Abstract

We present the methodology of an integration of a dot generation scheme by a molecular-dynamics (MD) method and the subsequent software optical design phase by software. The MD dot generation scheme proposed has great advantages when integrated into the optical design phase. These advantages include the variable r-cut and reflective boundary condition techniques, both of which could achieve a high-density variation of dot distribution. In addition, we use a cell technique where the domain is divided into a number of smaller cells, allowing for flexibility in adjusting the dot density within each cell, as well as for using the add-on or remove-from technique of the dots in one cell to achieve an equal-luminance condition. In addition, a simple proportional rule of luminance to dot density is also proposed to perform dot optimization. Finally, an illustration is shown for the optimal dot distribution of a LED backlight. The result that a two-dimensional dot density distribution near the light source changes gradually to a one-dimensional dot density distribution with increasing distance from the light source shows the validity of the present integration of the MD dot generation scheme into the optical design phase.

© 2007 Optical Society of America

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References

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  1. C. A. Rudisill and S. P. Ryan, "Discretely applied diffusor structure on lightguides," U.S. patent 5,940,215 (17 August 1999).
  2. G. T. Sung and C. H. Liu, "Lightguide and method for manufacturing the same," U.S. patent 6680010 (20 January 2001).
  3. J. G. Chang, Y. B. Fang, and C. F. Lin, "Solution strategy of optimal dot pattern design for light guide using in backlight," Proc. SPIE 6034, 210-217 (2006).
  4. J. G. Chang and Y. B. Fang, "Dot pattern design of light guide in edge-lit backlight using regional partition approach," Opt. Eng. (Bellingham) (to be published).
  5. W. Y. Lee, T. K. Lim, Y. W. Lee, and I. W. Lee, "Fast ray-tracing methods for LCD backlight simulation using the characteristics of the pattern," Opt. Eng. (Bellingham) 44, 014004 (2005).
    [CrossRef]
  6. T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
    [CrossRef]
  7. T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
    [CrossRef]
  8. T. Idé, H. Mizuta, Y. Taira, and A. Nishikai, "Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern," U.S. patent 6,865,325 (8 March 2005).
  9. Breault Research Organization, "Arrays and bounds in ASAP," 9 June 2006, http://www.breault.com/k-base.php?kbaseID=30&CatID=44.
  10. J. F. Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," Proc. SPIE 4445, 119-129 (2001).
    [CrossRef]
  11. J. G. Chang, C. C. Hwang, S. P. Ju, and S. H. Huang, "A molecular dynamics simulation investigation into the structure of fullerene C60 grown on a diamond substrate," Carbon 42, 2609-2616 (2004).
    [CrossRef]
  12. M. H. Su, C. C. Hwang, J. G. Chang, and S. H. Wang, "Microstructure evolution analysis in Co/Cu layers during the annealing process," J. Appl. Phys. 93, 4566-4575 (2003).
    [CrossRef]
  13. C. C. Hwang, G. J. Huang, S. P. Ju, and J. G. Chang, "Incident ion characteristics in ionized physical vapor deposition using molecular dynamics simulation," Surf. Sci. 512, 135-150 (2002).
    [CrossRef]
  14. C. C. Hwang, J. G. Chang, J. M. Lu, and H. C. Lin, "Dual Damascene simulation for ionized physical vapor deposition process: investigation on incident energy and via geometry effects," J. Phys. Soc. Jpn. 72, 3151-5157 (2003).
    [CrossRef]
  15. J. G. Chang, M. H. Su, C. T. Lee, and C. C. Hwang, "Generating random and non-overlapping dot patterns for LCD backlight light guides using molecular dynamics method," J. Appl. Phys. 98, 114910 (2005).
    [CrossRef]
  16. J. M. Haile, Molecular Dynamics Simulation (Wiley, 1992).
  17. LightTools, Optical Design Tools for Backlight Displays (Optical Research Associates, 2005).
  18. Breault Research Organization, "The ASAP Primer," http://www.breault.com/k-base.php.
  19. American National Standards Institute (ANSI), "Measuring method of optical characteristics for backlight unit," SEMI D33-0703 (ANSI, 2003).
  20. J. G. Chang, Y. B. Fang, and C. F. Lin, "Photometric quantity analysis of backlight for a dual-panel display," Opt. Eng. (Bellingham) 45, 056402 (2006).
    [CrossRef]
  21. W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
    [CrossRef]
  22. F. Balena, Programming Microsoft Visual Basic 6.0 (Microsoft, 1999).

2006 (2)

J. G. Chang, Y. B. Fang, and C. F. Lin, "Solution strategy of optimal dot pattern design for light guide using in backlight," Proc. SPIE 6034, 210-217 (2006).

J. G. Chang, Y. B. Fang, and C. F. Lin, "Photometric quantity analysis of backlight for a dual-panel display," Opt. Eng. (Bellingham) 45, 056402 (2006).
[CrossRef]

2005 (2)

W. Y. Lee, T. K. Lim, Y. W. Lee, and I. W. Lee, "Fast ray-tracing methods for LCD backlight simulation using the characteristics of the pattern," Opt. Eng. (Bellingham) 44, 014004 (2005).
[CrossRef]

J. G. Chang, M. H. Su, C. T. Lee, and C. C. Hwang, "Generating random and non-overlapping dot patterns for LCD backlight light guides using molecular dynamics method," J. Appl. Phys. 98, 114910 (2005).
[CrossRef]

2004 (1)

J. G. Chang, C. C. Hwang, S. P. Ju, and S. H. Huang, "A molecular dynamics simulation investigation into the structure of fullerene C60 grown on a diamond substrate," Carbon 42, 2609-2616 (2004).
[CrossRef]

2003 (4)

M. H. Su, C. C. Hwang, J. G. Chang, and S. H. Wang, "Microstructure evolution analysis in Co/Cu layers during the annealing process," J. Appl. Phys. 93, 4566-4575 (2003).
[CrossRef]

C. C. Hwang, J. G. Chang, J. M. Lu, and H. C. Lin, "Dual Damascene simulation for ionized physical vapor deposition process: investigation on incident energy and via geometry effects," J. Phys. Soc. Jpn. 72, 3151-5157 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

2002 (1)

C. C. Hwang, G. J. Huang, S. P. Ju, and J. G. Chang, "Incident ion characteristics in ionized physical vapor deposition using molecular dynamics simulation," Surf. Sci. 512, 135-150 (2002).
[CrossRef]

2001 (2)

J. F. Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," Proc. SPIE 4445, 119-129 (2001).
[CrossRef]

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Balena, F.

F. Balena, Programming Microsoft Visual Basic 6.0 (Microsoft, 1999).

Chang, J. G.

J. G. Chang, Y. B. Fang, and C. F. Lin, "Photometric quantity analysis of backlight for a dual-panel display," Opt. Eng. (Bellingham) 45, 056402 (2006).
[CrossRef]

J. G. Chang, Y. B. Fang, and C. F. Lin, "Solution strategy of optimal dot pattern design for light guide using in backlight," Proc. SPIE 6034, 210-217 (2006).

J. G. Chang, M. H. Su, C. T. Lee, and C. C. Hwang, "Generating random and non-overlapping dot patterns for LCD backlight light guides using molecular dynamics method," J. Appl. Phys. 98, 114910 (2005).
[CrossRef]

J. G. Chang, C. C. Hwang, S. P. Ju, and S. H. Huang, "A molecular dynamics simulation investigation into the structure of fullerene C60 grown on a diamond substrate," Carbon 42, 2609-2616 (2004).
[CrossRef]

C. C. Hwang, J. G. Chang, J. M. Lu, and H. C. Lin, "Dual Damascene simulation for ionized physical vapor deposition process: investigation on incident energy and via geometry effects," J. Phys. Soc. Jpn. 72, 3151-5157 (2003).
[CrossRef]

M. H. Su, C. C. Hwang, J. G. Chang, and S. H. Wang, "Microstructure evolution analysis in Co/Cu layers during the annealing process," J. Appl. Phys. 93, 4566-4575 (2003).
[CrossRef]

C. C. Hwang, G. J. Huang, S. P. Ju, and J. G. Chang, "Incident ion characteristics in ionized physical vapor deposition using molecular dynamics simulation," Surf. Sci. 512, 135-150 (2002).
[CrossRef]

J. G. Chang and Y. B. Fang, "Dot pattern design of light guide in edge-lit backlight using regional partition approach," Opt. Eng. (Bellingham) (to be published).

Chong, G. S.

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Derlofske, J. F.

J. F. Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," Proc. SPIE 4445, 119-129 (2001).
[CrossRef]

Fang, X. M.

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Fang, Y. B.

J. G. Chang, Y. B. Fang, and C. F. Lin, "Photometric quantity analysis of backlight for a dual-panel display," Opt. Eng. (Bellingham) 45, 056402 (2006).
[CrossRef]

J. G. Chang, Y. B. Fang, and C. F. Lin, "Solution strategy of optimal dot pattern design for light guide using in backlight," Proc. SPIE 6034, 210-217 (2006).

J. G. Chang and Y. B. Fang, "Dot pattern design of light guide in edge-lit backlight using regional partition approach," Opt. Eng. (Bellingham) (to be published).

Feng, M.

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Gao, K. L.

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Hai, W. H.

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Haile, J. M.

J. M. Haile, Molecular Dynamics Simulation (Wiley, 1992).

Huang, G. J.

C. C. Hwang, G. J. Huang, S. P. Ju, and J. G. Chang, "Incident ion characteristics in ionized physical vapor deposition using molecular dynamics simulation," Surf. Sci. 512, 135-150 (2002).
[CrossRef]

Huang, S. H.

J. G. Chang, C. C. Hwang, S. P. Ju, and S. H. Huang, "A molecular dynamics simulation investigation into the structure of fullerene C60 grown on a diamond substrate," Carbon 42, 2609-2616 (2004).
[CrossRef]

Hwang, C. C.

J. G. Chang, M. H. Su, C. T. Lee, and C. C. Hwang, "Generating random and non-overlapping dot patterns for LCD backlight light guides using molecular dynamics method," J. Appl. Phys. 98, 114910 (2005).
[CrossRef]

J. G. Chang, C. C. Hwang, S. P. Ju, and S. H. Huang, "A molecular dynamics simulation investigation into the structure of fullerene C60 grown on a diamond substrate," Carbon 42, 2609-2616 (2004).
[CrossRef]

C. C. Hwang, J. G. Chang, J. M. Lu, and H. C. Lin, "Dual Damascene simulation for ionized physical vapor deposition process: investigation on incident energy and via geometry effects," J. Phys. Soc. Jpn. 72, 3151-5157 (2003).
[CrossRef]

M. H. Su, C. C. Hwang, J. G. Chang, and S. H. Wang, "Microstructure evolution analysis in Co/Cu layers during the annealing process," J. Appl. Phys. 93, 4566-4575 (2003).
[CrossRef]

C. C. Hwang, G. J. Huang, S. P. Ju, and J. G. Chang, "Incident ion characteristics in ionized physical vapor deposition using molecular dynamics simulation," Surf. Sci. 512, 135-150 (2002).
[CrossRef]

Idé, T.

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

T. Idé, H. Mizuta, Y. Taira, and A. Nishikai, "Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern," U.S. patent 6,865,325 (8 March 2005).

Ju, S. P.

J. G. Chang, C. C. Hwang, S. P. Ju, and S. H. Huang, "A molecular dynamics simulation investigation into the structure of fullerene C60 grown on a diamond substrate," Carbon 42, 2609-2616 (2004).
[CrossRef]

C. C. Hwang, G. J. Huang, S. P. Ju, and J. G. Chang, "Incident ion characteristics in ionized physical vapor deposition using molecular dynamics simulation," Surf. Sci. 512, 135-150 (2002).
[CrossRef]

Katsu, Y.

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

Lee, C. T.

J. G. Chang, M. H. Su, C. T. Lee, and C. C. Hwang, "Generating random and non-overlapping dot patterns for LCD backlight light guides using molecular dynamics method," J. Appl. Phys. 98, 114910 (2005).
[CrossRef]

Lee, I. W.

W. Y. Lee, T. K. Lim, Y. W. Lee, and I. W. Lee, "Fast ray-tracing methods for LCD backlight simulation using the characteristics of the pattern," Opt. Eng. (Bellingham) 44, 014004 (2005).
[CrossRef]

Lee, W. Y.

W. Y. Lee, T. K. Lim, Y. W. Lee, and I. W. Lee, "Fast ray-tracing methods for LCD backlight simulation using the characteristics of the pattern," Opt. Eng. (Bellingham) 44, 014004 (2005).
[CrossRef]

Lee, Y. W.

W. Y. Lee, T. K. Lim, Y. W. Lee, and I. W. Lee, "Fast ray-tracing methods for LCD backlight simulation using the characteristics of the pattern," Opt. Eng. (Bellingham) 44, 014004 (2005).
[CrossRef]

Lim, T. K.

W. Y. Lee, T. K. Lim, Y. W. Lee, and I. W. Lee, "Fast ray-tracing methods for LCD backlight simulation using the characteristics of the pattern," Opt. Eng. (Bellingham) 44, 014004 (2005).
[CrossRef]

Lin, C. F.

J. G. Chang, Y. B. Fang, and C. F. Lin, "Solution strategy of optimal dot pattern design for light guide using in backlight," Proc. SPIE 6034, 210-217 (2006).

J. G. Chang, Y. B. Fang, and C. F. Lin, "Photometric quantity analysis of backlight for a dual-panel display," Opt. Eng. (Bellingham) 45, 056402 (2006).
[CrossRef]

Lin, H. C.

C. C. Hwang, J. G. Chang, J. M. Lu, and H. C. Lin, "Dual Damascene simulation for ionized physical vapor deposition process: investigation on incident energy and via geometry effects," J. Phys. Soc. Jpn. 72, 3151-5157 (2003).
[CrossRef]

Liu, C. H.

G. T. Sung and C. H. Liu, "Lightguide and method for manufacturing the same," U.S. patent 6680010 (20 January 2001).

Lu, J. M.

C. C. Hwang, J. G. Chang, J. M. Lu, and H. C. Lin, "Dual Damascene simulation for ionized physical vapor deposition process: investigation on incident energy and via geometry effects," J. Phys. Soc. Jpn. 72, 3151-5157 (2003).
[CrossRef]

Mizuta, H.

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

T. Idé, H. Mizuta, Y. Taira, and A. Nishikai, "Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern," U.S. patent 6,865,325 (8 March 2005).

Nishikai, A.

T. Idé, H. Mizuta, Y. Taira, and A. Nishikai, "Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern," U.S. patent 6,865,325 (8 March 2005).

Noguchi, M.

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

Numata, H.

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

Rudisill, C. A.

C. A. Rudisill and S. P. Ryan, "Discretely applied diffusor structure on lightguides," U.S. patent 5,940,215 (17 August 1999).

Ryan, S. P.

C. A. Rudisill and S. P. Ryan, "Discretely applied diffusor structure on lightguides," U.S. patent 5,940,215 (17 August 1999).

Shi, L.

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Su, M. H.

J. G. Chang, M. H. Su, C. T. Lee, and C. C. Hwang, "Generating random and non-overlapping dot patterns for LCD backlight light guides using molecular dynamics method," J. Appl. Phys. 98, 114910 (2005).
[CrossRef]

M. H. Su, C. C. Hwang, J. G. Chang, and S. H. Wang, "Microstructure evolution analysis in Co/Cu layers during the annealing process," J. Appl. Phys. 93, 4566-4575 (2003).
[CrossRef]

Sung, G. T.

G. T. Sung and C. H. Liu, "Lightguide and method for manufacturing the same," U.S. patent 6680010 (20 January 2001).

Suzuki, M.

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

Taira, Y.

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "Dot pattern generation technique using molecular dynamics," J. Opt. Soc. Am. A 20, 248-255 (2003).
[CrossRef]

T. Idé, H. Mizuta, Y. Taira, and A. Nishikai, "Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern," U.S. patent 6,865,325 (8 March 2005).

Wang, S. H.

M. H. Su, C. C. Hwang, J. G. Chang, and S. H. Wang, "Microstructure evolution analysis in Co/Cu layers during the annealing process," J. Appl. Phys. 93, 4566-4575 (2003).
[CrossRef]

Zhu, X. W.

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

Carbon (1)

J. G. Chang, C. C. Hwang, S. P. Ju, and S. H. Huang, "A molecular dynamics simulation investigation into the structure of fullerene C60 grown on a diamond substrate," Carbon 42, 2609-2616 (2004).
[CrossRef]

J. Appl. Phys. (2)

M. H. Su, C. C. Hwang, J. G. Chang, and S. H. Wang, "Microstructure evolution analysis in Co/Cu layers during the annealing process," J. Appl. Phys. 93, 4566-4575 (2003).
[CrossRef]

J. G. Chang, M. H. Su, C. T. Lee, and C. C. Hwang, "Generating random and non-overlapping dot patterns for LCD backlight light guides using molecular dynamics method," J. Appl. Phys. 98, 114910 (2005).
[CrossRef]

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

J. Phys. A (1)

W. H. Hai, X. W. Zhu, M. Feng, L. Shi, K. L. Gao, X. M. Fang, and G. S. Chong, "Numerical instability in Rayleigh-Schrodinger quantum mechanics," J. Phys. A 34, L79-L87 (2001).
[CrossRef]

J. Phys. Soc. Jpn. (1)

C. C. Hwang, J. G. Chang, J. M. Lu, and H. C. Lin, "Dual Damascene simulation for ionized physical vapor deposition process: investigation on incident energy and via geometry effects," J. Phys. Soc. Jpn. 72, 3151-5157 (2003).
[CrossRef]

J. Soc. Inf. Disp. (1)

T. Idé, H. Mizuta, H. Numata, Y. Taira, M. Suzuki, M. Noguchi, and Y. Katsu, "A novel dot-pattern generation to improve luminance uniformity of LCD backlight," J. Soc. Inf. Disp. 11, 659-665 (2003).
[CrossRef]

Opt. Eng. (Bellingham) (2)

W. Y. Lee, T. K. Lim, Y. W. Lee, and I. W. Lee, "Fast ray-tracing methods for LCD backlight simulation using the characteristics of the pattern," Opt. Eng. (Bellingham) 44, 014004 (2005).
[CrossRef]

J. G. Chang, Y. B. Fang, and C. F. Lin, "Photometric quantity analysis of backlight for a dual-panel display," Opt. Eng. (Bellingham) 45, 056402 (2006).
[CrossRef]

Proc. SPIE (2)

J. F. Derlofske, "Computer modeling of LED light pipe systems for uniform display illumination," Proc. SPIE 4445, 119-129 (2001).
[CrossRef]

J. G. Chang, Y. B. Fang, and C. F. Lin, "Solution strategy of optimal dot pattern design for light guide using in backlight," Proc. SPIE 6034, 210-217 (2006).

Surf. Sci. (1)

C. C. Hwang, G. J. Huang, S. P. Ju, and J. G. Chang, "Incident ion characteristics in ionized physical vapor deposition using molecular dynamics simulation," Surf. Sci. 512, 135-150 (2002).
[CrossRef]

Other (10)

J. M. Haile, Molecular Dynamics Simulation (Wiley, 1992).

LightTools, Optical Design Tools for Backlight Displays (Optical Research Associates, 2005).

Breault Research Organization, "The ASAP Primer," http://www.breault.com/k-base.php.

American National Standards Institute (ANSI), "Measuring method of optical characteristics for backlight unit," SEMI D33-0703 (ANSI, 2003).

J. G. Chang and Y. B. Fang, "Dot pattern design of light guide in edge-lit backlight using regional partition approach," Opt. Eng. (Bellingham) (to be published).

C. A. Rudisill and S. P. Ryan, "Discretely applied diffusor structure on lightguides," U.S. patent 5,940,215 (17 August 1999).

G. T. Sung and C. H. Liu, "Lightguide and method for manufacturing the same," U.S. patent 6680010 (20 January 2001).

T. Idé, H. Mizuta, Y. Taira, and A. Nishikai, "Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern," U.S. patent 6,865,325 (8 March 2005).

Breault Research Organization, "Arrays and bounds in ASAP," 9 June 2006, http://www.breault.com/k-base.php?kbaseID=30&CatID=44.

F. Balena, Programming Microsoft Visual Basic 6.0 (Microsoft, 1999).

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Figures (7)

Fig. 1
Fig. 1

Repulsive force as a function of atomic distance, r i j .

Fig. 2
Fig. 2

(a) Schematics diagram of the cell-division technique and cell notation; (b) schematic diagram of the variable r-cut technique (top) and reflective boundary condition (bottom).

Fig. 3
Fig. 3

(a) Anticipated dot density distribution, (b) initial dot distribution by random number generator, and (c) final dot distribution after regulation and an enlarged view.

Fig. 4
Fig. 4

(a) Anticipated dot density distribution, (b) initial dot distribution by random-number generator (dot distribution remains unchanged for those regions marked with arrow lines), (c) final dot distribution and an enlarged view.

Fig. 5
Fig. 5

Dot distribution during optimization: (a) initial estimate of dot distribution at initial stage and an enlarged view, (b) intermediate stage of dot distribution, (c) final stage of dot distribution, (d) dot density distribution.

Fig. 6
Fig. 6

Dot density variation during optimization at (a) center region; (b) top-most region, along Z axis; and (c) uniformity change during optimization.

Fig. 7
Fig. 7

Illuminance in the final stage.

Equations (14)

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m d 2 r i d t 2 + c d d r i d t = j n f i j ( r i , r j ) ,
f ( r i j ) = r i j r i j e ( r i j c k l ) ,
c k l = ln f re r cut , k l ,
D k l = A dot A cell = m k l π r 2 A cell ,
A r ̱ min , k l = A cell m k l .
r cut , k l = a m A cell π m k l ,
L ( θ ) = L 0 e ( 1 2 ) ( θ σ ) 2 for ϕ = 0 2 π ,
L 0 , i j = 4 2 π 3 2 1 σ e 2 σ 2 1 [ Erfi ( 2 σ 2 + i θ 2 σ ) Erfi ( 2 σ 2 + i θ 2 σ ) ] 0 π 2 Φ i j A i j ,
E a v = k , l = 1 n , m E k l n m ,
E k l = D k l A cell π r 2 E dot ,
Δ D k l = π r 2 A cell E a v E k l E dot = D k l ( E a v E k l 1 ) ,
D ¯ k l = D k l + Δ D k l = D k l E a v E k l .
m ¯ k l = m k l + Δ m k l = m k l E a v E k l .
U ( % ) = 100 min ( E k l ) max ( E k l ) for k = 1 n , l = 1 m ,

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