Abstract

We propose a novel method that synthesizes computer-generated holograms from light field data. Light field, or ray space, is the spatio-angular distribution of light rays coming from three-dimensional scene, and it can also be represented using a large number of views from different observation directions. The proposed method synthesizes a hologram by applying the complex field recovery technique from its Wigner distribution function to the light field data. Unlike conventional approaches, the proposed method synthesizes holograms without hogel configuration, generating a converging parabolic wave for each object point with continuous wavefront. The proposed method does not trade the spatial resolution with angular resolution like conventional hogel-based approaches. Moreover, the proposed method works not only for random phase light field like conventional approaches, but also for arbitrary phase distribution with corresponding carrier waves. Therefore, the proposed method is useful in synthesizing holographic contents for a wide range of applications. The proposed method is verified by simulations and optical experiments, showing successful reconstruction of three-dimensional objects.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
  3. K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22(20), 24450–24465 (2014).
    [Crossref] [PubMed]
  4. M. Askari, S.-B. Kim, K.-S. Shin, S.-B. Ko, S.-H. Kim, D.-Y. Park, Y.-G. Ju, and J.-H. Park, “Occlusion handling using angular spectrum convolution in fully analytical mesh based computer generated hologram,” Opt. Express 25(21), 25867–25878 (2017).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  12. 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]
  13. 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]
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    [Crossref] [PubMed]
  19. N. T. Shaked, J. Rosen, and A. Stern, “Integral holography: white-light single-shot hologram acquisition,” Opt. Express 15(9), 5754–5760 (2007).
    [Crossref] [PubMed]
  20. J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009).
    [Crossref] [PubMed]
  21. H.-S. Kim, K.-M. Jeong, S.-I. Hong, N.-Y. Jo, and J.-H. Park, “Analysis of image distortion based on light ray field by multi-view and horizontal parallax only integral imaging display,” Opt. Express 20(21), 23755–23768 (2012).
    [Crossref] [PubMed]
  22. H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and tis optical production,” Opt. Commun. 32(1), 32–38 (1980).
    [Crossref]
  23. Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” 2009 IEEE International Conference on Computational Photography (ICCP), San Francisco, CA, 2009, pp. 1–10.
    [Crossref]
  24. J.-H. Park, S. K. Lee, N. Y. Jo, H. J. Kim, Y. S. Kim, and H. G. Lim, “Light ray field capture using focal plane sweeping and its optical reconstruction using 3D displays,” Opt. Express 22(21), 25444–25454 (2014).
    [Crossref] [PubMed]

2018 (2)

2017 (2)

2016 (4)

2015 (1)

2014 (2)

2013 (4)

2012 (2)

2011 (1)

2010 (1)

2009 (1)

2007 (1)

1980 (1)

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and tis optical production,” Opt. Commun. 32(1), 32–38 (1980).
[Crossref]

Askari, M.

Baasantseren, G.

Bartelt, H. O.

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and tis optical production,” Opt. Commun. 32(1), 32–38 (1980).
[Crossref]

Brenner, K.-H.

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and tis optical production,” Opt. Commun. 32(1), 32–38 (1980).
[Crossref]

Cao, L.

Cao, S.

Ding, S.

Ewing, R. L.

Feng, Q.

Hamann, S.

Hong, S.-I.

Ichihashi, Y.

Ichikawa, T.

Ito, T.

Jeong, K.-M.

Jin, G.

Jo, N. Y.

Jo, N.-Y.

Ju, Y.-G.

Kang, H.

Kim, H. J.

Kim, H.-S.

Kim, M.-S.

Kim, N.

Kim, S.-B.

Kim, S.-H.

Kim, Y. S.

Kim, Y.-S.

Ko, S.-B.

Kurita, T.

Lee, S. K.

Lee, S.-K.

Levoy, M.

Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” 2009 IEEE International Conference on Computational Photography (ICCP), San Francisco, CA, 2009, pp. 1–10.
[Crossref]

Lim, H. G.

Lim, H.-G.

Lohmann, A. W.

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and tis optical production,” Opt. Commun. 32(1), 32–38 (1980).
[Crossref]

Lv, G.

Masuda, N.

Matsushima, K.

Ming, H.

Nakahara, S.

Nakamura, M.

Nakayama, H.

Ohsawa, Y.

Oi, R.

Park, D.-Y.

Park, J.-H.

Rosen, J.

Sakamoto, Y.

Senoh, T.

Shaked, N. T.

Shi, L.

Shimobaba, T.

Shin, K.-S.

Solgaard, O.

Stern, A.

Stoykova, E.

Wakunami, K.

Wang, A.

Wang, Z.

Wetzstein, G.

Yamaguchi, K.

Yamaguchi, M.

Yamamoto, K.

Yamashita, H.

Yoshikawa, H.

Zhang, H.

Zhang, Z.

Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” 2009 IEEE International Conference on Computational Photography (ICCP), San Francisco, CA, 2009, pp. 1–10.
[Crossref]

Zhao, Y.

Zheng, Y. F.

Appl. Opt. (5)

J. Inform. Display (1)

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

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and tis optical production,” Opt. Commun. 32(1), 32–38 (1980).
[Crossref]

Opt. Express (13)

S.-K. Lee, S.-I. Hong, Y.-S. Kim, H.-G. Lim, N.-Y. Jo, and J.-H. Park, “Hologram synthesis of three-dimensional real objects using portable integral imaging camera,” Opt. Express 21(20), 23662–23670 (2013).
[Crossref] [PubMed]

J.-H. Park, S. K. Lee, N. Y. Jo, H. J. Kim, Y. S. Kim, and H. G. Lim, “Light ray field capture using focal plane sweeping and its optical reconstruction using 3D displays,” Opt. Express 22(21), 25444–25454 (2014).
[Crossref] [PubMed]

N. T. Shaked, J. Rosen, and A. Stern, “Integral holography: white-light single-shot hologram acquisition,” Opt. Express 15(9), 5754–5760 (2007).
[Crossref] [PubMed]

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009).
[Crossref] [PubMed]

H.-S. Kim, K.-M. Jeong, S.-I. Hong, N.-Y. Jo, and J.-H. Park, “Analysis of image distortion based on light ray field by multi-view and horizontal parallax only integral imaging display,” Opt. Express 20(21), 23755–23768 (2012).
[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]

K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22(20), 24450–24465 (2014).
[Crossref] [PubMed]

M. Askari, S.-B. Kim, K.-S. Shin, S.-B. Ko, S.-H. Kim, D.-Y. Park, Y.-G. Ju, and J.-H. Park, “Occlusion handling using angular spectrum convolution in fully analytical mesh based computer generated hologram,” Opt. Express 25(21), 25867–25878 (2017).
[Crossref] [PubMed]

Z. Wang, G. Lv, Q. Feng, A. Wang, and H. Ming, “Simple and fast calculation algorithm for computer-generated hologram based on integral imaging using look-up table,” Opt. Express 26(10), 13322–13330 (2018).
[Crossref] [PubMed]

Y. Ichihashi, R. Oi, T. Senoh, K. Yamamoto, and T. Kurita, “Real-time capture and reconstruction system with multiple GPUs for a 3D live scene by a generation from 4K IP images to 8K holograms,” Opt. Express 20(19), 21645–21655 (2012).
[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]

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]

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]

Opt. Lett. (1)

Other (2)

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a handheld plenoptic camera,” Stanford Tech. Rep. CTSR 2005–02 (Stanford University, 2005).

Z. Zhang and M. Levoy, “Wigner distributions and how they relate to the light field,” 2009 IEEE International Conference on Computational Photography (ICCP), San Francisco, CA, 2009, pp. 1–10.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Computation scheme of the proposed method in comparison with conventional hogel based methods.
Fig. 2
Fig. 2 Maximum depth for different spatial bandwidth of the object (λ = 532nm).
Fig. 3
Fig. 3 Examples of orthographic view images used for the hologram synthesis.
Fig. 4
Fig. 4 Holograms synthesized by the proposed method and their reconstructions. 1st and 2nd columns show amplitude and phase of the synthesized holograms. 3rd column is angular spectrum, i.e. amplitude of Fourier transform of the hologram. 4th and 5th columns are numerical reconstructions at z = −3mm and 2mm. Each row corresponds to different carrier wave.
Fig. 5
Fig. 5 Comparison of reconstruction resolution between the proposed method and conventional hogel based method. In both cases, 10 × 10 orthographic view images are used and the pixel resolution of the hologram is 1000(H) × 1060(V). The object, i.e. resolution target pattern is apart from the hologram plane by 1.9mm. Amplitude and phase of the hologram and its numerical reconstruction at z = 1.9mm for the (a) proposed method, and (b) conventional hogel based method.
Fig. 6
Fig. 6 Experimental setup.
Fig. 7
Fig. 7 Optical experimental result for 3D reconstruction. The reconstruction was captured with the camera focus at (a) front and (b) rear object.
Fig. 8
Fig. 8 Optical experimental result for resolution comparison. Reconstructions of the holograms synthesized by (a) the proposed method and (b) the conventional hogel based method.

Equations (16)

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L( x,y,u,v )= m a m 2 δ( u+ x x m λ z m ,v+ y y m λ z m ) ,
H(x,y)= H( x,y; x c , y c )W( x c , y c )d x c d y c ,
H( x,y; x c , y c )= L( x+ x c 2 , y+ y c 2 ,u,v ) e j2π{ u( x x c )+v( y y c ) } dudv .
H( x,y; x c , y c )= m a m 2 δ( u+ x+ x c 2 x m λ z m ,v+ y+ y c 2 y m λ z m ) e j2π{ u( x x c )+v( y y c ) } dudv = m a m 2 exp[ j π λ z m { ( x x m ) 2 + ( y y m ) 2 } ]exp[ j π λ z m { ( x c x m ) 2 + ( y c y m ) 2 } ].
x= t x + τ x 2 ,y= t y + τ y 2 , x c = t x τ x 2 , y c = t y τ y 2 .
H( x,y; x c , y c )=H( t x + τ x 2 , t y + τ y 2 ; t x τ x 2 , t y τ y 2 ) = L( t x , t y ,u,v )exp[ j2π( u τ x +v τ y ) ] dudv = L ˜ ( t x , t y , τ x , τ y )= L ˜ ( x+ x c 2 , y+ y c 2 ,x x c ,y y c ),
H(x,y)= L ˜ ( x+ x c 2 , y+ y c 2 ,x x c ,y y c )W( x c , y c ) d x c d y c ,
U(x)= m U m (x) = m a m e j ϕ m exp[ j π λ z m ( x x m ) 2 ] ,
WDF( t x ,u)= U( t x + τ x 2 ) U * ( t x τ x 2 ) e j2πu τ x d τ x = m U m ( t x + τ x 2 ) U m * ( t x τ x 2 ) e j2πu τ x d τ x + m,n(m) U m ( t x + τ x 2 ) U n * ( t x τ x 2 ) e j2πu τ x d τ x = m a m 2 δ( u+ t x x m λ z m ) + m,n(m) U m ( t x + τ x 2 ) U n * ( t x τ x 2 ) e j2πu τ x d τ x =L( t x ,u)+ m,n(m) U m ( t x + τ x 2 ) U n * ( t x τ x 2 ) e j2πu τ x d τ x ,
WDF( t x ,u) e j2πu τ x du | t x = x+ x c 2 , τ x =x x c =U( x ) U * ( x c )= m U m (x) n U n * ( x c ) ,
L( t x ,u) e j2πu τ x du | t x = x+ x c 2 , τ x =x x c = L ˜ ( t x , τ x )| t x = x+ x c 2 , τ x =x x c = m U m (x) U m * ( x c ) = m a m 2 exp[ j π λ z m ( x x m ) 2 ] exp[ j π λ z m ( x c x m ) 2 ]=H(x; x c ),
Δ t x =Δx, N tx = N x .
Δu N u = 1 Δ τ x = 1 Δx = sin θ full λ ,
B tx = B x , B u =λ| z | B x ,
Δ t x 1 B x ,Δu 1 λ| z | B x .
N u λ| z | B x 2 .

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