Abstract

A compression method of phase-shifting digital holographic data is presented. Three interference patterns are recorded, and holographic information is extracted from them by phase-shifting interferometry. The scheme uses standard baseline Joint Photographic Experts Group (JPEG) or standard JPEG-2000 image compression techniques on the recorded interference patterns to reduce the amount of data to be stored. High compression rates are achieved for good reconstructed object image quality. The utility of the proposed method is experimentally verified with real holographic data. Results for compression rates using JPEG-2000 and JPEG of approximately 27 and 20, respectively, for a normalized root-mean-square error of 0.7 are demonstrated.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  18. 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]
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    [CrossRef]
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  24. T. Acharya and P.-S. Tsai, JPEG2000 Standard for Image Compression: Concepts, Algorithms and VLSI Architectures (Wiley, 2005).

2005

2004

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

2003

M. Liebling, T. Blu, and M. A. Unser, "Non-linear Fresnelet approximation for interference term suppression in digital holography," in Wavelets: Applications in Signal and Image Processing X, M. A. Unser, A. Aldroubi, and A. F. Laine, eds., Proc. SPIE 5207, 553-559 (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

2000

1999

1997

T. M. Kreis and W. P. O. Juptner, "Suppression of the dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

T. M. Kreis, M. Adams, and W. P. O. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
[CrossRef] [PubMed]

1996

1967

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

1948

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

Acharya, T.

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

Adams, M.

T. M. Kreis, M. Adams, and W. P. O. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Bertaux, N.

Blu, T.

M. Liebling, T. Blu, and M. A. Unser, "Non-linear Fresnelet approximation for interference term suppression in digital holography," in Wavelets: Applications in Signal and Image Processing X, M. A. Unser, A. Aldroubi, and A. F. Laine, eds., Proc. SPIE 5207, 553-559 (2003).
[CrossRef]

Chang, H. T.

H. T. Chang, "Preliminary studies on compressing interference patterns in electronic holography," in Three-Dimensional Holographic Imaging, C.J.Kuo and M.H.Tsai, eds. (Wiley, 2002), pp. 99-117.
[CrossRef]

Cuche, E.

Depeursinge, C.

Frauel, Y.

Gabor, D.

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

Goodman, J. W.

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

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Javidi, B.

Juptner, W. P. O.

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

T. M. Kreis and W. P. O. Juptner, "Suppression of the dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

T. M. Kreis, M. Adams, and W. P. O. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Kato, J.

Kreis, T. M.

T. M. Kreis, M. Adams, and W. P. O. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

T. M. Kreis and W. P. O. Juptner, "Suppression of the dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

Krile, T. F.

Lawrence, R.

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

Liebling, M.

M. Liebling, T. Blu, and M. A. Unser, "Non-linear Fresnelet approximation for interference term suppression in digital holography," in Wavelets: Applications in Signal and Image Processing X, M. A. Unser, A. Aldroubi, and A. F. Laine, eds., Proc. SPIE 5207, 553-559 (2003).
[CrossRef]

Marquet, P.

Matoba, O.

O. Matoba, T. J. Naughton, Y. Frauel, N. Bertaux, and B. Javidi, "Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram," Appl. Opt. 41, 6187-6192 (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.

Matsumura, T.

McDonald, J. B.

Merzlyakov, N. S.

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).

Mills, G. A.

Mitchell, J. L.

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

Naughton, T. J.

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]

O. Matoba, T. J. Naughton, Y. Frauel, N. Bertaux, and B. Javidi, "Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram," Appl. Opt. 41, 6187-6192 (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.

Naughton, T.J.

Pennebaker, W. B.

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

Schnars, U.

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

Shahnaz, R.

Surrel, Y.

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.

Tsai, P.-S.

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

Unser, M. A.

M. Liebling, T. Blu, and M. A. Unser, "Non-linear Fresnelet approximation for interference term suppression in digital holography," in Wavelets: Applications in Signal and Image Processing X, M. A. Unser, A. Aldroubi, and A. F. Laine, eds., Proc. SPIE 5207, 553-559 (2003).
[CrossRef]

Walkup, J. F.

Yamaguchi, I.

Yaroslavskii, L. P.

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).

Zhang, T.

Appl. Opt.

Appl. Phys. Lett.

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

Meas. Sci. Technol.

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

Nature

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

Opt. Eng.

T. M. Kreis and W. P. O. Juptner, "Suppression of the dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

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

Opt. Lett.

Proc. SPIE

M. Liebling, T. Blu, and M. A. Unser, "Non-linear Fresnelet approximation for interference term suppression in digital holography," in Wavelets: Applications in Signal and Image Processing X, M. A. Unser, A. Aldroubi, and A. F. Laine, eds., Proc. SPIE 5207, 553-559 (2003).
[CrossRef]

T. M. Kreis, M. Adams, and W. P. O. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Other

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).

International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC) standard 10918-1:1994 for production of International Telecommunication Union Telecommunication Standardization Sector (ITU-T) recommendation T.81 (1994).

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

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.

H. T. Chang, "Preliminary studies on compressing interference patterns in electronic holography," in Three-Dimensional Holographic Imaging, C.J.Kuo and M.H.Tsai, eds. (Wiley, 2002), pp. 99-117.
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC) standard 15444-1:2004 for production of International Telecommunication Union Telecommunication Standardization Sector (ITU-T) recommendation T.800 (2004).

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

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Figures (6)

Fig. 1
Fig. 1

Phase-shifting hologram recording and reconstruction setup: BS's beam splitters; PZT, piezoelectric transducer mirror; PSI, phase-shifting interferometry algorithm.

Fig. 2
Fig. 2

(a) Magnitude and (b) phase of the measured wavefront (data courtesy of Fucai Zhang, Gunma University, Kiryu, Japan).

Fig. 3
Fig. 3

Compression approaches: (a) complex wavefront compressed, (b) interference patterns compressed. PSIs, phase-shifting interferometry algorithms.

Fig. 4
Fig. 4

One of the three interference patterns: (a) original interference pattern (data courtesy of Fucai Zhang, Gunma University, Kiryu, Japan), (b) the same interference pattern compressed by the JPEG algorithm.

Fig. 5
Fig. 5

Reconstructed object's images resulting (a) from the uncompressed interference patterns and (b) from the JPEG compressed interference patterns.

Fig. 6
Fig. 6

NRMS error of the reconstructed image for several compression rates obtained with JPEG and JPEG-2000 compression.

Tables (4)

Tables Icon

Table 1 Numerical Results of Quantization of the Complex Wavefront at the CCD Plane

Tables Icon

Table 2 Numerical Results of Quantization of the Interference Patterns

Tables Icon

Table 3 Numerical Results of JPEG Compression

Tables Icon

Table 4 Numerical Results of JPEG-2000 Compression

Equations (52)

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

0.7
U 0 ( x , y )  =  A 0 ( x , y ) exp [ i ϕ 0 ( x , y ) ] ,
A 0 ( x , y )
ϕ 0 ( x , y )
( x , y )
d 0
U ( x , y ) = + + U 0 ( x , y ) exp { i k 2 d 0 [ ( x x ) 2 + ( y y ) 2 ] } d x d y = U 0 G d 0 ,
k = 2 π / λ
G d ( x , y ) = exp [ ( i k / 2 d ) ( x 2 + y 2 ) ]
( d = d 0
ϕ = 0 ,
π / 2 ,
π )
U R ( x , y ; ϕ ) = A R ( x , y ) exp ( i ϕ ) ,
A R ( x , y )
( x , y )
I ( x , y ; ϕ ) = | U R ( x , y ; ϕ ) + U ( x , y ) | 2 .
U ( x , y ) = 1 i 4 A R { [ I ( x , y ; 0 ) I ( x , y ; π / 2 ) ] + i [ I ( x , y ; π / 2 ) I ( x , y ; π ) ] } .
U ( X , Y , d ) = + + U ( x , y ) exp { i k 2 d [ ( X x ) 2 + ( Y y ) 2 ] } d x d y = U G d .
U ( X , Y , d 0 ) = U 0 ( x , y )
ϕ = 0
( ϕ = π / 2   and   π )
d 0 = 115   mm
λ =632 .8   nm
ϕ =0,  
π / 2 ,
1024 × 1024   pixels
6 .7   μm
I ( n , m ; ϕ ) = | U R ( n , m ; ϕ ) + U ( n , m ) | 2 ,
n = 1 , 2 , , N x   and   m = 1 , 2 , , N y
U ( n , m ) = 1 i 4 A R { [ I ( n , m ; 0 ) I ( n , m ; π / 2 ) ] + i [ I ( n , m ; π / 2 ) I ( n , m ; π ) ] } ,
U ( n , m , d 0 )
I ( n , m ; ϕ )
I ^ ( n , m ; ϕ )
U ^ ( n , m )
I ^ ( n , m ; ϕ )
I ( n , m ; ϕ )
U ^ ( n , m , d 0 )
U ^ ( n , m )
d = d 0
D = { n = 0 N x 1 m = 0 N y 1 [ | U ( n , m , d 0 ) | 2 | U ^ ( n , m , d 0 ) | 2 ] 2 } 1 / 2 ×  { n = 0 N x 1 m = 0 N y 1 [ | U ( n , m , d 0 ) | 2 ] 2 } 1 / 2 .
r = uncompressed   size sum   of   compressed   files'   size ,
1024 × 1024   pixels
3   Mbytes
1024 × 1024
8   bits
( 2   MBytes
2   MBytes
8   bits
2   MBytes
2   MBytes
NRMS = 0.7

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