Abstract

In this paper, we propose a new ultrafast layer based CGH calculation that exploits the sparsity of hologram fringe pattern in 3-D object layer. Specifically, we devise a sparse template holographic fringe pattern. The holographic fringe pattern on a depth layer can be rapidly calculated by adding the sparse template holographic fringe patterns at each object point position. Since the size of sparse template holographic fringe pattern is much smaller than that of the CGH plane, the computational load can be significantly reduced. Experimental results show that the proposed method achieves 10-20 msec for 1024x1024 pixels providing visually plausible results.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Accelerated computer generated holography using sparse bases in the STFT domain

David Blinder and Peter Schelkens
Opt. Express 26(2) 1461-1473 (2018)

References

  • View by:
  • |
  • |
  • |

  1. J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20(4), 4018–4023 (2012).
    [PubMed]
  2. C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38, 46–53 (2005).
  3. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
  4. S.-C. Kim and E.-S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48(6), 1030–1041 (2009).
    [PubMed]
  5. T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
    [PubMed]
  6. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39(35), 6587–6594 (2000).
    [PubMed]
  7. H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).
  8. T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
    [PubMed]
  9. A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
    [PubMed]
  10. D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23(2), 1740–1747 (2015).
    [PubMed]
  11. D. Arai, T. Shimobaba, T. Nishitsuji, T. KaKue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).
  12. Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
    [PubMed]
  13. D. Im, J. Cho, J. Hahn, B. Lee, and H. Kim, “Accelerated synthesis algorithm of polygon computer-generated holograms,” Opt. Express 23(3), 2863–2871 (2015).
    [PubMed]
  14. X. Li, J. Liu, Y. Pan, and Y. Wang, “Improved polygon-based method for subwavelength pixel pitch computer generated holograms,” Opt. Commun. 390, 22–25 (2017).
  15. J. S. Chen and D. P. Chu, “Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications,” Opt. Express 23(14), 18143–18155 (2015).
    [PubMed]
  16. Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
    [PubMed]
  17. P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).
  18. H. G. Kim, H. Jeong, and Y. Man Ro, “Acceleration of the calculation speed of computer-generated holograms using the sparsity of the holographic fringe pattern for a 3D object,” Opt. Express 24(22), 25317–25328 (2016).
    [PubMed]
  19. T. Shimobaba and T. Ito, “Fast generation of computer-generated holograms using wavelet shrinkage,” Opt. Express 25(1), 77–87 (2017).
    [PubMed]
  20. A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
  21. M. Levoy, J. Gerth, B. Curless, and K. Pull, “The Stanford 3D Scanning Repository,” (2005) [online], http://graphics.stanford.edu/data/3Dscanrep/ .

2017 (3)

D. Arai, T. Shimobaba, T. Nishitsuji, T. KaKue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).

X. Li, J. Liu, Y. Pan, and Y. Wang, “Improved polygon-based method for subwavelength pixel pitch computer generated holograms,” Opt. Commun. 390, 22–25 (2017).

T. Shimobaba and T. Ito, “Fast generation of computer-generated holograms using wavelet shrinkage,” Opt. Express 25(1), 77–87 (2017).
[PubMed]

2016 (2)

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

H. G. Kim, H. Jeong, and Y. Man Ro, “Acceleration of the calculation speed of computer-generated holograms using the sparsity of the holographic fringe pattern for a 3D object,” Opt. Express 24(22), 25317–25328 (2016).
[PubMed]

2015 (6)

2013 (1)

2012 (1)

2009 (2)

2005 (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38, 46–53 (2005).

2000 (2)

K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39(35), 6587–6594 (2000).
[PubMed]

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).

1993 (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).

Abbeel, P.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.

Achim, T.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.

Arai, D.

D. Arai, T. Shimobaba, T. Nishitsuji, T. KaKue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23(2), 1740–1747 (2015).
[PubMed]

Blinder, D.

Cameron, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38, 46–53 (2005).

Cao, L.

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[PubMed]

Cao, W.

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

Chen, J. S.

Cheng, B.

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

Cho, J.

Chu, D. P.

Endo, Y.

Hahn, J.

Hirayama, R.

Hiyama, D.

Im, D.

Ito, T.

Iwase, S.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).

Jeong, H.

Jia, J.

Jin, C.

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

Jin, G.

KaKue, T.

Kim, E.-S.

Kim, H.

Kim, H. G.

Kim, S.-C.

Kong, D.

Lee, B.

Li, X.

X. Li, J. Liu, Y. Pan, and Y. Wang, “Improved polygon-based method for subwavelength pixel pitch computer generated holograms,” Opt. Commun. 390, 22–25 (2017).

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[PubMed]

Liang, X.

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

Liu, J.

X. Li, J. Liu, Y. Pan, and Y. Wang, “Improved polygon-based method for subwavelength pixel pitch computer generated holograms,” Opt. Commun. 390, 22–25 (2017).

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[PubMed]

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).

Ma, J.

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

Man Ro, Y.

Masuda, N.

Matsushima, K.

Munteanu, A.

Murano, K.

Nakayama, H.

Narayan, K. S.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.

Nishitsuji, T.

D. Arai, T. Shimobaba, T. Nishitsuji, T. KaKue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).

T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
[PubMed]

Oikawa, M.

Okada, N.

Oneda, T.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).

Pan, Y.

X. Li, J. Liu, Y. Pan, and Y. Wang, “Improved polygon-based method for subwavelength pixel pitch computer generated holograms,” Opt. Commun. 390, 22–25 (2017).

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[PubMed]

Schelkens, P.

Sha, J.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.

Shimobaba, T.

Singh, A.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.

Slinger, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38, 46–53 (2005).

Stanley, M.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38, 46–53 (2005).

Su, P.

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

Symeonidou, A.

Takai, M.

Wang, Y.

X. Li, J. Liu, Y. Pan, and Y. Wang, “Improved polygon-based method for subwavelength pixel pitch computer generated holograms,” Opt. Commun. 390, 22–25 (2017).

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[PubMed]

Weng, J.

Yoshikawa, H.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).

Zhang, H.

Zhao, Y.

Appl. Opt. (3)

Computer (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38, 46–53 (2005).

J. Disp. Technol. (1)

P. Su, W. Cao, J. Ma, B. Cheng, X. Liang, L. Cao, and C. Jin, “Fast computer-generated hologram generation method for three-dimensional point cloud model,” J. Disp. Technol. 12(12), 1688–1694 (2016).

J. Electron. Imaging (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).

Opt. Commun. (2)

X. Li, J. Liu, Y. Pan, and Y. Wang, “Improved polygon-based method for subwavelength pixel pitch computer generated holograms,” Opt. Commun. 390, 22–25 (2017).

D. Arai, T. Shimobaba, T. Nishitsuji, T. KaKue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).

Opt. Express (9)

J. S. Chen and D. P. Chu, “Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications,” Opt. Express 23(14), 18143–18155 (2015).
[PubMed]

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[PubMed]

T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
[PubMed]

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20(4), 4018–4023 (2012).
[PubMed]

H. G. Kim, H. Jeong, and Y. Man Ro, “Acceleration of the calculation speed of computer-generated holograms using the sparsity of the holographic fringe pattern for a 3D object,” Opt. Express 24(22), 25317–25328 (2016).
[PubMed]

T. Shimobaba and T. Ito, “Fast generation of computer-generated holograms using wavelet shrinkage,” Opt. Express 25(1), 77–87 (2017).
[PubMed]

D. Im, J. Cho, J. Hahn, B. Lee, and H. Kim, “Accelerated synthesis algorithm of polygon computer-generated holograms,” Opt. Express 23(3), 2863–2871 (2015).
[PubMed]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[PubMed]

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23(2), 1740–1747 (2015).
[PubMed]

Opt. Lett. (1)

Proc. SPIE (1)

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).

Other (2)

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.

M. Levoy, J. Gerth, B. Curless, and K. Pull, “The Stanford 3D Scanning Repository,” (2005) [online], http://graphics.stanford.edu/data/3Dscanrep/ .

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 Overview of the proposed ultrafast CGH calculation method using the sparse template holographic fringe pattern on depth layer.
Fig. 2
Fig. 2 Example of the proposed multiple sub-layer at i-th depth distance.
Fig. 3
Fig. 3 Example of holographic fringe pattern on a sub-layer including a few points. (a) One sub-layer with a few object point light source. (b) Holographic fringe pattern of (a), (c) Sparse holographic fringe pattern including a few dominant signals and zero values (black area), (d) Numerical reconstruction result from (c).
Fig. 4
Fig. 4 Holographic fringe pattern of a sub-layer (a) Proposed sparse template holographic fringe pattern generation, (b) Sparse object points (e.g., five points) in the sub-layer, (c) Holographic fringe pattern of the sub-layer sparse template fringe patterns.
Fig. 5
Fig. 5 Ultrafast layer-based CGH calculation using the sparsity based sparse template holographic fringe pattern (ti) for 3-D point cloud.
Fig. 6
Fig. 6 Visual results of the numerical reconstruction from the CGHs generated by five existing methods and the proposed method for each data set. (a) Results of the ray tracing, (b) Results of the LUT based method [3], (c) Results of the recurrence based method [6], (d) Results of the WRP based method [8], (e) Results of the sparsity based method using sFFT [18], (f) Results of the proposed method.

Tables (5)

Tables Icon

Table 1 Data sets in our experiments

Tables Icon

Table 2 CGH calculation conditions in our experiments

Tables Icon

Table 3 Memory size of LUT for each data set

Tables Icon

Table 4 Computational times [s] of the 1024x1024 CGH calculation

Tables Icon

Table 5 PSNR [dB] for visual quality of the numerical reconstruction from the generated CGH

Equations (3)

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

t i (ξ,η)= exp( j 2π λ z i ) jλ z i l i t (x,y) exp( j π λ z i ( ( ξx ) 2 + ( ηy ) 2 ) )dxdy , = exp( j 2π λ z i ) jλ z i F 1 [ F[ l i t (x,y) ]F[ g(x,y) ] ]
h i,j (ξ,η)= p=1 P i,j t i ( ξ ξ p + R 2 +1,η η p + R 2 +1 ) ,
u(ξ,η)= i=1 D j=1 K i h i,j (ξ,η) .

Metrics