Abstract

Fast calculation and correct depth cue are crucial issues in the calculation of computer-generated hologram (CGH) for high quality three-dimensional (3-D) display. An angular-spectrum based algorithm for layer-oriented CGH is proposed. Angular spectra from each layer are synthesized as a layer-corresponded sub-hologram based on the fast Fourier transform without paraxial approximation. The proposed method can avoid the huge computational cost of the point-oriented method and yield accurate predictions of the whole diffracted field compared with other layer-oriented methods. CGHs of versatile formats of 3-D digital scenes, including computed tomography and 3-D digital models, are demonstrated with precise depth performance and advanced image quality.

© 2015 Optical Society of America

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References

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2015 (2)

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (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]

2014 (3)

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photonics Lett. Pol. 6(3), 90–92 (2014).

K. Hong, J. Yeom, C. Jang, J. Hong, and B. Lee, “Full-color lens-array holographic optical element for three-dimensional optical see-through augmented reality,” Opt. Lett. 39(1), 127–130 (2014).
[Crossref] [PubMed]

J. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

2013 (3)

2012 (2)

Y. Zhao, L. C. Cao, H. Zhang, and Q. S. He, “Holographic display with LED illumination based on phase only spatial light modulator,” Proc. SPIE 8559, 85590B (2012).
[Crossref]

T. Shimobaba, K. Matsushima, T. Kakue, N. Masuda, and T. Ito, “Scaled angular spectrum method,” Opt. Lett. 37(19), 4128–4130 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (4)

F. Yaras, H. Kang, and L. Onural, “State of the art in holographic display: A survey,” J. Displ. Technol. 6(10), 443–454 (2010).
[Crossref]

Y. Z. Liu, J. W. Dong, Y. Y. Pu, B. C. Chen, H. X. He, and H. Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18(4), 3345–3351 (2010).
[Crossref] [PubMed]

K. Matsushima and S. Nakahara, “High-definition full-parallax CGHs created by using the polygon-based method and the shifted angular spectrum method,” Proc. SPIE 7619, 761913 (2010).
[Crossref]

M. Bayraktar and M. Özcan, “Method to calculate the far field of three-dimensional objects for computer-generated holography,” Appl. Opt. 49(24), 4647–4654 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (3)

2007 (1)

2006 (3)

2005 (1)

2004 (1)

1993 (1)

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

1976 (1)

Ahrenberg, L.

Bayraktar, M.

Benzie, P.

Cao, L.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Cao, L. C.

Y. Zhao, L. C. Cao, H. Zhang, and Q. S. He, “Holographic display with LED illumination based on phase only spatial light modulator,” Proc. SPIE 8559, 85590B (2012).
[Crossref]

Chen, B. C.

Chen, J.

J. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

Chen, J. S.

Chen, X.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Chu, D.

J. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

Chu, D. P.

Dong, J. W.

Gu, M.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Hahn, J.

Haist, T.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8(1), 8–13 (2006).
[Crossref]

He, H. X.

He, Q. S.

Y. Zhao, L. C. Cao, H. Zhang, and Q. S. He, “Holographic display with LED illumination based on phase only spatial light modulator,” Proc. SPIE 8559, 85590B (2012).
[Crossref]

Hong, J.

Hong, K.

Hu, B.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Ichihashi, Y.

Ito, T.

Jang, C.

Javidi, B.

Jia, J.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Jin, G.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Kakue, T.

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photonics Lett. Pol. 6(3), 90–92 (2014).

T. Shimobaba, K. Matsushima, T. Kakue, N. Masuda, and T. Ito, “Scaled angular spectrum method,” Opt. Lett. 37(19), 4128–4130 (2012).
[Crossref] [PubMed]

Kang, H.

F. Yaras, H. Kang, and L. Onural, “State of the art in holographic display: A survey,” J. Displ. Technol. 6(10), 443–454 (2010).
[Crossref]

H. Kang, T. Yamaguchi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47(19), D44–D54 (2008).
[Crossref] [PubMed]

Kim, H.

Lee, B.

Li, C.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Li, Q.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Li, X.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Liang, X.

Liu, J.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Liu, Y. Z.

Lucente, V. M.

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

Magnor, M.

Masuda, N.

Matsushima, K.

Muffoletto, R. P.

Nakahara, S.

K. Matsushima and S. Nakahara, “High-definition full-parallax CGHs created by using the polygon-based method and the shifted angular spectrum method,” Proc. SPIE 7619, 761913 (2010).
[Crossref]

Nakayama, H.

Niwa, M.

Oi, R.

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photonics Lett. Pol. 6(3), 90–92 (2014).

Okada, N.

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photonics Lett. Pol. 6(3), 90–92 (2014).

Onural, L.

F. Yaras, H. Kang, and L. Onural, “State of the art in holographic display: A survey,” J. Displ. Technol. 6(10), 443–454 (2010).
[Crossref]

Özcan, M.

Pan, Y.

Pu, Y. Y.

Reicherter, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8(1), 8–13 (2006).
[Crossref]

Ren, H.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Rivenson, Y.

Sahu, A.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Seifert, L.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8(1), 8–13 (2006).
[Crossref]

Shimobaba, T.

Shiraki, A.

Smithwick, Q.

J. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

Stern, A.

Sugie, T.

Takada, N.

Tanaka, T.

Tohline, J. E.

Tyler, J. M.

Wakunami, K.

Wang, H. Z.

Wang, Y.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Watson, J.

Wu, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8(1), 8–13 (2006).
[Crossref]

Xu, X.

Xue, G.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Yamaguchi, I.

Yamaguchi, M.

Yamaguchi, T.

Yamamoto, K.

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photonics Lett. Pol. 6(3), 90–92 (2014).

Yamashita, H.

Yaras, F.

F. Yaras, H. Kang, and L. Onural, “State of the art in holographic display: A survey,” J. Displ. Technol. 6(10), 443–454 (2010).
[Crossref]

Yaroslavsky, L. P.

Yatagai, T.

Yeom, J.

Yoshikawa, H.

Zhang, F.

Zhang, H.

Y. Zhao, L. C. Cao, H. Zhang, and Q. S. He, “Holographic display with LED illumination based on phase only spatial light modulator,” Proc. SPIE 8559, 85590B (2012).
[Crossref]

Zhao, Y.

Y. Zhao, L. C. Cao, H. Zhang, and Q. S. He, “Holographic display with LED illumination based on phase only spatial light modulator,” Proc. SPIE 8559, 85590B (2012).
[Crossref]

Appl. Opt. (8)

Comput. Sci. Eng. (1)

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8(1), 8–13 (2006).
[Crossref]

J. Displ. Technol. (1)

F. Yaras, H. Kang, and L. Onural, “State of the art in holographic display: A survey,” J. Displ. Technol. 6(10), 443–454 (2010).
[Crossref]

J. Electron. Imaging (2)

J. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

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

Nat. Commun. (1)

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6, 6984 (2015).
[Crossref] [PubMed]

Opt. Express (10)

Y. Z. Liu, J. W. Dong, Y. Y. Pu, B. C. Chen, H. X. He, and H. Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18(4), 3345–3351 (2010).
[Crossref] [PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14(17), 7636–7641 (2006).
[Crossref] [PubMed]

K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19(10), 9086–9101 (2011).
[Crossref] [PubMed]

Y. Ichihashi, H. Nakayama, T. Ito, N. Masuda, T. Shimobaba, A. Shiraki, and T. Sugie, “HORN-6 special-purpose clustered computing system for electroholography,” Opt. Express 17(16), 13895–13903 (2009).
[Crossref] [PubMed]

A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector,” Opt. Express 17(18), 16038–16045 (2009).
[Crossref] [PubMed]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14(2), 603–608 (2006).
[Crossref] [PubMed]

K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express 21(19), 21811–21822 (2013).
[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]

R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express 15(9), 5631–5640 (2007).
[Crossref] [PubMed]

K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17(22), 19662–19673 (2009).
[Crossref] [PubMed]

Opt. Lett. (3)

Photonics Lett. Pol. (1)

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photonics Lett. Pol. 6(3), 90–92 (2014).

Proc. SPIE (2)

Y. Zhao, L. C. Cao, H. Zhang, and Q. S. He, “Holographic display with LED illumination based on phase only spatial light modulator,” Proc. SPIE 8559, 85590B (2012).
[Crossref]

K. Matsushima and S. Nakahara, “High-definition full-parallax CGHs created by using the polygon-based method and the shifted angular spectrum method,” Proc. SPIE 7619, 761913 (2010).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Supplementary Material (1)

NameDescription
» Visualization 1: MOV (3622 KB)      The optical reconstruction of a rotating hall.

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Figures (8)

Fig. 1
Fig. 1 Diagram of angular-spectrum layer-oriented method.
Fig. 2
Fig. 2 The influence of calculation width and sampling number on the effective distance.
Fig. 3
Fig. 3 PSNR of the reconstruction with different bit-depth holograms and different sampling points.
Fig. 4
Fig. 4 Optical setup of the holographic display system.
Fig. 5
Fig. 5 Reconstructed images of the train. (a), (b) and (c) are numerical reconstructions of the train at distance d = 210mm, 220mm, 230mm, respectively. (d), (e) and (f) are optical reconstructions of the train at distance d = 210mm, 220mm, 230mm, respectively.
Fig. 6
Fig. 6 Reconstructed images of the headangio. (a) and (b) are numerical reconstructions at distance d = 210 mm, 220 mm, respectively. (c) and (d) are optical reconstructions at distance d = 210 mm, 220 mm, respectively.
Fig. 7
Fig. 7 Reconstructed images of a hall. (a) is the 3-D model and (b) is the optical reconstruction (see Visualization 1).
Fig. 8
Fig. 8 Numerical simulation of angular spectrum method and FFT based Fresnel diffraction. (a) Simulation diagram. (b) SNR of the algorithms.

Tables (2)

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Table 1 Computation time of the train and headangio

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Table 2 Parameters of computing the train and headangio with the layer-oriented method

Equations (9)

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H F ( u,v )=exp[ jkz 1- λ 2 u 2 - λ 2 v 2 ],
H F ( m,n )=exp[ jkz 1 λ 2 ( m u 0 ) 2 λ 2 ( n v 0 ) 2 ],
H(u;z)=exp[ j2πz λ -2 u 2 ].
f lu = 1 2π u ϕ(u)= zu λ 2 u 2 .
Δ u 1 2| f lu |.
zL λ 2 u 2 1 .
z L 4 L 2 λ 2 N 2 N .
zL 4 (Δx) 2 λ 2 1 .
PSNR=10log( 255 2 1 mn m,n ( I 0 (m,n) I r (m,n) ) 2 ),

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