Abstract

A versatile optical trap has been constructed to control the position of trapped objects and ultimately to apply specified forces using feedback control. While the design, development, and use of optical traps has been extensive and feedback control has played a critical role in pushing the state of the art, few comprehensive examinations of feedback control of optical traps have been undertaken. Furthermore, as the requirements are pushed to ever smaller distances and forces, the performance of optical traps reaches limits. It is well understood that feedback control can result in both positive and negative effects in controlled systems. We give an analysis of the trapping limits as well as introducing an optical trap with a feedback control scheme that dramatically improves an optical trap's sensitivity at low frequencies.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
  2. A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
    [CrossRef] [PubMed]
  3. A. Ashkin and J. M. Dziedzic, "Internal cell manipulation using infrared-laser traps," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
    [CrossRef] [PubMed]
  4. T. T. Perkins, D. E. Smith, and S. Chu, "Direct observation of tube-like motion of a single polymer-chain," Science 264, 819-822 (1994).
    [CrossRef] [PubMed]
  5. S. C. Kuo and M. P. Sheetz, "Force of single kinesin molecules measured with optical tweezers," Science 260, 232-234 (1993).
    [CrossRef] [PubMed]
  6. 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).
    [CrossRef] [PubMed]
  7. J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics--piconewton forces and nanometer steps," Nature 368, 113-119 (1994).
    [CrossRef] [PubMed]
  8. 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]
  9. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, "Stretching dna with optical tweezers," Biophys. J. 72, 1335-1346 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. K. Visscher and S. M. Block, "Versatile optical traps with feedback control," Methods Enzymol. 298, 460-489 (1998).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. M. Polin, K. Ladavac, S. H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
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  19. P. C. Mogensen and J. Gluckstad, "Dynamic away generation and pattern formation for optical tweezers," Opt. Commun. 175, 75-81 (2000).
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  20. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
    [CrossRef]
  21. J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
    [CrossRef]
  22. V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, "Optically controlled three-dimensional rotation of microscopic objects," Appl. Phys. Lett. 82, 829-831 (2003).
    [CrossRef]
  23. J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, "3d manipulation of particles into crystal structures using holographic optical tweezers," Opt. Express 12, 220-226 (2004).
    [CrossRef] [PubMed]
  24. 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]
  25. L. D. Landau and E. M. Lifshitz, Statistical Physics, Vol. 5 of Course of Theoretical Physics (Butterworth-Heinemann, 2001).
  26. K. Ogata, Modern Control Engineering, 3rd ed. (Prentice Hall, 1997).
  27. G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 3rd ed. (Addison-Wesley , 1994).
  28. C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
    [CrossRef]
  29. E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, "Extending the bandwidth of optical-tweezers interferometry," Rev. Sci. Instrum. 74, 3246-3249 (2003).
    [CrossRef]
  30. K. Berg-Sorensen, L. 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]
  31. J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, "Single-molecule mechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers," Biophys. J. 68, S298-S305 (1995).
  32. G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
    [CrossRef] [PubMed]

2006

2005

M. Polin, K. Ladavac, S. H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

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]

2004

2003

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, "Optically controlled three-dimensional rotation of microscopic objects," Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, "Extending the bandwidth of optical-tweezers interferometry," Rev. Sci. Instrum. 74, 3246-3249 (2003).
[CrossRef]

K. Berg-Sorensen, L. 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]

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

2001

L. D. Landau and E. M. Lifshitz, Statistical Physics, Vol. 5 of Course of Theoretical Physics (Butterworth-Heinemann, 2001).

2000

P. C. Mogensen and J. Gluckstad, "Dynamic away generation and pattern formation for optical tweezers," Opt. Commun. 175, 75-81 (2000).
[CrossRef]

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

1999

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]

1998

K. Visscher and S. M. Block, "Versatile optical traps with feedback control," Methods Enzymol. 298, 460-489 (1998).
[CrossRef] [PubMed]

F. Gittes and C. F. Schmidt, "Interference model for back-focal-plane displacement detection in optical tweezers," Opt. Lett. 23, 7-9 (1998).
[CrossRef]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

1997

K. Ogata, Modern Control Engineering, 3rd ed. (Prentice Hall, 1997).

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, "Stretching dna with optical tweezers," Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

1996

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).
[CrossRef]

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]

1995

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, "Single-molecule mechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers," Biophys. J. 68, S298-S305 (1995).

1994

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 3rd ed. (Addison-Wesley , 1994).

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics--piconewton forces and nanometer steps," Nature 368, 113-119 (1994).
[CrossRef] [PubMed]

T. T. Perkins, D. E. Smith, and S. Chu, "Direct observation of tube-like motion of a single polymer-chain," Science 264, 819-822 (1994).
[CrossRef] [PubMed]

1993

S. C. Kuo and M. P. Sheetz, "Force of single kinesin molecules measured with optical tweezers," Science 260, 232-234 (1993).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

1992

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).
[CrossRef] [PubMed]

1990

1989

A. Ashkin and J. M. Dziedzic, "Internal cell manipulation using infrared-laser traps," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef] [PubMed]

1987

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

Ashkin, A.

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).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Internal cell manipulation using infrared-laser traps," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

Bamieh, B.

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]

Berg-Sorensen, K.

K. Berg-Sorensen, L. 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]

Bingelyte, V.

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, "Optically controlled three-dimensional rotation of microscopic objects," Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

Block, S. M.

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]

K. Visscher and S. M. Block, "Versatile optical traps with feedback control," Methods Enzymol. 298, 460-489 (1998).
[CrossRef] [PubMed]

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, "Stretching dna with optical tweezers," Biophys. J. 72, 1335-1346 (1997).
[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, 1066-1076 (1996).
[CrossRef]

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).
[CrossRef] [PubMed]

Burns, J. E.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, "Single-molecule mechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers," Biophys. J. 68, S298-S305 (1995).

Bustamante, C.

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

Chu, S.

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]

T. T. Perkins, D. E. Smith, and S. Chu, "Direct observation of tube-like motion of a single polymer-chain," Science 264, 819-822 (1994).
[CrossRef] [PubMed]

Clark, R. L.

Cole, D. G.

Cooper, J.

Courtial, J.

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, "3d manipulation of particles into crystal structures using holographic optical tweezers," Opt. Express 12, 220-226 (2004).
[CrossRef] [PubMed]

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, "Optically controlled three-dimensional rotation of microscopic objects," Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Davenport, R. J.

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

Denk, W.

di Leonardo, R.

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, "An optically driven pump for microfluidics," Lab Chip 6, 735-739 (2006).
[CrossRef] [PubMed]

DiLeonardo, R.

Dufresne, E. R.

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Internal cell manipulation using infrared-laser traps," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

Emami-Naeini, A.

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 3rd ed. (Addison-Wesley , 1994).

Finer, J. T.

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]

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics--piconewton forces and nanometer steps," Nature 368, 113-119 (1994).
[CrossRef] [PubMed]

Florin, E. L.

K. Berg-Sorensen, L. 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.

K. Berg-Sorensen, L. 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]

Franklin, G. F.

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 3rd ed. (Addison-Wesley , 1994).

Gelles, J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, "Stretching dna with optical tweezers," Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Gibson, G.

Gittes, F.

Gluckstad, J.

P. C. Mogensen and J. Gluckstad, "Dynamic away generation and pattern formation for optical tweezers," Opt. Commun. 175, 75-81 (2000).
[CrossRef]

Grier, D. G.

M. Polin, K. Ladavac, S. H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

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, 1066-1076 (1996).
[CrossRef]

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Jordan, P.

Kapitein, L. C.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, "Extending the bandwidth of optical-tweezers interferometry," Rev. Sci. Instrum. 74, 3246-3249 (2003).
[CrossRef]

Kendrickjones, J.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, "Single-molecule mechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers," Biophys. J. 68, S298-S305 (1995).

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Kuo, S. C.

S. C. Kuo and M. P. Sheetz, "Force of single kinesin molecules measured with optical tweezers," Science 260, 232-234 (1993).
[CrossRef] [PubMed]

Laczik, Z. J.

Ladavac, K.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Statistical Physics, Vol. 5 of Course of Theoretical Physics (Butterworth-Heinemann, 2001).

Landick, R.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, "Stretching dna with optical tweezers," Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Leach, J.

Lee, S. H.

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Statistical Physics, Vol. 5 of Course of Theoretical Physics (Butterworth-Heinemann, 2001).

Macosko, J. C.

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

Mogensen, P. C.

P. C. Mogensen and J. Gluckstad, "Dynamic away generation and pattern formation for optical tweezers," Opt. Commun. 175, 75-81 (2000).
[CrossRef]

Molloy, J. E.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, "Single-molecule mechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers," Biophys. J. 68, S298-S305 (1995).

Mushfique, H.

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, "An optically driven pump for microfluidics," Lab Chip 6, 735-739 (2006).
[CrossRef] [PubMed]

Oddershede, L.

K. Berg-Sorensen, L. 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]

Ogata, K.

K. Ogata, Modern Control Engineering, 3rd ed. (Prentice Hall, 1997).

Padgett, M.

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, "An optically driven pump for microfluidics," Lab Chip 6, 735-739 (2006).
[CrossRef] [PubMed]

Padgett, M. J.

Perkins, T. T.

T. T. Perkins, D. E. Smith, and S. Chu, "Direct observation of tube-like motion of a single polymer-chain," Science 264, 819-822 (1994).
[CrossRef] [PubMed]

Peterman, E. J. G.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, "Extending the bandwidth of optical-tweezers interferometry," Rev. Sci. Instrum. 74, 3246-3249 (2003).
[CrossRef]

Polin, M.

Powell, J. D.

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 3rd ed. (Addison-Wesley , 1994).

Ranaweera, A.

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]

Rappaport, A.

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Roichman, Y.

Schmidt, C. F.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, "Extending the bandwidth of optical-tweezers interferometry," Rev. Sci. Instrum. 74, 3246-3249 (2003).
[CrossRef]

F. Gittes and C. F. Schmidt, "Interference model for back-focal-plane displacement detection in optical tweezers," Opt. Lett. 23, 7-9 (1998).
[CrossRef]

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).
[CrossRef] [PubMed]

Schnapp, B. J.

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Spudich, J. A.

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]

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[CrossRef] [PubMed]

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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).
[CrossRef] [PubMed]

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E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, "Extending the bandwidth of optical-tweezers interferometry," Rev. Sci. Instrum. 74, 3246-3249 (2003).
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[CrossRef]

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[CrossRef] [PubMed]

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G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
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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).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Free body diagram of a particle suspended in an optical trap where x is the relative displacement of the particle from the trapping laser, z is the absolute position of the particle, and u is the position of the trap.

Fig. 2
Fig. 2

Block diagram of servo controller for an optical trap.

Fig. 3
Fig. 3

Experimental optical trap setup with a FSM actuator and a quadrant photodiode sensor.

Fig. 4
Fig. 4

(Color online) Sensitivity of the QDP position sensor. The sensor has a sensitivity of 0.51 μm / V in the central linear region.

Fig. 5
Fig. 5

(Color online) Power spectral density of a 1 μ m polystyrene microsphere in an optical trap and the corresponding curve fit.

Fig. 6
Fig. 6

(Color online) Transfer function and curve fit of the actuator dynamics.

Fig. 7
Fig. 7

(Color online) Loop gain (L), sensitivity (S), and complementary sensitivity (T) of the closed-loop system. L and T were measured experimentally while S was calculated from L.

Fig. 8
Fig. 8

(Color online) Autospectrum of the absolute position of a trapped 1 μm polystyrene microsphere for the open- and closed-loop systems.

Fig. 9
Fig. 9

(Color online) Autospectrum (A) and time trace (B) of the absolute position of a trapped 1 μm polystyrene microsphere for the open- and closed-loop systems after digital filtering. The signals are filtered with a fifth-order low-pass Butterworth filter with ω c = 50   Hz . The rms displacement of the closed-loop signal is half that of the open-loop signal.

Equations (29)

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

σ f 2 = 2 γ k B T ,
σ d 2 = 2 γ k B T k 2 .
m x ¨ + γ x ˙ + k x = m u ¨ γ u ˙ + k d ˜ ,
Ω = k γ γ m .
x = G 1 d ˜ + G 2 u ,
G 1 ( s ) = X ( s ) D ˜ ( s ) = k γ s + k = Ω s + Ω ,
G 2 ( s ) = X ( s ) U ( s ) = γ s γ s + k = s s + Ω ,
z = G 1 d ˜ + ( 1 + G 2 ) u = G 1 ( d ˜ + u ) .
z ^ d ˜ = G 1 S ,
S = 1 1 + K ( G 2 G A + G ^ A ) .
| e o l ( j ω ) e c l ( j ω ) | = | S ( j ω ) | .
L ( s ) = ω c s ,
K ( s ) = L ( s ) G ( s ) = α ( s + Ω ) s .
S ( s ) = s s + ω c ,
T ( s ) = ω c s + ω c .
G S ( s ) = Ω s ( s + Ω ) ( s + ω c ) .
z 2 = G S 2 2 σ d 2 = 1 1 + α k B T k ,
u 2 = T 2 2 σ d 2 = α k B T k .
K S ( s ) = α s + Ω s + ω c .
x d ˜ = G S ( 1 + K ) = ( Ω + ω c ) s + ω c Ω ( s + Ω ) ( s + ω c ) ,
x n = K S ( 1 G ) = s s + ω c .
G S ( 1 + K ) { 1 + α α < 1 2 / 3 α = 1 , 1 + 1 / α α > 1 ,
x 2 ( 1 + α ) 2 k B T k < x max 2 .
α < x max x rms x rms ,
G A ( s ) = g ( s + z 1 ) ( s + p 1 ) ( s + p 2 ) ( s 2 + 2 ζ ω n s + ω n 2 ) , 
0 ln | S ( j ω ) | d ω = π i p i ,
S > M ω 1 / ( Ω ω 1 ) = M α / ( 1 α ) ,
0 ω 1 ln | S ( j ω ) | d ω + ω 1 Ω ln | S ( j ω ) | d ω = 0 .
( Ω ω 1 ) ln S > ω 1 Ω ln | S ( j ω ) | d ω > ω 1   ln   M .  

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