Abstract

Three principal strategies for the compression of phase-shifting digital holograms (interferogram domain-, hologram domain-, and reconstruction domain-based strategies) are reviewed and their effects in the reconstruction domain are investigated. Images of the reconstructions are provided to visually compare the performances of the methods. In addition to single reconstructions the compression effects on different depth reconstructions and reconstructions corresponding to different viewing angles are investigated so that a range of the 3D aspects of the holograms may be considered. Although comparable at low compression rates, it is found that depth and perspective information is degraded in different ways with the different techniques at high compression rates. A hologram of an object with sufficient details at different depths is used so that both parallax and depth effects can be illustrated.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]
  3. I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  6. T. J. Naughton, J. B. McDonald, and B. Javidi, "Efficient compression of Fresnel fields for Internet transmission of three-dimensional images," Appl. Opt. 42, 4758-4764 (2003).
    [CrossRef] [PubMed]
  7. T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
    [CrossRef]
  8. A. E. Shortt, T. J. Naughton, and B. Javidi, "Compression of digital holograms of three-dimensional objects using wavelets," Opt. Express 14, 2625-2630 (2006).
    [CrossRef] [PubMed]
  9. T. J. Naughton, Department of Computer Science, National University of Ireland, Maynooth, Ireland, A. E. Shortt, and B. Javidi are preparing a manuscript to be called "Nonuniform quantization compression of digital holograms."
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. E. Darakis and J. J. Soraghan, "Compression of phase-shifting digital holography interference patterns," in Photon Management II, J. T. Sheridan and F. Wyrowski, eds., Proc. SPIE 6187, 61870Y (2006).
  13. E. Darakis, T. J. Naughton, J. J. Soraghan, and B. Javidi, "Measurement of compression defects in phase-shifting digital holographic data," in Optical Information Systems IV, B. Javidi, D. Psaltis, and H. J. Caulfield, eds., Proc. SPIE 6311, 63110B (2006).
    [CrossRef]
  14. E. Darakis and J. J. Soraghan, "Reconstruction domain compression of phase-shifting interferometry digital holograms," Appl. Opt. 46, 351-356 (2007).
    [CrossRef] [PubMed]
  15. E. Darakis and J. J. Soraghan, "Use of Fresnelets for phase-shifting digital hologram compression," IEEE Trans. Image Process. 15, 3804-3811 (2006).
    [CrossRef] [PubMed]
  16. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
  17. W. B. Pennebaker and J. L. Mitchell, JPEG Still Image Data Compression Standard (Van Nostrand Reinhold, 1993).
  18. T. Acharya and P.-S. Tsai, JPEG2000 Standard for Image Compression: Concepts, Algorithms and VLSI Architectures (Wiley, 2005).
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    [CrossRef]
  20. A. E. Shortt, T. J. Naughton, and B. Javidi, "A companding approach for nonuniform quantization of digital holograms of three-dimensional objects," Opt. Express 14, 5129-5134 (2006).
    [CrossRef] [PubMed]
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  22. M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
    [CrossRef]
  23. M. Unser, "Splines: a perfect fit for signal and image processing," IEEE Signal Process Mag. 16, 22-38 (1999).
    [CrossRef]
  24. M. Unser, P. Thevenaz, and A. Aldroubi, "Shift-orthogonal wavelet bases using splines," IEEE Signal Process Lett. 3, 85-88 (1996).
    [CrossRef]
  25. D. Kayser, T. Kreis, and W. Juptner, "Compression of digital holographic data using its electromagnetic field properties," Proc. SPIE 5908, 59080C-59089 (2005).
    [CrossRef]

2007 (1)

2006 (6)

E. Darakis and J. J. Soraghan, "Use of Fresnelets for phase-shifting digital hologram compression," IEEE Trans. Image Process. 15, 3804-3811 (2006).
[CrossRef] [PubMed]

E. Darakis and J. J. Soraghan, "Compression of interference patterns with application to phase-shifting digital holography," Appl. Opt. 45, 2437-2443 (2006).
[CrossRef] [PubMed]

E. Darakis and J. J. Soraghan, "Compression of phase-shifting digital holography interference patterns," in Photon Management II, J. T. Sheridan and F. Wyrowski, eds., Proc. SPIE 6187, 61870Y (2006).

E. Darakis, T. J. Naughton, J. J. Soraghan, and B. Javidi, "Measurement of compression defects in phase-shifting digital holographic data," in Optical Information Systems IV, B. Javidi, D. Psaltis, and H. J. Caulfield, eds., Proc. SPIE 6311, 63110B (2006).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, "A companding approach for nonuniform quantization of digital holograms of three-dimensional objects," Opt. Express 14, 5129-5134 (2006).
[CrossRef] [PubMed]

A. E. Shortt, T. J. Naughton, and B. Javidi, "Compression of digital holograms of three-dimensional objects using wavelets," Opt. Express 14, 2625-2630 (2006).
[CrossRef] [PubMed]

2005 (2)

G. A. Mills and I. Yamaguchi, "Effects of quantization in phase-shifting digital holography," Appl. Opt. 44, 1216-1225 (2005).
[CrossRef] [PubMed]

D. Kayser, T. Kreis, and W. Juptner, "Compression of digital holographic data using its electromagnetic field properties," Proc. SPIE 5908, 59080C-59089 (2005).
[CrossRef]

2004 (1)

T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
[CrossRef]

2003 (2)

T. J. Naughton, J. B. McDonald, and B. Javidi, "Efficient compression of Fresnel fields for Internet transmission of three-dimensional images," Appl. Opt. 42, 4758-4764 (2003).
[CrossRef] [PubMed]

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

2002 (3)

1999 (2)

R. Shahnaz, J. F. Walkup, and T. F. Krile, "Image compression in signal-dependent noise," Appl. Opt. 38, 5560-5567 (1999).
[CrossRef]

M. Unser, "Splines: a perfect fit for signal and image processing," IEEE Signal Process Mag. 16, 22-38 (1999).
[CrossRef]

1997 (1)

1996 (2)

M. Unser, P. Thevenaz, and A. Aldroubi, "Shift-orthogonal wavelet bases using splines," IEEE Signal Process Lett. 3, 85-88 (1996).
[CrossRef]

A. Said and W. A. Pearlman, "A new, fast, and efficient image codec based on set partitioning in hierarchical trees," IEEE Trans. Circuits Syst. Video Technol. 6, 243-250 (1996).
[CrossRef]

Appl. Opt. (6)

IEEE Signal Process Lett. (1)

M. Unser, P. Thevenaz, and A. Aldroubi, "Shift-orthogonal wavelet bases using splines," IEEE Signal Process Lett. 3, 85-88 (1996).
[CrossRef]

IEEE Signal Process Mag. (1)

M. Unser, "Splines: a perfect fit for signal and image processing," IEEE Signal Process Mag. 16, 22-38 (1999).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol. (1)

A. Said and W. A. Pearlman, "A new, fast, and efficient image codec based on set partitioning in hierarchical trees," IEEE Trans. Circuits Syst. Video Technol. 6, 243-250 (1996).
[CrossRef]

IEEE Trans. Image Process. (2)

E. Darakis and J. J. Soraghan, "Use of Fresnelets for phase-shifting digital hologram compression," IEEE Trans. Image Process. 15, 3804-3811 (2006).
[CrossRef] [PubMed]

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

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Opt. Eng. (1)

T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (3)

D. Kayser, T. Kreis, and W. Juptner, "Compression of digital holographic data using its electromagnetic field properties," Proc. SPIE 5908, 59080C-59089 (2005).
[CrossRef]

E. Darakis and J. J. Soraghan, "Compression of phase-shifting digital holography interference patterns," in Photon Management II, J. T. Sheridan and F. Wyrowski, eds., Proc. SPIE 6187, 61870Y (2006).

E. Darakis, T. J. Naughton, J. J. Soraghan, and B. Javidi, "Measurement of compression defects in phase-shifting digital holographic data," in Optical Information Systems IV, B. Javidi, D. Psaltis, and H. J. Caulfield, eds., Proc. SPIE 6311, 63110B (2006).
[CrossRef]

Other (5)

T. J. Naughton, Department of Computer Science, National University of Ireland, Maynooth, Ireland, A. E. Shortt, and B. Javidi are preparing a manuscript to be called "Nonuniform quantization compression of digital holograms."

M. Burrows and D. Wheeler, A Block-Sorting Lossless Data Compression Algorithm (Digital Systems Research Center, Palo Alto, 1994).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

W. B. Pennebaker and J. L. Mitchell, JPEG Still Image Data Compression Standard (Van Nostrand Reinhold, 1993).

T. Acharya and P.-S. Tsai, JPEG2000 Standard for Image Compression: Concepts, Algorithms and VLSI Architectures (Wiley, 2005).

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Figures (8)

Fig. 1
Fig. 1

Simplified PSI hologram recording setup.

Fig. 2
Fig. 2

PSI data at different stages: (a) Captured interference pattern, (b) magnitude of the PSI hologram, (c) reconstruction at 263   mm , and (d) at 277   mm .

Fig. 3
Fig. 3

Magnitude of the Fresnelet coefficients at scale j = 5 .

Fig. 4
Fig. 4

NRMS numerical results for the investigated coding methods.

Fig. 5
Fig. 5

Depth effects from low compressed data. (a)–(d) Reconstructions from the original, JPEG2000, quantized, and SPIHT coded data, respectively, for reconstruction distance 263   mm . (e)–(h) Same for distance 277   mm .

Fig. 6
Fig. 6

Depth effects from highly compressed data. (a)–(d) Reconstructions from the original, JPEG2000, quantized, and SPIHT coded data, respectively, for reconstruction distance 263   mm . (e)–(h) Same for distance 277   mm .

Fig. 7
Fig. 7

Parallax effects from low compressed data. (a)–(d) Corresponding to the left view reconstructions from the original, JPEG2000, quantized, and SPIHT coded data. (e)–(h) Same for a view from the right.

Fig. 8
Fig. 8

Parallax effects from highly compressed data. (a)–(d) Corresponding to the left view reconstructions from the original, JPEG2000, quantized, and SPIHT coded data. (e)–(h) Same for a view from the right.

Equations (18)

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

U ( x , y ) = A 0 ( x , y ) exp [ i φ 0 ( x , y ) ] ,
I ( x , y ; ϕ ) = | U 0 ( x , y ) + U R ( x , y ; ϕ ) | 2 ,
U ( x , y ) = 1 4 A R { [ I ( x , y ; 0 ) I ( x , y ; π ) ] + i [ I ( x , y ; π / 2 ) I ( x , y ; 3 π / 2 ) ] } ,
U d ( x , y ) = 1 τ 2 + + U ( x , y ) exp { i π τ 2 [ ( x x ) 2 + ( y y ) 2 ] } d x d y = ( U G τ ) ( x , y ) ,
G τ ( x , y ) = 1 τ 2 exp [ i π τ 2 ( x 2 + y 2 ) ] ,
U ^ ( x , y ) = round [ U ( x , y ) × ( 2 m 1 1 ) / U max ] ,
β n ( x ) = β 0   .   .   .   β 0 n + 1   times ( x ) ,
β 0 ( x ) = 1 , 1 / 2 < x < 1 / 2 1 / 2 , | x | = 1 / 2 0 , otherwise.
β n ( x 2 ) = k h ( k ) β n ( x k ) ,
{ ψ j , k n = 2 ( j / 2 ) ψ n ( 2 j x k ) } j , k Z ,
ψ n ( x 2 ) = k g ( k ) β n ( x k ) ,
β ˜ τ n ( x ) = ( β n G τ ) ( x ) .
β ˜ τ / 2 n ( x 2 ) = k h ( k ) β ˜ τ n ( x k ) .
ψ ˜ τ / 2 n ( x 2 ) = k g ( k ) β ˜ τ n ( x k ) .
β n ( x , y ) = β n ( x ) β n ( y ) ,
L L ( x 2 , y 2 ) = U * [ β ˜ τ / 2 n ( x 2 , y 2 ) β ˜ τ / 2 n ( x 2 , y 2 ) ] H L ( x 2 , y 2 ) = U * [ ψ ˜ τ / 2 n ( x 2 , y 2 ) β ˜ τ / 2 n ( x 2 , y 2 ) ] L H ( x 2 , y 2 ) = U * [ β ˜ τ / 2 n ( x 2 , y 2 ) ψ ˜ τ / 2 n ( x 2 , y 2 ) ] H H ( x 2 , y 2 ) = U * [ ψ ˜ τ / 2 n ( x 2 , y 2 ) ψ ˜ τ / 2 n ( x 2 , y 2 ) ] .
NRMS = [ N x N y [ | U d | 2 | U ^ d | 2 ] 2 / N x N y [ | U d | 2 ] 2 ] 1 / 2 ,
r = s s ^ ,

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