Abstract

In photonic force microscopes, the position detection with high temporal and spatial resolution is usually implemented by a quadrant position detector placed in the back focal plane of a condenser. An objective with high numerical aperture (NA) for the optical trap has also been used to focus a detection beam. In that case the displacement of the probe at a fixed position of the detector produces a unique and linear response only in a restricted region of the probe displacement, usually several hundred nanometers. There are specific experiments where the absolute position of the probe is a relevant measure together with the probe position relative the optical trap focus. In our scheme we introduce the detection beam into the condenser with low NA through a pinhole with tunable size. This combination permits us to create a wide detection spot and to achieve the linear range of several micrometers by the probe position detection without reducing the trapping force.

© 2012 Optical Society of America

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  1. L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. 18, 1678–1680 (1993).
    [CrossRef]
  2. L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
    [CrossRef]
  3. K. Visscher, S. P. Gross, and S. M. Block, “Construction of mutiple-beam optical traps with nanometric-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066–1076 (1996).
    [CrossRef]
  4. A. Prälle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and 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]
  5. 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]
  6. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
    [CrossRef]
  7. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
    [CrossRef]
  8. S. R. Quake, H. Babcock, and S. Chu, “The dynamics of partially extended single molecules of DNA,” Nature 388, 151–154 (1997).
    [CrossRef]
  9. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335–1346 (1997).
    [CrossRef]
  10. J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17, 1422–1430 (2010).
    [CrossRef]
  11. L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic forcing of a Brownian particle,” Phys. Rev. E 51, 5239–5250 (1995).
    [CrossRef]
  12. G. Wang, E. Sevick, E. Mittag, D. Searles, and D. Evans, “Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales,” Phys. Rev. Lett. 89, 050601 (2002).
    [CrossRef]
  13. A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, “Work and heat probability distribution of an optically driven Brownian particle: theory and experiments,” Phys. Rev. E 76, 050101 (2007).
    [CrossRef]
  14. A. Simon and A. Libchaber, “Escape and synchronization of a Brownian particle,” Phys. Rev. Lett. 68, 3375–3378(1992).
    [CrossRef]
  15. L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785–787 (1999).
    [CrossRef]
  16. C. Schmidt, B. Dybiec, P. Hänggi, and C. Bechinger, “Stochastic resonance vs. resonant activation,” Europhys. Lett. 74, 937–943 (2006).
    [CrossRef]
  17. K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
    [CrossRef]
  18. J. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, “Experimental verification of a modified fluctuation–dissipation relation for a micron-sized particle in a nonequilibrium steady state,” Phys. Rev. Lett. 103, 040601 (2009).
    [CrossRef]
  19. P. Hänggi and F. Marchesoni, “Artificial Brownian motors: controlling transport on the nanoscale,” Rev. Mod. Phys. 81, 387–442 (2009).
    [CrossRef]
  20. J. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
    [CrossRef]
  21. M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491–501 (2002).
    [CrossRef]
  22. 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]
  23. G. Volpe, G. Kozyreff, and D. Petrov, “Backscattering position detection for photonic force microscopy,” J. Appl. Phys. 102, 084701 (2007).
    [CrossRef]
  24. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II,” Proc. R. Soc. A 253, 358–379 (1959).
    [CrossRef]
  25. F. Gittes and C. F. Schmidt, “Signals and noise in micromechanical measurements,” Methods Cell Biol. 55, 129–156 (1998).
    [CrossRef]
  26. S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum. 79, 106101 (2008).
    [CrossRef]

2010 (2)

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17, 1422–1430 (2010).
[CrossRef]

K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[CrossRef]

2009 (2)

J. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, “Experimental verification of a modified fluctuation–dissipation relation for a micron-sized particle in a nonequilibrium steady state,” Phys. Rev. Lett. 103, 040601 (2009).
[CrossRef]

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: controlling transport on the nanoscale,” Rev. Mod. Phys. 81, 387–442 (2009).
[CrossRef]

2008 (1)

S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum. 79, 106101 (2008).
[CrossRef]

2007 (2)

G. Volpe, G. Kozyreff, and D. Petrov, “Backscattering position detection for photonic force microscopy,” J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, “Work and heat probability distribution of an optically driven Brownian particle: theory and experiments,” Phys. Rev. E 76, 050101 (2007).
[CrossRef]

2006 (1)

C. Schmidt, B. Dybiec, P. Hänggi, and C. Bechinger, “Stochastic resonance vs. resonant activation,” Europhys. Lett. 74, 937–943 (2006).
[CrossRef]

2004 (1)

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]

2003 (1)

2002 (2)

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491–501 (2002).
[CrossRef]

G. Wang, E. Sevick, E. Mittag, D. Searles, and D. Evans, “Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales,” Phys. Rev. Lett. 89, 050601 (2002).
[CrossRef]

1999 (2)

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785–787 (1999).
[CrossRef]

A. Prälle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and 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]

1998 (2)

F. Gittes and C. F. Schmidt, “Signals and noise in micromechanical measurements,” Methods Cell Biol. 55, 129–156 (1998).
[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]

1997 (2)

S. R. Quake, H. Babcock, and S. Chu, “The dynamics of partially extended single molecules of DNA,” Nature 388, 151–154 (1997).
[CrossRef]

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

1996 (3)

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef]

J. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

K. Visscher, S. P. Gross, and S. M. Block, “Construction of mutiple-beam optical traps with nanometric-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066–1076 (1996).
[CrossRef]

1995 (1)

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic forcing of a Brownian particle,” Phys. Rev. E 51, 5239–5250 (1995).
[CrossRef]

1994 (1)

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

1993 (1)

1992 (1)

A. Simon and A. Libchaber, “Escape and synchronization of a Brownian particle,” Phys. Rev. Lett. 68, 3375–3378(1992).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II,” Proc. R. Soc. A 253, 358–379 (1959).
[CrossRef]

Asbury, C. L.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491–501 (2002).
[CrossRef]

Babcock, H.

S. R. Quake, H. Babcock, and S. Chu, “The dynamics of partially extended single molecules of DNA,” Nature 388, 151–154 (1997).
[CrossRef]

Bechinger, C.

C. Schmidt, B. Dybiec, P. Hänggi, and C. Bechinger, “Stochastic resonance vs. resonant activation,” Europhys. Lett. 74, 937–943 (2006).
[CrossRef]

Block, S. M.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491–501 (2002).
[CrossRef]

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

K. Visscher, S. P. Gross, and S. M. Block, “Construction of mutiple-beam optical traps with nanometric-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066–1076 (1996).
[CrossRef]

Boyce, M. C.

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17, 1422–1430 (2010).
[CrossRef]

Bustamante, C.

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef]

Castro, C. E.

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17, 1422–1430 (2010).
[CrossRef]

Chetrite, R.

J. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, “Experimental verification of a modified fluctuation–dissipation relation for a micron-sized particle in a nonequilibrium steady state,” Phys. Rev. Lett. 103, 040601 (2009).
[CrossRef]

Chu, S.

S. R. Quake, H. Babcock, and S. Chu, “The dynamics of partially extended single molecules of DNA,” Nature 388, 151–154 (1997).
[CrossRef]

Ciliberto, S.

J. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, “Experimental verification of a modified fluctuation–dissipation relation for a micron-sized particle in a nonequilibrium steady state,” Phys. Rev. Lett. 103, 040601 (2009).
[CrossRef]

Crocker, J.

J. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Cui, Y.

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef]

Dholakia, K.

K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[CrossRef]

Dong, J.

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17, 1422–1430 (2010).
[CrossRef]

Dybiec, B.

C. Schmidt, B. Dybiec, P. Hänggi, and C. Bechinger, “Stochastic resonance vs. resonant activation,” Europhys. Lett. 74, 937–943 (2006).
[CrossRef]

Dykman, M.

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785–787 (1999).
[CrossRef]

Evans, D.

G. Wang, E. Sevick, E. Mittag, D. Searles, and D. Evans, “Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales,” Phys. Rev. Lett. 89, 050601 (2002).
[CrossRef]

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]

Florin, E.-L.

A. Prälle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and 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]

Gawedzki, K.

J. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, “Experimental verification of a modified fluctuation–dissipation relation for a micron-sized particle in a nonequilibrium steady state,” Phys. Rev. Lett. 103, 040601 (2009).
[CrossRef]

Gelles, J.

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

Ghislain, L. P.

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

L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. 18, 1678–1680 (1993).
[CrossRef]

Gittes, F.

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

F. Gittes and C. F. Schmidt, “Signals and noise in micromechanical measurements,” Methods Cell Biol. 55, 129–156 (1998).
[CrossRef]

Golding, B.

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785–787 (1999).
[CrossRef]

Gomez-Solano, J.

J. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, “Experimental verification of a modified fluctuation–dissipation relation for a micron-sized particle in a nonequilibrium steady state,” Phys. Rev. Lett. 103, 040601 (2009).
[CrossRef]

Grier, D. G.

J. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of mutiple-beam optical traps with nanometric-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066–1076 (1996).
[CrossRef]

Hänggi, P.

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: controlling transport on the nanoscale,” Rev. Mod. Phys. 81, 387–442 (2009).
[CrossRef]

C. Schmidt, B. Dybiec, P. Hänggi, and C. Bechinger, “Stochastic resonance vs. resonant activation,” Europhys. Lett. 74, 937–943 (2006).
[CrossRef]

Hörber, J. K. H.

A. Prälle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and 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]

Imparato, A.

A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, “Work and heat probability distribution of an optically driven Brownian particle: theory and experiments,” Phys. Rev. E 76, 050101 (2007).
[CrossRef]

Kozyreff, G.

G. Volpe, G. Kozyreff, and D. Petrov, “Backscattering position detection for photonic force microscopy,” J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

Kress, H.

Landick, R.

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

Lang, M. J.

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17, 1422–1430 (2010).
[CrossRef]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491–501 (2002).
[CrossRef]

Libchaber, A.

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic forcing of a Brownian particle,” Phys. Rev. E 51, 5239–5250 (1995).
[CrossRef]

A. Simon and A. Libchaber, “Escape and synchronization of a Brownian particle,” Phys. Rev. Lett. 68, 3375–3378(1992).
[CrossRef]

Lindquist, S.

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17, 1422–1430 (2010).
[CrossRef]

Marchesoni, F.

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: controlling transport on the nanoscale,” Rev. Mod. Phys. 81, 387–442 (2009).
[CrossRef]

McCann, L. I.

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785–787 (1999).
[CrossRef]

Mittag, E.

G. Wang, E. Sevick, E. Mittag, D. Searles, and D. Evans, “Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales,” Phys. Rev. Lett. 89, 050601 (2002).
[CrossRef]

Neumayer, D.

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]

Peliti, L.

A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, “Work and heat probability distribution of an optically driven Brownian particle: theory and experiments,” Phys. Rev. E 76, 050101 (2007).
[CrossRef]

Perrone, S.

S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum. 79, 106101 (2008).
[CrossRef]

Pesce, G.

A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, “Work and heat probability distribution of an optically driven Brownian particle: theory and experiments,” Phys. Rev. E 76, 050101 (2007).
[CrossRef]

Petrosyan, A.

J. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, and K. Gawedzki, “Experimental verification of a modified fluctuation–dissipation relation for a micron-sized particle in a nonequilibrium steady state,” Phys. Rev. Lett. 103, 040601 (2009).
[CrossRef]

Petrov, D.

S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum. 79, 106101 (2008).
[CrossRef]

G. Volpe, G. Kozyreff, and D. Petrov, “Backscattering position detection for photonic force microscopy,” J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

Prälle, A.

A. Prälle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and 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]

Prummer, M.

A. Prälle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and 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]

Quake, S. R.

S. R. Quake, H. Babcock, and S. Chu, “The dynamics of partially extended single molecules of DNA,” Nature 388, 151–154 (1997).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II,” Proc. R. Soc. A 253, 358–379 (1959).
[CrossRef]

Rohrbach, A.

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]

Rusciano, G.

A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, “Work and heat probability distribution of an optically driven Brownian particle: theory and experiments,” Phys. Rev. E 76, 050101 (2007).
[CrossRef]

Sasso, A.

A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, “Work and heat probability distribution of an optically driven Brownian particle: theory and experiments,” Phys. Rev. E 76, 050101 (2007).
[CrossRef]

Schmidt, C.

C. Schmidt, B. Dybiec, P. Hänggi, and C. Bechinger, “Stochastic resonance vs. resonant activation,” Europhys. Lett. 74, 937–943 (2006).
[CrossRef]

Schmidt, C. F.

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

F. Gittes and C. F. Schmidt, “Signals and noise in micromechanical measurements,” Methods Cell Biol. 55, 129–156 (1998).
[CrossRef]

Searles, D.

G. Wang, E. Sevick, E. Mittag, D. Searles, and D. Evans, “Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales,” Phys. Rev. Lett. 89, 050601 (2002).
[CrossRef]

Sevick, E.

G. Wang, E. Sevick, E. Mittag, D. Searles, and D. Evans, “Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales,” Phys. Rev. Lett. 89, 050601 (2002).
[CrossRef]

Shaevitz, J. W.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491–501 (2002).
[CrossRef]

Simon, A.

A. Simon and A. Libchaber, “Escape and synchronization of a Brownian particle,” Phys. Rev. Lett. 68, 3375–3378(1992).
[CrossRef]

Smith, S. B.

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef]

Stelzer, E. H. K.

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]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the BFP position detection system. (a) The trapping beam introduced by a trapping objective OT is also used to detect the probe position. (b) An additional beam of other wavelength (or polarization) introduced through the trapping objective OT is the detection beam. In both schemes the condenser objective OD collimates the detection beam before sending it to the QPD. In (c) the detection beam is introduced by the objective OD. By choosing the NA of OD and the size of a pinhole PH, one may tune the size of the detection spot in the focal plane of OT.

Fig. 2.
Fig. 2.

Normalized electric field intensity in the focal plane versus distance from the focus calculated for the objectives with (a) NA=1.3 (focal distance f=2.7mm) and (b) NA=0.1 (focal distance f=28.9mm). In both cases the input Gaussian beam has the waist 0.5 cm. The results are shown for two radii of the aperture 0.5 cm (1) and 0.05 cm (2). The Gaussian fitting of the numerically obtained results gives w0=0.18μm (curve 1) and w0=0.68μm (curve 2) for the objective with NA=1.3 and w0=0.78μm (curve 1) and w0=7.05μm (curve 2) for the objective with NA=0.1. The values of the focal distances are from www.edmundsoptics.com. The wavelength in vacuum is 0.63 μm.

Fig. 3.
Fig. 3.

Experimental setup.

Fig. 4.
Fig. 4.

Trapped 2 μm sphere inside the spot of the detection beam in the focal plane of the trapping objective.

Fig. 5.
Fig. 5.

Position detector output signal (the probe diameter is 1 μm, blue line, and 2 μm, red line) as a function of probe displacements shows a nonlinear character when the probe displacement exceeds the size of the detection spot 8 μm. However, at probe shifts less than ±1500nm (the 1 μm probe diameter), there is a linear dependence between the QPD output and the probe position. The minor deviations from the linear dependence in the linear part of the QPD response are due to the nonuniformity in the detection beam intensity as well as Brownian fluctuations of the probe position. For the probe with diameter 2 μm, the linear range is ±3500nm. The insets show the images of the interference rings of the detection beam observed at the plane of the QPD for the 1 and 2 μm probes.

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