Abstract

We present a parallel implementation of the Fresnel transform suitable for reconstructing large digital holograms. Our method has a small memory footprint and utilizes the spare resources of a distributed set of desktop PCs connected by a network. We show how we parallelize the Fresnel transform and discuss how it is constrained by computer and communication resources. Finally, we demonstrate how a 4.3 gigapixel digital hologram can be reconstructed and how the efficiency of the method changes for different memory and processor configurations.

© 2008 Optical Society of America

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References

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  1. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional object reconstruction and recognition," Appl. Opt. 41, 4124-4132 (2002).
    [CrossRef] [PubMed]
  2. B. Munjuluri, M. Huebschman, and H. R. Garner, "Rapid hologram updates for real-time volumetric information displays," Appl. Opt. 44, 5076-5085 (2005).
    [CrossRef] [PubMed]
  3. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, "Computer generated holography using parallel commodity graphics hardware," Opt. Express 14, 7636-7641 (2006).
    [CrossRef] [PubMed]
  4. N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, "Computer generated holography using a graphics processing unit," Opt. Express 14, 603-608 (2006).
    [CrossRef] [PubMed]
  5. M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, "Fast digital hologram generation and adaptive force measurement in liquid-crystal-display-based holographic tweezers," Appl. Opt. 45, 888-896 (2006).
    [CrossRef] [PubMed]
  6. T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1923-1932 (2005).
    [CrossRef] [PubMed]
  7. N. Masuda, T. Ito, K. Kayama, H. Kono, S. Satake, T. Kunugi, and K. Sato, "Special purpose computer for digital holographic particle tracking velocimetry," Opt. Express 14, 587-592 (2006).
    [CrossRef] [PubMed]
  8. B. Hennelly and J. Sheridan, "Fast numerical algorithm for the linear canonical transform," J. Opt. Soc. Am. A 22, 928-937 (2005).
    [CrossRef]
  9. T. Janse, V. von Rymon-Lipinski, N. Hanssen, and E. Keeve, "Fourier volume rendering on the GPU using a split-stream-FFT," in Proc. of the VMV’04, Stanford, CA, (IOS Press BV, 2004) pp. 395-403.
  10. M. C. Pease, "An adaptation of the Fast Fourier Transform for parallel processing," J. ACM 15, 252-264 (1968).
    [CrossRef]
  11. Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, "Three-dimensional imaging and processing using computational holographic imaging," Proc. IEEE 94, 636-653 (2006).
    [CrossRef]
  12. T. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2005).
  13. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods (Athena Scientific, 1997).
  14. T. M. Keane, A. J. Page, T. J. Naughton, S. A. A. Travers, and J. O. McInerney, "Building large phylogenetic trees on coarse-grained parallel machines," Algorithmica 45, 285-300 (2006).
    [CrossRef]

2006

2005

2002

1968

M. C. Pease, "An adaptation of the Fast Fourier Transform for parallel processing," J. ACM 15, 252-264 (1968).
[CrossRef]

Algorithmica

T. M. Keane, A. J. Page, T. J. Naughton, S. A. A. Travers, and J. O. McInerney, "Building large phylogenetic trees on coarse-grained parallel machines," Algorithmica 45, 285-300 (2006).
[CrossRef]

Appl. Opt.

J. ACM

M. C. Pease, "An adaptation of the Fast Fourier Transform for parallel processing," J. ACM 15, 252-264 (1968).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Proc. IEEE

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, "Three-dimensional imaging and processing using computational holographic imaging," Proc. IEEE 94, 636-653 (2006).
[CrossRef]

Other

T. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2005).

D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods (Athena Scientific, 1997).

T. Janse, V. von Rymon-Lipinski, N. Hanssen, and E. Keeve, "Fourier volume rendering on the GPU using a split-stream-FFT," in Proc. of the VMV’04, Stanford, CA, (IOS Press BV, 2004) pp. 395-403.

Supplementary Material (1)

» Media 1: MOV (331 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Three stage parallelized reconstruction algorithm based on Eq. (1). The text shows the computations performed, where QPT denotes multiplication by the quadratic phase term of Eq. (1). The cubes represent processors operating on rows or columns individually.

Fig. 2.
Fig. 2.

Animation of the 216 × 216 reconstruction, from (a) zoomed-in view to (b) full field (330 KB - QuickTime).[Media 1]

Fig. 3.
Fig. 3.

Results: (a) Reconstruction time for 214×214 digital hologram using varying numbers of processors. (b) Execution time with varying sized units for a 212×212 reconstruction, using the hard disk as intermediate storage versus keeping the whole computation in memory.

Equations (3)

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R ( m Δ x , n Δ y ; d ) = 𝓕 1 ( 𝓕 [ H ( m Δ x , n Δ y ) ] × exp { i π λ d [ u 2 ( Δ x N X ) 2 + v 2 ( Δ y N y ) 2 ] } ) ,
log 2 N ( N 1 ) .
N = 2 1 P + 1 B ,

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