Abstract

Much effort is put into minimizing noise in optical tweezers experiments because noise and drift can mask fundamental behaviours of, e.g., single molecule assays. Various initiatives have been taken to reduce or eliminate noise but it has been difficult to quantify their effect. We propose to use Allan variance as a simple and efficient method to quantify noise in optical tweezers setups. We apply the method to determine the optimal measurement time, frequency, and detection scheme, and quantify the effect of acoustic noise in the lab. The method can also be used on-the-fly for determining optimal parameters of running experiments.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. C. Neuman, and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  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. P. Hansen, V. Bhatia, N. Harrit, and L. B. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
    [CrossRef] [PubMed]
  4. L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, "Efficient Optical Trapping and Visualization of Silver Nanoparticles," Nano Lett. 8, 1486-1491 (2008).
    [CrossRef] [PubMed]
  5. C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
    [CrossRef] [PubMed]
  6. L. Jauffred, A. C. Richardson, and L. B. Oddershede, "Three-Dimensional Optical Control of Individual Quantum Dots," Nano Lett. 8, 3376-3380 (2008).
    [CrossRef] [PubMed]
  7. E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
    [CrossRef] [PubMed]
  8. J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
    [CrossRef] [PubMed]
  9. A. R. Carter, Y. Seol, and T. T. Perkins, "Precision surface-coupled optical-trapping assay with one-basepair resolution," Biophys. J. 96, 2926-2934 (2009).
    [CrossRef] [PubMed]
  10. F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," Methods Cell. Biol. 55, 129-156 (1998).
    [CrossRef]
  11. M. Klein, M. Andersson, O. Axner, and E. Fallman, "Dual-trap technique for reduction of low-frequency noise in force measuring optical tweezers," Appl. Opt. 46, 405-412 (2007).
    [CrossRef] [PubMed]
  12. D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
    [CrossRef]
  13. P. Banerjee, A. Chatterjee, and A. Suman, "Determination of Allan deviation of Cesium atomic clock for lower averaging time," Indian J. Pure Appl. Phys. 45, 945-949 (2007).
  14. G. M. 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]
  15. F. Czerwinski and L. B. Oddershede, "Reliable Data-Streaming Software for Photodiode Readout in LABVIEW," in. prep. (2009).
  16. K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, "Unintended filtering in a typical photodiode detection system for optical tweezers," J. Appl. Phys. 93, 3167-3176 (2003).
    [CrossRef]
  17. L. B. Oddershede, S. Grego, S. Nørrelykke, and K. Berg-Sørensen, "Optical tweezers: probing biological surfaces," Probe Microsc 2, 129-137 (2001).
  18. K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594- 612 (2004).
    [CrossRef]
  19. P. M. Hansen, I. Tolic¸-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers," Comput. Phys. Commun. 175, 572-573 (2006).
    [CrossRef]
  20. F. Czerwinski, "BeadFluct v1.0," MatlabCentral 24196 (2009), http://www.mathworks.com/matlabcentral/fileexchange/24196.
  21. P. Kartaschoff, Frequency and Time (Academic Press, 1978).
  22. F. Czerwinski, "allan v1.71," MatlabCentral 21727 (2008), http://www.mathworks.com/matlabcentral/fileexchange/21727.

2009

A. R. Carter, Y. Seol, and T. T. Perkins, "Precision surface-coupled optical-trapping assay with one-basepair resolution," Biophys. J. 96, 2926-2934 (2009).
[CrossRef] [PubMed]

2008

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, "Efficient Optical Trapping and Visualization of Silver Nanoparticles," Nano Lett. 8, 1486-1491 (2008).
[CrossRef] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

L. Jauffred, A. C. Richardson, and L. B. Oddershede, "Three-Dimensional Optical Control of Individual Quantum Dots," Nano Lett. 8, 3376-3380 (2008).
[CrossRef] [PubMed]

G. M. 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

P. Banerjee, A. Chatterjee, and A. Suman, "Determination of Allan deviation of Cesium atomic clock for lower averaging time," Indian J. Pure Appl. Phys. 45, 945-949 (2007).

M. Klein, M. Andersson, O. Axner, and E. Fallman, "Dual-trap technique for reduction of low-frequency noise in force measuring optical tweezers," Appl. Opt. 46, 405-412 (2007).
[CrossRef] [PubMed]

2006

P. M. Hansen, I. Tolic¸-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers," Comput. Phys. Commun. 175, 572-573 (2006).
[CrossRef]

2005

P. Hansen, V. Bhatia, N. Harrit, and L. B. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

2004

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

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

2003

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, "Unintended filtering in a typical photodiode detection system for optical tweezers," J. Appl. Phys. 93, 3167-3176 (2003).
[CrossRef]

2001

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

J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
[CrossRef] [PubMed]

1998

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

1987

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]

1966

D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
[CrossRef]

Aabo, T.

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, "Efficient Optical Trapping and Visualization of Silver Nanoparticles," Nano Lett. 8, 1486-1491 (2008).
[CrossRef] [PubMed]

Abbondanzieri, E. A.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

Allan, D. W.

D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
[CrossRef]

Andersson, M.

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]

Axner, O.

Banerjee, P.

P. Banerjee, A. Chatterjee, and A. Suman, "Determination of Allan deviation of Cesium atomic clock for lower averaging time," Indian J. Pure Appl. Phys. 45, 945-949 (2007).

Bendix, P. M.

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, "Efficient Optical Trapping and Visualization of Silver Nanoparticles," Nano Lett. 8, 1486-1491 (2008).
[CrossRef] [PubMed]

Berg-Sørensen, K.

P. M. Hansen, I. Tolic¸-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers," Comput. Phys. Commun. 175, 572-573 (2006).
[CrossRef]

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

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, "Unintended filtering in a typical photodiode detection system for optical tweezers," J. Appl. Phys. 93, 3167-3176 (2003).
[CrossRef]

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

Bhatia, V.

P. Hansen, V. Bhatia, N. Harrit, and L. B. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

Block, S. M.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

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

Bosanac, L.

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, "Efficient Optical Trapping and Visualization of Silver Nanoparticles," Nano Lett. 8, 1486-1491 (2008).
[CrossRef] [PubMed]

Bustamante, C.

J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
[CrossRef] [PubMed]

Carter, A. R.

A. R. Carter, Y. Seol, and T. T. Perkins, "Precision surface-coupled optical-trapping assay with one-basepair resolution," Biophys. J. 96, 2926-2934 (2009).
[CrossRef] [PubMed]

Chatterjee, A.

P. Banerjee, A. Chatterjee, and A. Suman, "Determination of Allan deviation of Cesium atomic clock for lower averaging time," Indian J. Pure Appl. Phys. 45, 945-949 (2007).

Czerwinski, F.

F. Czerwinski and L. B. Oddershede, "Reliable Data-Streaming Software for Photodiode Readout in LABVIEW," in. prep. (2009).

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]

Fallman, E.

Florin, E. L.

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, "Unintended filtering in a typical photodiode detection system for optical tweezers," J. Appl. Phys. 93, 3167-3176 (2003).
[CrossRef]

Flyvbjerg, H.

P. M. Hansen, I. Tolic¸-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers," Comput. Phys. Commun. 175, 572-573 (2006).
[CrossRef]

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

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, "Unintended filtering in a typical photodiode detection system for optical tweezers," J. Appl. Phys. 93, 3167-3176 (2003).
[CrossRef]

Gibson, G. M.

Gittes, F.

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

Greenleaf, W. J.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

Grego, S.

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

Hansen, P.

P. Hansen, V. Bhatia, N. Harrit, and L. B. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

Hansen, P. M.

P. M. Hansen, I. Tolic¸-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers," Comput. Phys. Commun. 175, 572-573 (2006).
[CrossRef]

Harrit, N.

P. Hansen, V. Bhatia, N. Harrit, and L. B. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

Jauffred, L.

L. Jauffred, A. C. Richardson, and L. B. Oddershede, "Three-Dimensional Optical Control of Individual Quantum Dots," Nano Lett. 8, 3376-3380 (2008).
[CrossRef] [PubMed]

Keen, S.

Klein, M.

Landick, R.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

Leach, J.

Liphardt, J.

J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
[CrossRef] [PubMed]

Neuman, K. C.

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

Nørrelykke, S.

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

Oddershede, L. B.

L. Jauffred, A. C. Richardson, and L. B. Oddershede, "Three-Dimensional Optical Control of Individual Quantum Dots," Nano Lett. 8, 3376-3380 (2008).
[CrossRef] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, "Efficient Optical Trapping and Visualization of Silver Nanoparticles," Nano Lett. 8, 1486-1491 (2008).
[CrossRef] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

P. Hansen, V. Bhatia, N. Harrit, and L. B. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, "Unintended filtering in a typical photodiode detection system for optical tweezers," J. Appl. Phys. 93, 3167-3176 (2003).
[CrossRef]

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

F. Czerwinski and L. B. Oddershede, "Reliable Data-Streaming Software for Photodiode Readout in LABVIEW," in. prep. (2009).

Onoa, B.

J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
[CrossRef] [PubMed]

Padgett, M. J.

Perkins, T. T.

A. R. Carter, Y. Seol, and T. T. Perkins, "Precision surface-coupled optical-trapping assay with one-basepair resolution," Biophys. J. 96, 2926-2934 (2009).
[CrossRef] [PubMed]

Richardson, A. C.

L. Jauffred, A. C. Richardson, and L. B. Oddershede, "Three-Dimensional Optical Control of Individual Quantum Dots," Nano Lett. 8, 3376-3380 (2008).
[CrossRef] [PubMed]

S¨onnichsen, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Schmidt, C. F.

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

Schubert, O.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Selhuber-Unkel, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Seol, Y.

A. R. Carter, Y. Seol, and T. T. Perkins, "Precision surface-coupled optical-trapping assay with one-basepair resolution," Biophys. J. 96, 2926-2934 (2009).
[CrossRef] [PubMed]

Shaevitz, J. W.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

Smith, S. B.

J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
[CrossRef] [PubMed]

Suman, A.

P. Banerjee, A. Chatterjee, and A. Suman, "Determination of Allan deviation of Cesium atomic clock for lower averaging time," Indian J. Pure Appl. Phys. 45, 945-949 (2007).

Tinoco, I.

J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
[CrossRef] [PubMed]

Tolic¸-Nørrelykke, I.

P. M. Hansen, I. Tolic¸-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers," Comput. Phys. Commun. 175, 572-573 (2006).
[CrossRef]

Wright, A. J.

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]

Zins, I.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Appl. Opt.

Biophys. J.

A. R. Carter, Y. Seol, and T. T. Perkins, "Precision surface-coupled optical-trapping assay with one-basepair resolution," Biophys. J. 96, 2926-2934 (2009).
[CrossRef] [PubMed]

Comput. Phys. Commun.

P. M. Hansen, I. Tolic¸-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers," Comput. Phys. Commun. 175, 572-573 (2006).
[CrossRef]

Indian J. Pure Appl. Phys.

P. Banerjee, A. Chatterjee, and A. Suman, "Determination of Allan deviation of Cesium atomic clock for lower averaging time," Indian J. Pure Appl. Phys. 45, 945-949 (2007).

J. Appl. Phys.

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, "Unintended filtering in a typical photodiode detection system for optical tweezers," J. Appl. Phys. 93, 3167-3176 (2003).
[CrossRef]

Methods Cell. Biol.

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

Nano Lett.

P. Hansen, V. Bhatia, N. Harrit, and L. B. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, "Efficient Optical Trapping and Visualization of Silver Nanoparticles," Nano Lett. 8, 1486-1491 (2008).
[CrossRef] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. S¨onnichsen, and L. B. Oddershede, "Quantitative optical trapping of single gold nanorods," Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

L. Jauffred, A. C. Richardson, and L. B. Oddershede, "Three-Dimensional Optical Control of Individual Quantum Dots," Nano Lett. 8, 3376-3380 (2008).
[CrossRef] [PubMed]

Nature

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

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. Express

Probe Microsc

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

Proc. IEEE

D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
[CrossRef]

Rev. Sci. Instrum.

K. Berg-Sørensen 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]

Science

J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante, "Reversible unfolding of single RNA molecules by mechanical force," Science 292, 733-737 (2001).
[CrossRef] [PubMed]

Other

F. Czerwinski and L. B. Oddershede, "Reliable Data-Streaming Software for Photodiode Readout in LABVIEW," in. prep. (2009).

F. Czerwinski, "BeadFluct v1.0," MatlabCentral 24196 (2009), http://www.mathworks.com/matlabcentral/fileexchange/24196.

P. Kartaschoff, Frequency and Time (Academic Press, 1978).

F. Czerwinski, "allan v1.71," MatlabCentral 21727 (2008), http://www.mathworks.com/matlabcentral/fileexchange/21727.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Schematic drawing of the experimental setup. An infrared laser beam was focused into a sealed measurement chamber which was mounted onto a piezo stage. A polystyrene sphere was trapped in the middle of the measurement chamber which was filled with water (zoom in). The scatter light was collected onto a photodiode. The positional signal of the sphere inside the trap was streamed onto a hard drive. Acoustic noise might have interfered with the experiment.

Fig. 2.
Fig. 2.

(a) Experimental (green) and simulated (grey) position time series of an optically-trapped polystyrene sphere in water. The traces are centered around 0 nm, and the dashed lines indicate the interval ±σ, respectively ±3σ. (b) Variance σ is obtained by fitting a Gaussian to the overlapping positional histogram. (c) The power spectral density of experimental (green) and simulated (grey) positional sequences. Each graph is the average of 10 individually calculated power spectra for traces of about 3 s. The band from 20 to 6000 Hz was used to obtain corrected Lorentzian fits (experimental: black; simulation: grey). The inset shows the spread in corner frequencies from individual calibrations. This spread follows a Gaussian distribution.

Fig. 3.
Fig. 3.

Variances of individual optical tweezers experiments. The variances were calculated from the position of a polystyrene sphere trapped with κ=67.7 pN/µm (orange) or with κ=33.6 pN/µm (green). Grey graphs show results of Monte-Carlo simulations using the same physical parameters. Dashed lines are the thermal limits according to Eq. (6). The dotted lines are graphs of the normal variances using Eq. (5). Remarkably, the Allan variance provides half an order of magnitude higher sensitivity for τ>1 s.

Fig. 4.
Fig. 4.

Allan variance depends on the acquisition frequency (a) and on the number of data points (b). Each time series had a length of about 13 min, the acquisition frequency f acq was varied, and the trap stiffness was κ=67.7 pN/µm.

Fig. 5.
Fig. 5.

Impact of measurement-chamber construction and acoustic noise in the laboratory. (a) Allan variance for the position of a trapped sphere, κ=53.4 pN/µm. x (green) is the longest lateral dimension of the measurement chamber. Accordingly, y (orange) denotes the shortest lateral dimension. The upper cover slip has a thickness of 1 mm. Solid lines are measured in virtual silence, dash-dotted lines are measured with acoustic noise in the laboratory. (b) Same conditions as in (a), but using an upper cover slip of a thickness of 0.13–0.16 mm. The solid black curves represent the thermal limit and grey line is a guide to the eye at 0.17 nm. The blue lines indicate the slope for low-frequency drift, 1 for (a) and 1/2 for (b).

Fig. 6.
Fig. 6.

Impact of piezo stage on Allan variance for a trapped sphere. When the piezo is switched on a hill in the Allan variance within the interval 0.5 s<τ<110 s is observed (grey shading). It is more pronounced for a weaker trapped sphere, κ=15.3 pN/µm (red), than for a strongly trapped sphere, κ=33.6 pN/µm (violet). The Allan variance of the piezo itself is plotted in black. When the piezo is switched off (green), the hill disappears.

Fig. 7.
Fig. 7.

Effect of photodiodes on Allan variance, PSD (green) and QPD (orange), κ=33.6 pN/µm. The solid black line gives the thermal limit. The dashed lines mark the Allan variance when the diodes are shined on by the laser with nothing trapped. The dotted line marks the purely electronic noise when every illumination was blocked. It drops below the best resolution possible for the given photodiode-based detection system with the used acquisition settings (dash-dotted line).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

fc=κ2πγ.
σx2(τ)=12(xi+1xi)2τ
σx˜2(τ)=12(x˜i+1x˜i)2=β2σx2 (τ).
SEσ(τ)=σx(τ)n=mNσx(τ)=τtacqσx(τ).
σ2(τ)=12(xixˉ)2τ.
SEx=1nx22kBTγk2τ .

Metrics