Abstract

The power spectrum density (PSD) has long been explored for calibrating optical tweezers stiffness. Fast Fourier Transform (FFT) based spectral estimator is typically used. This approach requires a relatively longer data acquisition time to achieve adequate spectral resolution. In this paper, an autoregressive (AR) model is proposed to obtain the Spectrum Density using a limited number of samples. According to our method, the arithmetic model has been established with burg arithmetic, and the final prediction error criterion has been used to select the most appropriate order of the AR model, the power spectrum density has been estimated based the AR model. Then, the optical tweezers stiffness has been determined with the simple calculation from the power spectrum. Since only a small number of samples are used, the data acquisition time is significantly reduced and real-time stiffness calibration becomes feasible. To test this calibration method, we study the variation of the trap stiffness as a function of the parameters of the data length and the trapping depth. Both of the simulation and experiment results have showed that the presented method returns precise results and outperforms the conventional FFT method when using a limited number of samples.

© 2014 Optical Society of America

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References

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  1. M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
    [CrossRef] [PubMed]
  2. R. Reyes-Lamothe, D. J. Sherratt, and M. C. Leake, “Stoichiometry and Architecture of Active DNA Replication Machinery in Escherichia coli,” Science 328(5977), 498–501 (2010).
    [CrossRef] [PubMed]
  3. F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
    [CrossRef] [PubMed]
  4. T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
    [CrossRef] [PubMed]
  5. 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(4), 1687–1696 (2002).
    [CrossRef]
  6. K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
    [CrossRef]
  7. K. Berg-, Sørensen, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
    [CrossRef]
  8. W. P. Wong and K. Halvorsen, “The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur,” Opt. Express 14(25), 12517–12531 (2006).
    [CrossRef] [PubMed]
  9. B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
    [CrossRef] [PubMed]
  10. K. D. Wulff, D. G. Cole, and R. L. Clark, “An adaptive system identification approach to optical trap calibration,” Opt. Express 16(7), 4420–4425 (2008).
    [CrossRef] [PubMed]
  11. C.-K. Yeh and P.-C. Li, “Doppler angle estimation using AR modeling,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 683–692 (2002).
    [CrossRef] [PubMed]
  12. S. Nassar, K.-P. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation 51, 259–268 (2004).
  13. Z. Li, J. Shen, X. Sun, and Y. Wang, “Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model,” Laser Phys. Lett. 10(9), 095701 (2013).
    [CrossRef]
  14. E. D. Übeylı and İ. Güler, “Comparison of eigenvector methods with classical and model-based methods in analysis of internal carotid arterial Doppler signals,” Comput. Biol. Med. 33(6), 473–493 (2003).
    [CrossRef] [PubMed]
  15. Z. Q. Wang, “calibration OT based AR spectrum,” MatlabCentral (2014) http://www.mathworks.cn/matlabcentral/fileexchange/47059 .
  16. F. Czerwinski, A. C. Richardson, and L. B. Oddershede, “Quantifying Noise in Optical Tweezers by Allan Variance,” Opt. Express 17(15), 13255–13269 (2009).
    [CrossRef] [PubMed]
  17. K. Svoboda and S. M. Block, “Biological Applications of Optical Forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
    [CrossRef] [PubMed]
  18. H. Felgner, O. Müller, and M. Schliwa, “Calibration of Light Forces in Optical Tweezers,” Appl. Opt. 34(6), 977–982 (1995).
    [CrossRef] [PubMed]
  19. L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of Small Forces Using an Optical Trap,” Rev. Sci. Instrum. 65(9), 2762–2768 (1994).
    [CrossRef]
  20. K. C. Vermeulen, G. J. L. Wuite, G. J. M. Stienen, and C. F. Schmidt, “Optical trap stiffness in the presence and absence of spherical aberrations,” Appl. Opt. 45(8), 1812–1819 (2006).
    [CrossRef] [PubMed]
  21. K. C. Neuman, E. A. Abbondanzieri, and S. M. Block, “Measurement of the effective focal shift in an optical trap,” Opt. Lett. 30(11), 1318–1320 (2005).
    [CrossRef] [PubMed]

2013 (2)

M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
[CrossRef] [PubMed]

Z. Li, J. Shen, X. Sun, and Y. Wang, “Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model,” Laser Phys. Lett. 10(9), 095701 (2013).
[CrossRef]

2012 (1)

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[CrossRef] [PubMed]

2011 (1)

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

2010 (1)

R. Reyes-Lamothe, D. J. Sherratt, and M. C. Leake, “Stoichiometry and Architecture of Active DNA Replication Machinery in Escherichia coli,” Science 328(5977), 498–501 (2010).
[CrossRef] [PubMed]

2009 (2)

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

F. Czerwinski, A. C. Richardson, and L. B. Oddershede, “Quantifying Noise in Optical Tweezers by Allan Variance,” Opt. Express 17(15), 13255–13269 (2009).
[CrossRef] [PubMed]

2008 (1)

2006 (2)

2005 (1)

2004 (2)

S. Nassar, K.-P. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation 51, 259–268 (2004).

K. Berg-, Sørensen, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

2003 (1)

E. D. Übeylı and İ. Güler, “Comparison of eigenvector methods with classical and model-based methods in analysis of internal carotid arterial Doppler signals,” Comput. Biol. Med. 33(6), 473–493 (2003).
[CrossRef] [PubMed]

2002 (2)

C.-K. Yeh and P.-C. Li, “Doppler angle estimation using AR modeling,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 683–692 (2002).
[CrossRef] [PubMed]

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(4), 1687–1696 (2002).
[CrossRef]

1996 (1)

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

1995 (1)

1994 (2)

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of Small Forces Using an Optical Trap,” Rev. Sci. Instrum. 65(9), 2762–2768 (1994).
[CrossRef]

K. Svoboda and S. M. Block, “Biological Applications of Optical Forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[CrossRef] [PubMed]

Abbondanzieri, E. A.

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(4), 1687–1696 (2002).
[CrossRef]

Berg-, K.

K. Berg-, Sørensen, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

Block, S. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

K. C. Neuman, E. A. Abbondanzieri, and S. M. Block, “Measurement of the effective focal shift in an optical trap,” Opt. Lett. 30(11), 1318–1320 (2005).
[CrossRef] [PubMed]

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

K. Svoboda and S. M. Block, “Biological Applications of Optical Forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[CrossRef] [PubMed]

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(4), 1687–1696 (2002).
[CrossRef]

Chemla, Y. R.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

Chubiz, L. M.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

Clark, R. L.

Cole, D. G.

Czerwinski, F.

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(4), 1687–1696 (2002).
[CrossRef]

El-Sheimy, N.

S. Nassar, K.-P. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation 51, 259–268 (2004).

Fazal, F. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

Felgner, H.

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(4), 1687–1696 (2002).
[CrossRef]

Flyvbjerg, H.

K. Berg-, Sørensen, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[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(9), 2762–2768 (1994).
[CrossRef]

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(4), 1687–1696 (2002).
[CrossRef]

Golding, I.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

Güler, I.

E. D. Übeylı and İ. Güler, “Comparison of eigenvector methods with classical and model-based methods in analysis of internal carotid arterial Doppler signals,” Comput. Biol. Med. 33(6), 473–493 (2003).
[CrossRef] [PubMed]

Halvorsen, K.

Lansdorp, B. M.

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[CrossRef] [PubMed]

Leake, M. C.

R. Reyes-Lamothe, D. J. Sherratt, and M. C. Leake, “Stoichiometry and Architecture of Active DNA Replication Machinery in Escherichia coli,” Science 328(5977), 498–501 (2010).
[CrossRef] [PubMed]

Li, P.-C.

C.-K. Yeh and P.-C. Li, “Doppler angle estimation using AR modeling,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 683–692 (2002).
[CrossRef] [PubMed]

Li, Y. M.

M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
[CrossRef] [PubMed]

Li, Z.

Z. Li, J. Shen, X. Sun, and Y. Wang, “Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model,” Laser Phys. Lett. 10(9), 095701 (2013).
[CrossRef]

Mears, P. J.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

Min, T. L.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

Müller, O.

Nassar, S.

S. Nassar, K.-P. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation 51, 259–268 (2004).

Neuman, K. C.

Noureldin, A.

S. Nassar, K.-P. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation 51, 259–268 (2004).

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(4), 1687–1696 (2002).
[CrossRef]

Rao, C. V.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

Reyes-Lamothe, R.

R. Reyes-Lamothe, D. J. Sherratt, and M. C. Leake, “Stoichiometry and Architecture of Active DNA Replication Machinery in Escherichia coli,” Science 328(5977), 498–501 (2010).
[CrossRef] [PubMed]

Richardson, A. C.

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(4), 1687–1696 (2002).
[CrossRef]

Saleh, O. A.

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[CrossRef] [PubMed]

Schliwa, M.

Schmidt, C. F.

Schwarz, K.-P.

S. Nassar, K.-P. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation 51, 259–268 (2004).

Shen, J.

Z. Li, J. Shen, X. Sun, and Y. Wang, “Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model,” Laser Phys. Lett. 10(9), 095701 (2013).
[CrossRef]

Sherratt, D. J.

R. Reyes-Lamothe, D. J. Sherratt, and M. C. Leake, “Stoichiometry and Architecture of Active DNA Replication Machinery in Escherichia coli,” Science 328(5977), 498–501 (2010).
[CrossRef] [PubMed]

Sørensen,

K. Berg-, Sørensen, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

Stienen, G. J. M.

Sun, X.

Z. Li, J. Shen, X. Sun, and Y. Wang, “Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model,” Laser Phys. Lett. 10(9), 095701 (2013).
[CrossRef]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological Applications of Optical Forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[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(9), 2762–2768 (1994).
[CrossRef]

Übeyli, E. D.

E. D. Übeylı and İ. Güler, “Comparison of eigenvector methods with classical and model-based methods in analysis of internal carotid arterial Doppler signals,” Comput. Biol. Med. 33(6), 473–493 (2003).
[CrossRef] [PubMed]

Vermeulen, K. C.

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

Wang, Y.

Z. Li, J. Shen, X. Sun, and Y. Wang, “Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model,” Laser Phys. Lett. 10(9), 095701 (2013).
[CrossRef]

Wang, Z. Q.

M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
[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(9), 2762–2768 (1994).
[CrossRef]

Wei, X. B.

M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
[CrossRef] [PubMed]

Wong, W. P.

Wuite, G. J. L.

Wulff, K. D.

Yeh, C.-K.

C.-K. Yeh and P.-C. Li, “Doppler angle estimation using AR modeling,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 683–692 (2002).
[CrossRef] [PubMed]

Zhong, M. C.

M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
[CrossRef] [PubMed]

Zhou, J. H.

M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
[CrossRef] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda and S. M. Block, “Biological Applications of Optical Forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[CrossRef] [PubMed]

Appl. Opt. (2)

Comput. Biol. Med. (1)

E. D. Übeylı and İ. Güler, “Comparison of eigenvector methods with classical and model-based methods in analysis of internal carotid arterial Doppler signals,” Comput. Biol. Med. 33(6), 473–493 (2003).
[CrossRef] [PubMed]

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

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

C.-K. Yeh and P.-C. Li, “Doppler angle estimation using AR modeling,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 683–692 (2002).
[CrossRef] [PubMed]

Laser Phys. Lett. (1)

Z. Li, J. Shen, X. Sun, and Y. Wang, “Nanoparticle size measurement from dynamic light scattering data based on an autoregressive model,” Laser Phys. Lett. 10(9), 095701 (2013).
[CrossRef]

Nat Commun (1)

M. C. Zhong, X. B. Wei, J. H. Zhou, Z. Q. Wang, and Y. M. Li, “Trapping red blood cells in living animals using optical tweezers,” Nat Commun 4, 1768 (2013).
[CrossRef] [PubMed]

Nat. Methods (1)

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6(11), 831–835 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

Navigation (1)

S. Nassar, K.-P. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation 51, 259–268 (2004).

Opt. Express (3)

Opt. Lett. (1)

Rev. Sci. Instrum. (4)

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of Small Forces Using an Optical Trap,” Rev. Sci. Instrum. 65(9), 2762–2768 (1994).
[CrossRef]

B. M. Lansdorp and O. A. Saleh, “Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments,” Rev. Sci. Instrum. 83(2), 025115 (2012).
[CrossRef] [PubMed]

K. Berg-, Sørensen, and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (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(4), 1687–1696 (2002).
[CrossRef]

Science (1)

R. Reyes-Lamothe, D. J. Sherratt, and M. C. Leake, “Stoichiometry and Architecture of Active DNA Replication Machinery in Escherichia coli,” Science 328(5977), 498–501 (2010).
[CrossRef] [PubMed]

Other (1)

Z. Q. Wang, “calibration OT based AR spectrum,” MatlabCentral (2014) http://www.mathworks.cn/matlabcentral/fileexchange/47059 .

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Figures (4)

Fig. 1
Fig. 1

AR spectrum of position signal for a 1 μm radius polystyrene bead immersed in water solution at room temperature. The laser power is 0.4 W, and the AR spectrum has been normalized.

Fig. 2
Fig. 2

The OT setup.

Fig. 3
Fig. 3

Calibration of the optical tweezers at different data lengths where the polystyrene bead radius is 0.5μm and the trap depth is 15μm. These error bars are determined by calculating the standard deviation from a set of seven different measurements.

Fig. 4
Fig. 4

Calibration of the optical tweezers at different trapping depth. The polystyrene bead radius is 1 μm. These error bars are determined by calculating the standard deviation from a set of seven different measurements.

Tables (2)

Tables Icon

Table 1 A comparison of the calibration methods performed on different stiffness simulation signal (data length is 1 × 106, each stiffness signal is simulated with 10 times)

Tables Icon

Table 2 A Comparison of the calibration methods performed on different data length based on Monte-Carlo simulation signal (kx = 20 pN/μm, each length data signal is simulated with 10 times)

Equations (12)

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

x( n )= i=1 p a i x( ni )+ω( n ) 0nN1
P( e jω )= σ 2 | 1+ i=1 p a i e jωi z i | 2 .
FPE( i )= ρ i 2 N+i+1 Ni1 ,
P i =< | x i | 2 / T msr >= k B T/2 π 2 γ f c 2 + f i 2 = A f c 2 + f i 2 .
e ^ p f ( n )=x( n )+ i=1 p a ^ p ( i )x( ni ) , n=p+1,...,N,
e ^ p b ( n )=x( np )+ i=1 p a ^ * p ( i ) x( np+i ), n=p+1,...,N.
ρ p fb = 1 2 [ ρ p f + ρ p b ]= 1 Np n=p N1 | e p f ( n ) | 2 + 1 Np n=p N1 | e p b ( n ) | 2
e m f ( n )= e m1 f ( n )+ u m e m1 b ( n1 ) e m b ( n )= e m1 b ( n )+ u m * e m1 f ( n1 ), m=1,2,,p e 0 f ( n )= e 0 b ( n )=x( n ) }
u ^ m = 2 n=m+1 N e ^ m1 f ( n ) e m1 b* ( n1 ) n=m+1 N | e m1 f ( n ) | 2 + n=m+1 N | e m1 b ( n1 ) | 2 .
a ^ m ( i )={ a ^ m1 ( i )+ u ^ m a m1 ( mi ), i=1,...,p1, u ^ p , i=p.
ρ m fb =( 1 u m 2 ) ρ m1 fb .
e 0 f ( n )=x( n ), e 0 b ( n )=x( n ) .

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