Abstract

We have developed a novel experimental technique for tracking small particles in three dimensions with nanometer accuracy. The longitudinal positioning of a micrometer-sized particle is determined by using the Fresnel approximation to describe the transverse distribution of the wavefront that originated in the particle. The method utilizes the high-sensitivity quantitative phase imaging capability of diffraction phase microscopy recently developed in our laboratory. We demonstrate the principle of the technique with experiments on Brownian particles jittering in water both in bulk and in the vicinity of a boundary. The particles are localized in space within an error cube of 20nm×20nm×20nm for a 33Hz acquisition rate and 20s recording time.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2006 (4)

2005 (4)

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

T. A. Waigh, Rep. Prog. Phys. 68, 685 (2005).
[CrossRef]

G. Popescu and A. Dogariu, Eur. Phys. J.: Appl. Phys. 32, 73 (2005).
[CrossRef]

2003 (1)

2002 (3)

G. Popescu, A. Dogariu, and R. Rajagopalan, Phys. Rev. E 65041504 (2002).
[CrossRef]

Y. Tseng, T. P. Kole, and D. Wirtz, Biophys. J. 83, 3162 (2002).
[CrossRef] [PubMed]

A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. E 66, 011916 (2002).
[CrossRef]

2001 (1)

1999 (1)

F. C. MacKintosh and C. F. Schmidt, Curr. Opin. Colloid Interface Sci. 4, 300 (1999).
[CrossRef]

1998 (1)

T. Gisler and D. A. Weitz, Curr. Opin. Colloid Interface Sci. 3, 586 (1998).
[CrossRef]

1905 (1)

A. Einstein, Ann. Phys. 17, 549 (1905).
[CrossRef]

Badizadegan, K.

Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Express 14, 8263 (2006).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

Best, C. A.

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

Boccara, A. C.

Butler, J. P.

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

Caspi, A.

A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. E 66, 011916 (2002).
[CrossRef]

Chasles, F.

Dasari, R. R.

Deng, L. H.

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

Dogariu, A.

G. Popescu and A. Dogariu, Eur. Phys. J.: Appl. Phys. 32, 73 (2005).
[CrossRef]

G. Popescu, A. Dogariu, and R. Rajagopalan, Phys. Rev. E 65041504 (2002).
[CrossRef]

G. Popescu and A. Dogariu, Opt. Lett. 26, 551 (2001).
[CrossRef]

Dubertret, B.

Einstein, A.

A. Einstein, Ann. Phys. 17, 549 (1905).
[CrossRef]

Elbaum, M.

A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. E 66, 011916 (2002).
[CrossRef]

Feld, M. S.

Florin, E. L.

Fredberg, J. J.

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

Gisler, T.

T. Gisler and D. A. Weitz, Curr. Opin. Colloid Interface Sci. 3, 586 (1998).
[CrossRef]

Granek, R.

A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. E 66, 011916 (2002).
[CrossRef]

Ikeda, T.

Jonas, A.

Kole, T. P.

Y. Tseng, T. P. Kole, and D. Wirtz, Biophys. J. 83, 3162 (2002).
[CrossRef] [PubMed]

MacKintosh, F. C.

F. C. MacKintosh and C. F. Schmidt, Curr. Opin. Colloid Interface Sci. 4, 300 (1999).
[CrossRef]

Millet, E.

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

Morgan, K. G.

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

Park, Y. K.

Popescu, G.

Rajagopalan, R.

G. Popescu, A. Dogariu, and R. Rajagopalan, Phys. Rev. E 65041504 (2002).
[CrossRef]

Schmidt, C. F.

F. C. MacKintosh and C. F. Schmidt, Curr. Opin. Colloid Interface Sci. 4, 300 (1999).
[CrossRef]

Speidel, M.

Trepat, X.

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

Tseng, Y.

Y. Tseng, T. P. Kole, and D. Wirtz, Biophys. J. 83, 3162 (2002).
[CrossRef] [PubMed]

Waigh, T. A.

T. A. Waigh, Rep. Prog. Phys. 68, 685 (2005).
[CrossRef]

Weitz, D. A.

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

T. Gisler and D. A. Weitz, Curr. Opin. Colloid Interface Sci. 3, 586 (1998).
[CrossRef]

Wirtz, D.

Y. Tseng, T. P. Kole, and D. Wirtz, Biophys. J. 83, 3162 (2002).
[CrossRef] [PubMed]

Ann. Phys. (1)

A. Einstein, Ann. Phys. 17, 549 (1905).
[CrossRef]

Biophys. J. (1)

Y. Tseng, T. P. Kole, and D. Wirtz, Biophys. J. 83, 3162 (2002).
[CrossRef] [PubMed]

Curr. Opin. Colloid Interface Sci. (2)

T. Gisler and D. A. Weitz, Curr. Opin. Colloid Interface Sci. 3, 586 (1998).
[CrossRef]

F. C. MacKintosh and C. F. Schmidt, Curr. Opin. Colloid Interface Sci. 4, 300 (1999).
[CrossRef]

Eur. Phys. J.: Appl. Phys. (1)

G. Popescu and A. Dogariu, Eur. Phys. J.: Appl. Phys. 32, 73 (2005).
[CrossRef]

J. Biomed. Opt. (1)

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

Nat. Mater. (1)

L. H. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Nat. Mater. 5, 636 (2006).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. E (2)

A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. E 66, 011916 (2002).
[CrossRef]

G. Popescu, A. Dogariu, and R. Rajagopalan, Phys. Rev. E 65041504 (2002).
[CrossRef]

Rep. Prog. Phys. (1)

T. A. Waigh, Rep. Prog. Phys. 68, 685 (2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Algorithm for retrieving the z position of a particle from the xy distribution of the scattered wavefront.

Fig. 2
Fig. 2

a, Measured phase distribution of the light scattered from the bead. b, Simulated wavefront distributions for various values of the particle position, z. c, Result of the 2D cross correlations between the phase in a and each of the simulated phases in b. The cross correlation of highest value provides the value of z 0 .

Fig. 3
Fig. 3

a, Retrieved and expected z positions for a bead affixed to a microscope slide as the focus is adjusted. b, 3D trajectories of a 2 μ m diameter bead under Brownian motion in water (red circles) and affixed to a cover glass (blue cross). c, Retrieved trajectory for the fixed bead in b. d, Histogram of z-axis rms displacement for the fixed bead.

Fig. 4
Fig. 4

a, Total and individual axis MSD for Brownian particle in water, as indicated. b, The y and z axis MSD for a particle embedded in water, in the vicinity of the cover glass.

Equations (2)

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U S ( x , y ; z ) U F ( x , y ) U W ( x x , y y ; z ) d x d y .
D = k B T 3 π η d .

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