Abstract

In the calculation of large-scale computer-generated holograms, an approach called “tiling,” which divides the hologram plane into small rectangles, is often employed due to limitations on computational memory. However, the total amount of computational complexity severely increases with the number of divisions. In this paper, we propose an efficient method for calculating tiled large-scale holograms using ray-wavefront conversion. In experiments, the effectiveness of the proposed method was verified by comparing its calculation cost with that using the previous method. Additionally, a hologram of 128K × 128K pixels was calculated and fabricated by a laser-lithography system, and a high-quality 105 mm × 105 mm 3D image including complicated reflection and translucency was optically reconstructed.

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

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References

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    [Crossref]
  2. 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).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).
    [Crossref]
  6. 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).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  11. Y.-M. Ji, H. Yeom, and J.-H. Park, “Efficient texture mapping by adaptive mesh division in mesh-based computer generated hologram,” Opt. Express 24(24), 28154–28169 (2016).
    [Crossref] [PubMed]
  12. H. Nishi and K. Matsushima, “Rendering of specular curved objects in polygon-based computer holography,” Appl. Opt. 56(13), F37–F44 (2017).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  17. 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(4), 3901–3913 (2015).
    [Crossref] [PubMed]
  18. K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19(10), 9086–9101 (2011).
    [Crossref] [PubMed]
  19. 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]
  20. H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
    [Crossref] [PubMed]
  21. S. Igarashi, T. Nakamura, and M. Yamaguchi, “Fast method of calculating a photorealistic hologram based on orthographic ray-wavefront conversion,” Opt. Lett. 41(7), 1396–1399 (2016).
    [Crossref] [PubMed]
  22. 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]
  23. N. Takada, T. Shimobaba, H. Nakayama, A. Shiraki, N. Okada, M. Oikawa, N. Masuda, and T. Ito, “Fast high-resolution computer-generated hologram computation using multiple graphics processing unit cluster system,” Appl. Opt. 51(30), 7303–7307 (2012).
    [Crossref] [PubMed]
  24. Y. Pan, X. Xu, and X. Liang, “Fast distributed large-pixel-count hologram computation using a GPU cluster,” Appl. Opt. 52(26), 6562–6571 (2013).
    [Crossref] [PubMed]
  25. P. Lobaz, “Reference calculation of light propagation between parallel planes of different sizes and sampling rates,” Opt. Express 19(1), 32–39 (2011).
    [Crossref] [PubMed]
  26. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  27. K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18(17), 18453–18463 (2010).
    [Crossref] [PubMed]
  28. Blender Foundation, “Blender,” https://www.blender.org .
  29. Kansai University, “Kan-Dai Digital Holo Studio,” http://holography.ordist.kansai-u.ac.jp/digitalholostudio .

2017 (1)

2016 (4)

2015 (3)

2013 (3)

2012 (1)

2011 (2)

2010 (2)

2009 (2)

2008 (2)

2007 (1)

2001 (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).
[Crossref]

1993 (2)

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

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

1988 (1)

1976 (1)

Cao, L.

Chong, T.-C.

Frère, C.

Hahn, J.

Honda, T.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Hoshino, H.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Ichihashi, Y.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated-hologram on AMD HD5000 series GPU and OpenCL,” Opt. Express 18(10), 9955–9960 (2010).
[Crossref] [PubMed]

Ichikawa, T.

Igarashi, S.

Ito, T.

Ji, Y.-M.

Jin, G.

Kakue, T.

Kang, H.

Kim, E.-S.

Kim, H.

Kim, S.-C.

Lee, B.

Leseberg, D.

Liang, X.

Lobaz, P.

Lucente, M.

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

Masuda, N.

Matsushima, K.

Muffoletto, R. P.

Nakamura, T.

Nakayama, H.

Nishi, H.

Nishitsuji, T.

Ohyama, N.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Oi, R.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Oikawa, M.

Okada, N.

Pan, Y.

Park, J.-H.

Sakamoto, Y.

Sasaki, H.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Senoh, T.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Shimobaba, T.

Shiraki, A.

Solanki, S.

Stoykova, E.

Takada, N.

Tan, C.

Tanjung, R. B. A.

Tohline, J. E.

Tyler, J. M.

Wakunami, K.

Xu, X.

Yamaguchi, M.

Yamamoto, K.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Yamashita, H.

Yatagai, T.

Yeom, H.

Yoneyama, T.

Yoshikawa, H.

Zhang, H.

Zhao, Y.

Appl. Opt. (8)

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]

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]

N. Takada, T. Shimobaba, H. Nakayama, A. Shiraki, N. Okada, M. Oikawa, N. Masuda, and T. Ito, “Fast high-resolution computer-generated hologram computation using multiple graphics processing unit cluster system,” Appl. Opt. 51(30), 7303–7307 (2012).
[Crossref] [PubMed]

Y. Pan, X. Xu, and X. Liang, “Fast distributed large-pixel-count hologram computation using a GPU cluster,” Appl. Opt. 52(26), 6562–6571 (2013).
[Crossref] [PubMed]

T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15(11), 2722–2729 (1976).
[Crossref] [PubMed]

D. Leseberg and C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27(14), 3020–3024 (1988).
[Crossref] [PubMed]

H. Kang, E. Stoykova, and H. Yoshikawa, “Fast phase-added stereogram algorithm for generation of photorealistic 3D content,” Appl. Opt. 55(3), A135–A143 (2016).
[Crossref] [PubMed]

H. Nishi and K. Matsushima, “Rendering of specular curved objects in polygon-based computer holography,” Appl. Opt. 56(13), F37–F44 (2017).
[Crossref] [PubMed]

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. Opt. Soc. Am. A (1)

Opt. Express (11)

Y.-M. Ji, H. Yeom, and J.-H. Park, “Efficient texture mapping by adaptive mesh division in mesh-based computer generated hologram,” Opt. Express 24(24), 28154–28169 (2016).
[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]

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(21), 18543–18555 (2009).
[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]

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]

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(4), 3901–3913 (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]

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated-hologram on AMD HD5000 series GPU and OpenCL,” Opt. Express 18(10), 9955–9960 (2010).
[Crossref] [PubMed]

K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18(17), 18453–18463 (2010).
[Crossref] [PubMed]

P. Lobaz, “Reference calculation of light propagation between parallel planes of different sizes and sampling rates,” Opt. Express 19(1), 32–39 (2011).
[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]

Opt. Lett. (2)

Opt. Rev. (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).
[Crossref]

Proc. SPIE (1)

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Sci. Rep. (1)

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Other (3)

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

Blender Foundation, “Blender,” https://www.blender.org .

Kansai University, “Kan-Dai Digital Holo Studio,” http://holography.ordist.kansai-u.ac.jp/digitalholostudio .

Supplementary Material (1)

NameDescription
» Visualization 1       Reconstructed 3D image

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Figures (12)

Fig. 1
Fig. 1 Scheme of the CGH calculation using the ORS plane.
Fig. 2
Fig. 2 Schematic of the original concept of (a) the conventional tiling and (b) the proposed tiling.
Fig. 3
Fig. 3 Calculation of CGH using the rectangular-tiling technique.
Fig. 4
Fig. 4 Concept of the efficient calculation of a tiled hologram using reassembly of orthographic rays.
Fig. 5
Fig. 5 Propagation between two planes and the tiling technique. (a) Original calculation of a hologram using an object plane and (b) the calculation using rectangular tiling.
Fig. 6
Fig. 6 Estimated computational complexity to calculate a 16K × 16K hologram, with conventional tiling, and with the proposed method.
Fig. 7
Fig. 7 Geometrical setup of the ORS and hologram planes for evaluating calculation time.
Fig. 8
Fig. 8 Experimental calculation-time results for the conventional and proposed RS methods.
Fig. 9
Fig. 9 Simulated reconstruction of the 3D image (left and right view).
Fig. 10
Fig. 10 Examples of rendered orthographic images.
Fig. 11
Fig. 11 Geometrical setup of the synthesized CGH.
Fig. 12
Fig. 12 Optical reconstruction of 3D images from the fabricated CGH. (a) Left, (b) right (c) far, and (d) close up views (see Visualization 1).

Equations (29)

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w h ( x )= F 1 [ F[ w RS ( x ) ]H( f x ;z ) ]= F 1 [ W RS ( f x )H( f x ;z ) ].
W RS ( f x )= k O α k ( f x sin α k )
O α k ( f x )=F[ o α k ( x ) ].
w CGH ( x;n )= F 1 [ k=1 K [ F[ w RS ( x;k ) ] H n, k ( f x ;z ) ] ]
o α k ( x;n )= o α k ( x )rect( x( n W tile ztan α k ) W ray )
δ ray = λz Δo .
Δo=z θ eye .
δ ray = λz Δo = λ θ eye =const.
W ray = W tile + δ ray = W tile + λ  θ eye =const.
O α k ( f x ;n )=F[ o α k ( x )rect( x( n W tile ztan α k ) W tile + λ  θ eye ) ].
w CGH ( x;n )= F 1 [ k=1 K O α k ( f x sin α k ;n ) H n,k ( f x ;z ) ].
r= W ray mN W tile = 1+ λ W tile θ eye mN .
r= 1+ 2.2× 10 3 W tile mN .
C= C w +2 X 2 logX+ X 2 .
C conv = N 2 ( C AS + C H + C HOLO )
C AS = C W tile + N 2 ( X N ) 2 log( X N )
C H = ( mN ) 2 ( X N ) 2
C HOLO =  ( X N ) 2 log( X N )
C conv = N 2 C W tile + ( mN ) 2 X 2 log( X N )+ N 2 X 2 + X 2 log( X N ).
C ORS = N 2 ( C AS ORS + C H ORS + C HOLO ORS ).
C AS ORS = A ¯ ( K x N ) 2 log K x .
C H ORS = A ¯ ( K x N ) 2 .
C HOLO ORS = ( X N ) 2 log( X N ).
C ORS = A ¯ K x 2 log N x + A ¯ K x 2 + X 2 log X N .
C max ORS = ( A x K x ) 2 log K x + ( A x K x ) 2 + X 2 log X N
= X 2 log K x + X 2 + X 2 log X N .
θ max = sin 1 ( λ 2Δx )=23.3 [ degree ].
tan θ x =( n A x 2 ) 2 A x tan θ max
tan θ y =( m A y 2 ) 2 A y tan θ max

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