Feedback Control of Optically Trapped Particles

  • Jason J. Gorman
  • Arvind Balijepalli
  • Thomas W. LeBrun


Optical trapping is a method for manipulating micro- and nanoscale particles that are widely used in biophysics and colloid science, among other areas. This method uses optical forces to confine a particle to a localized region, which is referred to as a trap. This chapter examines the application of feedback control to optical trapping to improve particle localization, manipulation precision, and trap stability. Although control systems have been used in optical trapping for almost two decades, their perceived importance has largely been secondary to the scientific experiments that they support. As a result, only limited effort has been taken to explore the performance and stability of control systems in optical trapping. This chapter provides an introduction to the field and an overview of many of the issues relevant to a control systems perspective in optical trapping, including sensor and actuator performance, trap modeling, and instrument design. It also describes the design and implementation of a control system that has been used to dramatically improve the localization of a trapped particle with respect to the center of the trap. Many of the challenges in controlling optically trapped particles and future research directions for addressing these challenges are also described.


Brownian Motion Trap Particle Optical Trap Optical Trapping Optical Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    A. Ashkin. History of optical trapping and manipulation of small-neutral particle, atoms, and molecules. IEEE J. Sel. Top. Quantum Electron., 6:841–856, 2000.CrossRefGoogle Scholar
  2. 2.
    D.C. Grier. A revolution in optical manipulation. Nature, 424:810–816, 2003.CrossRefGoogle Scholar
  3. 3.
    K.C. Neuman and S.M. Block. Optical trapping. Rev. Sci. Instrum., 75:2787–2809, 2004.CrossRefGoogle Scholar
  4. 4.
    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., 2:1066–1076, 1996.CrossRefGoogle Scholar
  5. 5.
    A. Ashkin, J.M. Dziedzic, J.E. Bjorkhom, and S. Chu. Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett., 11:288–290, 1986.CrossRefGoogle Scholar
  6. 6.
    D.T. Gillespie. The mathematics of Brownian motion and Johnson noise. Am. J. Phys., 64:225–240, 1995.CrossRefGoogle Scholar
  7. 7.
    R.M. Mazo. Brownian motion: Fluctuations, dynamics and application, New York, Oxford, 2002.Google Scholar
  8. 8.
    A. Ashkin. Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime. Biophys. J., 61:569–582, 1992.CrossRefGoogle Scholar
  9. 9.
    A. Rohrbach. Stiffness of optical traps: Quantitative agreement between experiment and electromagnetic theory. Phys. Rev. Lett., 95:168102, 2005.CrossRefGoogle Scholar
  10. 10.
    A.A.R. Neves et al. Electromagnetic forces for an arbitrary optical trapping of a spherical dielectric. Opt. Express, 14:13101–13106, 2006.CrossRefGoogle Scholar
  11. 11.
    G. Gouesbet, B. Maheu, and G. Grehan. Light-scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation. J. Opt. Soc. Am. A, 5:1427–1443, 1988.CrossRefMathSciNetGoogle Scholar
  12. 12.
    J.A. Lock. Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz–Mie Theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration. Appl. Opt., 43:2532–2544, 2004.Google Scholar
  13. 13.
    K. Svoboda and S.M. Block. Optical trapping of metallic Rayleigh particles. Opt. Lett., 19:930–932, 1994.CrossRefGoogle Scholar
  14. 14.
    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.CrossRefGoogle Scholar
  15. 15.
    Y. Liu, D.K. Cheng, G.J. Sonek, M.W. Berns, C.F. Chapman, and B.J. Tromberg. Evidence for localized cell heating induced by infrared optical tweezers. Biophys. J., 68:2137–2144, 1995.CrossRefGoogle Scholar
  16. 16.
    K.C. Neuman, E.H. Chadd, G.F. Liou, K. Bergman, and S.M. Block. Characterization of photodamage to Escherichia coli in optical traps. Biophys. J., 77:2856–2863, 1999.CrossRefGoogle Scholar
  17. 17.
    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.CrossRefGoogle Scholar
  18. 18.
    A. Balijepalli, T.W. LeBrun, and S.K. Gupta. A flexible system framework for a nanoassembly cell using optical tweezers. Proceedings of the ASME IDETC/CIE, Philadelphia, PA, 2006, DETC2006–99563.Google Scholar
  19. 19.
    M.D. Wang, H. Yin, R. Landick, J. Gelles, and S.M. Block. Stretching DNA with optical tweezers. Biophys. J., 72:1335–1346, 1997.CrossRefGoogle Scholar
  20. 20.
    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.CrossRefGoogle Scholar
  21. 21.
    C. Cecconi, E.A. Shank, C. Bustamante, and S. Marqusee. Direct observation of the three-state folding of a single protein molecule. Science, 309:2057–2060, 2005.CrossRefGoogle Scholar
  22. 22.
    J.T. Finer, R.M. Simmons, and J.A. Spudich. Single myosin molecule mechanics: piconewton forces and nanometer steps. Nature, 368:113–119, 1994.CrossRefGoogle Scholar
  23. 23.
    K. Visscher, M.J. Schnitzer, and S.M. Block. Single kinesin molecules studied with a molecular force clamp. Nature, 400:184–189, 1999.CrossRefGoogle Scholar
  24. 24.
    J. Sleep, D. Wilson, R. Simmons, and W. Gratzer. Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study. Biophys. J., 77:3085–3095, 1999.CrossRefGoogle Scholar
  25. 25.
    M. Dao, C.T. Lim, and S. Suresh. Mechanics of the human red blood cell deformed by optical tweezers. J. Mech. Phys. Solids, 51:2259–2280, 2003.CrossRefGoogle Scholar
  26. 26.
    M.M. Wang et al. Microfluidic sorting of mammalian cells by optical force switching. Nat. Biotechnol., 23:83–87, 2005.CrossRefGoogle Scholar
  27. 27.
    B.A. Nemet and M. Cronin-Golomb. Microscopic flow measurements with optically trapped probes. Opt. Lett., 27:1357–1359, 2002.CrossRefGoogle Scholar
  28. 28.
    B.A. Nemet, Y. Shabtai, and M. Cronin-Golomb. Imaging microscopic viscosity with confocal scanning optical tweezers. Opt. Lett., 27:264–266, 2002.CrossRefGoogle Scholar
  29. 29.
    L.P. Ghislain and W.W. Webb. Scanning-force microscope based on an optical trap. Opt. Lett., 18:1678–1680, 1993.CrossRefGoogle Scholar
  30. 30.
    M.E.J. Friese, A.G. Truscott, H. Rubinsztein, and N.R. Heckenberg. Three-dimensional imaging with optical tweezers. Appl. Opt., 38:6597–6603, 1999.CrossRefGoogle Scholar
  31. 31.
    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.CrossRefGoogle Scholar
  32. 32.
    T. Li, S. Kheifets, D. Medellin, and M.G. Raizen. Measurement of the instantaneous velocity of a Brownian particle. Science, 328:1673–1675, 2010.CrossRefGoogle Scholar
  33. 33.
    R.E. Holmlin, M. Schiavoni, C.Y. Chen, S.P. Smith, M.G. Prentiss, and G.M. Whitesides. Light-driven microfabrication: assembly of multicomponent, three-dimensional structures by using optical tweezers. Angew. Chem. Int. Ed., 39:3503–3506, 2000.CrossRefGoogle Scholar
  34. 34.
    A. Terray, J. Oakey, and D.W.M. Marr. Fabrication of linear colloidal structures for microfluidic applications. Appl. Phys. Lett., 81:1555–1557, 2002.CrossRefGoogle Scholar
  35. 35.
    P.J. Rodrigo, L. Kelemen, C.A. Alonzo, I.R. Perch-Nielsen, J.S. Dam, P. Ormos, and J. Glückstad. 2D optical manipulation and assembly of shape-complementary planar microstructures. Opt. Express, 15:9009–9014, 2007.CrossRefGoogle Scholar
  36. 36.
    R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C.M. Lieber, and D.G. Lieber. Manipulation and assembly of nanowires with holographic optical traps. Opt. Express, 13:8906–8912, 2005.CrossRefGoogle Scholar
  37. 37.
    P.J. Pauzauskie, A. Radenovic, E. Trepagnier, H. Shroff, P. Yang, and J. Liphardt. Optical trapping and integration of semiconductor nanowire assemblies in water. Nat. Mater., 5:97–101, 2006.CrossRefGoogle Scholar
  38. 38.
    M.J. Guffey and N.F. Scherer. All-optical patterning of Au nanoparticles on surfaces using optical traps. Nano Lett., 10:4302–4308, 2010.CrossRefGoogle Scholar
  39. 39.
    A. Ashkin and J.M. Dziedzic. Feedback stabilization of optically levitated particles. Appl. Phys. Lett., 30:202–204, 1977.CrossRefGoogle Scholar
  40. 40.
    J.E. Molloy, J.E. Burns, J. Kendrick-Jones, R.T. Tregear, and D.C.S. White. Movement and force produced by a single myosin head. Nature. 378:209–212, 1995.CrossRefGoogle Scholar
  41. 41.
    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.CrossRefGoogle Scholar
  42. 42.
    W.H. Guilford, D.E. Dupuis, G. Kennedy, J. Wu, J.B. Patlak, and D.M. Warshaw. Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap. Biophys. J., 72:1006–1021, 1997.CrossRefGoogle Scholar
  43. 43.
    K. Visscher and S.M. Block. Versatile optical traps with feedback control. Methods Enzymol., 298:460–489, 1998.CrossRefGoogle Scholar
  44. 44.
    M.J. Lang, C.L. Asbury, J.W. Shaevitz, and S.M. Block. An automated two-dimensional optical force clamp for single molecule studies. Biophys. J., 83:491–501, 2002.CrossRefGoogle Scholar
  45. 45.
    K.D. Wulff, D.G. Cole, and R.L. Clark. Servo control of an optical trap. Appl. Opt., 46:4923–4931, 2007.CrossRefGoogle Scholar
  46. 46.
    K.D. Wulff, D.G. Cole, and R.L. Clark. Adaptive disturbance rejection in an optical trap. Appl. Opt., 47:3585–3589, 2008.CrossRefGoogle Scholar
  47. 47.
    A.E. Wallin, H. Ojala, E. Hæggström, and R. Tuma. Stiffer optical tweezers through real-time feedback control. Appl. Phys. Lett., 92:224104, 2008.CrossRefGoogle Scholar
  48. 48.
    H. Ojala, A. Korsbäck, A.E. Wallin, and E. Hæggström. Optical position clamping with predictive control. Appl. Phys. Lett., 95:181104, 2009.CrossRefGoogle Scholar
  49. 49.
    J.J. Gorman, A. Balijepalli, and T.W. LeBrun. Control of optically trapped particles for Brownian motion suppression. IEEE Trans. Control Syst. Technol., in press, 2011.Google Scholar
  50. 50.
    A. Ranaweera, B. Bamieh, and A.R. Teel. Nonlinear stabilization of a spherical particle trapped in an optical tweezer. IEEE Conference on Decision and Control, Maui, HI, 2003, 3431–3436.Google Scholar
  51. 51.
    A. Ranaweera and B. Bamieh. Modeling, identification, and control of a spherical particle trapped in an optical tweezer. Int. J. Robust Nonlinear Control, 15:747–768, 2005.CrossRefMATHMathSciNetGoogle Scholar
  52. 52.
    C. Aguilar-Ibañez, M.S. Suarez-Castanon, and L.I. Rosas-Soriano. A simple control scheme for the manipulation of a particle by means of optical tweezers. Int. J. Robust Nonlinear Control, 21:328–337, 2011.CrossRefMATHGoogle Scholar
  53. 53.
    A.K. Balijepalli. Modeling and experimental techniques to demonstrate nanomanipulation with optical tweezers. Ph.D. Thesis, University of Maryland, 2011.Google Scholar
  54. 54.
    E Fallman and O Axner. Design for fully steerable dual-trap optical tweezers. Appl. Opt., 36:2107–2113, 1997.Google Scholar
  55. 55.
    E.R. Dufresne, G.C. Spalding, M.T. Dearing, S.A. Sheets, and D.G. Grier. Computer-generated holographic optical tweezer arrays. Rev. Sci. Instrum., 72:1810–1816, 2001.CrossRefGoogle Scholar
  56. 56.
    P.J. Rodrigo, V.R. Daria, and J. Glückstad. Real-time three-dimensional optical micromanipulation of multiple particles and living cells. Opt. Lett., 29:2270–2272, 2004.CrossRefGoogle Scholar
  57. 57.
    A.P. Goutzoulis and D.R. Pape. Design and fabrication of acousto-optic devices, New York, Marcel Dekker, 1994.Google Scholar
  58. 58.
    M. Gottlieb, C.L.M. Ireland, and J.M. Ley. Electro-optic and acousto-optic scanning and deflection, New York, Marcel Dekker, 1983.Google Scholar
  59. 59.
    M.T. Valentine, N.R. Guydosh, B. Gutiérrez-Medina, A.N. Fehr, J.O. Andreasson, and S.M. Block. Precision steering of an optical trap by electro-optic deflection. Opt. Lett., 33:599–601, 2008.CrossRefGoogle Scholar
  60. 60.
    N. Kaplan, A. Friedman, and N. Davidson. Acousto-optic lens with very fast focus scanning. Opt. Lett., 26:1078–1080, 2001.CrossRefGoogle Scholar
  61. 61.
    V.X.D. Yang et al. Doppler optical coherence tomography with a micro-electro-mechanical membrane mirror for high-speed dynamic focus tracking. Opt. Lett., 31:1262–1264, 2006.CrossRefGoogle Scholar
  62. 62.
    F. Gittes and C.F. Schmidt. Interference model for back-focal-plane displacement detection in optical tweezers. Opt. Lett., 23:7–9, 1998.CrossRefGoogle Scholar
  63. 63.
    M.W. Allersma, F. Gittes, M.J. deCastro, R.J. Stewart, and C.F. Schmidt. Two-dimensional tracking for ncd motility by back focal plane interferometry. Biophys. J., 74:1074–1085, 1998.Google Scholar
  64. 64.
    L. Nugent-Glandorf and T.T. Perkins. Measuring 0.1 nm motion in 1 ms in an optical microscope with differential back-focal-plane detection. Opt. Lett., 29:2611–2613, 2004.Google Scholar
  65. 65.
    W. Denk and W.W. Webb. Optical measurement of picometer displacements of transparent microscopic objects. Appl. Opt., 29:2382–2391, 1990.CrossRefGoogle Scholar
  66. 66.
    K. Svoboda, C.F. Schmidt, B.J. Schnapp, and S.M. Block. Direct observation of kinesin stepping by optical trapping interferometry. Nature, 365:721–727, 1993.CrossRefGoogle Scholar
  67. 67.
    J.C. Crocker and D.G. Grier. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci., 179:298–310, 1996.CrossRefGoogle Scholar
  68. 68.
    M.K. Cheezum, W.F. Walker, and W.H. Guilford. Quantitative comparison of algorithms for tracking single fluorescent particles. Biophys. J., 81:2378–2388, 2001.CrossRefGoogle Scholar
  69. 69.
    M. Capitanio, R. Cicchi, and F.S. Pavone. Position control and optical manipulation for nanotechnology applications. Eur. Phys. J. B, 46:1–8, 2005.Google Scholar
  70. 70.
    O. Otto, C. Gutsche, F. Kremer, and U.F. Keyser. Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis. Rev. Sci. Instrum., 79:023710, 2008.Google Scholar
  71. 71.
    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.CrossRefMATHGoogle Scholar
  72. 72.
    I.M. Peters, B.G. de Grooth, J.M. Schins, C.G. Figdor, and J. Greve. Three dimensional single-particle tracking with nanometer resolution. Rev. Sci. Instrum., 69:2762–2766, 1998.CrossRefGoogle Scholar
  73. 73.
    A. Pralle, M. Prummer, E.-L. Florin, E.H.K. Stelzer, and J.K.H. Hörber. Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light. Microsc. Res. Tech., 44:378–386, 1999.CrossRefGoogle Scholar
  74. 74.
    A. Rohrbach and E.H.K. Stelzer. Three-dimensional position detection of optically trapped dielectric particles. J. Appl. Phys., 91:5474–5488, 2002.CrossRefGoogle Scholar
  75. 75.
    F. Gittes and C.F. Schmidt. Signals and noise in micromechanical measurements. Methods in Cell Biol., 55:129–156, 1998.CrossRefGoogle Scholar
  76. 76.
    A. Rohrbach and E.H.K. Stelzer. Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations. Appl. Opt., 41:2494–2507, 2002.CrossRefGoogle Scholar
  77. 77.
    H. Risken. The fokker-planck equation: Methods of solution and applications. New York, Springer, 1996.MATHGoogle Scholar
  78. 78.
    Y.K. Nahmias and D.J. Odde. Analysis of radiation forces in laser trapping and laser-guided direct writing applications. IEEE J. Quantum Electron., 38:131–141, 2002.CrossRefGoogle Scholar
  79. 79.
    A. Balijepalli, T.W. Lebrun, and S.K. Gupta. Stochastic simulations with graphics hardware: Characterization of accuracy and performance. J. Comput. Inf. Sci. Eng., 10: 011010, 2010.CrossRefGoogle Scholar
  80. 80.
    J.H. Ginsberg, Advanced engineering dynamics, 2nd edition, New York, NY, Cambridge University Press, 1995.MATHGoogle Scholar
  81. 81.
    B.J. Kuo, Automatic Control Systems, 7th edition, Englewood Cliffs, NJ, Prentice-Hall, 1995.Google Scholar
  82. 82.
    K.J. Åström and T. Hägglund, Advanced PID control, Research Triangle Park, NC, ISA, 2005.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Jason J. Gorman
    • 1
  • Arvind Balijepalli
    • 1
  • Thomas W. LeBrun
    • 1
  1. 1.National Institute of Standards and TechnologyGaithersburgUSA

Personalised recommendations