Abstract

We investigate the viewing angle enhancement of a lenticular three-dimensional (3D) display with a triplet lens array. The theoretical limitations of the viewing angle and view number of the lenticular 3D display with the triplet lens array are analyzed numerically. For this, the genetic-algorithm-based design method of the triplet lens is developed. We show that a lenticular 3D display with viewing angle of 120° and 144 views without interview cross talk can be realized with the use of an optimally designed triplet lens array.

© 2011 Optical Society of America

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References

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  1. A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “An interactive 360° light field display,” in Proceedings of ACM SIGGRAPH 2007 Emerging Technologies (ACM, 2007), p. 13.
  2. R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, “gCubik: a cubic autostereoscopic display for multiuser interaction: grasp and group-share virtual images,” in Proceedings of ACM SIGGRAPH 2008 Posters (ACM, 2008), p. 133.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.
  9. C. Van Berkel and J. A. Clarke, “Characterisation and optimisation of 3D-LCD module design,” Proc. SPIE 3012, 179–187 (1997).
    [CrossRef]
  10. H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Disp. 8, 23–26 (2007).
    [CrossRef]
  11. Y.-G. Lee and J. B. Ra, “Image distortion correction for lenticular misalignment in three-dimensional lenticular displays,” Opt. Eng. 45, 017007 (2006).
    [CrossRef]
  12. Z. Michalewicz, Genetic Algorithms+Data structures=Evolution Programs (Springer, 1999).
    [PubMed]
  13. J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
    [CrossRef]

2010 (1)

2009 (1)

2008 (2)

2007 (2)

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Disp. 8, 23–26 (2007).
[CrossRef]

J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
[CrossRef]

2006 (1)

Y.-G. Lee and J. B. Ra, “Image distortion correction for lenticular misalignment in three-dimensional lenticular displays,” Opt. Eng. 45, 017007 (2006).
[CrossRef]

2004 (1)

1997 (1)

C. Van Berkel and J. A. Clarke, “Characterisation and optimisation of 3D-LCD module design,” Proc. SPIE 3012, 179–187 (1997).
[CrossRef]

Agocs, T.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Balet, O.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Balogh, T.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Bettio, F.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Bolas, M.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “An interactive 360° light field display,” in Proceedings of ACM SIGGRAPH 2007 Emerging Technologies (ACM, 2007), p. 13.

Bouvier, E.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Choi, H.

Clarke, J. A.

C. Van Berkel and J. A. Clarke, “Characterisation and optimisation of 3D-LCD module design,” Proc. SPIE 3012, 179–187 (1997).
[CrossRef]

Debevec, P.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “An interactive 360° light field display,” in Proceedings of ACM SIGGRAPH 2007 Emerging Technologies (ACM, 2007), p. 13.

Forgács, T.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Gobbetti, E.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Hahn, J.

He, Q.

J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
[CrossRef]

Hong, H.-K.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Disp. 8, 23–26 (2007).
[CrossRef]

Im, H.-J.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Disp. 8, 23–26 (2007).
[CrossRef]

Inoue, N.

R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, “gCubik: a cubic autostereoscopic display for multiuser interaction: grasp and group-share virtual images,” in Proceedings of ACM SIGGRAPH 2008 Posters (ACM, 2008), p. 133.

Jin, G.

J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
[CrossRef]

Jones, A.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “An interactive 360° light field display,” in Proceedings of ACM SIGGRAPH 2007 Emerging Technologies (ACM, 2007), p. 13.

Jung, S.

Kim, H.

Kim, Y.

Lee, B.

Lee, B.-J.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Disp. 8, 23–26 (2007).
[CrossRef]

Lee, Y.-G.

Y.-G. Lee and J. B. Ra, “Image distortion correction for lenticular misalignment in three-dimensional lenticular displays,” Opt. Eng. 45, 017007 (2006).
[CrossRef]

Lim, Y.

Lopez-Gulliver, R.

R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, “gCubik: a cubic autostereoscopic display for multiuser interaction: grasp and group-share virtual images,” in Proceedings of ACM SIGGRAPH 2008 Posters (ACM, 2008), p. 133.

McDowall, I.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “An interactive 360° light field display,” in Proceedings of ACM SIGGRAPH 2007 Emerging Technologies (ACM, 2007), p. 13.

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithms+Data structures=Evolution Programs (Springer, 1999).
[PubMed]

Min, S.-W.

Nago, N.

Park, G.

Park, J.-H.

Ra, J. B.

Y.-G. Lee and J. B. Ra, “Image distortion correction for lenticular misalignment in three-dimensional lenticular displays,” Opt. Eng. 45, 017007 (2006).
[CrossRef]

Shin, H.-H.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Disp. 8, 23–26 (2007).
[CrossRef]

Takaki, Y.

Van Berkel, C.

C. Van Berkel and J. A. Clarke, “Characterisation and optimisation of 3D-LCD module design,” Proc. SPIE 3012, 179–187 (1997).
[CrossRef]

Wang, M.

J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
[CrossRef]

Yamada, H.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “An interactive 360° light field display,” in Proceedings of ACM SIGGRAPH 2007 Emerging Technologies (ACM, 2007), p. 13.

Yan, Y.

J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
[CrossRef]

Yano, S.

R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, “gCubik: a cubic autostereoscopic display for multiuser interaction: grasp and group-share virtual images,” in Proceedings of ACM SIGGRAPH 2008 Posters (ACM, 2008), p. 133.

Yoshida, S.

R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, “gCubik: a cubic autostereoscopic display for multiuser interaction: grasp and group-share virtual images,” in Proceedings of ACM SIGGRAPH 2008 Posters (ACM, 2008), p. 133.

Zanetti, G.

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Zeng, J.

J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
[CrossRef]

J. Inf. Disp. (1)

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Disp. 8, 23–26 (2007).
[CrossRef]

Opt. Eng. (2)

Y.-G. Lee and J. B. Ra, “Image distortion correction for lenticular misalignment in three-dimensional lenticular displays,” Opt. Eng. 45, 017007 (2006).
[CrossRef]

J. Zeng, G. Jin, M. Wang, Q. He, and Y. Yan, “Design of a short-focal-length double-Fourier-transform-lens system for holographic storage,” Opt. Eng. 46, 033002 (2007).
[CrossRef]

Opt. Express (5)

Proc. SPIE (1)

C. Van Berkel and J. A. Clarke, “Characterisation and optimisation of 3D-LCD module design,” Proc. SPIE 3012, 179–187 (1997).
[CrossRef]

Other (4)

T. Balogh, T. Forgács, T. Agocs, O. Balet, E. Bouvier, F. Bettio, E. Gobbetti, and G. Zanetti, “A scalable hardware and software system for the holographic display of interactive graphics applications,” in EUROGRAPHICS 2005 Short Papers Proceedings (ACM, 2005), pp. 109–112.

Z. Michalewicz, Genetic Algorithms+Data structures=Evolution Programs (Springer, 1999).
[PubMed]

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “An interactive 360° light field display,” in Proceedings of ACM SIGGRAPH 2007 Emerging Technologies (ACM, 2007), p. 13.

R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, “gCubik: a cubic autostereoscopic display for multiuser interaction: grasp and group-share virtual images,” in Proceedings of ACM SIGGRAPH 2008 Posters (ACM, 2008), p. 133.

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Figures (7)

Fig. 1
Fig. 1

(a) Basic structure of the lenticular 3D display and (b) simulation images of the single 3D unit pixel observed at different observation viewing angles of 0 ° , 10 ° , 20 ° , and 40 ° obtained by a self-developed ray-tracing simulator.

Fig. 2
Fig. 2

(a) Schematic of the triplet lenticular lens and (b) elements of the designed merit function of the genetic algorithm.

Fig. 3
Fig. 3

Designed triplet lenses for viewing angles of (a)  20 ° , (b)  40 ° , (c)  60 ° , (d)  80 ° , (e)  100 ° , and (f)  120 ° .

Fig. 4
Fig. 4

3D pixel simulation of the designed triplet with viewing angle of 60 ° : (a) pixel patterns of 9-, 36-, 144-, and 288-view and simulation images of 3D unit pixels at observation angles of (b)  10 ° , (c)  20 ° , (d)  30 ° , (e)  40 ° , and (f)  50 ° .

Fig. 5
Fig. 5

3D pixel simulation of the designed triplet with viewing angle of 80 ° : (a) pixel patterns of 9-, 36-, 144-, and 288-view and simulation images of 3D unit pixels at observation angles of (b)  20 ° , (c)  30 ° , (d)  40 ° , (e)  50 ° , and (f)  60 ° .

Fig. 6
Fig. 6

Classification of 3D modes with respect to the viewing angle and the number of views: pupil diameter, 5 mm ; maximum acceptance angle of eye, 0.5 ° ; observation distance, 50 cm ; interpupilary distance, 65 mm ; and convergence angle, 7.5 ° .

Fig. 7
Fig. 7

Results of design and evaluation of 3D unit pixel with triplet lens.

Equations (3)

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V ( θ ) = 1 M i = 1 M I θ 2 ( x i ) ( 1 M i = 1 M I θ ( x i ) ) 2 ,
P ( θ ) = i x i I θ ( x i ) / i I θ ( x i ) .
E = { 1 , 000 , 000 for     T e < T min α 0 θ max ( ° ) | 1 600 V ( θ ) | 2 d θ + β 0 θ max ( ° ) | P ( θ ) f eff sin θ | 2 d θ for     T e T min .

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