Abstract

High-Speed tracking of several particles allows measuring dynamic long-range interactions relevant to biotechnology and colloidal physics. In this paper we extend the successful technique of 3D back-focal plane interferometry to oscillating laser beams and show that two or more particles can be trapped and tracked with a precision of a few nanometers in all three dimensions. The tracking rate of several kHz is only limited by the scan speed of the beam steering device. Several tests proof the linearity and orthogonality of our detection scheme, which is of interest to optical tweezing applications and various metrologies. As an example we show the position cross-correlations of three diffusing particles in a scanning line optical trap.

© 2009 Optical Society of America

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  1. D. Weihs, T. G. Mason, and M. A. Teitell, "Bio-Microrheology: A Frontier in Microrheology," Biophys. J. 91, 4296-4305 (2006).
    [CrossRef] [PubMed]
  2. M. Brunner, J. Dobnikar, H. H. von Grunberg, and C. Bechinger, "Direct measurement of three-body interactions amongst charged colloids," Phys. Rev. Lett. 92, 078301 (2004).
    [CrossRef] [PubMed]
  3. J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, "Entropic attraction and repulsion in binary colloids probed with a line optical tweezer," Phys. Rev. Lett. 82, 4352-4355 (1999).
    [CrossRef]
  4. J.-C. Meiners and S. R. Quake, "Direct Measurement of Hydrodynamic Cross Correlations between Two Particles in an External Potential," Phys. Rev. Lett. 82, 2211 (1999).
    [CrossRef]
  5. S. Henderson, S. Mitchell, and P. Bartlett, "Direct measurements of colloidal friction coefficients," Phys.Rev. E 64, 061403 (2001).
    [CrossRef]
  6. M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instr. 79, 043103 (2008).
    [CrossRef]
  7. M. Polin, Y. Roichman, and D. G. Grier, "Autocalibrated colloidal interaction measurements with extended optical traps," Phys.Rev. E 77, 051401-051407 (2008).
    [CrossRef]
  8. G. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, "Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy," Opt. Express 16, 14561-14570 (2008).
    [CrossRef] [PubMed]
  9. M. Speidel, A. Jonas, and E. L. Florin, "Three-dimensional tracking of fluoroscent nanoparticles with subnanometer precision by use of off-focus imaging," Opt. Lett. 28, 69-71 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, "Characterizing and tracking single colloidal particles with video holographic microscopy," Opt. Express 15, 18275-18282 (2007).
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    [CrossRef]
  13. R. Verma, J. C. Crocker, T. C. Lubensky, and A. G. Yodh, "Entropic colloidal interactions in concentrated DNA solutions," Phys. Rev. Lett. 81, 4004-4007 (1998).
    [CrossRef]
  14. J. Dobnikar, M. Brunner, H. H. von Grunberg, and C. Bechinger, "Three-body interactions in colloidal systems," Phys. Rev. E 69, 031402 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
    [CrossRef]
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    [CrossRef]
  19. D. Neumayer, P. Kaiser, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of two particles with dynamic optical traps," Proc. SPIE 5859, 33-39 (2005).
  20. A. Rohrbach, H. Kress, and E. H. K. Stelzer, "Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture," Opt. Lett. 28, 411 - 413 (2003).
    [CrossRef] [PubMed]
  21. J. K. Dreyer, K. Berg-Sorensen, and L. Oddershede, "Improved axial position detection in optical tweezers measurements," Appl. Opt. 43, 1991-1995 (2004).
    [CrossRef] [PubMed]
  22. A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optically trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
    [CrossRef]
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  24. P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of optically trapped probes behind structured surfaces: a phase correction method," Appl. Opt. 45, 7903-7915 (2006).
    [CrossRef]

2008

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instr. 79, 043103 (2008).
[CrossRef]

M. Polin, Y. Roichman, and D. G. Grier, "Autocalibrated colloidal interaction measurements with extended optical traps," Phys.Rev. E 77, 051401-051407 (2008).
[CrossRef]

Z. Zhang and C.-H. Menq, "Three-dimensional particle tracking with subnanometer resolution using off-focus images," Appl. Opt. 47, 2361-2370 (2008).
[CrossRef] [PubMed]

G. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, "Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy," Opt. Express 16, 14561-14570 (2008).
[CrossRef] [PubMed]

2007

2006

D. Weihs, T. G. Mason, and M. A. Teitell, "Bio-Microrheology: A Frontier in Microrheology," Biophys. J. 91, 4296-4305 (2006).
[CrossRef] [PubMed]

P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of optically trapped probes behind structured surfaces: a phase correction method," Appl. Opt. 45, 7903-7915 (2006).
[CrossRef]

2005

D. Neumayer, P. Kaiser, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of two particles with dynamic optical traps," Proc. SPIE 5859, 33-39 (2005).

2004

J. Dobnikar, M. Brunner, H. H. von Grunberg, and C. Bechinger, "Three-body interactions in colloidal systems," Phys. Rev. E 69, 031402 (2004).
[CrossRef]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004).
[CrossRef]

M. Brunner, J. Dobnikar, H. H. von Grunberg, and C. Bechinger, "Direct measurement of three-body interactions amongst charged colloids," Phys. Rev. Lett. 92, 078301 (2004).
[CrossRef] [PubMed]

J. K. Dreyer, K. Berg-Sorensen, and L. Oddershede, "Improved axial position detection in optical tweezers measurements," Appl. Opt. 43, 1991-1995 (2004).
[CrossRef] [PubMed]

2003

2002

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

R. Nambiar and J. C. Meiners, "Fast position measurements with scanning line optical tweezers," Opt. Lett. 27, 836-838 (2002).
[CrossRef]

2001

S. Henderson, S. Mitchell, and P. Bartlett, "Direct measurements of colloidal friction coefficients," Phys.Rev. E 64, 061403 (2001).
[CrossRef]

1999

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, "Entropic attraction and repulsion in binary colloids probed with a line optical tweezer," Phys. Rev. Lett. 82, 4352-4355 (1999).
[CrossRef]

J.-C. Meiners and S. R. Quake, "Direct Measurement of Hydrodynamic Cross Correlations between Two Particles in an External Potential," Phys. Rev. Lett. 82, 2211 (1999).
[CrossRef]

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

1998

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

R. Verma, J. C. Crocker, T. C. Lubensky, and A. G. Yodh, "Entropic colloidal interactions in concentrated DNA solutions," Phys. Rev. Lett. 81, 4004-4007 (1998).
[CrossRef]

1995

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, "Periodic Forcing of a Brownian Particle," Phys.Rev. E 51, 5239-5250 (1995).
[CrossRef]

Addas, K. M.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instr. 79, 043103 (2008).
[CrossRef]

Atakhorrami, M.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instr. 79, 043103 (2008).
[CrossRef]

Bartlett, P.

S. Henderson, S. Mitchell, and P. Bartlett, "Direct measurements of colloidal friction coefficients," Phys.Rev. E 64, 061403 (2001).
[CrossRef]

Bechinger, C.

J. Dobnikar, M. Brunner, H. H. von Grunberg, and C. Bechinger, "Three-body interactions in colloidal systems," Phys. Rev. E 69, 031402 (2004).
[CrossRef]

M. Brunner, J. Dobnikar, H. H. von Grunberg, and C. Bechinger, "Direct measurement of three-body interactions amongst charged colloids," Phys. Rev. Lett. 92, 078301 (2004).
[CrossRef] [PubMed]

Berg-Sorensen, K.

Brunner, M.

M. Brunner, J. Dobnikar, H. H. von Grunberg, and C. Bechinger, "Direct measurement of three-body interactions amongst charged colloids," Phys. Rev. Lett. 92, 078301 (2004).
[CrossRef] [PubMed]

J. Dobnikar, M. Brunner, H. H. von Grunberg, and C. Bechinger, "Three-body interactions in colloidal systems," Phys. Rev. E 69, 031402 (2004).
[CrossRef]

Crocker, J. C.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, "Entropic attraction and repulsion in binary colloids probed with a line optical tweezer," Phys. Rev. Lett. 82, 4352-4355 (1999).
[CrossRef]

R. Verma, J. C. Crocker, T. C. Lubensky, and A. G. Yodh, "Entropic colloidal interactions in concentrated DNA solutions," Phys. Rev. Lett. 81, 4004-4007 (1998).
[CrossRef]

Dinsmore, A. D.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, "Entropic attraction and repulsion in binary colloids probed with a line optical tweezer," Phys. Rev. Lett. 82, 4352-4355 (1999).
[CrossRef]

Dobnikar, J.

M. Brunner, J. Dobnikar, H. H. von Grunberg, and C. Bechinger, "Direct measurement of three-body interactions amongst charged colloids," Phys. Rev. Lett. 92, 078301 (2004).
[CrossRef] [PubMed]

J. Dobnikar, M. Brunner, H. H. von Grunberg, and C. Bechinger, "Three-body interactions in colloidal systems," Phys. Rev. E 69, 031402 (2004).
[CrossRef]

Dreyer, J. K.

Faucheux, L. P.

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, "Periodic Forcing of a Brownian Particle," Phys.Rev. E 51, 5239-5250 (1995).
[CrossRef]

Florin, E. L.

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004).
[CrossRef]

M. Speidel, A. Jonas, and E. L. Florin, "Three-dimensional tracking of fluoroscent nanoparticles with subnanometer precision by use of off-focus imaging," Opt. Lett. 28, 69-71 (2003).
[CrossRef] [PubMed]

Florin, E.-L.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

Gibson, G.

Gittes, F.

Grier, D. G.

Henderson, S.

S. Henderson, S. Mitchell, and P. Bartlett, "Direct measurements of colloidal friction coefficients," Phys.Rev. E 64, 061403 (2001).
[CrossRef]

Hörber, J. K. H.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

Jonas, A.

Kaiser, P.

D. Neumayer, P. Kaiser, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of two particles with dynamic optical traps," Proc. SPIE 5859, 33-39 (2005).

Keen, S.

Kim, S.-H.

Kress, H.

Leach, J.

Lee, S.-H.

Libchaber, A.

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, "Periodic Forcing of a Brownian Particle," Phys.Rev. E 51, 5239-5250 (1995).
[CrossRef]

Lubensky, T. C.

R. Verma, J. C. Crocker, T. C. Lubensky, and A. G. Yodh, "Entropic colloidal interactions in concentrated DNA solutions," Phys. Rev. Lett. 81, 4004-4007 (1998).
[CrossRef]

Mason, T. G.

D. Weihs, T. G. Mason, and M. A. Teitell, "Bio-Microrheology: A Frontier in Microrheology," Biophys. J. 91, 4296-4305 (2006).
[CrossRef] [PubMed]

Matteo, J. A.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, "Entropic attraction and repulsion in binary colloids probed with a line optical tweezer," Phys. Rev. Lett. 82, 4352-4355 (1999).
[CrossRef]

Meiners, J. C.

Meiners, J.-C.

J.-C. Meiners and S. R. Quake, "Direct Measurement of Hydrodynamic Cross Correlations between Two Particles in an External Potential," Phys. Rev. Lett. 82, 2211 (1999).
[CrossRef]

Menq, C.-H.

Mitchell, S.

S. Henderson, S. Mitchell, and P. Bartlett, "Direct measurements of colloidal friction coefficients," Phys.Rev. E 64, 061403 (2001).
[CrossRef]

Nambiar, R.

Neumayer, D.

D. Neumayer, P. Kaiser, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of two particles with dynamic optical traps," Proc. SPIE 5859, 33-39 (2005).

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004).
[CrossRef]

Oddershede, L.

Padgett, M. J.

Polin, M.

M. Polin, Y. Roichman, and D. G. Grier, "Autocalibrated colloidal interaction measurements with extended optical traps," Phys.Rev. E 77, 051401-051407 (2008).
[CrossRef]

Pralle, A.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

Prummer, M.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

Quake, S. R.

J.-C. Meiners and S. R. Quake, "Direct Measurement of Hydrodynamic Cross Correlations between Two Particles in an External Potential," Phys. Rev. Lett. 82, 2211 (1999).
[CrossRef]

Rohrbach, A.

P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of optically trapped probes behind structured surfaces: a phase correction method," Appl. Opt. 45, 7903-7915 (2006).
[CrossRef]

D. Neumayer, P. Kaiser, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of two particles with dynamic optical traps," Proc. SPIE 5859, 33-39 (2005).

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004).
[CrossRef]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, "Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture," Opt. Lett. 28, 411 - 413 (2003).
[CrossRef] [PubMed]

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

Roichman, Y.

Schmidt, C. F.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instr. 79, 043103 (2008).
[CrossRef]

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

Seitz, P. C.

P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of optically trapped probes behind structured surfaces: a phase correction method," Appl. Opt. 45, 7903-7915 (2006).
[CrossRef]

Speidel, M.

Stelzer, E. H. K.

P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of optically trapped probes behind structured surfaces: a phase correction method," Appl. Opt. 45, 7903-7915 (2006).
[CrossRef]

D. Neumayer, P. Kaiser, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of two particles with dynamic optical traps," Proc. SPIE 5859, 33-39 (2005).

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004).
[CrossRef]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, "Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture," Opt. Lett. 28, 411 - 413 (2003).
[CrossRef] [PubMed]

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

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

Stolovitzky, G.

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, "Periodic Forcing of a Brownian Particle," Phys.Rev. E 51, 5239-5250 (1995).
[CrossRef]

Teitell, M. A.

D. Weihs, T. G. Mason, and M. A. Teitell, "Bio-Microrheology: A Frontier in Microrheology," Biophys. J. 91, 4296-4305 (2006).
[CrossRef] [PubMed]

Tischer, C.

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004).
[CrossRef]

van Blaaderen, A.

van Oostrum, P.

Verma, R.

R. Verma, J. C. Crocker, T. C. Lubensky, and A. G. Yodh, "Entropic colloidal interactions in concentrated DNA solutions," Phys. Rev. Lett. 81, 4004-4007 (1998).
[CrossRef]

von Grunberg, H. H.

M. Brunner, J. Dobnikar, H. H. von Grunberg, and C. Bechinger, "Direct measurement of three-body interactions amongst charged colloids," Phys. Rev. Lett. 92, 078301 (2004).
[CrossRef] [PubMed]

J. Dobnikar, M. Brunner, H. H. von Grunberg, and C. Bechinger, "Three-body interactions in colloidal systems," Phys. Rev. E 69, 031402 (2004).
[CrossRef]

Weihs, D.

D. Weihs, T. G. Mason, and M. A. Teitell, "Bio-Microrheology: A Frontier in Microrheology," Biophys. J. 91, 4296-4305 (2006).
[CrossRef] [PubMed]

Wright, A. J.

Yang, S.-M.

Yi, G.-R.

Yodh, A. G.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, "Entropic attraction and repulsion in binary colloids probed with a line optical tweezer," Phys. Rev. Lett. 82, 4352-4355 (1999).
[CrossRef]

R. Verma, J. C. Crocker, T. C. Lubensky, and A. G. Yodh, "Entropic colloidal interactions in concentrated DNA solutions," Phys. Rev. Lett. 81, 4004-4007 (1998).
[CrossRef]

Zhang, Z.

Appl. Opt.

Biophys. J.

D. Weihs, T. G. Mason, and M. A. Teitell, "Bio-Microrheology: A Frontier in Microrheology," Biophys. J. 91, 4296-4305 (2006).
[CrossRef] [PubMed]

J. Appl. Phys.

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

Microscopy Research and Techniques

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

J. Dobnikar, M. Brunner, H. H. von Grunberg, and C. Bechinger, "Three-body interactions in colloidal systems," Phys. Rev. E 69, 031402 (2004).
[CrossRef]

Phys. Rev. Lett.

M. Brunner, J. Dobnikar, H. H. von Grunberg, and C. Bechinger, "Direct measurement of three-body interactions amongst charged colloids," Phys. Rev. Lett. 92, 078301 (2004).
[CrossRef] [PubMed]

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, "Entropic attraction and repulsion in binary colloids probed with a line optical tweezer," Phys. Rev. Lett. 82, 4352-4355 (1999).
[CrossRef]

J.-C. Meiners and S. R. Quake, "Direct Measurement of Hydrodynamic Cross Correlations between Two Particles in an External Potential," Phys. Rev. Lett. 82, 2211 (1999).
[CrossRef]

R. Verma, J. C. Crocker, T. C. Lubensky, and A. G. Yodh, "Entropic colloidal interactions in concentrated DNA solutions," Phys. Rev. Lett. 81, 4004-4007 (1998).
[CrossRef]

Phys.Rev. E

S. Henderson, S. Mitchell, and P. Bartlett, "Direct measurements of colloidal friction coefficients," Phys.Rev. E 64, 061403 (2001).
[CrossRef]

M. Polin, Y. Roichman, and D. G. Grier, "Autocalibrated colloidal interaction measurements with extended optical traps," Phys.Rev. E 77, 051401-051407 (2008).
[CrossRef]

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, "Periodic Forcing of a Brownian Particle," Phys.Rev. E 51, 5239-5250 (1995).
[CrossRef]

Proc. SPIE

D. Neumayer, P. Kaiser, E. H. K. Stelzer, and A. Rohrbach, "Interferometric tracking of two particles with dynamic optical traps," Proc. SPIE 5859, 33-39 (2005).

Rev. Sci. Instr.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instr. 79, 043103 (2008).
[CrossRef]

Rev. Sci. Instrum.

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004).
[CrossRef]

Other

J. Baumgartl, "Like-charge attraction in confinement: myth or truth?," Soft Matter 2, 631-635 (2006).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

(Color online) Schematic of the trapping and tracking setup. A NIR-laser is modulated by an AOM and deflected in phase by two galvanometric scan mirrors (SM). The rotational motion is translated into a lateral displacement by the scan lenses (L1, L2) and the objective lens (OL). The back focal plane of the detection lens (DL) is imaged onto two quadrant photodiodes for axial (QPD2) and lateral (QPD1) position detection. The inset shows a magnification of the focal plane, where the oscillating laser focus probes the positions b1 and b2 of two particles.

Fig. 2.
Fig. 2.

(Color online) Time series Sx′(t),and Sz′(t) of the x (green) and z (blue) detector responses of two trapped particles. The trap positions xtr (t) correspond to the black line. The axial sum signal is superimposed by the modulated laser intensity. Due to the back and forth motion of the trap, the positions (peaks) of each particle are horizontally flipped per scan. Right: z-raw data and “empty-scan” (red and black lines) and the resulting post processed z-data (blue) for two particles with z-positions, i.e. peak heights indicated by the arrows.

Fig. 3.
Fig. 3.

(Color online) Left: time series of two 970 nm particles (red and blue traces) in a line trap. The distance between the x positions reveal the bead diameter. Center: Three 1D histograms of a single particle reflect the trap stiffnesses. Right: 2D histograms show how the particles distribute in the trap, which is also sketched above in 3D.

Fig. 4.
Fig. 4.

(Color online) Linear detection range of the detector response of a 970nm silica sphere. Fixed on the coverslip, the particle is moved downwards in axial direction (see arrows) while the laser sweeps across it in x-direction. The method is illustrated for three different axial coverslip positions (I, II, III). The resulting detector response has a linear range (blue line) and the slope of a line fit encodes the axial sensitivity gz(bz). A lateral movement of the coverslip results in the sensitivity gy(by). The contor plots for gy(by) and gz(bz) are shown and the linear range is indicated by a black line.

Fig. 5.
Fig. 5.

(Color online) Detector responses Sy, Sz at the positions A, B and C within the optical potential. Points B and C are 3μm away from the center point A.

Fig. 6.
Fig. 6.

Three different types of errors are summarized in the figures (a)–(c). In a) the influence of electronical and mechanical noise is characterized, b) describes optically induced errors and c) the influence of changes in the sample frequency.

Fig. 7.
Fig. 7.

(a). (Color online) The z-positions of two adjacent particles can be independently tracked. (b). Increase in the x-position reconstruction error as a function of the sphere overlap Δx between two particles (see text for details).

Fig. 8.
Fig. 8.

(a). (Color online) Histogram of x-positions of a single particle and optical potential derived from Boltzmann statistics. (b). If two particles diffuse in the optical potential left, bead distances Δb = |b 1-b 2| vary. The histogram H(Δb) of the 3D bead separation is compared to the histogram H(Δbx) calculated from the distances Δbx = |bx1-bx2| of lateral x- positions only. The bead diameter D is indicated by the red line (for details see text).

Fig. 9.
Fig. 9.

(Color online) Cross correlation data of three 970nm particles in the line optical tweezers. The data reveal an anti-correlated motion due to hydrodynamic coupling between the particles in the y and z- direction, whereas the x-lateral direction shows a positively correlated motion. Cross talk between directly neighbored particles is pronounced compared to the outer most particles.

Tables (1)

Tables Icon

Table 1: Kick-displacements Δxkick in nm for various speeds vtrap of the passing trap in mm/s.

Equations (10)

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I(xtr,b)=A(xtr)·E˜i(xtr)+E˜s(xtr,b)2A(xtr)·E˜i(xtr)2+A(xtr)·E˜s(xtr,b)2+
A (xtr) · 2 · E˜i(xtr) E˜s(xtr,b) · cos (Δϕx(bx) +Δϕy(by)+Δϕz(bz))
Sm (b(t),xtr(t)) ~ ∫∫Am A (xtr) ·E˜i(kx,ky,xtr)+E˜s(kx,ky,xtr,b)2 H (kx,ky) d kx d ky
S(b(t),xtr(t))Ses(xtr(t)) ~ ∫∫A A (xtr) · (E˜i(xtr)+E˜s(b+xtr(t))2E˜i(xtr)2) · H dA
bx(t0)=xtr(0)+vx·minpos[ddtSx(t)]t0Δtt0+Δt
by(t0)=gyy1·extval[Sy(t)]t0Δtt0+Δt
bz(t0)=gzz1·extval[Sy(t)S'es(t)]t0Δtt0+Δt
Fgrad(bx)=αn2cV V(bead) I (rbx·ex) dV Dλ αn2c bx (I0·exp((bx/Δx)2)) bx<<Δx κx·bx
Veff(bx)=L/2bx Fgradxt dx =RL/2bx(4R)1(4R)1A(vxt)·Fgrad(xvxt) dt dx bx<<L2 12 · κx,eff · bx2
I (b1,b2) ~ Ei+ES1+ES22 Ei+ES12 +Ei+ES22 +Re{ES1·ES2*} .

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