Abstract

We propose a speckle noise reduction method for generation of coherent holographic stereograms. The method employs densely sampled light field (DSLF) of the scene together with depth information acquired for each ray in the captured DSLF. Speckle reduction is achieved based on the ray separation technique where the scene is first described as a superposition of sparse sets of point sources corresponding to separated sets of rays and then the holographic reconstructions corresponding to these sparse sets of point sources are added incoherently (intensity-wise) to obtain the final reconstruction. The proposed method handles the light propagation between the sparse scene points and hologram elements accurately by utilizing ray resampling based on the notion of DSLF. As a result, as demonstrated via numerical simulations, significant speckle suppression is achieved at no cost of sampling related reconstruction artifacts.

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

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References

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  1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  7. V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. T. Kurihara and Y. Takaki, “Speckle-free, shaded 3d images produced by computer-generated holography,” Opt. Express 21(4), 4044–4054 (2013).
    [Crossref] [PubMed]
  14. T. Utsugi and M. Yamaguchi, “Speckle-suppression in hologram calculation using ray-sampling plane,” Opt. Express 22(14), 17193–17206 (2014).
    [Crossref] [PubMed]
  15. M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, (ACM, 1996), pp. 31–42.
  16. 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]
  17. 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]
  18. M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (Massachusetts Institute of Technology1994).
  19. Z. Lin and H.-Y. Shum, “A geometric analysis of light field rendering,” International Journal of Computer Vision 58(2), 121–138 (2004).
    [Crossref]
  20. C. H. J. Howard, “A Test for the Judgment of Distance,” American Journal of Ophthalmology 2, 656–675 (1919).
    [Crossref]
  21. J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).
  22. Blender Foundation, http://www.blender.org .

2016 (2)

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

Y. Takaki and K. Taira, “Speckle regularization and miniaturization of computer-generated holographic stereograms,” Opt. Express 24(6), 6328–6340 (2016).
[Crossref] [PubMed]

2014 (2)

2013 (1)

2011 (1)

2010 (2)

L. Rong, W. Xiao, F. Pan, S. Liu, and R. Li, “Speckle noise reduction in digital holography by use of multiple polarization holograms,” Chin. Opt. Lett. 8(7), 653–655 (2010).
[Crossref]

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, “Interactive holographic stereograms with accommodation cues,” Proc. SPIE 7619, 761903 (2010).
[Crossref]

2009 (1)

2008 (1)

2004 (1)

Z. Lin and H.-Y. Shum, “A geometric analysis of light field rendering,” International Journal of Computer Vision 58(2), 121–138 (2004).
[Crossref]

1995 (1)

1994 (1)

1993 (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]

1991 (1)

P. W. McOwan, W. J. Hossack, and R. E. Burge, “Three-dimensional stereoscopic display using ray traced computer generated holograms,” Opt. Commun. 82(1–2), 6–11 (1991).
[Crossref]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

1919 (1)

C. H. J. Howard, “A Test for the Judgment of Distance,” American Journal of Ophthalmology 2, 656–675 (1919).
[Crossref]

Amako, J.

Barabas, J.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, “Interactive holographic stereograms with accommodation cues,” Proc. SPIE 7619, 761903 (2010).
[Crossref]

Bianco, V.

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22(21), 25768–25775 (2014).
[Crossref] [PubMed]

Bove, V. M.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, “Interactive holographic stereograms with accommodation cues,” Proc. SPIE 7619, 761903 (2010).
[Crossref]

Burge, R. E.

P. W. McOwan, W. J. Hossack, and R. E. Burge, “Three-dimensional stereoscopic display using ray traced computer generated holograms,” Opt. Commun. 82(1–2), 6–11 (1991).
[Crossref]

Endoh, H.

Ferraro, P.

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22(21), 25768–25775 (2014).
[Crossref] [PubMed]

Finizio, A.

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).

Hanrahan, P.

M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, (ACM, 1996), pp. 31–42.

Honda, T.

M. Yamaguchi, H. Endoh, T. Honda, and N. Ohyama, “High-quality recording of a full-parallax holographic stereogram with a digital diffuser,” Opt. Lett. 19(2), 135–137 (1994).
[Crossref] [PubMed]

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]

Hossack, W. J.

P. W. McOwan, W. J. Hossack, and R. E. Burge, “Three-dimensional stereoscopic display using ray traced computer generated holograms,” Opt. Commun. 82(1–2), 6–11 (1991).
[Crossref]

Howard, C. H. J.

C. H. J. Howard, “A Test for the Judgment of Distance,” American Journal of Ophthalmology 2, 656–675 (1919).
[Crossref]

Javidi, B.

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22(21), 25768–25775 (2014).
[Crossref] [PubMed]

Kang, H.

Kurihara, T.

Levoy, M.

M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, (ACM, 1996), pp. 31–42.

Li, R.

Lin, Z.

Z. Lin and H.-Y. Shum, “A geometric analysis of light field rendering,” International Journal of Computer Vision 58(2), 121–138 (2004).
[Crossref]

Liu, S.

Lucente, M.

M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (Massachusetts Institute of Technology1994).

McOwan, P. W.

P. W. McOwan, W. J. Hossack, and R. E. Burge, “Three-dimensional stereoscopic display using ray traced computer generated holograms,” Opt. Commun. 82(1–2), 6–11 (1991).
[Crossref]

Memmolo, P.

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22(21), 25768–25775 (2014).
[Crossref] [PubMed]

Miura, H.

Netti, P.

Ohyama, N.

M. Yamaguchi, H. Endoh, T. Honda, and N. Ohyama, “High-quality recording of a full-parallax holographic stereogram with a digital diffuser,” Opt. Lett. 19(2), 135–137 (1994).
[Crossref] [PubMed]

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]

Onural, L.

Pan, F.

Paturzo, M.

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22(21), 25768–25775 (2014).
[Crossref] [PubMed]

Rong, L.

Shum, H.-Y.

Z. Lin and H.-Y. Shum, “A geometric analysis of light field rendering,” International Journal of Computer Vision 58(2), 121–138 (2004).
[Crossref]

Smalley, D. E.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, “Interactive holographic stereograms with accommodation cues,” Proc. SPIE 7619, 761903 (2010).
[Crossref]

Smithwick, Q. Y. J.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, “Interactive holographic stereograms with accommodation cues,” Proc. SPIE 7619, 761903 (2010).
[Crossref]

Sonehara, T.

Taira, K.

Takaki, Y.

Utsugi, T.

Xiao, W.

Yamaguchi, M.

Yamaguchi, T.

Yaras, F.

Yokouchi, M.

Yoshikawa, H.

American Journal of Ophthalmology (1)

C. H. J. Howard, “A Test for the Judgment of Distance,” American Journal of Ophthalmology 2, 656–675 (1919).
[Crossref]

Appl. Opt. (3)

Chin. Opt. Lett. (1)

International Journal of Computer Vision (1)

Z. Lin and H.-Y. Shum, “A geometric analysis of light field rendering,” International Journal of Computer Vision 58(2), 121–138 (2004).
[Crossref]

Light: Science & Applications (1)

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light: Science & Applications 5(9), e16142 (2016).
[Crossref]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Opt. Commun. (1)

P. W. McOwan, W. J. Hossack, and R. E. Burge, “Three-dimensional stereoscopic display using ray traced computer generated holograms,” Opt. Commun. 82(1–2), 6–11 (1991).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Proc. SPIE (2)

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, “Interactive holographic stereograms with accommodation cues,” Proc. SPIE 7619, 761903 (2010).
[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]

Other (5)

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).

Blender Foundation, http://www.blender.org .

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (Massachusetts Institute of Technology1994).

M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, (ACM, 1996), pp. 31–42.

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Figures (7)

Fig. 1
Fig. 1 Discrete light field and hologram definitions according to two-plane parametrization.
Fig. 2
Fig. 2 Capture setup and parameters for DSLF. A set of cameras capture the scene at intervals of Δs, sampling the (recentered) image plane at Δx. The area between zb and zf fulfills the DSLF requirement.
Fig. 3
Fig. 3 General structure of the ray separation based speckle suppression method. (a) Assigning emission coordinates to the captured light rays, (b) quantizing each emission point to a voxel (highlighted in red) center point, (c) detailed look at the original and quantized ray distributions, (d) assigning quantized ray intensities based on summation of original ray intensities within the voxels.
Fig. 4
Fig. 4 The reconstructed images via the viewing simulation for different speckle suppression methods and object distances. The plane distance from the hologram plane is 6 mm (top row), 9 mm (middle row) or 12 mm (bottom row). The speckle suppression methods used: (a) without speckle reduction, (b) random averaging, (c) ray separation [14] and (d) proposed method.
Fig. 5
Fig. 5 Scene and LF capture setup for the second experiment utilizing the Pony car model. (The 3D model Pony Cartoon by Slava Zhuravlev is licensed under CC BY 4.0.)
Fig. 6
Fig. 6 Reconstructed images obtained via the viewing simulation. The viewer position is (−15, −15) mm in the top row, (0, 0) mm in the middle row and (15, 15) mm in the bottom row. From left to right: reference image, no speckle suppression, random averaging, ray separation [14], and proposed accurate ray separation.
Fig. 7
Fig. 7 Resolution comparison of reference image (left) and the reconstructed image for the proposed method (right), magnifying the detail on the front of the car.

Tables (3)

Tables Icon

Table 1 Parameters of the CGH and LF capture for the car scene.

Tables Icon

Table 2 Speckle contrasts of each different scene and speckle suppression method.

Tables Icon

Table 3 PSNRs (dB) for the view images corresponding to different methods.

Equations (21)

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O D S C P ( x ) = m rect ( x m Δ x Δ x ) i L i [ m , i ] r m i exp [ j 2 π λ ( ( x x m i ) 2 + z m i 2 z m i ) ] ,
Δ s = min { Δ x z b z b z 0 , Δ x z f z 0 z f } .
z o p t = 2 z b z f z b + z f .
z b = Δ s z 0 Δ s Δ x ,
z f = Δ s z 0 Δ s + Δ x .
L x 2.44 λ l T ,
x m i = m Δ x + z m i ( i Δ s m Δ x ) d ,
z m i = D [ m , i ] ,
Δ x ˜ 1.22 λ d T .
δ z ( z ) = z 2 δ γ c B ,
( x ˜ m i , z ˜ m i ) = arg min ( x ˜ , z ˜ ) S q { ( x ˜ x m i ) 2 + ( z ˜ z m i ) 2 } ,
L ˜ 1 ( m Δ x , s m k ) = i V m k L 1 [ m , i ] ,
V m k = 1 Δ s [ m Δ x d Z m k ( X m k m Δ x ) ] ,
s m k = m Δ x d ( x ˜ m k m Δ x ) z ˜ m k .
i 1 = arg min i s m k / Δ s | i Δ s s m k | ,
i 2 = arg min i > s m k / Δ s | i Δ s s m k | .
L ˜ 1 ( m Δ x , s m k ) = L 1 [ m , i 1 ] ( i 2 Δ s s m k ) + L 1 [ m , i 2 ] ( s m k i 1 Δ s ) Δ s .
O ( x ) = m rect ( x m Δ x Δ x ) k L ˜ 1 ( m Δ x , s m k ) r ˜ m k exp [ j 2 π λ ( ( x x ˜ m k ) 2 + z ˜ m k 2 z ˜ m k ) ] ,
I ( u , v ) = | l { T ( s , t ) z e y e { O D S C P ( x , y ) } } | 2 ,
f = ( 1 d f + 1 l ) 1 .
C = σ I ˜ ,

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