Abstract

Optical tweezers are very often used for measurement of piconewton range forces. Depending on the displacement of the trapped bead, the trap may become stiffer which causes considerable underestimation of the measured force. We have shown, both by theory and experiment, that such a stiffening occurs for beads larger than 0.5μm in radius. For the first time, we have shown that the displacement at which the stiffening starts is size dependent and that the stiffening starts at higher forces for larger beads. We have shown that for the applications, which simultaneous force measurement and position sensing are on demand (such as biopolymer stretching), mid-range sized (1.5μm in radius) beads could be the best choice.

© 2011 Optical Society of America

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[CrossRef]

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830(2007).
[CrossRef] [PubMed]

S. N. S. Reihani and L. B. Oddershede, Opt. Lett. 32, 1998 (2007).
[CrossRef] [PubMed]

2005

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, Phys. Rev. Lett. 95, 208102 (2005).
[CrossRef] [PubMed]

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J. F. Allemand, D. Bensimon, and V. Croquette, Curr. Opin. Struct. Biol. 13, 266 (2003).
[CrossRef] [PubMed]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, Opt. Lett. 28, 411 (2003).
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Hajizadeh, F.

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T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

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Jannasch, A.

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T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

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Laczik, Z.

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

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[CrossRef]

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P. M. Bendix, S. N. S. Reihani, and L. B. Oddershede, ACS Nano 4, 2256 (2010).
[CrossRef] [PubMed]

A. C. Richardson, S. N. S. Reihani, and L. B. Oddershede, Opt. Express 16, 15709 (2008).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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Schäffer, E.

Sørensen, M. A.

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830(2007).
[CrossRef] [PubMed]

Stelzer, E. H. K.

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Török, P.

Varga, P.

Woodside, M. T.

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, Phys. Rev. Lett. 95, 208102 (2005).
[CrossRef] [PubMed]

ACS Nano

P. M. Bendix, S. N. S. Reihani, and L. B. Oddershede, ACS Nano 4, 2256 (2010).
[CrossRef] [PubMed]

Curr. Opin. Struct. Biol.

J. F. Allemand, D. Bensimon, and V. Croquette, Curr. Opin. Struct. Biol. 13, 266 (2003).
[CrossRef] [PubMed]

J. Opt. A

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, Phys. Rev. Lett. 95, 208102 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830(2007).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Left panel: the procedure used to measure the displacement of the bead from the trap center. The upper (lower) raw shows the images when the stage is moved at v = 0 μm / s ( v = 200 μm / s ). Right panel: the pixel size calibration graph with a result of 14 nm / pixel .

Fig. 2
Fig. 2

(a)–(e) Measured lateral trapping force as a function of displacement for 1.48, 1.65, 2.10, 3.0, and 5.5 μm beads, respectively. A (pN), and B (pN/nm) values represent the result of a double-linear fit to the data points (one and two indices represent the low and high force parts, respectively). Each data point represents the average over five measurements. (f) α as a function of the bead radius. The dashed line represents the exponential fit to the data points.

Fig. 3
Fig. 3

(a) Theoretical force-displacement graphs for different bead sizes calculated based on the AIG (hollow symbols) and T-matrix (filled symbols) methods. (b) α as a function of the bead radius calculated using the T-matrix (black squares) and AIG (red circles) methods. The transverse (c) and axial (d) cross section of the intensity profile at the focus.

Equations (1)

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I 0 = 0 α 0 exp [ ( f sin θ ) 2 w 2 ] cos θ 1 sin θ 1 × ( τ s + τ p cos θ 2 ) exp [ i k 0 ψ ( θ 1 , θ 2 , d ) ] × J 0 ( k 0 n 1 r sin θ 1 ) exp ( i k 0 n 2 z cos θ 2 ) d θ 1 ,

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