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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 14 — Jul. 14, 2014
  • pp: 16956–16964

Calibration of optical tweezers based on an autoregressive model

Zi-Qiang Wang, Jin-Hua Zhou, Min-Cheng Zhong, Di Li, and Yin-Mei Li  »View Author Affiliations

Optics Express, Vol. 22, Issue 14, pp. 16956-16964 (2014)

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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

OCIS Codes
(120.4640) Instrumentation, measurement, and metrology : Optical instruments
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

Original Manuscript: March 3, 2014
Revised Manuscript: May 23, 2014
Manuscript Accepted: June 13, 2014
Published: July 3, 2014

Virtual Issues
Vol. 9, Iss. 9 Virtual Journal for Biomedical Optics

Zi-Qiang Wang, Jin-Hua Zhou, Min-Cheng Zhong, Di Li, and Yin-Mei Li, "Calibration of optical tweezers based on an autoregressive model," Opt. Express 22, 16956-16964 (2014)

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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]

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