Abstract

The huge computational complexity is a challenge for computer-generated hologram (CGH) calculation in a holographic display. In this paper, we propose a symmetric compressed look-up-table algorithm to accelerate CGH computation based on the Fresnel diffraction theory and compressed look-up-table algorithm. In offline computation, the memory usage of horizontal and vertical modulation factors is reduced to the order of Kilobytes by using translational symmetric compression and wavelength separation. In online computation, we develop a one-time generation of color holograms method which is accelerated by matrix convolution operation. Numerical simulation results show at least 13 times faster than existing algorithms without sacrificing the computation precision. The optical experiments are performed to demonstrate its feasibility. It is believed that the proposed method is an effective algorithm to accelerate the computation of CGH in color holographic display.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. Y. Pan, J. Liu, X. Li, and Y. Wang, “A review of dynamic holographic 3D display: algorithms, devices, and systems,” IEEE Trans. Industr. Inform. 12(4), 1599–1610 (2015).
    [Crossref]
  2. Y. Hayasaki, J. P. Liu, and M. Georges, “Feature issue of digital holography and 3D imaging (DH): introduction,” Appl. Opt. 54(1), DH1–DH2 (2015).
    [Crossref] [PubMed]
  3. J. H. Park, “Recent progresses in computer generated holography for three-dimensional scene,” J. Inf. Displ. 18(1), 1–12 (2017).
    [Crossref]
  4. A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
    [Crossref]
  5. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
    [Crossref]
  6. S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47(19), D55–D62 (2008).
    [Crossref] [PubMed]
  7. S. C. Kim, J. M. Kim, and E. S. Kim, “Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe patterns in computer-generated holograms,” Opt. Express 20(11), 12021–12034 (2012).
    [Crossref] [PubMed]
  8. S. C. Kim, X. B. Dong, M. W. Kwon, and E. S. Kim, “Fast generation of video holograms of three-dimensional moving objects using a motion compensation-based novel look-up table,” Opt. Express 21(9), 11568–11584 (2013).
    [Crossref] [PubMed]
  9. S. C. Kim, X. B. Dong, and E. S. Kim, “Accelerated one-step generation of full-color holographic videos using a color-tunable novel-look-up-table method for holographic three-dimensional television broadcasting,” Sci. Rep. 5(1), 14056 (2015).
    [Crossref] [PubMed]
  10. 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).
    [Crossref] [PubMed]
  11. S. Jiao, Z. Zhuang, and W. Zou, “Fast computer generated hologram calculation with a mini look-up table incorporated with radial symmetric interpolation,” Opt. Express 25(1), 112–123 (2017).
    [Crossref] [PubMed]
  12. Z. Zeng, H. Zheng, Y. Yu, and A. K. Asundic, “Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm,” Opt. Lasers Eng. 93, 47–54 (2017).
    [Crossref]
  13. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17(21), 18543–18555 (2009).
    [Crossref] [PubMed]
  14. J. Jia, Y. Wang, J. Liu, X. Li, Y. Pan, Z. Sun, B. Zhang, Q. Zhao, and W. Jiang, “Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display,” Appl. Opt. 52(7), 1404–1412 (2013).
    [Crossref] [PubMed]
  15. C. Gao, J. Liu, X. Li, G. Xue, J. Jia, and Y. Wang, “Accurate compressed look up table method for CGH in 3D holographic display,” Opt. Express 23(26), 33194–33204 (2015).
    [Crossref] [PubMed]
  16. 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).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  18. 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).
    [Crossref] [PubMed]
  19. 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).
    [Crossref] [PubMed]
  20. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
    [Crossref] [PubMed]
  21. 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).
    [Crossref] [PubMed]
  22. 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).
    [Crossref] [PubMed]
  23. C. Chang, J. Wu, Y. Qi, C. Yuan, S. Nie, and J. Xia, “Simple calculation of a computer-generated hologram for lensless holographic 3D projection using a nonuniform sampled wavefront recording plane,” Appl. Opt. 55(28), 7988–7996 (2016).
    [Crossref] [PubMed]
  24. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. McGraw-Hill College, (Roberts & Co. Publishers, 2005).

2017 (3)

J. H. Park, “Recent progresses in computer generated holography for three-dimensional scene,” J. Inf. Displ. 18(1), 1–12 (2017).
[Crossref]

Z. Zeng, H. Zheng, Y. Yu, and A. K. Asundic, “Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm,” Opt. Lasers Eng. 93, 47–54 (2017).
[Crossref]

S. Jiao, Z. Zhuang, and W. Zou, “Fast computer generated hologram calculation with a mini look-up table incorporated with radial symmetric interpolation,” Opt. Express 25(1), 112–123 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (9)

Y. Pan, J. Liu, X. Li, and Y. Wang, “A review of dynamic holographic 3D display: algorithms, devices, and systems,” IEEE Trans. Industr. Inform. 12(4), 1599–1610 (2015).
[Crossref]

S. C. Kim, X. B. Dong, and E. S. Kim, “Accelerated one-step generation of full-color holographic videos using a color-tunable novel-look-up-table method for holographic three-dimensional television broadcasting,” Sci. Rep. 5(1), 14056 (2015).
[Crossref] [PubMed]

Y. Hayasaki, J. P. Liu, and M. Georges, “Feature issue of digital holography and 3D imaging (DH): introduction,” Appl. Opt. 54(1), DH1–DH2 (2015).
[Crossref] [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).
[Crossref] [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).
[Crossref] [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).
[Crossref] [PubMed]

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).
[Crossref] [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).
[Crossref] [PubMed]

C. Gao, J. Liu, X. Li, G. Xue, J. Jia, and Y. Wang, “Accurate compressed look up table method for CGH in 3D holographic display,” Opt. Express 23(26), 33194–33204 (2015).
[Crossref] [PubMed]

2013 (3)

2012 (1)

2010 (1)

2009 (1)

2008 (1)

1993 (1)

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

1992 (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Arai, D.

Asundic, A. K.

Z. Zeng, H. Zheng, Y. Yu, and A. K. Asundic, “Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm,” Opt. Lasers Eng. 93, 47–54 (2017).
[Crossref]

Cao, L.

Chang, C.

Chen, J. S.

Cho, J.

Chong, T. C.

Chu, D. P.

Dong, X. B.

S. C. Kim, X. B. Dong, and E. S. Kim, “Accelerated one-step generation of full-color holographic videos using a color-tunable novel-look-up-table method for holographic three-dimensional television broadcasting,” Sci. Rep. 5(1), 14056 (2015).
[Crossref] [PubMed]

S. C. Kim, X. B. Dong, M. W. Kwon, and E. S. Kim, “Fast generation of video holograms of three-dimensional moving objects using a motion compensation-based novel look-up table,” Opt. Express 21(9), 11568–11584 (2013).
[Crossref] [PubMed]

Endo, Y.

Gao, C.

Georges, M.

Hahn, J.

Hayasaki, Y.

Hirayama, R.

Hiyama, D.

Im, D.

Ito, T.

Jeong, H.

Jia, J.

Jiang, W.

Jiao, S.

Jin, G.

Kakue, T.

Kim, E. S.

Kim, H.

Kim, H. G.

Kim, J. M.

Kim, S. C.

Kong, D.

Kwon, M. W.

Lee, B.

Leigh, J. J. S.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Li, X.

Liang, X.

Liu, J.

Liu, J. P.

Lucente, M.

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

Man Ro, Y.

Masuda, N.

Murano, K.

Nakayama, H.

Nie, S.

Nishitsuji, T.

Pan, Y.

Park, J. H.

J. H. Park, “Recent progresses in computer generated holography for three-dimensional scene,” J. Inf. Displ. 18(1), 1–12 (2017).
[Crossref]

Qi, Y.

Shimobaba, T.

Solanki, S.

Stein, A. D.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Sun, Z.

Tan, C.

Tanjung, R. B.

Wang, Y.

Wang, Z.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Wu, J.

Xia, J.

Xu, X.

Xue, G.

Yu, Y.

Z. Zeng, H. Zheng, Y. Yu, and A. K. Asundic, “Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm,” Opt. Lasers Eng. 93, 47–54 (2017).
[Crossref]

Yuan, C.

Zeng, Z.

Z. Zeng, H. Zheng, Y. Yu, and A. K. Asundic, “Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm,” Opt. Lasers Eng. 93, 47–54 (2017).
[Crossref]

Zhang, B.

Zhang, H.

Zhao, Q.

Zhao, Y.

Zheng, H.

Z. Zeng, H. Zheng, Y. Yu, and A. K. Asundic, “Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm,” Opt. Lasers Eng. 93, 47–54 (2017).
[Crossref]

Zhuang, Z.

Zou, W.

Appl. Opt. (5)

Comput. Phys. (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

IEEE Trans. Industr. Inform. (1)

Y. Pan, J. Liu, X. Li, and Y. Wang, “A review of dynamic holographic 3D display: algorithms, devices, and systems,” IEEE Trans. Industr. Inform. 12(4), 1599–1610 (2015).
[Crossref]

J. Electron. Imaging (1)

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

J. Inf. Displ. (1)

J. H. Park, “Recent progresses in computer generated holography for three-dimensional scene,” J. Inf. Displ. 18(1), 1–12 (2017).
[Crossref]

Opt. Express (12)

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).
[Crossref] [PubMed]

S. Jiao, Z. Zhuang, and W. Zou, “Fast computer generated hologram calculation with a mini look-up table incorporated with radial symmetric interpolation,” Opt. Express 25(1), 112–123 (2017).
[Crossref] [PubMed]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17(21), 18543–18555 (2009).
[Crossref] [PubMed]

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
[Crossref] [PubMed]

S. C. Kim, J. M. Kim, and E. S. Kim, “Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe patterns in computer-generated holograms,” Opt. Express 20(11), 12021–12034 (2012).
[Crossref] [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).
[Crossref] [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).
[Crossref] [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).
[Crossref] [PubMed]

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).
[Crossref] [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).
[Crossref] [PubMed]

C. Gao, J. Liu, X. Li, G. Xue, J. Jia, and Y. Wang, “Accurate compressed look up table method for CGH in 3D holographic display,” Opt. Express 23(26), 33194–33204 (2015).
[Crossref] [PubMed]

S. C. Kim, X. B. Dong, M. W. Kwon, and E. S. Kim, “Fast generation of video holograms of three-dimensional moving objects using a motion compensation-based novel look-up table,” Opt. Express 21(9), 11568–11584 (2013).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

Z. Zeng, H. Zheng, Y. Yu, and A. K. Asundic, “Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm,” Opt. Lasers Eng. 93, 47–54 (2017).
[Crossref]

Sci. Rep. (1)

S. C. Kim, X. B. Dong, and E. S. Kim, “Accelerated one-step generation of full-color holographic videos using a color-tunable novel-look-up-table method for holographic three-dimensional television broadcasting,” Sci. Rep. 5(1), 14056 (2015).
[Crossref] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. McGraw-Hill College, (Roberts & Co. Publishers, 2005).

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Figures (6)

Fig. 1
Fig. 1 Computation process of symmetrical compressed LUT algorithm.
Fig. 2
Fig. 2 Offline computation time of S-LUT, C-LUT, AC-LUT and SC-LUT algorithms. (a) is the computation time of monochrome LUTs, and (b) is the computation time of color LUTs.
Fig. 3
Fig. 3 Online computation time of S-LUT, C-LUT, AC-LUT and SC-LUT algorithms. (a) is the computation time of monochrome holograms, and (b) is the time of color holograms.
Fig. 4
Fig. 4 Numerical reconstructed results of 3D scene. (a) and (b) are the monochrome results reconstructed at d = 500mm and d = 550mm, respectively. (c) and (d) are the color results reconstructed at d = 500mm and d = 550mm, respectively.
Fig. 5
Fig. 5 Optical experimental reconstructed results of 3D scene. (a) and (b) are the monochrome results reconstructed at d = 500mm and d = 550mm, respectively. (c) and (d) are the color results reconstructed at d = 500mm and d = 550mm, respectively.
Fig. 6
Fig. 6 Optical experimental results of different algorithms reconstructed at d = 500mm and d = 550mm. (a) and (b), (c) and (d), (e) and (f), (g) and (h) are the S-LUT, C-LUT, AC-LUT and SC-LUT reconstructed results, respectively.

Tables (6)

Tables Icon

Algorithm 1 Algorithm 1.

Tables Icon

Algorithm 2 Algorithm 2

Tables Icon

Table 1 Complexity and memory usage among S-LUT, C-LUT, AC-LUT, and SC-LUT

Tables Icon

Table 2 Distortion of reconstructed object among S-LUT, C-LUT, AC-LUT and SC-LUT

Tables Icon

Table 3 Memory usage among S-LUT, C-LUT, AC-LUT and SC-LUT

Tables Icon

Table 4 Results of reconstructed distortion ratio among S-LUT, C-LUT, AC-LUT and SC-LUT

Equations (9)

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

E ( x h , y h ) = j = 1 N A j exp [ i k ( x h x j ) 2 + ( y h y j ) 2 + ( d z j ) 2 ] .
E ( x h , y h ) = j = 1 N A j exp { i k [ ( d z j ) + ( x h x j ) 2 + ( y h y j ) 2 2 ( d z j ) ] } .
E ( x h , y h ) = j = 1 N A j exp ( i k d ) exp { i k ( x h x j ) 2 + ( y h y j ) 2 2 ( d z j ) } .
E ( x h , y h ) = j = 1 N A j [ exp ( i k ( x h x j ) 2 2 ( d z j ) ) ] [ exp ( i k ( y h y j ) 2 2 ( d z j ) ) ] .
E ( x h , y h ) = j = 1 N A j { [ exp ( ( x h x m ) 2 2 ) ] i k d z j [ exp ( ( y h y m ) 2 2 ) ] i k d z j } = j = 1 N A j ( H m w V m w ) .
E ( x , y ) = j = 1 N A j H m w V m w .
E ( x , y ) = j z = 1 N z ( j x , y = 1 N x N y A j H m w V m w ) .
Resolution of H m : [ N x + p ] . Resolution of V m : [ N y + q ] .
r = D / p × 100 % .

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