Abstract

A powerful technique is presented for occlusion processing in computer holography. The technique offers an improvement on the conventional silhouette method, which is a general wave optics-based occlusion processing method. The proposed technique dramatically reduces the computation time required for computer-generated holograms (CGH) of self-occluded objects. Performance measurements show that a full-parallax high-definition CGH composed of billions of pixels and a small CGH intended to be reconstructed in electro-holography can be computed in only 1.7 h and 4.5 s, respectively, without any hardware acceleration. Optical reconstruction of the high-definition CGH shows natural and continuous motion parallax in the self-occluded object.

© 2014 Optical Society of America

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References

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  1. A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967).
    [Crossref] [PubMed]
  2. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
    [Crossref] [PubMed]
  3. H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50(34), H245–H252 (2011).
    [Crossref] [PubMed]
  4. K. Matsushima, Y. Arima, and S. Nakahara, “Digitized holography: modern holography for 3D imaging of virtual and real objects,” Appl. Opt. 50(34), H278–H284 (2011).
    [Crossref] [PubMed]
  5. K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
    [Crossref]
  6. H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
    [Crossref]
  7. K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).
  8. K. Matsushima and S. Nakahara, “Stepping closer to the perfect 3D digital image,” SPIE Newsroom (6 Nov. 2012), http://spie.org/x90909.xml .
    [Crossref]
  9. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
    [Crossref] [PubMed]
  10. J. Underkoffler, “Occlusion processing and smooth shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997).
    [Crossref]
  11. 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]
  12. J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966).
    [Crossref]
  13. R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48(21), 4246–4255 (2009).
    [Crossref] [PubMed]
  14. R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram from point cloud using graphics processor,” Appl. Opt. 48(36), 6841–6850 (2009).
    [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. T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21(26), 32019–32031 (2013).
    [Crossref] [PubMed]
  17. I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Visual Comput. J. 26(2), 83–96 (2010).
    [Crossref]
  18. I. Hanák, A. Herout, and P. Zemcik, “Acceleration of detail driven method for hologram generation,” Opt. Eng. 49(8), 085802 (2010).
    [Crossref]
  19. K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19(10), 9086–9101 (2011).
    [Crossref] [PubMed]
  20. T. Fuji and H. Yoshikawa, “Improvement of hidden-surface removal for computer-generated holograms from CG,” in Digital Holography and Three-Dimensional Imaging, (Optical Society of America, 2007), paper DWB3.
  21. K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
    [Crossref]
  22. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47(10), 1567–1574 (2008).
    [Crossref] [PubMed]
  23. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
    [Crossref] [PubMed]
  24. 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]
  25. K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
    [Crossref]
  26. A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53–61 (2007).
    [Crossref]
  27. DigInfo TV, “Computer-synthesized holograms - The ultimate in 3D images” (Digitized Information, Inc., July 22, 2010), http://www.diginfo.tv/2010/07/22/10-0130-r-en.php .
  28. 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]

2013 (3)

2012 (2)

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

2011 (4)

2010 (3)

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]

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Visual Comput. J. 26(2), 83–96 (2010).
[Crossref]

I. Hanák, A. Herout, and P. Zemcik, “Acceleration of detail driven method for hologram generation,” Opt. Eng. 49(8), 085802 (2010).
[Crossref]

2009 (4)

2008 (2)

2007 (1)

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53–61 (2007).
[Crossref]

2005 (2)

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
[Crossref] [PubMed]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
[Crossref]

2004 (1)

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

1997 (1)

J. Underkoffler, “Occlusion processing and smooth shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997).
[Crossref]

1967 (1)

1966 (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966).
[Crossref]

Ahrenberg, L.

Arima, Y.

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

K. Matsushima, Y. Arima, and S. Nakahara, “Digitized holography: modern holography for 3D imaging of virtual and real objects,” Appl. Opt. 50(34), H278–H284 (2011).
[Crossref] [PubMed]

Benzie, P.

Chen, B. C.

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.

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]

Dong, J. W.

Hahn, J.

Hanák, I.

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Visual Comput. J. 26(2), 83–96 (2010).
[Crossref]

I. Hanák, A. Herout, and P. Zemcik, “Acceleration of detail driven method for hologram generation,” Opt. Eng. 49(8), 085802 (2010).
[Crossref]

He, H. X.

Herout, A.

I. Hanák, A. Herout, and P. Zemcik, “Acceleration of detail driven method for hologram generation,” Opt. Eng. 49(8), 085802 (2010).
[Crossref]

Ichikawa, T.

Janda, M.

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Visual Comput. J. 26(2), 83–96 (2010).
[Crossref]

Kim, H.

Kondoh, A.

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53–61 (2007).
[Crossref]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

Lee, B.

Liu, Y. Z.

Lohmann, A. W.

Magnor, M.

Matsushima, K.

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50(34), H245–H252 (2011).
[Crossref] [PubMed]

K. Matsushima, Y. Arima, and S. Nakahara, “Digitized holography: modern holography for 3D imaging of virtual and real objects,” Appl. Opt. 50(34), H278–H284 (2011).
[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]

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
[Crossref] [PubMed]

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53–61 (2007).
[Crossref]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
[Crossref]

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
[Crossref] [PubMed]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

Nakahara, S.

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50(34), H245–H252 (2011).
[Crossref] [PubMed]

K. Matsushima, Y. Arima, and S. Nakahara, “Digitized holography: modern holography for 3D imaging of virtual and real objects,” Appl. Opt. 50(34), H278–H284 (2011).
[Crossref] [PubMed]

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
[Crossref] [PubMed]

Nishi, H.

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50(34), H245–H252 (2011).
[Crossref] [PubMed]

Ogawa, K.

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

Paris, D. P.

Pu, Y. Y.

Sakamoto, Y.

Shimobaba, T.

Skala, V.

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Visual Comput. J. 26(2), 83–96 (2010).
[Crossref]

Underkoffler, J.

J. Underkoffler, “Occlusion processing and smooth shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997).
[Crossref]

Wakunami, K.

Wang, H. Z.

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966).
[Crossref]

Watson, 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]

Yamaguchi, M.

Yamashita, H.

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]

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

Yoneyama, T.

Yoshizaki, Y.

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

Zemcik, P.

I. Hanák, A. Herout, and P. Zemcik, “Acceleration of detail driven method for hologram generation,” Opt. Eng. 49(8), 085802 (2010).
[Crossref]

Zhang, H.

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]

Appl. Opt. (9)

A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967).
[Crossref] [PubMed]

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
[Crossref] [PubMed]

H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50(34), H245–H252 (2011).
[Crossref] [PubMed]

K. Matsushima, Y. Arima, and S. Nakahara, “Digitized holography: modern holography for 3D imaging of virtual and real objects,” Appl. Opt. 50(34), H278–H284 (2011).
[Crossref] [PubMed]

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
[Crossref] [PubMed]

R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48(21), 4246–4255 (2009).
[Crossref] [PubMed]

R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram from point cloud using graphics processor,” Appl. Opt. 48(36), 6841–6850 (2009).
[Crossref] [PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47(10), 1567–1574 (2008).
[Crossref] [PubMed]

H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966).
[Crossref]

J. Electron. Imaging (1)

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

J. Phys.: Conf. Ser. (1)

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” J. Phys.: Conf. Ser. 415, 012053 (2013).

Opt. Eng. (2)

I. Hanák, A. Herout, and P. Zemcik, “Acceleration of detail driven method for hologram generation,” Opt. Eng. 49(8), 085802 (2010).
[Crossref]

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 (5)

Proc. SPIE (4)

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
[Crossref]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

J. Underkoffler, “Occlusion processing and smooth shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

Syst. Comput. Jpn. (1)

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53–61 (2007).
[Crossref]

Visual Comput. J. (1)

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Visual Comput. J. 26(2), 83–96 (2010).
[Crossref]

Other (3)

T. Fuji and H. Yoshikawa, “Improvement of hidden-surface removal for computer-generated holograms from CG,” in Digital Holography and Three-Dimensional Imaging, (Optical Society of America, 2007), paper DWB3.

K. Matsushima and S. Nakahara, “Stepping closer to the perfect 3D digital image,” SPIE Newsroom (6 Nov. 2012), http://spie.org/x90909.xml .
[Crossref]

DigInfo TV, “Computer-synthesized holograms - The ultimate in 3D images” (Digitized Information, Inc., July 22, 2010), http://www.diginfo.tv/2010/07/22/10-0130-r-en.php .

Supplementary Material (1)

» Media 1: MP4 (15001 KB)     

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Figures (16)

Fig. 1
Fig. 1

(a) Schematic illustration of light-shielding of a real opaque object, and (b) emulation of light-shielding by the silhouette method.

Fig. 2
Fig. 2

(a) Schematic illustration of object-by-object light-shielding, and (b) silhouette mask of the current object.

Fig. 3
Fig. 3

Comparison between (a) object-by-object and (b) polygon-by-polygon light-shielding methods.

Fig. 4
Fig. 4

Schematic illustration of (a) polygon-by-polygon light shielding, and (b) the silhouette mask of a polygon.

Fig. 5
Fig. 5

Three types of masking procedure. The final masked field is given by the subtraction of two fields in procedures (ii) and (iii).

Fig. 6
Fig. 6

Schematic illustration of the advantages of the silhouette aperture over the silhouette mask.

Fig. 7
Fig. 7

(a) Forward propagation of the localized field to the object plane, and (b) backward propagation of the small part of the accumulated field in the object plane to the current aperture.

Fig. 8
Fig. 8

Schematic explanation of the procedure for the switch-back technique: (a) switch-back for the current polygon n, and (b) for the next polygon n + 1.

Fig. 9
Fig. 9

Schematic illustration of maximum diffraction areas and the minimum sampling window required for avoiding arising errors in switch-back propagation.

Fig. 10
Fig. 10

Schematic illustration of the division of an object and the multiple object planes.

Fig. 11
Fig. 11

3D scene used for the performance measurements. The sizes and distances indicated are those of the full-size hologram.

Fig. 12
Fig. 12

Object models used for the performance measurements. The number of polygons indicated in brackets in each case is the total number of polygons. The number of front-face polygons is simply half of the total number. Model 5 is used to create the actual HD-CGH.

Fig. 13
Fig. 13

Computation time vs. number of sub-objects. The measured times are for (a) high-definition CGHs and (b) electro-holography.

Fig. 14
Fig. 14

Computation time vs. number of front-face polygons. The measured times are for (a) high-definition CGHs and (b) electro-holography.

Fig. 15
Fig. 15

Optical reconstruction of a fabricated high-definition CGH using (a) the reflected illumination of a red LED, and (b) the transmitted illumination of a He-Ne laser.

Fig. 16
Fig. 16

Close-up photographs of the optical reconstruction using illumination from a red LED. The photographs are taken from various viewpoints. Occlusions and continuous motion parallax are appropriately reconstructed (see Media 1).

Tables (2)

Tables Icon

Table 1 Parameters used for high-definition CGH computation.

Tables Icon

Table 2 Specifications of the hardware and software used for the performance measurements.

Equations (14)

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M n (x,y)={ 1 0 inside orthogonal projection of object n otherwise
u n+1 (x,y)= P n+1,n { M n (x,y) u n (x,y)+ O n (x,y) },
u 3 (x,y)= P 3,2 [ P 2,1 { u 1 (x,y)} M 2 (x,y)]
A n (x,y)=1 M n (x,y).
u 3 (x,y)= P 3,2 [ P 2,1 { u 1 (x,y)} P 2,1 { u 1 (x,y)} A 2 (x,y)] = P 3,1 { u 1 (x,y)} P 3,2 [ P 2,1 { u 1 (x,y)} A 2 (x,y)],
u 3 (x,y)= P 3,1 { u 1 (x,y)}.
u 3 (x,y)= u 3 (x,y) P 3,2 [ P 2,3 { u 3 (x,y)} A 2 (x,y)].
P obj,n+1 { u n+1 (x,y) }= P obj,n+1 [ P n+1,n { M n (x,y) u n (x,y)+ O n (x,y) } ] = P obj,n { M n (x,y) u n (x,y)+ O n (x,y) },
P obj,n+1 { u n+1 (x,y) }= P obj,n { u n (x,y) } P obj,n { A n (x,y) u n (x,y) O n (x,y) }.
u n obj (x,y) P obj,n { u n (x,y) },
u n+1 obj (x,y)= u n obj (x,y)+ P obj,n { O n (x,y) A n (x,y) u n (x,y) }.
u n (x,y)= P n,obj { u n obj (x,y) }.
u n ( x , y ) = P ^ n , obj { u n obj ( x , y ) } ,
u n + 1 obj ( x , y ) = u n obj ( x , y ) + P ^ obj , n { O n ( x , y ) A n ( x , y ) u n ( x , y ) } ,

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