Abstract

Phase-shifting digital hologram compression has been mainly studied in the recording domain, where data possess a rather randomlike appearance, yielding reduced compression efficiency. We carry out the compression of such data in the reconstruction domain, which benefits from the spatial correlation of the data yielding, increased efficiency. Real holographic data are used to demonstrate the performance of the new approach. It is also shown that the reconstruction is not limited to the initially obtained view, as additional views can still be obtained with appropriate postprocessing.

© 2007 Optical Society of America

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  1. D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
    [CrossRef] [PubMed]
  2. U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Measurement Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]
  3. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef] [PubMed]
  4. I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
    [CrossRef]
  5. H. Yusuke, S. Kunihiro, M. Masakazu, and F. Kensaku, "Recording and reconstruction of 3D color images of practical objects by phase-shifting holography," in Display Devices and Systems, U. Tatsuo, L. Xu, and S. Hang, eds., Proc. SPIE 6030, 603005 (2006).
  6. T. J. Naughton, Y. Frauel, O. Matoba, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional video," in Three-Dimensional Television, Video, and Display Technologies, B. Javidi and F. Okano, eds. (Springer-Verlag, 2002), pp. 273-295.
  7. 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]
  8. 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]
  9. T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
    [CrossRef]
  10. A. E. Shortt, T. J. Naughton, and B. Javidi, "Nonuniform quantization compression techniques for digital holograms of three-dimensional objects," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 30-41 (2004).
  11. 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]
  12. I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, "Image reconstruction only by phase data in phase-shifting digital holography," Appl. Opt. 45, 975-983 (2006).
    [CrossRef] [PubMed]
  13. G. A. Mills and I. Yamaguchi, "Effects of quantization in phase-shifting digital holography," Appl. Opt. 44, 1216-1225 (2005).
    [CrossRef] [PubMed]
  14. 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]
  15. 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).
  16. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
  17. M. Liebling, T. Blu, and M. Unser, "Fresnelets:new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
    [CrossRef]
  18. E. Darakis and J. J. Soraghan, "Use of Fresnelets for phase-shifting digital hologram compression," IEEE Trans. Image Process. 15, 3804-3811 (2006).
  19. M. Burrows and D. Wheeler, "A block-sorting lossless data compression algorithm," (Digital Systems Research Center, Palo Alto, California, 1994).
  20. M. Liebling and M. Unser, "Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion," J. Opt. Soc. Am. A 21, 2424-2430 (2004).
    [CrossRef]

2006 (3)

2005 (1)

2004 (2)

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

M. Liebling and M. Unser, "Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion," J. Opt. Soc. Am. A 21, 2424-2430 (2004).
[CrossRef]

2003 (2)

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

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]

2002 (3)

1997 (1)

1948 (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Blu, T.

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

Burrows, M.

M. Burrows and D. Wheeler, "A block-sorting lossless data compression algorithm," (Digital Systems Research Center, Palo Alto, California, 1994).

Darakis, E.

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

Frauel, Y.

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]

T. J. Naughton, Y. Frauel, O. Matoba, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional video," in Three-Dimensional Television, Video, and Display Technologies, B. Javidi and F. Okano, eds. (Springer-Verlag, 2002), pp. 273-295.

Gabor, D.

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Goodman, J. W.

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

Javidi, B.

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]

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

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]

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]

A. E. Shortt, T. J. Naughton, and B. Javidi, "Nonuniform quantization compression techniques for digital holograms of three-dimensional objects," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 30-41 (2004).

T. J. Naughton, Y. Frauel, O. Matoba, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional video," in Three-Dimensional Television, Video, and Display Technologies, B. Javidi and F. Okano, eds. (Springer-Verlag, 2002), pp. 273-295.

Juptner, W. P. O.

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

Kato, J.

Kensaku, F.

H. Yusuke, S. Kunihiro, M. Masakazu, and F. Kensaku, "Recording and reconstruction of 3D color images of practical objects by phase-shifting holography," in Display Devices and Systems, U. Tatsuo, L. Xu, and S. Hang, eds., Proc. SPIE 6030, 603005 (2006).

Kunihiro, S.

H. Yusuke, S. Kunihiro, M. Masakazu, and F. Kensaku, "Recording and reconstruction of 3D color images of practical objects by phase-shifting holography," in Display Devices and Systems, U. Tatsuo, L. Xu, and S. Hang, eds., Proc. SPIE 6030, 603005 (2006).

Liebling, M.

M. Liebling and M. Unser, "Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion," J. Opt. Soc. Am. A 21, 2424-2430 (2004).
[CrossRef]

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

Masakazu, M.

H. Yusuke, S. Kunihiro, M. Masakazu, and F. Kensaku, "Recording and reconstruction of 3D color images of practical objects by phase-shifting holography," in Display Devices and Systems, U. Tatsuo, L. Xu, and S. Hang, eds., Proc. SPIE 6030, 603005 (2006).

Matoba, O.

T. J. Naughton, Y. Frauel, O. Matoba, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional video," in Three-Dimensional Television, Video, and Display Technologies, B. Javidi and F. Okano, eds. (Springer-Verlag, 2002), pp. 273-295.

Matsumura, T.

McDonald, J. B.

Mills, G. A.

Naughton, T. J.

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]

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

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]

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]

A. E. Shortt, T. J. Naughton, and B. Javidi, "Nonuniform quantization compression techniques for digital holograms of three-dimensional objects," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 30-41 (2004).

T. J. Naughton, Y. Frauel, O. Matoba, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional video," in Three-Dimensional Television, Video, and Display Technologies, B. Javidi and F. Okano, eds. (Springer-Verlag, 2002), pp. 273-295.

Schnars, U.

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

Shortt, A. E.

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]

A. E. Shortt, T. J. Naughton, and B. Javidi, "Nonuniform quantization compression techniques for digital holograms of three-dimensional objects," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 30-41 (2004).

Soraghan, J. J.

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

Tajahuerce, E.

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]

T. J. Naughton, Y. Frauel, O. Matoba, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional video," in Three-Dimensional Television, Video, and Display Technologies, B. Javidi and F. Okano, eds. (Springer-Verlag, 2002), pp. 273-295.

Unser, M.

M. Liebling and M. Unser, "Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion," J. Opt. Soc. Am. A 21, 2424-2430 (2004).
[CrossRef]

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

Wheeler, D.

M. Burrows and D. Wheeler, "A block-sorting lossless data compression algorithm," (Digital Systems Research Center, Palo Alto, California, 1994).

Yamaguchi, I.

Yamamoto, K.

Yokota, M.

Yusuke, H.

H. Yusuke, S. Kunihiro, M. Masakazu, and F. Kensaku, "Recording and reconstruction of 3D color images of practical objects by phase-shifting holography," in Display Devices and Systems, U. Tatsuo, L. Xu, and S. Hang, eds., Proc. SPIE 6030, 603005 (2006).

Zhang, T.

Appl. Opt. (5)

IEEE Trans. Image Process. (1)

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

J. Opt. Soc. Am. A (1)

Measurement Sci. Technol. (1)

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

Nature (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

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 (1)

Opt. Lett. (2)

Other (7)

H. Yusuke, S. Kunihiro, M. Masakazu, and F. Kensaku, "Recording and reconstruction of 3D color images of practical objects by phase-shifting holography," in Display Devices and Systems, U. Tatsuo, L. Xu, and S. Hang, eds., Proc. SPIE 6030, 603005 (2006).

T. J. Naughton, Y. Frauel, O. Matoba, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three-dimensional video," in Three-Dimensional Television, Video, and Display Technologies, B. Javidi and F. Okano, eds. (Springer-Verlag, 2002), pp. 273-295.

A. E. Shortt, T. J. Naughton, and B. Javidi, "Nonuniform quantization compression techniques for digital holograms of three-dimensional objects," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 30-41 (2004).

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

M. Burrows and D. Wheeler, "A block-sorting lossless data compression algorithm," (Digital Systems Research Center, Palo Alto, California, 1994).

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).

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

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Figures (7)

Fig. 1
Fig. 1

PSI interferograms recording setup.

Fig. 2
Fig. 2

Coordinate system in use.

Fig. 3
Fig. 3

PSI DH data:(a) an interference pattern, (b) the magnitude of the complex wavefront at the plane of the camera, and (c) the magnitude of the propagated wavefront at the plane of the object (data courtesy of Fucai Zhang, Gunma University, Kiryu, Japan).

Fig. 4
Fig. 4

Numerical results for a reconstruction distance d = z 0 .

Fig. 5
Fig. 5

Numerical results for another reconstruction distance d = z 1 . For quantization on the reconstruction plane, the coding was done on the plane d = z 0 .

Fig. 6
Fig. 6

Obtaining reconstructions from a different viewing angle by selecting a portion of the PSI hologram.

Fig. 7
Fig. 7

Numerical results for a view obtained by a 512   pixel × 1024   pixel section of the PSI hologram.

Equations (12)

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U z 0 ( x , y ) = A z 0 ( x , y ) exp [ i ϕ z 0 ( x , y ) ] ,
U 0 ( x , y ) = + + U z 0 ( x , y ) × exp { i k 2 z 0 [ ( x x ) 2 + ( y y ) 2 ] } d x d y
= U z 0 G z 0 ,
G d = exp [ i k 2 d ( x 2 + y 2 ) ]
U R ( x , y ) = A R ( x , y ) exp { i [ ϕ R ( x , y ) + ϕ ] } ,
I ( x , y ; ϕ ) = | U R ( x , y ; ϕ ) + U ( x , y ) | 2 = U R 2 + U 0 2 + 2 U R U 0  cos [ ϕ 0 ( x , y ) ϕ R ( x , y ) ϕ ] ,
U 0 ( 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 ˜ z 0 ( x , y ) = r o u n d [ U z 0 ( x , y ) × ( 2 m 1 1 ) / U z 0 ,max ] ,
D = [ N x N y ( U 2 U ˜ 2 ) 2 / N x N y ( U 2 ) 2 ] 1 / 2 ,
r = S / s ,
θ max, x = tan - 1 ( N x W x ) Δ x 2 z 0 ,
θ max, y = tan - 1 ( N y W y ) Δ y 2 z 0 ,

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