OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 30 — Oct. 20, 2009
  • pp: 5871–5880

Minimum-variance Brownian motion control of an optically trapped probe

Yanan Huang, Zhipeng Zhang, and Chia-Hsiang Menq  »View Author Affiliations

Applied Optics, Vol. 48, Issue 30, pp. 5871-5880 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (712 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



This paper presents a theoretical and experimental investigation of the Brownian motion control of an optically trapped probe. The Langevin equation is employed to describe the motion of the probe experiencing random thermal force and optical trapping force. Since active feedback control is applied to suppress the probe’s Brownian motion, actuator dynamics and measurement delay are included in the equation. The equation of motion is simplified to a first-order linear differential equation and transformed to a discrete model for the purpose of controller design and data analysis. The derived model is experimentally verified by comparing the model prediction to the measured response of a 1.87 μm trapped probe subject to proportional control. It is then employed to design the optimal controller that minimizes the variance of the probe’s Brownian motion. Theoretical analysis is derived to evaluate the control performance of a specific optical trap. Both experiment and simulation are used to validate the design as well as theoretical analysis, and to illustrate the performance envelope of the active control. Moreover, adaptive minimum variance control is implemented to maintain the optimal performance in the case in which the system is time varying when operating the actively controlled optical trap in a complex environment.

© 2009 Optical Society of America

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(230.1040) Optical devices : Acousto-optical devices
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Lasers and Laser Optics

Original Manuscript: July 7, 2009
Manuscript Accepted: September 21, 2009
Published: October 19, 2009

Virtual Issues
Vol. 4, Iss. 12 Virtual Journal for Biomedical Optics

Yanan Huang, Zhipeng Zhang, and Chia-Hsiang Menq, "Minimum-variance Brownian motion control of an optically trapped probe," Appl. Opt. 48, 5871-5880 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004). [CrossRef]
  2. C. Gosse and V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82, 3314-3329 (2002). [CrossRef] [PubMed]
  3. A. E. Cohen and W. E. Moerner, “Method for trapping and manipulating nanoscale objects in solution,” Appl. Phys. Lett. 86, 093109 (2005). [CrossRef]
  4. A. E. Cohen and W. E. Moerner, “Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer,” Opt. Express 16, 6941-6956 (2008). [CrossRef] [PubMed]
  5. M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902-907 (1998). [CrossRef] [PubMed]
  6. K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184-189 (1999). [CrossRef] [PubMed]
  7. C. Bustamante, J. C. Macosko, and G. J. Wuite, “Grabbing the cat by the tail: manipulating molecules one by one,” Nat. Rev. Mol. Cell. Biol. 1, 130-136 (2000). [CrossRef]
  8. C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421, 423-427(2003). [CrossRef] [PubMed]
  9. J. Zlatanova and S. H. Leuba, “Magnetic tweezers: a sensitive tool to study DNA and chromatin at the single-molecule level,” Biochem. Cell Biol. 81, 151-159 (2003). [CrossRef] [PubMed]
  10. H. Huang, R. D. Kamm, and R. T. Lee, “Cell mechanics and mechanotransduction: pathways, probes, and physiology,” Am. J. Physiol., Cell Physiol. 287, C1-C11 (2004). [CrossRef] [PubMed]
  11. M.- T. Wei, A. Zaorski, H. C. Yalcin, J. Wang, M. Hallow, S. N. Ghadiali, A. Chiou, and H. D. Ou-Yang, “A comparative study of living cell micromechanical properties by oscillatory optical tweezers,” Opt. Express 16, 8594-8603 (2008). [CrossRef] [PubMed]
  12. R. M. Mazo, Brownian Motion: Fluctuations, Dynamics, and Applications (Oxford University Press, 2002).
  13. P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937-1942 (2005). [CrossRef] [PubMed]
  14. P. Kollmannsberger and B. Fabry, “High-force magnetic tweezers with force feedback for biological applications,” Rev. Sci. Instrum. 78, 114301 (2007). [CrossRef] [PubMed]
  15. S. Ayano, Y. Wakamoto, S. Yamashita, and K. Yasuda, “Quantitative measurement of damage caused by 1064 nm wavelength optical trapping of Escherichia coli cells using on-chip single cell cultivation system,” Biochem. Biophys. Res. Commun. 350, 678-684 (2006). [CrossRef] [PubMed]
  16. M. B. Rasmussen, L. B. Oddershede, and H. Siegumfeldt, “Optical tweezers cause physiological damage to Escherichia coli and Listeria bacteria,” Appl. Environ. Microbiol. 74, 2441-2446 (2008). [CrossRef] [PubMed]
  17. 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]
  18. K. D. Wulff, D. G. Cole, and R. L. Clark, “Servo control of an optical trap,” Appl. Opt. 46, 4923-4931 (2007). [CrossRef] [PubMed]
  19. A. E. Wallin, H. Ojala, E. Haggstrom, and R. Tuma, “Stiffer optical tweezers through real-time feedback control,” Appl. Phys. Lett. 92, 224104 (2008). [CrossRef]
  20. Y. Huang, J. Wan, M.- C. Cheng, Z. Zhang, S. M. Jhiang, and C.- H. Menq, “Three-axis rapid steering of optically propelled micro/nano particles,” Rev. Sci. Instrum. 80, 063107 (2009). [CrossRef] [PubMed]
  21. A. Ranaweera and B. Bamieh, “Modelling, identification, and control of a spherical particle trapped in an optical tweezer,” Int. J. Robust Nonlinear Control 15, 747-768 (2005). [CrossRef]
  22. A. Rohrbach and E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474-5488 (2002). [CrossRef]
  23. A. R. Carter, G. M. King, T. A. Ulrich, W. Halsey, D. Alchenberger, and T. T. Perkins, “Stabilization of an optical microscope to 0.1 nm in three dimensions,” Appl. Opt. 46, 421-427 (2007). [CrossRef] [PubMed]
  24. F. Gittes and C. F. Schmidt, “Thermal noise limitations on micromechanical experiments,” Eur. Biophys. J. 27, 75-81(1998). [CrossRef]
  25. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529-541 (1996). [CrossRef]
  26. “LTC1564 10 kHz to 150 kHz digitally controlled anti-aliasing filter and 4 bit P.G.A.,” http://cds.linear.com/docs/Datasheet/1564fa.pdf.
  27. K. Berg-Sorensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004). [CrossRef]
  28. G. Box, G. M. Jenkins, and G. Reinsel, Time Series Analysis: Forecasting and Control, 3rd ed. (Prentice-Hall, 1994).
  29. A. V. Oppenheim, A. S. Willsky, and S. Hamid, Signals and Systems, 2nd ed. (Prentice-Hall, 1996).
  30. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).
  31. G. F. Franklin, J. D. Powell, and M. Workman, Digital Control of Dynamic Systems, 3rd ed. (Addison-Wesley, 1998).
  32. K. J. Astrom, Introduction to Stochastic Control Theory (Academic, 1970).
  33. P. R. Kumar, “Convergence of adaptive control schemes using least-squares parameter estimates,” IEEE Trans. Autom. Control. 35, 416-424 (1990). [CrossRef]
  34. A. Patete, K. Furuta, and M. Tomizuka, “Self-tuning control based on generalized minimum variance criterion for auto-regressive models,” Automatica 44, 1970-1975(2008). [CrossRef]
  35. J. Wan, Y. Huang, S. M. Jhiang, and C.-H. Menq, “Real-time in situ calibration of an optically trapped probing system,” Appl. Opt. 48, 4832-4841 (2009). [CrossRef] [PubMed]
  36. J. M. Mendel, Lessons in Etimation Theory for Signal Processing, Communications, and Control, 2nd ed. (Prentice-Hall, 1995).
  37. Q. Zhang, “Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems,” IEEE Trans. Autom. Control 47, 525-529 (2002). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited