Abstract

An approximation for fast digital hologram generation is implemented on a central processing unit (CPU), a graphics processing unit (GPU), and a multi-GPU computational platform. The computational performance of the method on each platform is measured and compared. The computational speed on the GPU platform is much faster than on a CPU, and the algorithm could be further accelerated on a multi-GPU platform. In addition, the accuracy of the algorithm for single- and double-precision arithmetic is evaluated. The quality of the reconstruction from the algorithm using single-precision arithmetic is comparable with the quality from the double-precision arithmetic, and thus the implementation using single-precision arithmetic on a multi-GPU platform can be used for holographic video displays.

© 2009 Optical Society of America

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  1. Y. Ichihashi, H. Nakayama, T. Ito, N. Masuda, T. Shimobaba, A. Shiraki, and T. Sugie, “Horn-6 special-purpose clustered computing system for electroholography,” Opt. Express 17, 13895-13903 (2009).
    [CrossRef]
  2. J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).
  3. T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).
  4. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
    [CrossRef]
  5. M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (Massachusetts Institute of Technology, 1994).
  6. H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
    [CrossRef]
  7. M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphic technique,” Proc. SPIE 1914, 25-33 (1993).
  8. H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).
  9. J. Tamai and H. Yoshikawa, “Faster computation of subsampled coherent stereogram,” J. ITEJ 50, 1612-1615 (1996). in Japanese, http://ci.nii.ac.jp/naid/110003336607.
  10. H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “The compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
  11. H. Kang, T. Yamaguchi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44-D54 (2008).
    [CrossRef]
  12. H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.
  13. H. Kang, T. Yamaguchi, H. Yoshikawa, S. C. Kim, and E. S. Kim, “Acceleration method of computing a compensated phase-added stereogram on a graphic processing unit,” Appl. Opt. 47, 5784-5789 (2008).
    [CrossRef]
  14. L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).
  15. H. Kang, F. Yaraş, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in 3DTV CONFERENCE 2009 (IEEE, 2009).
  16. “http://www.nvidia.com/,”.
  17. M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).

2009 (2)

Y. Ichihashi, H. Nakayama, T. Ito, N. Masuda, T. Shimobaba, A. Shiraki, and T. Sugie, “Horn-6 special-purpose clustered computing system for electroholography,” Opt. Express 17, 13895-13903 (2009).
[CrossRef]

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).

2008 (2)

2007 (1)

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “The compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

2001 (1)

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

1996 (1)

J. Tamai and H. Yoshikawa, “Faster computation of subsampled coherent stereogram,” J. ITEJ 50, 1612-1615 (1996). in Japanese, http://ci.nii.ac.jp/naid/110003336607.

1995 (3)

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

1993 (2)

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

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphic technique,” Proc. SPIE 1914, 25-33 (1993).

1992 (1)

M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).

Ahrenberg, L.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).

Bove, V. M.

J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Fujii, T.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “The compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

Hennelly, B. M.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).

Honda, T.

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphic technique,” Proc. SPIE 1914, 25-33 (1993).

Hoshino, H.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphic technique,” Proc. SPIE 1914, 25-33 (1993).

Ichihashi, Y.

Ito, T.

Iwata, S.

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

Kameyama, H.

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

Kang, H.

H. Kang, T. Yamaguchi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44-D54 (2008).
[CrossRef]

H. Kang, T. Yamaguchi, H. Yoshikawa, S. C. Kim, and E. S. Kim, “Acceleration method of computing a compensated phase-added stereogram on a graphic processing unit,” Appl. Opt. 47, 5784-5789 (2008).
[CrossRef]

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “The compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

H. Kang, F. Yaraş, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in 3DTV CONFERENCE 2009 (IEEE, 2009).

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

Kim, E. S.

Kim, S. C.

Lucente, M.

J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

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

M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).

M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (Massachusetts Institute of Technology, 1994).

Masuda, N.

Matsumoto, K.

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

McDonald, J. B.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).

Nakayama, H.

Naughton, T. J.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).

Nishikawa, O.

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

Ohyama, N.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphic technique,” Proc. SPIE 1914, 25-33 (1993).

Okada, T.

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

Onural, L.

H. Kang, F. Yaraş, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in 3DTV CONFERENCE 2009 (IEEE, 2009).

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

Page, A. J.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).

Sato, K.

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

Shimobaba, T.

Shiraki, A.

Sparrell, C. J.

J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Sugie, T.

Tamai, J.

J. Tamai and H. Yoshikawa, “Faster computation of subsampled coherent stereogram,” J. ITEJ 50, 1612-1615 (1996). in Japanese, http://ci.nii.ac.jp/naid/110003336607.

Tamitani, I.

J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Watlington, J. A.

J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Yamaguchi, M.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphic technique,” Proc. SPIE 1914, 25-33 (1993).

Yamaguchi, T.

Yaras, F.

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

H. Kang, F. Yaraş, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in 3DTV CONFERENCE 2009 (IEEE, 2009).

Yoshikawa, H.

H. Kang, T. Yamaguchi, H. Yoshikawa, S. C. Kim, and E. S. Kim, “Acceleration method of computing a compensated phase-added stereogram on a graphic processing unit,” Appl. Opt. 47, 5784-5789 (2008).
[CrossRef]

H. Kang, T. Yamaguchi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44-D54 (2008).
[CrossRef]

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “The compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

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

J. Tamai and H. Yoshikawa, “Faster computation of subsampled coherent stereogram,” J. ITEJ 50, 1612-1615 (1996). in Japanese, http://ci.nii.ac.jp/naid/110003336607.

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

Appl. Opt. (2)

J. Disp. Technol. (1)

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111-119 (2009).

J. Electron. Imaging (1)

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

J. ITEJ (1)

J. Tamai and H. Yoshikawa, “Faster computation of subsampled coherent stereogram,” J. ITEJ 50, 1612-1615 (1996). in Japanese, http://ci.nii.ac.jp/naid/110003336607.

Opt. Eng. (1)

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “The compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

Opt. Express (1)

Opt. Rev. (1)

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

Proc. SPIE (5)

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphic technique,” Proc. SPIE 1914, 25-33 (1993).

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

T. Okada, S. Iwata, O. Nishikawa, K. Matsumoto, H. Yoshikawa, K. Sato, and T. Honda, “The fast computation of holograms for the interactive holographic 3d display system,” Proc. SPIE 2577, 33-40 (1995).

M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).

Other (4)

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

H. Kang, F. Yaraş, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in 3DTV CONFERENCE 2009 (IEEE, 2009).

“http://www.nvidia.com/,”.

M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (Massachusetts Institute of Technology, 1994).

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Figures (7)

Fig. 1
Fig. 1

Computational performance of the algorithms for a different number of object points.

Fig. 2
Fig. 2

Parallel digital hologram computation methods on a multi-GPU platform. The gray levels indicate the associated GPU number: (a) fringe pattern partitioned according to the available number of GPUs with each partition computed on the assigned GPU and (b) each fringe of a fringe sequence is computed on the assigned GPU.

Fig. 3
Fig. 3

Image difference between the ACPAS computed using double-precision and single-precision floating points.

Fig. 4
Fig. 4

Measured PSNR results corresponding to fringe patterns generated by using the ACPAS and the reconstruction from them. The dotted curve indicates the PSNR between low- and high-precision fringe patterns; the solid curve indicates the PSNR between the reconstructions from these low- and high-precision holograms. These reconstructions are normalized to be [ 0 , 255 ] by using the lowest and highest values among their fringe patterns. As the number of points increase, other distortion and noise factors dominate the computational noise that is due to lower precision.

Fig. 5
Fig. 5

Measured PSNR corresponding to different floating-point precision and the high-precision ACPAS hologram. The circles on the solid curve indicate the PSNR between the reconstructions from the reference hologram and the high-precision ACPAS hologram. The X on the solid curve represents the PSNR between the reconstructions from the reference hologram and the low-precision ACPAS hologram. In both cases these reconstructions are normalized by using the lowest and highest values among their fringe patterns. The error that is due to the ACPAS approximation is dominant; the additional error that is due to computational noise as a consequence of lower precision is negligible.

Fig. 6
Fig. 6

Horizontal central profiles of the reconstructed images that correspond to a single object point.

Fig. 7
Fig. 7

Reconstruction of a random point cloud from (a) the reference hologram, (b)  the double-precision ACPAS, and (c) the single-precision ACPAS.

Tables (1)

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Table 1 Computing the Environment and Parameters

Equations (6)

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I ACPAS ( ξ , η ) = p = 1 N a p r p exp { j 2 π [ ( ξ - ξ c ) f p ξ c int + ( η - η c ) f p η c int ] + j k r p + j ϕ p + j C ξ η } ,
C ξ η = 2 π [ ( f p ξ c - f p ξ c int ) ( ξ c - x p ) + ( f p η c - f p η c int ) ( η c y p ) ] ,
f p ξ c = ( sin θ p ξ c - sin θ ξ ref ) / λ ,
f p η c = ( sin θ p η c - sin θ η ref ) / λ ,
MSE = 1 m n i = 0 m - 1 j = 0 n - 1 [ H dp ( i , j ) - H sp ( i , j ) ] 2 ,
PSNR = 10 log 10 ( 255 2 MSE ) .

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