Abstract

We compress phase-shift digital holograms (whole Fresnel fields) for the transmission of three-dimensional images. For real-time networking applications, the time required to compress can be as critical as the compression rate. We achieve lossy compression through quantization of both the real and imaginary streams, followed by a bit packing operation. Compression losses in the reconstructed objects were quantified. We define a speedup metric that combines space gains due to compression with temporal overheads due to the compression routine and the transmission serialization. We empirically verify transmission speedup due to compression using a special-purpose Internet-based networking application.

© 2003 Optical Society of America

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    [CrossRef]
  2. L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
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    [CrossRef] [PubMed]
  4. U. Schnars, W. P. O. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
    [CrossRef]
  8. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  9. B. Javidi, E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
    [CrossRef]
  10. B. Javidi, F. Okano, eds., Three-Dimensional Television, Video, and Display Technologies (Springer, Berlin, 2002).
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    [CrossRef] [PubMed]
  12. H. J. Caulfield, ed., Handbook of Optical Holography (Academic, New York, 1979).
  13. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  14. M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
    [CrossRef]
  15. O. Matoba, T. J. Naughton, Y. Frauel, N. Bertaux, B. Javidi, “Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram,” Appl. Opt. 41, 6187–6192 (2002).
    [CrossRef] [PubMed]
  16. M. Rabbani, ed., Selected Papers on Image Coding and Compression, SPIE Milestone Series MS48, (SPIE Press, Bellingham, Wa., 1992).
  17. T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 235–242 (2001).
    [CrossRef]
  18. L. Ding, Y. Yan, Q. Xue, G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
    [CrossRef]
  19. M. Liebling, T. Blu, M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
    [CrossRef]
  20. J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
    [CrossRef]
  21. W. J. Dallas, A. W. Lohmann, “Phase quantization in holograms,” Appl. Opt. 11, 192–194 (1972).
    [CrossRef] [PubMed]
  22. E. Tajahuerce, O. Matoba, B. Javidi, “Shift-invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40, 3877–3886 (2001).
    [CrossRef]
  23. Y. Frauel, E. Tajahuerce, M.-A. Castro, B. Javidi, “Distortion-tolerant three-dimensional object recognition with digital holography,” Appl. Opt. 40, 3887–3893 (2001).
    [CrossRef]
  24. Y. Frauel, B. Javidi, “Neural network for three-dimensional object recognition based on digital holography,” Opt. Lett. 26, 1478–1480 (2001).
    [CrossRef]
  25. http://hologram.cs.may.ie/online/jao2003/hologram.html

2003 (2)

L. Ding, Y. Yan, Q. Xue, G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
[CrossRef]

M. Liebling, T. Blu, M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

2002 (2)

2001 (3)

2000 (2)

M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
[CrossRef]

B. Javidi, E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
[CrossRef]

1997 (1)

1994 (1)

1987 (1)

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

1983 (1)

1979 (1)

1974 (1)

1972 (1)

1970 (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

1967 (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Bertaux, N.

Blu, T.

M. Liebling, T. Blu, M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Burow, B.

Castro, M.-A.

Dallas, W. J.

Ding, L.

L. Ding, Y. Yan, Q. Xue, G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
[CrossRef]

Elsner, K. E.

Frauel, Y.

Gallagher, J. E.

Goodman, J. W.

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Grzanna, J.

Herriott, D. R.

Javidi, B.

Jin, G.

L. Ding, Y. Yan, Q. Xue, G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
[CrossRef]

Jüptner, W. P. O.

Kameda, M.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 235–242 (2001).
[CrossRef]

Korpel, A.

Kujawinska, M.

M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
[CrossRef]

Lawrence, R. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Liebling, M.

M. Liebling, T. Blu, M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

Lohmann, A. W.

Matoba, O.

Merzlyakov, N. S.

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).

Morimoto, Y.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 235–242 (2001).
[CrossRef]

Naughton, T. J.

Nomura, T.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 235–242 (2001).
[CrossRef]

Okazaki, A.

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 235–242 (2001).
[CrossRef]

Onural, L.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Poon, T.-C.

Rosenfeld, D. P.

Schnars, U.

Schwider, J.

Scott, P. D.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Silvestri, A. M.

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Spolaczyk, R.

Sutkowski, M.

M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
[CrossRef]

Tajahuerce, E.

Unser, M.

M. Liebling, T. Blu, M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

White, A. D.

Xue, Q.

L. Ding, Y. Yan, Q. Xue, G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
[CrossRef]

Yamaguchi, I.

Yan, Y.

L. Ding, Y. Yan, Q. Xue, G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
[CrossRef]

Yaroslavsky, L. P.

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).

Zhang, T.

Appl. Opt. (8)

W. J. Dallas, A. W. Lohmann, “Phase quantization in holograms,” Appl. Opt. 11, 192–194 (1972).
[CrossRef] [PubMed]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef] [PubMed]

J. Schwider, B. Burow, K. E. Elsner, J. Grzanna, R. Spolaczyk, “Digital wavefront measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
[CrossRef]

U. Schnars, W. P. O. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

E. Tajahuerce, O. Matoba, B. Javidi, “Shift-invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40, 3877–3886 (2001).
[CrossRef]

Y. Frauel, E. Tajahuerce, M.-A. Castro, B. Javidi, “Distortion-tolerant three-dimensional object recognition with digital holography,” Appl. Opt. 40, 3887–3893 (2001).
[CrossRef]

T. J. Naughton, Y. Frauel, B. Javidi, E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41, 4124–4132 (2002).
[CrossRef] [PubMed]

O. Matoba, T. J. Naughton, Y. Frauel, N. Bertaux, B. Javidi, “Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram,” Appl. Opt. 41, 6187–6192 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

IBM J. Res. Dev. (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

IEEE Trans. Image Process. (1)

M. Liebling, T. Blu, M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

Opt. Commun. (1)

L. Ding, Y. Yan, Q. Xue, G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
[CrossRef]

Opt. Eng. (1)

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Opt. Lasers Eng. (1)

M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
[CrossRef]

Opt. Lett. (4)

Other (7)

B. Javidi, F. Okano, eds., Three-Dimensional Television, Video, and Display Technologies (Springer, Berlin, 2002).

http://hologram.cs.may.ie/online/jao2003/hologram.html

M. Rabbani, ed., Selected Papers on Image Coding and Compression, SPIE Milestone Series MS48, (SPIE Press, Bellingham, Wa., 1992).

T. Nomura, A. Okazaki, M. Kameda, Y. Morimoto, B. Javidi, “Digital holographic data reconstruction with data compression,” Algorithms and Systems for Optical Information Processing V, B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 235–242 (2001).
[CrossRef]

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).

H. J. Caulfield, ed., Handbook of Optical Holography (Academic, New York, 1979).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for PSI: BE, beam expander; BS, beam splitter; RP, retardation plate; M, mirror.

Fig. 2
Fig. 2

Illustration of the network-independent multiple-client system; U.I., user interface.

Fig. 3
Fig. 3

Internal operation of (a) server and (b) client processes.

Fig. 4
Fig. 4

Screenshot of client side of timings application. Top row (l to r): full Fresnel field with window indicated, uncompressed Fresnel field window data, uncompressed timings, and uncompressed reconstruction. Bottom row (l to r): control panel, compressed window, compressed timing information, and compressed reconstruction.

Fig. 5
Fig. 5

NRMS difference in the reconstructed intensity plotted versus the number of bits in each of the Fresnel field’s real and imaginary values for various degrees of subsampling.

Fig. 6
Fig. 6

Reconstructed views (with 4 × 4 subsampling) from a 1024 × 1024-pixel window from the Fresnel field stored with different quantization resolutions: (a) no quantization, (b) 4 bits, (c) 3 bits, (d) 2 bits of resolution in each real and imaginary value.

Fig. 7
Fig. 7

Speedup as a function of increasing compression, for various Fresnel field window sizes.

Tables (2)

Tables Icon

Table 1 Timings for Fresnel Field Windows of Side Length 512 Pixelsa

Tables Icon

Table 2 Timings Used to Calculate Speedup

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Ux, y, z=-iλzexpi 2πλ zH0x, y expiπ x2+y2λz,
H0x, y=roundH0x, yσ-1β
σ=max|minImH0|, |maxImH0|, |minReH0|, |maxReH0|.
D=m=0Nx-1n=0Ny-1|U0m, n|2-|U0m, n|22×m=0Nx-1n=0Ny-1|U0m, n|22-11/2,
r=uncompressed sizecompressed size.
s=tu¯c¯+tc¯+d¯,

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