Abstract

A light-folded projection three-dimensional (3D) display system with a single projection lens and a rectangular light tunnel which is composed of four folding mirrors on its inside walls is proposed. It is theoretically shown through the Wigner distribution function analysis that the proposed system can generate the same light field effectively as that of the conventional projection-type multiview 3D display system with plural projection lenses. Multiview 3D imaging of the proposed system configuration is experimentally demonstrated.

© 2013 Optical Society of America

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  1. J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50, H87–H115 (2011).
    [CrossRef]
  2. B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer, 2002).
  3. Y. Takaki, “High-density directional display for generating natural three-dimensional images,” Proc. IEEE 94, 654–663 (2006).
    [CrossRef]
  4. A. Stern and B. Javidi, “3-D computational synthetic aperture integral imaging (COMPSAII),” Opt. Express 11, 2446–2451 (2003).
    [CrossRef]
  5. H. Liao, M. Iwahara, H. Nobuhiko, and T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express 12, 1067–1076 (2004).
    [CrossRef]
  6. B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed. (Springer, 2006), pp. 333–378.
  7. G. E. Favalora, “Volumetric 3D displays and application infrastructure,” IEEE Comput. 38, 37–44 (2005).
    [CrossRef]
  8. A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
    [CrossRef]
  9. T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.
  10. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
    [CrossRef]
  11. M. A. Neifeld, “Information, resolution, and space-bandwidth product,” Opt. Lett. 23, 1477–1479 (1998).
    [CrossRef]
  12. M. J. Bastiaans, “Transport equations for the Wigner distribution function,” Opt. Acta 26, 1265–1272 (1979).
    [CrossRef]
  13. Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2009), pp. 1–10.
  14. H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
  15. 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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.
  16. T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.
  17. J. Hahn, Y. Kim, and B. Lee, “Uniform angular resolution integral imaging display with boundary folding mirrors,” Appl. Opt. 48, 504–511 (2009).
    [CrossRef]

2011 (1)

2009 (1)

2007 (1)

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
[CrossRef]

2006 (1)

Y. Takaki, “High-density directional display for generating natural three-dimensional images,” Proc. IEEE 94, 654–663 (2006).
[CrossRef]

2005 (1)

G. E. Favalora, “Volumetric 3D displays and application infrastructure,” IEEE Comput. 38, 37–44 (2005).
[CrossRef]

2004 (1)

2003 (1)

1998 (1)

1996 (1)

1979 (1)

M. J. Bastiaans, “Transport equations for the Wigner distribution function,” Opt. Acta 26, 1265–1272 (1979).
[CrossRef]

Agocs, T.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

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 Short Papers Proceedings (Eurographics, 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 Short Papers Proceedings (Eurographics, 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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

Bastiaans, M. J.

M. J. Bastiaans, “Transport equations for the Wigner distribution function,” Opt. Acta 26, 1265–1272 (1979).
[CrossRef]

Bettio, F.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.

Bolas, M.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
[CrossRef]

Bouvier, E.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.

Chen, N.

Choi, H.-J.

Curless, B.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.

Debevec, P.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
[CrossRef]

Dohi, T.

Dorsch, R. G.

Favalora, G. E.

G. E. Favalora, “Volumetric 3D displays and application infrastructure,” IEEE Comput. 38, 37–44 (2005).
[CrossRef]

Ferreira, C.

Forgacs, T.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.

Georgiev, T.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.

Gobbetti, E.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.

Hahn, J.

Hong, J.

Intwala, C.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.

Iwahara, M.

Javidi, B.

Jones, A.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
[CrossRef]

Kim, H.

Kim, Y.

Kutay, M. A.

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Lee, B.

Levoy, M.

Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2009), pp. 1–10.

Liao, H.

Lohmann, A. W.

McDowall, I.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
[CrossRef]

Mendlovic, D.

Min, S.-W.

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50, H87–H115 (2011).
[CrossRef]

B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed. (Springer, 2006), pp. 333–378.

Nayar, S.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.

Neifeld, M. A.

Nobuhiko, H.

Ozaktas, H. M.

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Park, J.-H.

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50, H87–H115 (2011).
[CrossRef]

B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed. (Springer, 2006), pp. 333–378.

Salesin, D.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.

Stern, A.

Takaki, Y.

Y. Takaki, “High-density directional display for generating natural three-dimensional images,” Proc. IEEE 94, 654–663 (2006).
[CrossRef]

Yamada, H.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
[CrossRef]

Zalevsky, Z.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
[CrossRef]

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Zanetti, G.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.

Zhang, Z.

Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2009), pp. 1–10.

Zheng, K. C.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.

ACM Trans. Graph. (1)

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26, 40 (2007).
[CrossRef]

Appl. Opt. (2)

IEEE Comput. (1)

G. E. Favalora, “Volumetric 3D displays and application infrastructure,” IEEE Comput. 38, 37–44 (2005).
[CrossRef]

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

Opt. Acta (1)

M. J. Bastiaans, “Transport equations for the Wigner distribution function,” Opt. Acta 26, 1265–1272 (1979).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. IEEE (1)

Y. Takaki, “High-density directional display for generating natural three-dimensional images,” Proc. IEEE 94, 654–663 (2006).
[CrossRef]

Other (7)

B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed. (Springer, 2006), pp. 333–378.

B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer, 2002).

Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2009), pp. 1–10.

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

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 Short Papers Proceedings (Eurographics, 2005), pp. 109–112.

T. Agocs, T. Balogh, T. Forgacs, F. Bettio, E. Gobbetti, G. Zanetti, and E. Bouvier, “A large scale interactive holographic display,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2006), pp. 311–312.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution trade-offs in integral photography,” in Proceedings of the 17th Eurographics Workshop on Rendering (Eurographics, 2006), pp. 263–272.

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Figures (10)

Fig. 1.
Fig. 1.

Schematics of 3D light-folded display with one projection lens and the light tunnel composed of light-folded mirrors.

Fig. 2.
Fig. 2.

Coordinates of a projection lens system. Here, the elemental image plane is projected on the image plane by a projection lens with focal length f. A ray in the elemental image plane is defined two space coordinates and two directional cosines. Its directional cosine is a product of the wavelength λ and the spatial frequency fEI.

Fig. 3.
Fig. 3.

(a) Propagation of light field through the projection lens and WDFs at (b) elemental image plane, (c) projection lens plane, and (d) image plane when the dimension of a projected image is equal to that of the aperture stop of the projection lens. A green dot in Fig. 3(a) is a point on the elemental image and the bundle of the rays appears as the green line in Figs. (b)–(d).

Fig. 4.
Fig. 4.

(a) Propagation of light field through the projection lens and WDFs at (b) projection lens plane and (c) image plane where there is no light tunnel and the dimension of a projected image is 5 times larger than that of the aperture stop of the projection lens.

Fig. 5.
Fig. 5.

(a) Propagation of light field through the projection lens and the light tunnel and WDFs at (b) the plane with propagation distance as 0.25d2, (c) the plane with propagation distance as 0.75d2, and (d) the image plane when the light field is folded by the light tunnel and the dimension of a projected image is 5 times larger than that of the aperture stop of the projection lens.

Fig. 6.
Fig. 6.

(a) Views of objects depending on the viewing directions and (b) positions and rotations of individual views in array of elemental images.

Fig. 7.
Fig. 7.

Array of elemental images applied for the experiment.

Fig. 8.
Fig. 8.

Experimental setup of the 3D light-folded display with one projection lens and the camera with telecentric lens for observation.

Fig. 9.
Fig. 9.

Perspective views of the 3D light-folded display with one projection lens at the positions; (a) View0,0, (b) View0,1, (c) View2,0, and (d) View1,2.

Fig. 10.
Fig. 10.

Reversely calculated array of elemental images under the condition mirrors in the light tunnel are wrongly tilted.

Equations (13)

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

xPL=xEI+λd1fx,EI,
fx,PL=(1/λf)xEI+(1d1/f)fx,EI.
f=ad1a+w/2.
w=2a×d1/d2.
xI=TriangleWave{xUnfolded/2a},
fx,I=SquareWave{xUnfolded/2a}fx,Unfolded,
TriangleWave(x)=2πsin1[sin(πx)],
SquareWave(x)=2jπ{tanh1[exp(jπx/2)]tanh1[exp(jπx/2)]}.
NTotal=NEI×NView.
ΘEI=2tan1(w2d1).
Directional cosine of Viewmn=mwd1f^x,I+nwd1f^y,I.
Viewmn=Viewmn(xI,yI).
EImn(xEI,yEI)=View(1)m+1m(1)n+1n[(1)m+1d2d1xI,(1)n+1d2d1yI].

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