Abstract

We demonstrate a new method of measuring quantitative phase in imaging of biological materials. This method, asynchronous digital holography, employs knowledge of a moving fringe created by acousto-optic modulators to execute phase-shifting interferometry using two near-simultaneous interferograms. The method can be used to obtain quantitative phase images of dynamic biological samples on millisecond time scales. We present results on a standard sample, and on live cell samples.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  6. L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. T. Kreis, "Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method," J. Opt. Soc. A 3, 847 (1986).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. E. B. Li, J. Q. Yao, D. Y. Xu, J. T. Xi, and J. Chicharo, "Optical phase shifting with acousto-optic devices," Opt. Lett. 30, 189 (2005).
    [CrossRef] [PubMed]
  11. U. Schnars. and W. Jueptner, Digital holography : digital hologram recording, numerical reconstruction, and related techniques (Berlin, Springer, 2005).
  12. S. L. Hahn, Hilbert transforms in signal processing (Artech House, Boston, 1996).
  13. D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping : theory, algorithms, and software (New York, Wiley, 1998).

2006

2005

2000

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214 (2000).
[CrossRef]

1999

1998

1986

T. Kreis, "Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method," J. Opt. Soc. A 3, 847 (1986).
[CrossRef]

Asundi, A.

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214 (2000).
[CrossRef]

Badizadegan, K.

Bevilacqua, F.

Chicharo, J.

Colomb, T.

Cuche, E.

Dasari, R. R.

Depeursinge, C.

Emery, Y.

Feld, M. S.

Ikeda, T.

Kreis, T.

T. Kreis, "Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method," J. Opt. Soc. A 3, 847 (1986).
[CrossRef]

Li, E. B.

Lue, N.

Magistretti, P. J.

Marquet, P.

Miao, J.

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214 (2000).
[CrossRef]

Popescu, G.

Rappaz, B.

Xi, J. T.

Xu, D. Y.

Xu, L.

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214 (2000).
[CrossRef]

Yamaguchi, I.

Yao, J. Q.

Zhang, T.

J. Opt. Soc. A

T. Kreis, "Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method," J. Opt. Soc. A 3, 847 (1986).
[CrossRef]

Opt. Eng.

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214 (2000).
[CrossRef]

Opt. Lett.

Other

T. Kreis, Holographic interferometry : principles and methods (Berlin: Akademie Verlag, 1996).

U. Schnars. and W. Jueptner, Digital holography : digital hologram recording, numerical reconstruction, and related techniques (Berlin, Springer, 2005).

S. L. Hahn, Hilbert transforms in signal processing (Artech House, Boston, 1996).

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping : theory, algorithms, and software (New York, Wiley, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

Setup for ADH system. The optical phase is tightly controlled with the AOMs (acousto-optical modulators). The MO and L1 form a 4f imaging system with L2, respectively, so that the CCD is in the image plane. The magnification of the sample beam is 33x, while the reference beam is expanded by a factor of 20.

Fig. 2.
Fig. 2.

At left, the complex analytic signal after the Hilbert transform. The AOMs impart a known phase shift α on the signal. At right, a flow chart of the ADH algorithm.

Fig. 3.
Fig. 3.

(a) and (b) depict two successive interferograms of the bottom-right quadrant of a water drop. A sine-wave is fit to the same section of each interferogram, and the wrapped phase (c) is determined from Eq. (3). The unwrapped phase is shown in (d).

Fig. 4.
Fig. 4.

At left, Four successive quantitative phase images of a water droplet receding due to evaporation. Each image was recorded 1 second apart. The maximum thickness of the water droplet in the image is (a) 8.34 μm, (b) 6.34 μm, (c) 5.75 μm, and (d) 3.67 μm. At right is a time profile of the phase stability over a 3 × 3 pixel area of a water sample. The standard deviation of the phase is 4.9 nm.

Fig. 5.
Fig. 5.

A quantitative phase image of a red blood cell (left) and a smooth muscle cell (right).

Equations (6)

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

I x y = A x y + C x y + C * x y ;
C x y = 1 2 B x y exp [ i Δ ϕ x y ]
I 1 = A x y + C x y exp ( iqx ) + c . c . ;
I 2 = A x y + C x y exp { i [ qx + α ] } + c c ;
G = HT { I 1 I 2 } exp ( iqx ) ( 1 exp ( ) ;
Δ ϕ x y = tan 1 ( Im G Re G ) .

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