Abstract

Successful commercialization of holographic printers based on holographic stereograms requires a tool for their numerical replaying and quality assessment before the time-consuming and expensive process of holographic recording. A holographic stereogram encodes 2D images of a 3D scene that are incoherently captured from multiple perspectives and rearranged before recording. This study presents a simulator which builds a full parallax and full color white light viewable holographic stereogram from the perspective images captured by a virtual recentering camera with its further numerical reconstruction for any viewer location. By tracking all steps from acquisition to recording, the simulator allows for analysis of radial distortions caused by the optical elements used at the recording stage. Numerical experiments conducted at increasing degree of pincushion distortion proved its insignificant influence on the reconstructed images in all practical cases by using a peak signal-to-noise ratio and the structural similarity as an image quality metrics.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. S. A. Benton, “Survey of holographic stereograms,” in 26th Annual Technical Symposium (International Society for Optics and Photonics, 1983), pp. 15–19.
  3. M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic 3-D printer,” in OE/LASE’90, 14–19 Jan., Los Angeles, CA (International Society for Optics and Photonics, 1990), pp. 84–92.
  4. M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic three-dimensional printer: new method,” Appl. Opt. 31, 217–222 (1992).
    [Crossref] [PubMed]
  5. S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” in Integrated Optoelectronic Devices 2008 (International Society for Optics and Photonics, 2008), 69120N.
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    [Crossref]
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    [Crossref]
  9. M. W. Halle, “The generalized holographic stereogram,” Ph.D. thesis, Massachusetts Institute of Technology (1993).
  10. M. Halle, “Multiple viewpoint rendering,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 243–254.
  11. A. J. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” in IS&T/SPIE’s Symposium on Electronic Imaging: Science and Technology (International Society for Optics and Photonics, 1993), pp. 36–48.
  12. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [Crossref] [PubMed]
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  14. 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, 23755–23768 (2012).
    [Crossref] [PubMed]

2013 (1)

2012 (2)

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, 23755–23768 (2012).
[Crossref] [PubMed]

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

1992 (1)

1948 (1)

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

Benton, S. A.

S. A. Benton, “Survey of holographic stereograms,” in 26th Annual Technical Symposium (International Society for Optics and Photonics, 1983), pp. 15–19.

Bjelkhagen, H.

H. Bjelkhagen and D. Brotherton-Ratcliffe, Ultra-realistic Imaging: Advanced Techniques in Analogue and Digital Colour Holography (CRC Press, 2013).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Brotherton-Ratcliffe, D.

H. Bjelkhagen and D. Brotherton-Ratcliffe, Ultra-realistic Imaging: Advanced Techniques in Analogue and Digital Colour Holography (CRC Press, 2013).
[Crossref]

Docherty, T.

A. J. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” in IS&T/SPIE’s Symposium on Electronic Imaging: Science and Technology (International Society for Optics and Photonics, 1993), pp. 36–48.

Gabor, D.

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

Halle, M.

M. Halle, “Multiple viewpoint rendering,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 243–254.

Halle, M. W.

M. W. Halle, “The generalized holographic stereogram,” Ph.D. thesis, Massachusetts Institute of Technology (1993).

Honda, T.

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic three-dimensional printer: new method,” Appl. Opt. 31, 217–222 (1992).
[Crossref] [PubMed]

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic 3-D printer,” in OE/LASE’90, 14–19 Jan., Los Angeles, CA (International Society for Optics and Photonics, 1990), pp. 84–92.

Hong, S.

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

Hong, S.-I.

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, 23755–23768 (2012).
[Crossref] [PubMed]

Javidi, B.

Jeong, K.-M.

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, 23755–23768 (2012).
[Crossref] [PubMed]

Jo, N.-Y.

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, 23755–23768 (2012).
[Crossref] [PubMed]

Jung, K.

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

Kang, H.

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

Kim, H.-S.

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, 23755–23768 (2012).
[Crossref] [PubMed]

Koch, R.

A. J. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” in IS&T/SPIE’s Symposium on Electronic Imaging: Science and Technology (International Society for Optics and Photonics, 1993), pp. 36–48.

Kuchin, J.

S. Zacharovas, A. Nikolskij, and J. Kuchin, “Dyi digital holography,” in SPIE OPTO (International Society for Optics and Photonics, 2011), 79570A.

Lee, S.

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

Martinez-Corral, M.

Maruyama, S.

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” in Integrated Optoelectronic Devices 2008 (International Society for Optics and Photonics, 2008), 69120N.

Nikolskij, A.

S. Zacharovas, A. Nikolskij, and J. Kuchin, “Dyi digital holography,” in SPIE OPTO (International Society for Optics and Photonics, 2011), 79570A.

Ohyama, N.

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic three-dimensional printer: new method,” Appl. Opt. 31, 217–222 (1992).
[Crossref] [PubMed]

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic 3-D printer,” in OE/LASE’90, 14–19 Jan., Los Angeles, CA (International Society for Optics and Photonics, 1990), pp. 84–92.

Ono, Y.

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” in Integrated Optoelectronic Devices 2008 (International Society for Optics and Photonics, 2008), 69120N.

Park, J.

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

Park, J.-H.

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, 23755–23768 (2012).
[Crossref] [PubMed]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Stern, A.

Stoykova, E.

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Woods, A. J.

A. J. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” in IS&T/SPIE’s Symposium on Electronic Imaging: Science and Technology (International Society for Optics and Photonics, 1993), pp. 36–48.

Xiao, X.

Yamaguchi, M.

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic three-dimensional printer: new method,” Appl. Opt. 31, 217–222 (1992).
[Crossref] [PubMed]

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” in Integrated Optoelectronic Devices 2008 (International Society for Optics and Photonics, 2008), 69120N.

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic 3-D printer,” in OE/LASE’90, 14–19 Jan., Los Angeles, CA (International Society for Optics and Photonics, 1990), pp. 84–92.

Zacharovas, S.

S. Zacharovas, A. Nikolskij, and J. Kuchin, “Dyi digital holography,” in SPIE OPTO (International Society for Optics and Photonics, 2011), 79570A.

3D Res. (1)

J. Park, E. Stoykova, H. Kang, S. Hong, S. Lee, and K. Jung, “Numerical reconstruction of full parallax holographic stereograms,” 3D Res. 3, 1–6 (2012).
[Crossref]

Appl. Opt. (2)

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Nature (1)

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

Opt Express (1)

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, 23755–23768 (2012).
[Crossref] [PubMed]

Other (8)

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” in Integrated Optoelectronic Devices 2008 (International Society for Optics and Photonics, 2008), 69120N.

H. Bjelkhagen and D. Brotherton-Ratcliffe, Ultra-realistic Imaging: Advanced Techniques in Analogue and Digital Colour Holography (CRC Press, 2013).
[Crossref]

S. Zacharovas, A. Nikolskij, and J. Kuchin, “Dyi digital holography,” in SPIE OPTO (International Society for Optics and Photonics, 2011), 79570A.

S. A. Benton, “Survey of holographic stereograms,” in 26th Annual Technical Symposium (International Society for Optics and Photonics, 1983), pp. 15–19.

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic 3-D printer,” in OE/LASE’90, 14–19 Jan., Los Angeles, CA (International Society for Optics and Photonics, 1990), pp. 84–92.

M. W. Halle, “The generalized holographic stereogram,” Ph.D. thesis, Massachusetts Institute of Technology (1993).

M. Halle, “Multiple viewpoint rendering,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 243–254.

A. J. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” in IS&T/SPIE’s Symposium on Electronic Imaging: Science and Technology (International Society for Optics and Photonics, 1993), pp. 36–48.

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Figures (17)

Fig. 1
Fig. 1 Acquisition of perspective images by using the recentering camera.
Fig. 2
Fig. 2 Perspectives acquired from multiple positions of the recentering camera.
Fig. 3
Fig. 3 The viewer position when perspective images are directly recorded onto the holographic emulsion
Fig. 4
Fig. 4 The viewer position, when the rearranged parallax-related images are recorded onto the holographic emulsion
Fig. 5
Fig. 5 Rearrangement of the perspective images: (a) perspective images, (b) rearranged hogel images.
Fig. 6
Fig. 6 Relationship between the holographic stereogram and the viewer
Fig. 7
Fig. 7 Relationship between the hogel images and the viewer position
Fig. 8
Fig. 8 Undistorted (a) and pincushion distorted (b) angular intensity distribution.
Fig. 9
Fig. 9 3D computer graphic models used in the numerical experiment
Fig. 10
Fig. 10 Perspective images acquired from different positions of the virtual camera (a) and some of the rearranged hogel images (b) for the KETI logo model.
Fig. 11
Fig. 11 Viewing geometry at different distances from the hologram
Fig. 12
Fig. 12 (a) undistorted reference hogel image for the KETI logo model, (b)–(e) pincussion distorted hogel images at different values of the distortion coefficient
Fig. 13
Fig. 13 Numerically reconstructed images for the KETI logo model at different values of the distortion coefficient
Fig. 14
Fig. 14 PSNR for distorted hogel images and distorted numerical reconstructions as a function of distortion
Fig. 15
Fig. 15 SSIM maps for distorted hogel images (top) and distorted numerical reconstructions (bottom) for the KETI logo model at increasing distortion
Fig. 16
Fig. 16 From left to right: SSIM maps for B, G and R channels of a distorted hogel image (70,41) for a KETI logo model (top) and a distorted numerical reconstruction (bottom) at a distortion coefficient 0.001.
Fig. 17
Fig. 17 MSSIM for distorted hogel images and distorted numerical reconstructions as a function of distortion.

Equations (8)

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H i j ( k , l ) = P k l ( i , j ) ; i = 1 I , j = 1 J , k = 1 K , l = 1 L
n p = n 2 + Θ ( ξ p Δ ξ )
ξ u = ξ d 1 + κ r d 2
η u = η d 1 + κ r d 2
r d = ξ d 2 + η d 2
PSNR = 10 log 10 ( MAX I 2 MSE ) = 20 log 10 ( MAX I MSE )
MSE = 1 m n i = 0 m 1 j = 0 n 1 | f ( x , y ) g ( x , y ) | 2
SSIM ( x , y ) = ( C 1 + 2 μ f μ g ) ( C 2 + 2 σ f g ) ( C 1 + μ f 2 + μ g 2 ) ( C 2 + σ f 2 + σ g 2 )

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