Abstract

We present real-time in situ calibration of an optically trapped probing system. In the probing system, a micro/nanobead is stably trapped around the minimum of the field potential to serve as the measurement probe, whereas the random thermal force tends to destabilize it and causes Brownian motion around the equilibrium. The weighted recursive least-squares algorithm is applied to recursively update the system’s parameters, such as the state transition coefficient, and to estimate specific system response and the unknown variance of the Gaussian white noise in real time according to the probe’s motion. The real-time recursive algorithm was first applied to real-time calibration of measurement sensitivity and trapping stiffness for the case that the local temperature and the damping coefficient of the probe are known. It was then applied to estimate the probe’s local temperature in real time. Two experiments were designed to illustrate the applicability of the real-time calibration method. The experimental results show that the recursive algorithm is able to real-time calibrate the trapping stiffness of the probing system and the measurement sensitivity of the back-focal-plane interferometry employed for position measurement. The experimental results also show that the method can estimate the probe’s local temperature in real time.

© 2009 Optical Society of America

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  2. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
    [CrossRef] [PubMed]
  3. 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]
  4. 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] [PubMed]
  5. A. E. Knight, C. Veigel, C. Chambers, and J. E. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Molec. Biol. 77, 45-72 (2001).
    [CrossRef]
  6. A. L. Stout, “Detection and characterization of individual intermolecular bounds using optical tweezers,” Biophys. J. 80, 2976-2986 (2001).
    [CrossRef] [PubMed]
  7. T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
    [CrossRef]
  8. F. Gittes and G. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7-9 (1998).
    [CrossRef]
  9. A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378-386 (1999).
    [CrossRef] [PubMed]
  10. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  11. M. E. J. Friese, H. Rubinsztein-Dunlop, N. R. Heckenberg, and E. W. Dearden, “Determination of the force constant of a single-beam gradient trap by measurement of backscattered light,” Appl. Opt. 35, 7112-7116 (1996).
    [CrossRef] [PubMed]
  12. K. Berg-Sorensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
    [CrossRef]
  13. K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
    [CrossRef]
  14. 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] [PubMed]
  15. M. Capitano, 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]
  16. E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316(2003).
    [CrossRef] [PubMed]
  17. Y. Seol, A. E. Carpenter, and T. T. Perkins, “Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating,” Opt. Lett. 31, 2429-2431 (2006).
    [CrossRef] [PubMed]
  18. Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
    [CrossRef] [PubMed]
  19. 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]
  20. A. Rohrbach and E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474-5488 (2002).
    [CrossRef]
  21. S. M. Pandit, Modal and Spectrum Analysis: Data Dependent Systems in State Space (Wiley, 1991).
  22. S. Haykin, Adaptive Filter Theory, 4th ed. (Prentice-Hall, 2002).
  23. Y. S. Touloukian, S. C. Saxena, and P. Hestermans, Viscosity (IFI/Plenum, 1975).
  24. S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
    [CrossRef]

2009 (1)

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

2006 (3)

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
[CrossRef]

Y. Seol, A. E. Carpenter, and T. T. Perkins, “Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating,” Opt. Lett. 31, 2429-2431 (2006).
[CrossRef] [PubMed]

2005 (1)

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[CrossRef]

2004 (3)

K. Berg-Sorensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (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]

2003 (1)

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316(2003).
[CrossRef] [PubMed]

2002 (2)

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

M. Capitano, 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]

2001 (2)

A. E. Knight, C. Veigel, C. Chambers, and J. E. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Molec. Biol. 77, 45-72 (2001).
[CrossRef]

A. L. Stout, “Detection and characterization of individual intermolecular bounds using optical tweezers,” Biophys. J. 80, 2976-2986 (2001).
[CrossRef] [PubMed]

1999 (1)

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

1998 (1)

1996 (3)

M. E. J. Friese, H. Rubinsztein-Dunlop, N. R. Heckenberg, and E. W. Dearden, “Determination of the force constant of a single-beam gradient trap by measurement of backscattered light,” Appl. Opt. 35, 7112-7116 (1996).
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

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]

1987 (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

1986 (1)

Altmann, S. M.

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[CrossRef]

Antognozzi, M.

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

Ballerini, R.

M. Capitano, 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]

Berg-Sorensen, K.

K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
[CrossRef]

K. Berg-Sorensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Brenner, B.

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[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] [PubMed]

Capitano, M.

M. Capitano, 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]

Carpenter, A. E.

Chambers, C.

A. E. Knight, C. Veigel, C. Chambers, and J. E. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Molec. Biol. 77, 45-72 (2001).
[CrossRef]

Cheng, M.-C.

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

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] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

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] [PubMed]

Dearden, E. W.

Dunlap, D.

M. Capitano, 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]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

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] [PubMed]

Finzi, L.

M. Capitano, 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]

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

Flyvbjerg, H.

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
[CrossRef]

K. Berg-Sorensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

Friese, M. E. J.

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]

Gittes, F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316(2003).
[CrossRef] [PubMed]

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

Giuntini, M.

M. Capitano, 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]

Haykin, S.

S. Haykin, Adaptive Filter Theory, 4th ed. (Prentice-Hall, 2002).

Heckenberg, N. R.

Heinrich, J. K.

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[CrossRef]

Hestermans, P.

Y. S. Touloukian, S. C. Saxena, and P. Hestermans, Viscosity (IFI/Plenum, 1975).

Horber, J. K. H.

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

Howard, J.

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Huang, Y.

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

Jhiang, S. M.

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

Julicher, F.

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Knight, A. E.

A. E. Knight, C. Veigel, C. Chambers, and J. E. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Molec. Biol. 77, 45-72 (2001).
[CrossRef]

Menq, C.-H.

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

Molloy, J. E.

A. E. Knight, C. Veigel, C. Chambers, and J. E. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Molec. Biol. 77, 45-72 (2001).
[CrossRef]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[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]

Pandit, S. M.

S. M. Pandit, Modal and Spectrum Analysis: Data Dependent Systems in State Space (Wiley, 1991).

Pavone, F. S.

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

M. Capitano, 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]

Perkins, T. T.

Peterman, E. J. G.

K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
[CrossRef]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316(2003).
[CrossRef] [PubMed]

Pralle, A.

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

Prummer, M.

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

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, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

Romano, G.

M. Capitano, 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]

Rubinsztein-Dunlop, H.

Saxena, S. C.

Y. S. Touloukian, S. C. Saxena, and P. Hestermans, Viscosity (IFI/Plenum, 1975).

Schaffer, E.

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Schmidt, C. F.

K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
[CrossRef]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316(2003).
[CrossRef] [PubMed]

Schmidt, G. F.

Scholz, T.

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[CrossRef]

Seol, Y.

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] [PubMed]

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] [PubMed]

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] [PubMed]

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, “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. Horber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

Stout, A. L.

A. L. Stout, “Detection and characterization of individual intermolecular bounds using optical tweezers,” Biophys. J. 80, 2976-2986 (2001).
[CrossRef] [PubMed]

Switz, N. A.

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]

Tischer, C.

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[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]

Tolic-Norrelykke, S. F.

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Touloukian, Y. S.

Y. S. Touloukian, S. C. Saxena, and P. Hestermans, Viscosity (IFI/Plenum, 1975).

Veigel, C.

A. E. Knight, C. Veigel, C. Chambers, and J. E. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Molec. Biol. 77, 45-72 (2001).
[CrossRef]

Wan, J.

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

Webb, W. W.

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]

Weber, T.

K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
[CrossRef]

Yamane, T.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

Zhang, Z.

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (4)

A. L. Stout, “Detection and characterization of individual intermolecular bounds using optical tweezers,” Biophys. J. 80, 2976-2986 (2001).
[CrossRef] [PubMed]

T. Scholz, S. M. Altmann, M. Antognozzi, C. Tischer, J. K. Heinrich, and B. Brenner, “Mechanical properties of single myosin molecules probed with the photonic force microscope,” Biophys. J. 88, 360-371 (2005).
[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] [PubMed]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308-1316(2003).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

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

Microsc. Res. Tech. (1)

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

Nature (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

Opt. Lett. (3)

Prog. Biophys. Molec. Biol. (1)

A. E. Knight, C. Veigel, C. Chambers, and J. E. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Molec. Biol. 77, 45-72 (2001).
[CrossRef]

Rev. Sci. Instrum. (8)

S. F. Tolic-Norrelykke, E. Schaffer, J. Howard, F. S. Pavone, F. Julicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Y. Huang, J. Wan, M.-C. Cheng, Z. Zhang, S. M. Jhiang, and C.-H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 063107(2009).
[CrossRef] [PubMed]

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]

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]

M. Capitano, 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]

K. Berg-Sorensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

K. Berg-Sorensen, E. J. G. Peterman, T. Weber, C. F. Schmidt, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers II: laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth,” Rev. Sci. Instrum. 77, 063106 (2006).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[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] [PubMed]

Other (3)

S. M. Pandit, Modal and Spectrum Analysis: Data Dependent Systems in State Space (Wiley, 1991).

S. Haykin, Adaptive Filter Theory, 4th ed. (Prentice-Hall, 2002).

Y. S. Touloukian, S. C. Saxena, and P. Hestermans, Viscosity (IFI/Plenum, 1975).

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Figures (4)

Fig. 1
Fig. 1

Schematic layout of the optically trapped probing system. The 1064 nm trapping laser propagates along the light path in the direction of HWP PBS QWP DM QWP PBS L 1 L 2 two- axis   AOD L 3 L 4 DiM and merges with the 830 nm measurement laser path through a DiM. The objective lens L 0 focuses the lasers at the specimen plane and the condenser collects the interference pattern at its back aperture. The QPD placed at the conjugated back-focal plane collects the probe’s motion signals through beam demagnification of the third lens pair ( L 5 and L 6 ).

Fig. 2
Fig. 2

Real-time calibration of measurement sensitivity and trapping stiffness with the laser power increased stepwise at 10, 20, 30, 40, and 50 mW : (a) Brownian motion of the trapped bead in the x direction, (b) estimated measurement sensitivity, (c) estimated corner frequency, and (d) estimated trapping stiffness, (inset) comparison of the average of the estimated trapping stiffness versus employed laser power (circle) to the linear fitting (solid curve).

Fig. 3
Fig. 3

Comparison of three pairs of experimental and reconstructed analytical power spectra. Each experimental PSD (solid curve) was computed from the measured position signal during the last second of one of the 4 s time intervals with laser power controlled at 10, 30, and 50 mW. The data were averaged every 20 data points in the frequency domain. The analytical power spectra (dashed curves) were reconstructed from the average of the real-time estimates of the same time windows.

Fig. 4
Fig. 4

Real-time calibration of corner frequency, measurement sensitivity, trapping stiffness, and the probe’s local temperature with the environmental temperature increased from 298.5 to 306.3 K: (a) estimated corner frequency, (b) estimated trapping stiffness, (c) estimated measurement sensitivity, (d) estimated local temperature of the probe (dotted curve) along with the direct measurement of the environmental temperature (solid curve), (e) the decomposed thermal fluctuation of the probe (solid curve) along with its measured motion (dotted curve), subject to a sine-wave excitation with 100 nm amplitude and 20 Hz frequency, and (f) comparison of their PSDs, averaged every 10 data points in frequency domain.

Equations (20)

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m x ¨ ( t ) inertia force 0 = [ γ x ˙ ( t ) friction force + F L ( t ) ] random force + F OT ( x u ) optical force + F E ( x , t ) external force ,
γ x ˙ + k OT ( x u ) = F L ( t ) + F E ( t ) .
x v ( k ) = φ x v ( k 1 ) + ( 1 φ ) u v ( k 1 ) + ( 1 φ ) k OT F E , v ( k 1 ) + v v ( k ) ,
x v ( k ) = φ x v ( k 1 ) + v v ( k ) .
k OT = ( γ / Δ t ) ln ( φ ) ,
f c = k OT / 2 π γ = ln ( φ ) / ( 2 π Δ t ) .
S v = [ k OT x v 2 k B T ] 1 / 2 .
S v = [ ln ( φ ) γ σ v 2 k B T Δ t ( 1 φ 2 ) ] 1 / 2 .
C ( n ) = i = 1 n λ n i [ x v ( i ) x ^ v ( i ) ] 2 = i = 1 n λ n i [ x v ( i ) h ^ T ( i 1 ) θ ( i 1 ) ] 2 ,
h ^ ( k ) = h ^ ( k 1 ) + L ( k ) [ x v ( k ) h ^ T ( k 1 ) θ ( k 1 ) ] ,
L ( k ) = P ( k 1 ) θ ( k 1 ) [ λ + θ T ( k 1 ) P ( k 1 ) θ ( k 1 ) ] 1 ,
P ( k ) = λ 1 [ P ( k 1 ) L ( k ) θ T ( k 1 ) P ( k 1 ) ] .
σ ^ v 2 ( k ) = λ σ ^ v 2 ( k 1 ) + ( 1 λ ) [ x v ( k ) h ^ T ( k 1 ) θ ( k 1 ) ] 2 ,
T = g 1 [ 6 π a ln ( φ ) σ v 2 S v 2 k B Δ t ( 1 φ 2 ) ] ,
x v ( k ) = φ x v ( k 1 ) + ( 1 φ ) u v ( k 1 ) + v v ( k ) ,
u v ( k ) = S v A ex [ cos θ 0 sin θ 0 ] [ cos ( ω 0 k ) sin ( ω 0 k ) ] ,
x v ( k ) = [ φ h 1 h 2 ] [ x v ( k 1 ) cos [ ω 0 ( k 1 ) ] sin [ ω 0 ( k 1 ) ] ] + v v ( k ) .
S v ( k ) = h ^ 1 ( k ) 2 + h ^ 2 ( k ) 2 A ex [ 1 φ ^ ( k ) ] .
{ x v , L ( k ) = [ φ h 1 h 2 ] [ x v , L ( k 1 ) 0 0 ] + v v ( k ) , x v , ex ( k ) = [ φ h 1 h 2 ] [ x v , ex ( k 1 ) cos [ ω 0 ( k 1 ) ] sin [ ω 0 ( k 1 ) ] ] .
P v ( f ) = S ¯ v 2 P ( f ) = S ¯ v 2 k B T π 2 γ ( f ¯ c 2 + f 2 ) ,

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