Abstract

We augment layered three-dimensional (3D) displays using a lens placed in front of or between attenuation layers. The lens, or similar optical element, improves the angular resolution of the system and enables translation of the displayed scene from a near-field image to a far-field projection. We analyze the relation between angular resolution (scene depth) and the number of layers and characterize the phase–space trade-offs between spatial and angular frequency components. We also introduce an algorithm for determining the layers of the display, which significantly reduces the computational requirements. The method is demonstrated on a standard 4D light field scene.

© 2013 Optical Society of America

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  1. R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).
  2. F. E. Ives, “A novel stereogram,” J. Franklin Inst. 153, 51–52 (1902).
  3. F. E. Ives, “Parallax stereogram and process of making same,” U. S. patent 725,567 (14April1903).
  4. G. Saxby, Practical Holography (Taylor & Francis, 2003).
  5. D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
    [CrossRef]
  6. G. Wetzstein, D. Lanman, W. Heidrich, and R. Raskar, “Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays,” ACM Trans. Graph. 30, 95 (2011).
  7. H. Gotoda, “A multilayer liquid crystal display for autostereoscopic 3D viewing,” Proc. SPIE 7524, 75240P (2010).
    [CrossRef]
  8. A. Loukianitsa and A. N. Putilin, “Stereo display with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
    [CrossRef]
  9. C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
    [CrossRef]
  10. C. C. Paige and M. A. Saunders, “LSQR: an algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8, 43–71 (1982).
    [CrossRef]
  11. M. Zwicker, W. Matusik, F. Durand, H. Pfister, and C. Forlines, “Antialiasing for automultiscopic 3D displays,” in ACM SIGGRAPH 2006 Sketches (ACM, 2006).
  12. J.-X. Chai, X. Tong, S.-C. Chan, and H.-Y. Shum, “Plenoptic sampling,” in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 307–318.

2011

G. Wetzstein, D. Lanman, W. Heidrich, and R. Raskar, “Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays,” ACM Trans. Graph. 30, 95 (2011).

2010

H. Gotoda, “A multilayer liquid crystal display for autostereoscopic 3D viewing,” Proc. SPIE 7524, 75240P (2010).
[CrossRef]

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[CrossRef]

2002

A. Loukianitsa and A. N. Putilin, “Stereo display with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[CrossRef]

1997

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

1982

C. C. Paige and M. A. Saunders, “LSQR: an algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8, 43–71 (1982).
[CrossRef]

1902

F. E. Ives, “A novel stereogram,” J. Franklin Inst. 153, 51–52 (1902).

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).

Byrd, R. H.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

Chai, J.-X.

J.-X. Chai, X. Tong, S.-C. Chan, and H.-Y. Shum, “Plenoptic sampling,” in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 307–318.

Chan, S.-C.

J.-X. Chai, X. Tong, S.-C. Chan, and H.-Y. Shum, “Plenoptic sampling,” in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 307–318.

Durand, F.

M. Zwicker, W. Matusik, F. Durand, H. Pfister, and C. Forlines, “Antialiasing for automultiscopic 3D displays,” in ACM SIGGRAPH 2006 Sketches (ACM, 2006).

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).

Forlines, C.

M. Zwicker, W. Matusik, F. Durand, H. Pfister, and C. Forlines, “Antialiasing for automultiscopic 3D displays,” in ACM SIGGRAPH 2006 Sketches (ACM, 2006).

Gotoda, H.

H. Gotoda, “A multilayer liquid crystal display for autostereoscopic 3D viewing,” Proc. SPIE 7524, 75240P (2010).
[CrossRef]

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).

Heidrich, W.

G. Wetzstein, D. Lanman, W. Heidrich, and R. Raskar, “Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays,” ACM Trans. Graph. 30, 95 (2011).

Hirsch, M.

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[CrossRef]

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).

Ives, F. E.

F. E. Ives, “A novel stereogram,” J. Franklin Inst. 153, 51–52 (1902).

F. E. Ives, “Parallax stereogram and process of making same,” U. S. patent 725,567 (14April1903).

Kim, Y.

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[CrossRef]

Lanman, D.

G. Wetzstein, D. Lanman, W. Heidrich, and R. Raskar, “Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays,” ACM Trans. Graph. 30, 95 (2011).

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[CrossRef]

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).

Loukianitsa, A.

A. Loukianitsa and A. N. Putilin, “Stereo display with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[CrossRef]

Lu, P.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

Matusik, W.

M. Zwicker, W. Matusik, F. Durand, H. Pfister, and C. Forlines, “Antialiasing for automultiscopic 3D displays,” in ACM SIGGRAPH 2006 Sketches (ACM, 2006).

Ng, R.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).

Nocedal, J.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

Paige, C. C.

C. C. Paige and M. A. Saunders, “LSQR: an algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8, 43–71 (1982).
[CrossRef]

Pfister, H.

M. Zwicker, W. Matusik, F. Durand, H. Pfister, and C. Forlines, “Antialiasing for automultiscopic 3D displays,” in ACM SIGGRAPH 2006 Sketches (ACM, 2006).

Putilin, A. N.

A. Loukianitsa and A. N. Putilin, “Stereo display with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[CrossRef]

Raskar, R.

G. Wetzstein, D. Lanman, W. Heidrich, and R. Raskar, “Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays,” ACM Trans. Graph. 30, 95 (2011).

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[CrossRef]

Saunders, M. A.

C. C. Paige and M. A. Saunders, “LSQR: an algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8, 43–71 (1982).
[CrossRef]

Saxby, G.

G. Saxby, Practical Holography (Taylor & Francis, 2003).

Shum, H.-Y.

J.-X. Chai, X. Tong, S.-C. Chan, and H.-Y. Shum, “Plenoptic sampling,” in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 307–318.

Tong, X.

J.-X. Chai, X. Tong, S.-C. Chan, and H.-Y. Shum, “Plenoptic sampling,” in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 307–318.

Wetzstein, G.

G. Wetzstein, D. Lanman, W. Heidrich, and R. Raskar, “Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays,” ACM Trans. Graph. 30, 95 (2011).

Zhu, C.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

Zwicker, M.

M. Zwicker, W. Matusik, F. Durand, H. Pfister, and C. Forlines, “Antialiasing for automultiscopic 3D displays,” in ACM SIGGRAPH 2006 Sketches (ACM, 2006).

ACM Trans. Graph.

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[CrossRef]

G. Wetzstein, D. Lanman, W. Heidrich, and R. Raskar, “Layered 3D: tomographic image synthesis for attenuation-based light field and high dynamic range displays,” ACM Trans. Graph. 30, 95 (2011).

ACM Trans. Math. Softw.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23, 550–560 (1997).
[CrossRef]

C. C. Paige and M. A. Saunders, “LSQR: an algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8, 43–71 (1982).
[CrossRef]

J. Franklin Inst.

F. E. Ives, “A novel stereogram,” J. Franklin Inst. 153, 51–52 (1902).

Proc. SPIE

H. Gotoda, “A multilayer liquid crystal display for autostereoscopic 3D viewing,” Proc. SPIE 7524, 75240P (2010).
[CrossRef]

A. Loukianitsa and A. N. Putilin, “Stereo display with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[CrossRef]

Other

M. Zwicker, W. Matusik, F. Durand, H. Pfister, and C. Forlines, “Antialiasing for automultiscopic 3D displays,” in ACM SIGGRAPH 2006 Sketches (ACM, 2006).

J.-X. Chai, X. Tong, S.-C. Chan, and H.-Y. Shum, “Plenoptic sampling,” in Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 307–318.

F. E. Ives, “Parallax stereogram and process of making same,” U. S. patent 725,567 (14April1903).

G. Saxby, Practical Holography (Taylor & Francis, 2003).

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. CSTR 2005-02 (Stanford University, 2005).

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Figures (4)

Fig. 1.
Fig. 1.

Layered 3D assembly, with attenuation slides spaced by acrylic sheets, and illumination from a uniform backlight. The assembly on the left is an unmodified layered structure and the assembly on the right contains a lens at the front of the stack.

Fig. 2.
Fig. 2.

Coordinate system convention for the spatial–angular resolution analysis. All coordinates are transformed to observer coordinates.

Fig. 3.
Fig. 3.

Plots of spatial–angular resolution phase space for layered displays with 5 (top) and 10 (bottom) slides. Frequencies that can be represented well are depicted with a higher intensity. Compare with Fig. 6 in [6]. Left: bare slides. Center: slides and front lens. Right: slides and center lens.

Fig. 4.
Fig. 4.

Simulated perspectives as seen by an observer. Top: the target view. Center: a five-slide display without a lens (left) and with a lens (right). Bottom: a 10-slide display without a lens (left) and with a lens (right).

Equations (8)

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Tα=v,
Si=(1itfnsdfnsdit+fitfns1fnsd+ffns)=(SAiSBiSCiSDi),
x=(SASBSCSD)xs+SBSDθ.
F(ν)=F0(Sm+1ν)i=1mαi(νTSABi),
ν=(xθ)=Si(xsiθsi)=(SAiSBiSCiSDi)(xsiθsi)SABi=(SAiSBi).
F{F0(Sm+1ν)}(ν^)=F^0((Sm+1)Tν^).
F{αi(νTSABi)}(ν^)=2πCiα^i(SABiSABi2·ν^)δ(SABiSABi2·ν^).
F^(ν^)=F^0((Sm+1)Tν^)i=1m2πCiα^i(SABiSABi2·ν^)δ(SABiSABi2·ν^),

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