Abstract

We investigate the axial position detection of a trapped microsphere in an optical trap by using a quadrant photodiode. By replacing the photodiode with a CCD camera, we obtain detailed information on the light scattered by the microsphere. The correlation of the interference pattern with the axial position displays complex behavior with regions of positive and negative interference. By analyzing the scattered light intensity as a function of the axial position of the trapped sphere, we propose a simple method to increase the sensitivity and control the linear range of axial position detection.

© 2004 Optical Society of America

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  1. M. J. Lang, S. M. Block, “Resource letter: Lbot-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
    [CrossRef]
  2. L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
    [CrossRef] [PubMed]
  3. M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
    [CrossRef] [PubMed]
  4. A. R. Clapp, R. B. Dickinson, “Direct measurement of static and dynamic forces between a colloidal particle and a flat surface using a single-beam gradient optical trap and evanescent wave light scattering,” Langmuir, 17, 2182–2191 (2001).
    [CrossRef]
  5. E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
    [CrossRef] [PubMed]
  6. F. Gittes, C. H. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
    [CrossRef]
  7. L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
    [CrossRef]
  8. A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
    [CrossRef] [PubMed]
  9. L. Oddershede, S. Grego, S. Nørrelykke, K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129–137 (2001).
  10. K. Berg-Sørensen, H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. (to be published).
  11. A. Rohrbach, E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474–5488 (2002).
    [CrossRef]
  12. K. Svoboda, S. M. Bloch, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef] [PubMed]
  13. K. Visscher, S. M. Block, “Versatile optical traps with feedback control,” Meth. Enzymol. 298, 460–489 (1998).
    [CrossRef] [PubMed]

2003 (1)

M. J. Lang, S. M. Block, “Resource letter: Lbot-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

2002 (2)

L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
[CrossRef] [PubMed]

A. Rohrbach, E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474–5488 (2002).
[CrossRef]

2001 (2)

L. Oddershede, S. Grego, S. Nørrelykke, K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129–137 (2001).

A. R. Clapp, R. B. Dickinson, “Direct measurement of static and dynamic forces between a colloidal particle and a flat surface using a single-beam gradient optical trap and evanescent wave light scattering,” Langmuir, 17, 2182–2191 (2001).
[CrossRef]

1999 (1)

A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

1998 (2)

K. Visscher, S. M. Block, “Versatile optical traps with feedback control,” Meth. Enzymol. 298, 460–489 (1998).
[CrossRef] [PubMed]

F. Gittes, C. H. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
[CrossRef]

1997 (2)

E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
[CrossRef] [PubMed]

M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
[CrossRef] [PubMed]

1994 (2)

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

K. Svoboda, S. M. Bloch, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Berg-Sørensen, K.

L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
[CrossRef] [PubMed]

L. Oddershede, S. Grego, S. Nørrelykke, K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129–137 (2001).

K. Berg-Sørensen, H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. (to be published).

Bloch, S. M.

K. Svoboda, S. M. Bloch, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Block, S. M.

M. J. Lang, S. M. Block, “Resource letter: Lbot-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

K. Visscher, S. M. Block, “Versatile optical traps with feedback control,” Meth. Enzymol. 298, 460–489 (1998).
[CrossRef] [PubMed]

M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
[CrossRef] [PubMed]

Brown, S.

L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
[CrossRef] [PubMed]

Dickinson, R. B.

A. R. Clapp, R. B. Dickinson, “Direct measurement of static and dynamic forces between a colloidal particle and a flat surface using a single-beam gradient optical trap and evanescent wave light scattering,” Langmuir, 17, 2182–2191 (2001).
[CrossRef]

Dreyer, J. K.

L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
[CrossRef] [PubMed]

Florin, E.-L.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
[CrossRef] [PubMed]

Flyvbjerg, H.

K. Berg-Sørensen, H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. (to be published).

Gelles, J.

M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
[CrossRef] [PubMed]

Ghislain, L. P.

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

Gittes, F.

Grego, S.

L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
[CrossRef] [PubMed]

L. Oddershede, S. Grego, S. Nørrelykke, K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129–137 (2001).

Hörber, J. K. H.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
[CrossRef] [PubMed]

Landick, R.

M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
[CrossRef] [PubMed]

Lang, M. J.

M. J. Lang, S. M. Block, “Resource letter: Lbot-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

Nørrelykke, S.

L. Oddershede, S. Grego, S. Nørrelykke, K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129–137 (2001).

Oddershede, L.

L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
[CrossRef] [PubMed]

L. Oddershede, S. Grego, S. Nørrelykke, K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129–137 (2001).

Pralle, A.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
[CrossRef] [PubMed]

Prummer, M.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

R. Clapp, A.

A. R. Clapp, R. B. Dickinson, “Direct measurement of static and dynamic forces between a colloidal particle and a flat surface using a single-beam gradient optical trap and evanescent wave light scattering,” Langmuir, 17, 2182–2191 (2001).
[CrossRef]

Rohrbach, A.

A. Rohrbach, E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474–5488 (2002).
[CrossRef]

Schmidt, C. H.

Stelzer, E. H. K

A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
[CrossRef] [PubMed]

Stelzer, E. H. K.

A. Rohrbach, E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474–5488 (2002).
[CrossRef]

Svoboda, K.

K. Svoboda, S. M. Bloch, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Switz, N. A.

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

Visscher, K.

K. Visscher, S. M. Block, “Versatile optical traps with feedback control,” Meth. Enzymol. 298, 460–489 (1998).
[CrossRef] [PubMed]

Wang, M. D.

M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
[CrossRef] [PubMed]

Webb, W. W.

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

Yin, Hong

M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
[CrossRef] [PubMed]

Am. J. Phys. (1)

M. J. Lang, S. M. Block, “Resource letter: Lbot-1: laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda, S. M. Bloch, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Biophys. J. (2)

L. Oddershede, J. K. Dreyer, S. Grego, S. Brown, K. Berg-Sørensen, “The motion of a single molecule, the λ-receptor, in the bacterial outer membrane,” Biophys. J. 83, 3152–3161 (2002).
[CrossRef] [PubMed]

M. D. Wang, Hong Yin, R. Landick, J. Gelles, S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

A. Rohrbach, E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474–5488 (2002).
[CrossRef]

J. Struct. Biol. (1)

E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
[CrossRef] [PubMed]

Langmuir (1)

A. R. Clapp, R. B. Dickinson, “Direct measurement of static and dynamic forces between a colloidal particle and a flat surface using a single-beam gradient optical trap and evanescent wave light scattering,” Langmuir, 17, 2182–2191 (2001).
[CrossRef]

Meth. Enzymol. (1)

K. Visscher, S. M. Block, “Versatile optical traps with feedback control,” Meth. Enzymol. 298, 460–489 (1998).
[CrossRef] [PubMed]

Microsc. Res. Tech. (1)

A. Pralle, M. Prummer, E.-L. Florin, E. H. K Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

Opt. Lett. (1)

Probe Microsc. (1)

L. Oddershede, S. Grego, S. Nørrelykke, K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129–137 (2001).

Rev. Sci. Instrum. (1)

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

Other (1)

K. Berg-Sørensen, H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Schematic illustration of the components forming the optical tweezers and the detection system. The laser beam enters the microscope via the side port, and the built-in tube lens, L2, must be incorporated into the optical path. Lens L3 images the back focal plane of the condenser onto the detection system, either a quadrant photodiode or a CCD camera. In this figure the beam expander, mirrors, and attenuating system have been omitted.

Fig. 2
Fig. 2

Analysis of forward-scattered light detected with a CCD camera. (a) Interference pattern of a trapped bead (diameter 1.07 μm). The physical diameter of the image is 5 mm. (b) Corresponding correlation matrix, C of Eq. (1). Each surface element in the plot is the mean of 5 × 5 entries of C. (c) Mean value of the correlation matrix C as a function of the detection angle θ. At angles θ below 35 deg, the light intensity of the image in (a) increases as the bead moves along the axis of the laser beam. At angles from 35 to 58 deg the correlation is negative, while a peak of positive correlation is visible close to the critical angle at 61 deg.

Fig. 3
Fig. 3

Total intensity on the quadrant photodiode with respect to the axial position of the trapped bead (diameter 1.07 μm). The legend provides the capture angle of the condenser, θcap, and the total range of linear detection. The inset shows the sensitivity of the axial position signal defined as the slope of the photodiode signal at the equilibrium position.

Fig. 4
Fig. 4

Probing the spatial resolution of the position detection system by moving a fixed bead with the piezo stage in 14-nm steps in the axial direction. The inset shows a position histogram taken at a typical step (indicated by an arrow). The positions obtained indicate a resolution of 2.8 nm in the axial direction. The capture angle of the condenser was set to 35 deg.

Fig. 5
Fig. 5

Power spectra of the fluctuations of a trapped bead, recorded with the quadrant photodiode at various opening angles of the condenser. The increase in signal strength is ∼2 orders of magnitude when the opening angle is decreased. Both signals have been high-pass filtered at 1 Hz. In the lower curve, the peaks are electronic noise, whereas in the upper curve only a 100 Hz peak is noticeable.

Equations (2)

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Ckl=pkliii-pkliiii.
γZ˙bead+κzZbead=γZ˙sample.

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