Abstract

We describe data compression in phase-shifting digital holography. We demonstrate by experimentation that an image of a diffusely reflecting object can be reconstructed only by phase data of the derived complex amplitude. It is shown that reduction of the bit depth of the phase data does not seriously damage the image even down to 1 bit. We observe enhancement of halo in the image with low bit depths. This tendency is verified quantitatively by a one-dimensional simulation. Our procedure for smoothing the images that result from the data-compression methods is shown to be effective.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2005 (2)

2004 (3)

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, "Algorithm for reconstruction of digital holograms with adjustable magnification," Opt. Lett. 29, 1668-1670 (2004).
[CrossRef] [PubMed]

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase-shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

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

2003 (2)

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

2002 (5)

2001 (2)

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, "Image formation in phase-shifting digital holography and applications to microscopy," Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, and S. Ohta, "Surface shape measurement by phase-shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

2000 (3)

1999 (1)

1998 (1)

1997 (1)

1994 (1)

1972 (1)

1970 (1)

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

1969 (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., "The kinoform, a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

1967 (1)

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

Bertaux, N.

Dallas, W. J.

Foster, R.

Frauel, Y.

Goodman, J. W.

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

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

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., "The kinoform, a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Indebetouw, G.

Javidi, B.

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., "The kinoform, a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Juptner, W.

Kato, J.

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

J. Kato, I. Yamaguchi, and T. Matsumura, "Multicolor digital holography with an achromatic phase-shifter," Opt. Lett. 27, 1403-1405 (2002).
[CrossRef]

I. Yamaguchi, J. Kato, and S. Ohta, "Surface shape measurement by phase-shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, "Image formation in phase-shifting digital holography and applications to microscopy," Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

Kim, T.

Lawrence, R. W.

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

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., "The kinoform, a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Lohmann, A. W.

Maghnouji, A. E.

Matoba, O.

Matsumura, T.

Matsuzaki, H.

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

McDonald, J. B.

Mills, G.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase-shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

Mills, G. H.

Mizuno, J.

Naughton, T. J.

Ohta, S.

I. Yamaguchi, J. Kato, and S. Ohta, "Surface shape measurement by phase-shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, "Image formation in phase-shifting digital holography and applications to microscopy," Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

Poon, T. C.

Poon, T.-C.

Schnars, U.

Silvestri, A. M.

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

Tajahuerce, E.

Tajahuerce, T.

Valera, J. D. R.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase-shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

Yamaguchi, I.

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

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase-shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, "Algorithm for reconstruction of digital holograms with adjustable magnification," Opt. Lett. 29, 1668-1670 (2004).
[CrossRef] [PubMed]

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

I. Yamaguchi, "Three-dimensional microscopy and measurement by phase-shifting digital holography," in Selected Papers from Fifth International Conference on Correlation Optics, O. F. Angelsky, ed., Proc. SPIE 4607, 153-160 (2002).
[CrossRef]

J. Kato, I. Yamaguchi, and T. Matsumura, "Multicolor digital holography with an achromatic phase-shifter," Opt. Lett. 27, 1403-1405 (2002).
[CrossRef]

I. Yamaguchi, J. Kato, and S. Ohta, "Surface shape measurement by phase-shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, "Image formation in phase-shifting digital holography and applications to microscopy," Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

T. Zhang and I. Yamaguchi, "Three-dimensional microscopy with phase-shifting digital holography," Opt. Lett. 23, 1221-1223 (1998).
[CrossRef]

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

Yaroslavsky, L. P.

Yokota, M.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase-shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

Zhang, F.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase-shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, "Algorithm for reconstruction of digital holograms with adjustable magnification," Opt. Lett. 29, 1668-1670 (2004).
[CrossRef] [PubMed]

Zhang, T.

Appl. Opt. (9)

IBM J. Res. Dev. (2)

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

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., "The kinoform, a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (3)

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

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

I. Yamaguchi, J. Kato, and H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography," Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

Opt. Lett. (6)

Opt. Rev. (2)

I. Yamaguchi, J. Kato, and S. Ohta, "Surface shape measurement by phase-shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase-shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

Phys. Lett. A (1)

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

Proc. SPIE (1)

I. Yamaguchi, "Three-dimensional microscopy and measurement by phase-shifting digital holography," in Selected Papers from Fifth International Conference on Correlation Optics, O. F. Angelsky, ed., Proc. SPIE 4607, 153-160 (2002).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Setup for phase-shifting digital holography.

Fig. 2
Fig. 2

Coordinate system for phase-shifting digital holography.

Fig. 3
Fig. 3

Images reconstructed by (a) 12 bit amplitude and phase, (b) only 12 bit phase, (c) only 12 bit amplitude, (d) 4 bit phase, (e) 2 bit phase, (f) and 1 bit phase.

Fig. 4
Fig. 4

Root-mean-square image difference between the image reconstructed from the full complex amplitude (dotted curve) and those from the complex amplitude and the phase only (solid curve) with a reduced bit depth.

Fig. 5
Fig. 5

Root-mean-square image difference between the image reconstructed from the full complex amplitude and those from only the phase with various bit depths.

Fig. 6
Fig. 6

Reconstructed images before and after smoothing with a matrix of 3 × 3 with various phase-only bit levels.

Fig. 7
Fig. 7

Distributions of (a) intensity and (b) phase of the object used for the computer simulation.

Fig. 8
Fig. 8

Outputs of a linear CCD for a phase difference equal to (a) 0, (b) π/2, and (c) π.

Fig. 9
Fig. 9

(Color online) (a) Complex amplitude and phase derived from the outputs in Fig. 7(a) and (b) their histograms.

Fig. 10
Fig. 10

(Color online) Intensities reconstructed from the complex amplitude. (a) Focused and (b) defocused images before and after spatial averaging.

Fig. 11
Fig. 11

(Color online) Intensities reconstructed from only the phase represented by 8 bits. (a) Focused and (b) defocused images before and after spatial averaging over 4 and 8 pixels.

Fig. 12
Fig. 12

(Color online) Reconstructed images in focus from only the phase distributions represented by lower bit depths (a) before and (b) after averaging over 8 pixels.

Fig. 13
Fig. 13

Cross sections of the averaged intensity of the images along the X–Z plane reconstructed from (a) the full complex amplitude and (b) the 1 bit phase. The horizontal dashed lines represent the focused plane.

Equations (10)

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U ( x , y ) = U O ( x , y ) exp [ i k z O + i k ( x x ) 2 + ( y y ) 2 2 z O ] d x d y ,
I H ( x , y ; δ ) = | U R ( x , y ) exp ( i δ ) + U ( x , y ) | 2
= | U R | 2 + | U | 2 + 2 [ U R U * exp ( i δ ) ] ,
U ( x , y ) = 1 - i 4 U R * { I H ( x , y ; 0 ) I H ( x , y ; π / 2 ) + i [ I H ( x , y ; π / 2 ) I H ( x , y ;  π ) ] }
U I ( X , Y , Z ) = U ( x , y ) exp [ i k Z + i k ( X x ) 2 + ( Y y ) 2 2 Z ] d x d y ,
U I ( X , Y , z O ) = U O ( X , Y )
U ( x , y ) = A ( x , y ) exp [ i ϕ ( x , y ) ] .
U q ( x , y ) = exp [ i ϕ q ( x , y ) ] ,
ϕ q ( x , y ) = F [ 2 q ϕ ( x , y ) 2 π ] 2 π 2 q ,
D ( q ) = { [ I q ( X , Y ) I ( X , Y ) ] d X d Y [ I ( X , Y ) ] 2 d X d Y } 1 / 2 .

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