consisting of 5 optical elements each.

Fig. 5
Fig. 5

Irradiance distributions in the planes z = 30 mm (a) and z = 40 mm (b) generated by a set of 10 optical elements (two linear arrays of 5 elements each) with a Lambertian reflecting surface (dashed curves show irradiance plots along the lines passing through the center of the image).

Equations (8)

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

dρ( α ) dα =ρ( α )cot( π/2 αβ( α ) 2 ),
x( α )= x 0 + [ ρ( α )cos( α )( x 0 ρ( α )sin( α ) )tg( β( α ) ) ] γ( α ) / [ nsin( β( α ) ) ] ,
sin( π/2α )( 0 π I( α,φ )dφ )dα=E( x )dx,
0 α max sin( π/2α )[ 0 π I( α,φ )dφ ]dα = x 1 x 2 E( x )dx .
x( α )= x 1 + 1 E 0 0 α cosα[ 0 π I( α,φ ) dφ ]dα .
I( α,φ )= I 0 cosαsinφ.
x( α )= x 1 +( x 2 x 1 ) 2α+sin( 2α ) 2 α max +sin( 2 α max ) .
dβ(α) dα =2 × nsin( β( α ) ) x ( α ) γ( α ) +sec( β( α ) )γ( α )[ sin( αβ( α ) )ρ( α )cos( αβ( α ) ) ρ ( α ) ] n 2 sec( β( α ) )sin( 2β( α ) )[ x 0 sin( β( α ) )cos( αβ( α ) )ρ( α ) ]2γ( α )g( α ) ,

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