Abstract

We propose a novel fast method for full parallax computer-generated holograms with occlusion processing, suitable for volumetric data such as point clouds. A novel light wave propagation strategy relying on the sequential use of the wavefront recording plane method is proposed, which employs look-up tables in order to reduce the computational complexity in the calculation of the fields. Also, a novel technique for occlusion culling with little additional computation cost is introduced. Additionally, the method adheres a Gaussian distribution to the individual points in order to improve visual quality. Performance tests show that for a full-parallax high-definition CGH a speedup factor of more than 2,500 compared to the ray-tracing method can be achieved without hardware acceleration.

© 2015 Optical Society of America

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References

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    [Crossref]
  9. 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,” Photon. Lett. Poland 6, 90–92 (2014).
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    [Crossref]
  11. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T.-C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009).
    [Crossref]
  12. N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
    [Crossref] [PubMed]
  13. D. Hiyama, T. Shimobaba, T. Kakue, and T. Ito, “Acceleration of color computer-generated hologram from RGB-D images using color space conversion,” Opt. Commun. 340, 121–125 (2015).
    [Crossref]
  14. J. Jia, J. Liu, G. Jin, and Y. Wang, “Fast and effective occlusion culling for 3D holographic displays by inverse orthographic projection with low angular sampling,” Appl. Opt. 53, 6287–6293 (2014).
    [Crossref] [PubMed]
  15. H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
    [Crossref]
  16. K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express 21, 21811–21822 (2013).
    [Crossref] [PubMed]
  17. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).
  18. A. Bronstein, M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes (Springer Publishing Company, Incorporated, 2008), 1st ed.

2015 (2)

D. Hiyama, T. Shimobaba, T. Kakue, and T. Ito, “Acceleration of color computer-generated hologram from RGB-D images using color space conversion,” Opt. Commun. 340, 121–125 (2015).
[Crossref]

H. Zhang, Y. Zhao, L. Cao, and G. Jin, “Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues,” Opt. Express 23, 3901–3913 (2015).
[Crossref] [PubMed]

2014 (3)

J. Jia, J. Liu, G. Jin, and Y. Wang, “Fast and effective occlusion culling for 3D holographic displays by inverse orthographic projection with low angular sampling,” Appl. Opt. 53, 6287–6293 (2014).
[Crossref] [PubMed]

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

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,” Photon. Lett. Poland 6, 90–92 (2014).

2013 (2)

2012 (1)

2011 (1)

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

2010 (1)

2009 (4)

2005 (1)

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25 (2005).
[Crossref]

1993 (1)

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

Alam, M. A.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Bronstein, A.

A. Bronstein, M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes (Springer Publishing Company, Incorporated, 2008), 1st ed.

Bronstein, M.

A. Bronstein, M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes (Springer Publishing Company, Incorporated, 2008), 1st ed.

Cao, L.

Chen, J.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Chen, R. H.-Y.

Chong, T.-C.

Chu, D.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Collings, N.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Crossland, B.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).

Hiyama, D.

D. Hiyama, T. Shimobaba, T. Kakue, and T. Ito, “Acceleration of color computer-generated hologram from RGB-D images using color space conversion,” Opt. Commun. 340, 121–125 (2015).
[Crossref]

Ichihashi, Y.

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,” Photon. Lett. Poland 6, 90–92 (2014).

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

Ito, T.

Jeon, S.-H.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Jia, J.

Jin, G.

Kakue, T.

D. Hiyama, T. Shimobaba, T. Kakue, and T. Ito, “Acceleration of color computer-generated hologram from RGB-D images using color space conversion,” Opt. Commun. 340, 121–125 (2015).
[Crossref]

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,” Photon. Lett. Poland 6, 90–92 (2014).

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

Kim, N.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Kimmel, R.

A. Bronstein, M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes (Springer Publishing Company, Incorporated, 2008), 1st ed.

Lee, J.-H.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Liang, X.

Liu, J.

Lucente, M. E.

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

Masuda, N.

Matsushima, K.

Nakahara, S.

Nakayama, H.

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,” Photon. Lett. Poland 6, 90–92 (2014).

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

Oikawa, M.

Okada, N.

Pan, Y.

Phan, A.-H.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Shimobaba, T.

Solanki, S.

Tan, C.

Tanjung, R. B. A.

Wakunami, K.

Wang, Y.

Weng, J.

Wilkinson, T. D.

Xie, J.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Xu, X.

Yamaguchi, M.

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,” Photon. Lett. Poland 6, 90–92 (2014).

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

Yamashita, H.

Zhang, H.

H. Zhang, Y. Zhao, L. Cao, and G. Jin, “Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues,” Opt. Express 23, 3901–3913 (2015).
[Crossref] [PubMed]

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Zhao, Y.

Appl. Opt. (3)

J. Elec. Imag. (1)

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

Opt. Commun. (1)

D. Hiyama, T. Shimobaba, T. Kakue, and T. Ito, “Acceleration of color computer-generated hologram from RGB-D images using color space conversion,” Opt. Commun. 340, 121–125 (2015).
[Crossref]

Opt. Eng. (1)

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Photon. Lett. Poland (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,” Photon. Lett. Poland 6, 90–92 (2014).

Proc. SPIE (2)

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25 (2005).
[Crossref]

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Other (2)

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).

A. Bronstein, M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes (Springer Publishing Company, Incorporated, 2008), 1st ed.

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (4061 KB)      Visualization of the occlusion culling by demonstrating numerical reconstructions of the hologram for different viewing angles of the object
» Visualization 2: MP4 (14296 KB)      Visualization of the full parallax by demonstrating numerical reconstruction of the hologram from different viewing angles

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Figures (8)

Fig. 1
Fig. 1 Previous WRP methods: (a) The WRP method as introduced in [5] with FFT, (b) The multiple WRP method [8] with FFT and (c) The WRP method with band-limited double step Fresnel diffraction (BL-DSF) for RGB and Depth data [9].
Fig. 2
Fig. 2 (a) The proposed multiple-WRP method with uniform segmentation of the 3D object/scene using intra- and inter-WRP propagation and (b) The look-up table with depth quantization levels for each WRP, showing the backward and forward propagation of the points.
Fig. 3
Fig. 3 Example of the propagation of 3 subsequently processed points A, B, C to the WRP. (a) The points and the WRP to which they propagate. (b) The occlusion of A by B, and the partial occlusion of A and B by C. (c) The occlusion mask and the optical field of a particular LUT depth level. (d) – (h) We alternatingly apply occlusion processing and the addition of the LUT field for all points assigned to the WRP, going from back to front.
Fig. 4
Fig. 4 Reconstruction of CGH generated by: (a) the ray tracing method and (b) the proposed method (17 WRPs).
Fig. 5
Fig. 5 (a) Object model of ”Perforated ball” (218,640 points) (b) and (c) Numerical reconstructions of CGH of the point cloud ”Perforated ball” with the proposed method at different positions with matching and non matching holes ( Visualization 1).
Fig. 6
Fig. 6 Digital reconstructions of various 3D point data sets. Table 2 lists the number of points, the computation time, the number of WRPs and the size of the occlusion mask used for each data set.
Fig. 7
Fig. 7 Numerical reconstruction results when viewing from (a) left, (b) right, (c) top and (d) bottom, showing occlusion effect and full parallax. ( Visualization 2).
Fig. 8
Fig. 8 (a) Computation time in seconds as a function of the number of WRPs. Absolute values in seconds are shown. (b) Computation gain as a function of the number of WRPs. Relative values, in reference to the computation time of 1 WRP only are shown. For example, for ”Bimba#2 Full” using 45 WRPs, makes the computation 19 times faster.

Tables (3)

Tables Icon

Table 1 Simulation parameters for all experiments

Tables Icon

Table 2 Results from numerical reconstruction of holograms from six 3D point data sets.

Tables Icon

Table 3 Computation time of data set Venus by 5 methods without occlusion processing.

Equations (8)

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u w ( x , y ) = j = 1 N A j R j exp ( i 2 π λ R j )
W j = | z j | tan ( sin 1 λ 2 p ) | z j z w | tan ( λ 2 p ) .
u H P ( ξ , η ) = exp ( i 2 π λ z w ) i λ z w u w ( x , y ) exp ( i π λ z wrp ( ( ξ x w ) 2 + ( η y w ) 2 ) d x w d y w = = exp ( i 2 π λ z w ) i λ z w 1 [ [ u w ( ξ , η ) ] [ h ( ξ , η ) ] ]
u 2 ( x 2 , y 2 ) = 1 [ [ u 1 ( x 1 , y 1 ) ] exp ( 2 π i z 1 / λ 2 ω x 2 ω y 2 ) ]
g ( x , y ) = exp ( x 2 + y 2 2 σ 2 )
ρ p = N H × W p 2
μ p = 1 2 p ρ p
O ( α N / L 2 ) + O ( β LD ) + O ( γ D 2 lnD )

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