Abstract

We suggest and study experimentally a time-sharing protocol for acousto-optical deflectors (AODs) that permits one to map the radial optical trapping force of optical tweezers without using a controllable flux control or an additional beam. Variations of the trapping potential due to modifications of the optical system are easily detected in terms of the force map. The protocol can be used in optical tweezers that already include an AOD without adding new elements in the existing optical system.

© 2012 Optical Society of America

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2012 (2)

A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

I. A. Martínez, S. Raj, and D. Petrov, “Colored noise in the fluctuations of an extended dna molecule detected by optical trapping,” Eur. Biophys. J. 41, 99–106 (2012).
[CrossRef]

2011 (2)

2010 (1)

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]

Y.-F. Chen, G. A. Blab, and J.-C. Meiners, “Stretching submicron biomolecules with constant-force axial optical tweezers,” Biophys. J. 96, 4701–4708 (2009).
[CrossRef]

2008 (3)

A. Balijepalli, T. W. LeBrun, J. J. Gorman, and S. K. Gupta, “Methods to directly measure the trapping potential in optical tweezers,” Proc. SPIE 7038, 70380V (2008).
[CrossRef]

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

A. C. Richardson, S. N. S. Reihani, and L. B. Oddershede, “Non-harmonic potential of a single beam optical trap,” Opt. Express 16, 15709–15717 (2008).
[CrossRef]

2007 (1)

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

2006 (2)

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)

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021–3041 (2003).
[CrossRef]

2002 (3)

A. Rohrbach, and E. H. K. Stelzer, “Trapping forces, force constants and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (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, 0506011 (2002).

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[CrossRef]

2000 (1)

W. Singer, S. Barnet, N. Hecker, and M. Ritsch-Marte, “Three-dimensional force calibration of optical tweezers,” J. Mod. Opt. 47, 2921–2931 (2000).

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 (1)

J. E. Molloy, “Optical chopsticks: digital synthesis of multiple optical traps,” Methods Cell Biol. 55, 205–216(1998).

1996 (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]

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]

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (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]

1993 (1)

Arakelyan, A.

A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

Balijepalli, A.

A. Balijepalli, T. W. LeBrun, J. J. Gorman, and S. K. Gupta, “Methods to directly measure the trapping potential in optical tweezers,” Proc. SPIE 7038, 70380V (2008).
[CrossRef]

Ballerini, R.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[CrossRef]

Barbosa, L. C.

Barnet, S.

W. Singer, S. Barnet, N. Hecker, and M. Ritsch-Marte, “Three-dimensional force calibration of optical tweezers,” J. Mod. Opt. 47, 2921–2931 (2000).

Behrndt, B.

Bérut, A.

A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

Blab, G. A.

Y.-F. Chen, G. A. Blab, and J.-C. Meiners, “Stretching submicron biomolecules with constant-force axial optical tweezers,” Biophys. J. 96, 4701–4708 (2009).
[CrossRef]

Block, S. M.

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]

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]

Capitanio, M.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[CrossRef]

Cesar, C. L.

Chen, Y.-F.

Y.-F. Chen, G. A. Blab, and J.-C. Meiners, “Stretching submicron biomolecules with constant-force axial optical tweezers,” Biophys. J. 96, 4701–4708 (2009).
[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]

Chillce, E.

Chiu, D. T.

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Chu, S.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
[CrossRef]

Ciliberto, S.

A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

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]

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]

de Thomaz, A. A.

Dholakia, K.

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

Dillenschneider, R.

A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

Dunlap, D.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[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]

Edgar, J. C.

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[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, 0506011 (2002).

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]

Finer, J. T.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
[CrossRef]

Finzi, L.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[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]

Fontes, A.

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]

Ghislain, L. P.

Giuntini, M.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[CrossRef]

Godazgar, T.

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]

Gorman, J. J.

A. Balijepalli, T. W. LeBrun, J. J. Gorman, and S. K. Gupta, “Methods to directly measure the trapping potential in optical tweezers,” Proc. SPIE 7038, 70380V (2008).
[CrossRef]

Grill, S. W.

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]

Gupta, S. K.

A. Balijepalli, T. W. LeBrun, J. J. Gorman, and S. K. Gupta, “Methods to directly measure the trapping potential in optical tweezers,” Proc. SPIE 7038, 70380V (2008).
[CrossRef]

Hecker, N.

W. Singer, S. Barnet, N. Hecker, and M. Ritsch-Marte, “Three-dimensional force calibration of optical tweezers,” J. Mod. Opt. 47, 2921–2931 (2000).

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]

Jahnel, M.

Jannasch, A.

Jeffries, G. D. M.

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

LeBrun, T. W.

A. Balijepalli, T. W. LeBrun, J. J. Gorman, and S. K. Gupta, “Methods to directly measure the trapping potential in optical tweezers,” Proc. SPIE 7038, 70380V (2008).
[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]

Lutz, E.

A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

Martínez, I. A.

I. A. Martínez, S. Raj, and D. Petrov, “Colored noise in the fluctuations of an extended dna molecule detected by optical trapping,” Eur. Biophys. J. 41, 99–106 (2012).
[CrossRef]

Mazolli, A.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021–3041 (2003).
[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]

McGloin, D.

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Meiners, J.-C.

Y.-F. Chen, G. A. Blab, and J.-C. Meiners, “Stretching submicron biomolecules with constant-force axial optical tweezers,” Biophys. J. 96, 4701–4708 (2009).
[CrossRef]

Mesquita, O. N.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

Milne, G.

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[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, 0506011 (2002).

Molloy, J. E.

J. E. Molloy, “Optical chopsticks: digital synthesis of multiple optical traps,” Methods Cell Biol. 55, 205–216(1998).

Neto, P. A. M.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021–3041 (2003).
[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]

Neves, A. A. R.

Nussenzveig, H. M.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021–3041 (2003).
[CrossRef]

Oddershede, L. B.

Pavone, F. S.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[CrossRef]

Petrosyan, A.

A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

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.

I. A. Martínez, S. Raj, and D. Petrov, “Colored noise in the fluctuations of an extended dna molecule detected by optical trapping,” Eur. Biophys. J. 41, 99–106 (2012).
[CrossRef]

G. Volpe and D. Petrov, “Torque detection using brownian fluctuations,” Phys. Rev. Lett. 97, 210603 (2006).
[CrossRef]

Pozzo, L. de Y.

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]

Raj, S.

I. A. Martínez, S. Raj, and D. Petrov, “Colored noise in the fluctuations of an extended dna molecule detected by optical trapping,” Eur. Biophys. J. 41, 99–106 (2012).
[CrossRef]

Reihani, S. N. S.

Richardson, A. C.

Ritsch-Marte, M.

W. Singer, S. Barnet, N. Hecker, and M. Ritsch-Marte, “Three-dimensional force calibration of optical tweezers,” J. Mod. Opt. 47, 2921–2931 (2000).

Rocha, M. S.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

Rodrigez, E.

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, and E. H. K. Stelzer, “Trapping forces, force constants and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (2002).
[CrossRef]

Romano, G.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[CrossRef]

Schaffer, E.

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, 0506011 (2002).

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, 0506011 (2002).

Shokri, R.

Simmons, R. M.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
[CrossRef]

Singer, W.

W. Singer, S. Barnet, N. Hecker, and M. Ritsch-Marte, “Three-dimensional force calibration of optical tweezers,” J. Mod. Opt. 47, 2921–2931 (2000).

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]

Spudich, J. A.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (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]

A. Rohrbach, and E. H. K. Stelzer, “Trapping forces, force constants and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (2002).
[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]

Stolovitzky, G.

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

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 Kampen, N. G.

N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, 1992).

Viana, N. B.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

Visscher, K.

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]

Volpe, G.

G. Volpe and D. Petrov, “Torque detection using brownian fluctuations,” Phys. Rev. Lett. 97, 210603 (2006).
[CrossRef]

Wang, G.

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, 0506011 (2002).

Webb, W. W.

Zemanek, P.

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

Zhao, Y.

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Zhao, G. Milne, J. C. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Biophys. J. (2)

Y.-F. Chen, G. A. Blab, and J.-C. Meiners, “Stretching submicron biomolecules with constant-force axial optical tweezers,” Biophys. J. 96, 4701–4708 (2009).
[CrossRef]

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
[CrossRef]

Eur. Biophys. J. (1)

I. A. Martínez, S. Raj, and D. Petrov, “Colored noise in the fluctuations of an extended dna molecule detected by optical trapping,” Eur. Biophys. J. 41, 99–106 (2012).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

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]

J. Mod. Opt. (1)

W. Singer, S. Barnet, N. Hecker, and M. Ritsch-Marte, “Three-dimensional force calibration of optical tweezers,” J. Mod. Opt. 47, 2921–2931 (2000).

Methods Cell Biol. (1)

J. E. Molloy, “Optical chopsticks: digital synthesis of multiple optical traps,” Methods Cell Biol. 55, 205–216(1998).

Microsc. Res. Tech. (1)

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]

Nature (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. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. E (2)

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

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

Phys. Rev. Lett. (3)

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, 0506011 (2002).

G. Volpe and D. Petrov, “Torque detection using brownian fluctuations,” Phys. Rev. Lett. 97, 210603 (2006).
[CrossRef]

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]

Proc. R. Soc. A (1)

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021–3041 (2003).
[CrossRef]

Proc. SPIE (1)

A. Balijepalli, T. W. LeBrun, J. J. Gorman, and S. K. Gupta, “Methods to directly measure the trapping potential in optical tweezers,” Proc. SPIE 7038, 70380V (2008).
[CrossRef]

Rev. Mod. Phys. (1)

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

Rev. Sci. Instrum. (2)

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. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002).
[CrossRef]

Science (1)

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]

Other (1)

N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, 1992).

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Figures (5)

Fig. 1.
Fig. 1.

A strong trap 1 holds the probe while the trapping force of a weak trap 2 at a distance x0 shifts the position of the probe to Δx. The stiffness of the trap 1 is strong enough such that Δx does not reach the limit of the harmonic approximation of its OTP. Therefore the force exerted by the trap 1 is equal to the stiffness of the trap 1 multiplied by Δx.

Fig. 2.
Fig. 2.

Protocol of the time-sharing regime. Signals of a modulation generator 1 U1(t) modulate the frequency of an RF generator in such a way that two traps with a controllable distance between the traps and a ratio of the trap’s stiffnesses are created in the focal plane of the trapping objective. When the amplitude of the square signal varies, the position of one of the traps remains fixed while the position of the other trap shifts. As seen, the duty cycle of the square wave provides the higher stiffness of the fixed trap compared with the stiffness of the movable trap. Signals of a modulation generator 2 U2(t) change the positions of both traps simultaneously.

Fig. 3.
Fig. 3.

Optical setup.

Fig. 4.
Fig. 4.

(a) Force exerted on 1 μm (red open squares) and 2 μm (blue squares) spheres versus radial distance. (b) Trap stiffness versus radial distance. The optical trap has a beam power of 3 mW. We confirmed that the force map is not affected by further increase of the strong trap stiffness by keeping the same intensity of the weak trap.

Fig. 5.
Fig. 5.

OTPs for 1 μm (red open squares) and 2 μm (blue squares) spheres.

Equations (1)

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U(r)=rF(r)dr.

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