Abstract

Whether or not an external force can make a trapped particle escape from optical tweezers can be used to measure optical forces. Combined with the linear dependence of optical forces on trapping power, a quantitative measurement of the force can be obtained. For this measurement, the particle is at the edge of the trap, away from the region near the equilbrium position where the trap can be described as a linear spring. This method provides the ability to measure higher forces for the same beam power, compared with using the linear region of the trap, with lower risk of optical damage to trapped specimens. Calibration is typically performed by using an increasing fluid flow to exert an increasing force on a trapped particle until it escapes. In this calibration technique, the particle is usually assumed to escape along a straight line in the direction of fluid-flow. Here, we show that the particle instead follows a curved trajectory, which depends on the rate of application of the force (i.e., the acceleration of the fluid flow). In the limit of very low acceleration, the particle follows the surface of zero axial optical force during the escape. The force required to produce escape depends on the trajectory, and hence the acceleration. This can result in variations in the escape force of a factor of two. This can have a major impact on calibration to determine the escape force efficiency. Even when calibration measurements are all performed in the low acceleration regime, variations in the escape force efficiency of 20% or more can still occur. We present computational simulations using generalized Lorenz–Mie theory and experimental measurements to show how the escape force efficiency depends on rate of increase of force and trapping power, and discuss the impact on calibration.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Escape trajectories of single-beam optically trapped micro-particles in a transverse fluid flow

Fabrice Merenda, Gerben Boer, Johann Rohner, Guy Delacrétaz, and René-Paul Salathé
Opt. Express 14(4) 1685-1699 (2006)

Calibration of light forces in optical tweezers

Harald Felgner, Otto Müller, and Manfred Schliwa
Appl. Opt. 34(6) 977-982 (1995)

Calibration of dynamic holographic optical tweezers for force measurements on biomaterials

Astrid van der Horst and Nancy R. Forde
Opt. Express 16(25) 20987-21003 (2008)

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [Crossref] [PubMed]
  2. J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
    [Crossref] [PubMed]
  3. A. Farré, F. Marsà, and M. Montes-Usategui, “Optimized back-focal-plane interferometry directly measures forces of optically trapped particles,” Opt. Express 20, 12270–12291 (2012).
    [Crossref] [PubMed]
  4. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [Crossref] [PubMed]
  5. W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
    [Crossref] [PubMed]
  6. A. van der Horst and N. R. Forde, “Power spectral analysis for optical trap stiffness calibration from high-speed camera position detection with limited bandwidth,” Opt. Express 18, 7670–7677 (2010).
    [Crossref] [PubMed]
  7. Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
    [Crossref] [PubMed]
  8. H. Felgner, O. Müller, and M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34, 977–982 (1995).
    [Crossref] [PubMed]
  9. N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
    [Crossref]
  10. N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
    [Crossref] [PubMed]
  11. A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
    [Crossref]
  12. A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
    [Crossref] [PubMed]
  13. F. Merenda, G. Boer, J. Rohner, G. Delacrétaz, and R.-P. Salathé, “Escape trajectories of single-beam optically trapped micro-particles in a transverse fluid flow,” Opt. Express 14, 1685–1699 (2006).
    [Crossref] [PubMed]
  14. Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
    [Crossref]
  15. Y. Cao, A. B. Stilgoe, L. Chen, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Equilibrium orientations and positions of non-spherical particles in optical traps,” Opt. Express 20, 12987–12996 (2012).
    [Crossref] [PubMed]
  16. A. A. M. Bui, A. B. Stilgoe, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Calibration of nonspherical particles in optical tweezers using only position measurement,” Opt. Lett. 38, 1244–1246 (2013).
    [Crossref] [PubMed]
  17. G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
    [Crossref]
  18. H. Faxén, “Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist,” Ann. Phys. 373, 89–119 (1922).
    [Crossref]
  19. M. Chaoui and F. Feuillebois, “Creeping flow around a sphere in a shear flow close to a wall,” Q. J. Mech. Appl. Math. 56, 381–410 (2003).
    [Crossref]
  20. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
    [Crossref]
  21. E. L. Botvinick and M. W. Berns, “Internet-based robotic laser scissors and tweezers microscopy,” Microsc. Res. Techniq. 68, 65–74 (2005).
    [Crossref]
  22. G. Thalhammer, L. Obmascher, and M. Ritsch-Marte, “Direct measurement of axial optical forces,” Opt. Express 23, 6112–6129 (2015).
    [Crossref] [PubMed]

2015 (1)

2014 (4)

Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
[Crossref] [PubMed]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

2013 (2)

2012 (2)

2010 (1)

2008 (2)

2007 (3)

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
[Crossref]

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

2006 (1)

2005 (1)

E. L. Botvinick and M. W. Berns, “Internet-based robotic laser scissors and tweezers microscopy,” Microsc. Res. Techniq. 68, 65–74 (2005).
[Crossref]

2003 (1)

M. Chaoui and F. Feuillebois, “Creeping flow around a sphere in a shear flow close to a wall,” Q. J. Mech. Appl. Math. 56, 381–410 (2003).
[Crossref]

1995 (1)

1994 (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[Crossref] [PubMed]

1986 (1)

1922 (1)

H. Faxén, “Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist,” Ann. Phys. 373, 89–119 (1922).
[Crossref]

Ashkin, A.

Berns, M. W.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

E. L. Botvinick and M. W. Berns, “Internet-based robotic laser scissors and tweezers microscopy,” Microsc. Res. Techniq. 68, 65–74 (2005).
[Crossref]

Bjorkholm, J. E.

Block, S. M.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[Crossref] [PubMed]

Boer, G.

Botvinick, E. L.

E. L. Botvinick and M. W. Berns, “Internet-based robotic laser scissors and tweezers microscopy,” Microsc. Res. Techniq. 68, 65–74 (2005).
[Crossref]

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Bui, A. A. M.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

A. A. M. Bui, A. B. Stilgoe, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Calibration of nonspherical particles in optical tweezers using only position measurement,” Opt. Lett. 38, 1244–1246 (2013).
[Crossref] [PubMed]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref] [PubMed]

Cao, Y.

Chaoui, M.

M. Chaoui and F. Feuillebois, “Creeping flow around a sphere in a shear flow close to a wall,” Q. J. Mech. Appl. Math. 56, 381–410 (2003).
[Crossref]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref] [PubMed]

Chen, L.

Chu, S.

Cruz, G.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

Cruz, G. M.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

Delacrétaz, G.

Dholakia, K.

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
[Crossref] [PubMed]

Dziedzic, J. M.

Farré, A.

Faxén, H.

H. Faxén, “Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist,” Ann. Phys. 373, 89–119 (1922).
[Crossref]

Felgner, H.

Feuillebois, F.

M. Chaoui and F. Feuillebois, “Creeping flow around a sphere in a shear flow close to a wall,” Q. J. Mech. Appl. Math. 56, 381–410 (2003).
[Crossref]

Forde, N. R.

Gong, Z.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
[Crossref]

Gross, S. P.

Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
[Crossref] [PubMed]

Heckenberg, N. R.

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Jun, Y.

Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
[Crossref] [PubMed]

Khatibzadeh, N.

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

Knöner, G.

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Lee, W. M.

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
[Crossref] [PubMed]

Li, Y.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
[Crossref]

Loke, V.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Lou, L.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
[Crossref]

Marchington, R. F.

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
[Crossref] [PubMed]

Marsà, F.

Mattson-Hoss, M. K.

Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
[Crossref] [PubMed]

Merenda, F.

Metzger, N. K.

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
[Crossref] [PubMed]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref] [PubMed]

Montes-Usategui, M.

Müller, O.

Narayanareddy, B. R. J.

Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
[Crossref] [PubMed]

Nieminen, T. A.

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

A. A. M. Bui, A. B. Stilgoe, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Calibration of nonspherical particles in optical tweezers using only position measurement,” Opt. Lett. 38, 1244–1246 (2013).
[Crossref] [PubMed]

Y. Cao, A. B. Stilgoe, L. Chen, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Equilibrium orientations and positions of non-spherical particles in optical traps,” Opt. Express 20, 12987–12996 (2012).
[Crossref] [PubMed]

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Obmascher, L.

Reece, P. J.

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
[Crossref] [PubMed]

Ritsch-Marte, M.

Rocha, Y.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

Rohner, J.

Rubinsztein-Dunlop, H.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

A. A. M. Bui, A. B. Stilgoe, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Calibration of nonspherical particles in optical tweezers using only position measurement,” Opt. Lett. 38, 1244–1246 (2013).
[Crossref] [PubMed]

Y. Cao, A. B. Stilgoe, L. Chen, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Equilibrium orientations and positions of non-spherical particles in optical traps,” Opt. Express 20, 12987–12996 (2012).
[Crossref] [PubMed]

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Salathé, R.-P.

Schliwa, M.

Shi, L. Z.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref] [PubMed]

Stilgoe, A. B.

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

A. A. M. Bui, A. B. Stilgoe, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Calibration of nonspherical particles in optical tweezers using only position measurement,” Opt. Lett. 38, 1244–1246 (2013).
[Crossref] [PubMed]

Y. Cao, A. B. Stilgoe, L. Chen, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Equilibrium orientations and positions of non-spherical particles in optical traps,” Opt. Express 20, 12987–12996 (2012).
[Crossref] [PubMed]

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[Crossref] [PubMed]

Thalhammer, G.

Tripathy, S. K.

Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
[Crossref] [PubMed]

van der Horst, A.

Volpe, G.

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

Wang, Z.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
[Crossref]

Xu, S.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
[Crossref]

Am. J. Phys. (1)

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

Ann. Phys. (1)

H. Faxén, “Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist,” Ann. Phys. 373, 89–119 (1922).
[Crossref]

Annu. Rev. Biochem. (1)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[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, 247–285 (1994).
[Crossref] [PubMed]

Appl. Opt. (1)

Biophys. J. (1)

Y. Jun, S. K. Tripathy, B. R. J. Narayanareddy, M. K. Mattson-Hoss, and S. P. Gross, “Calibration of optical tweezers for in vivo force measurements: How do different approaches compare?” Biophys. J. 107, 1474–1484 (2014).
[Crossref] [PubMed]

J. Opt. A (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Microsc. Res. Techniq. (1)

E. L. Botvinick and M. W. Berns, “Internet-based robotic laser scissors and tweezers microscopy,” Microsc. Res. Techniq. 68, 65–74 (2005).
[Crossref]

Nat. Protoc. (1)

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2, 3226–3238 (2007).
[Crossref] [PubMed]

Opt. Commun. (1)

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273, 37–42 (2007).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Proc. SPIE (2)

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. Cruz, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical trapping of isolated mammalian chromosomes,” Proc. SPIE 9164, 91642I (2014).
[Crossref]

A. A. M. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Optical tweezers escape forces,” Proc. SPIE 9164, 916413 (2014).
[Crossref]

Q. J. Mech. Appl. Math. (1)

M. Chaoui and F. Feuillebois, “Creeping flow around a sphere in a shear flow close to a wall,” Q. J. Mech. Appl. Math. 56, 381–410 (2003).
[Crossref]

Sci. Rep. (1)

N. Khatibzadeh, A. B. Stilgoe, A. A. M. Bui, Y. Rocha, G. M. Cruz, V. Loke, L. Z. Shi, T. A. Nieminen, H. Rubinsztein-Dunlop, and M. W. Berns, “Determination of motility forces on isolated chromosomes with laser tweezers,” Sci. Rep. 4, 6866 (2014).
[Crossref] [PubMed]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 Simulation showing regions of the force–position curve commonly used for force measurement with optical tweezers. The most common choice is the linear region A near the equilbrium, where the trap is approximately a Hookean spring. The maximum radial force region B allows higher forces to be measured for the same beam power, and at the same time reducing the risk of optical damage to live specimens.
Fig. 2
Fig. 2 Simulation showing that escape trajectories depend on the rate at which the force causing escape is applied. Extreme escape trajectories are shown for an optical trap, with the trapping beam propagating vertically upwards, and escape force applied horizontally to the right. The colour map shows the axial forces of the optical trap. One extreme case is a very rapid application of the escape force, when the particle escapes from the trap before the optical forces have time to move the particle significantly in the vertical direction. In this case, the escape trajectory is a horizontal straight line. The other extreme case is very slow application of the escape force, when the particle will follow a trajectory such that the vertical (i.e., axial) optical forces is zero. In this case, the trajectory lies on the (mathematical) surface where the vertical optical forces are in equilibrium, shown in white. Real trajectories will lie between these two extreme cases; if the escape forces are applied rapidly or slowly, the trajectory will be close to one of these extreme cases.
Fig. 3
Fig. 3 Experiment and simulation of escape of a 4.5 μm diameter polystyrene sphere, trapped by 10 mW 1070 nm laser beam focussed by a numerical aperture NA = 1.3 objective. a) Position of particle. The stage position is shown with an offset so that the stage and particle are shown at the same position after escape. b) Averaged velocity of particle over 15 data points. As the stage velocity is increased the the particle will be displaced from the trap by the viscous drag force. The particle escapes around the point the particle velocity changes behaviour such that it begins to approach the fluid velocity. The particle moves rapidly away from the trap, at the velocity of the surrounding fluid (i.e., the stage velocity). c) Simulated position. d) Simulated velocity. Due to the lag introduced by dynamics, the maximum optical trap force (×) is not coincident with the local minimum velocity prior to escape (○). Thus one cannot exactly know what the escape force is using only the particle position data.
Fig. 4
Fig. 4 Simulation showing the optical force field and the escape trajectories of a 4.5 μm diameter polystyrene sphere as it escapes from a 5 mW trap in water. Escape trajectories are shown for different stage accelerations. For low accelerations, the trajectory lies close to the zero axial force contour, and for high accelerations, it lies close to a straight horizontal line. The crosses mark the peak force, escape force, which correspond to the point of escape for each of the trajectories. The low acceleration particles escape by overcoming the axial trapping force, rather than the radial (x) trapping force. As the particle moves away from the beam axis, it moves upwards. At the radius where escape occurs, the particle ceases to be axially trapped. For high accelerations, escape occurs when the fluid flow force exceeds the maximum radial force encountered along the trajectory. These escapes of the particles along the different trajectories leads to different escape forces, as can be read from the x-force strength at the point of escape marked by the cross. Note that the sign of this radial force is negative as it points towards the centre of the trap, which is in the negative direction. The zero on the coordinates refers to the position of the focus: the equilibrium trapping position, before applying external fluid flow force, being beyond the focus.
Fig. 5
Fig. 5 Simulation showing optical force during escape. The radial normalised optical force efficiency, Qx, encountered during the escape is shown for a range of stage accelerations, that is, over a range of rates of applying the external fluid flow force, which correspond to the escape trajectories shown in Fig. 4. This is compared to the force acting on the particle which has an escape trajectory directly out of the trap in the x-direction. The low acceleration trajectories have lower maximum radial forces than if the particle was to go directly in the x-direction. This trap and particle are the same as for Fig. 4.
Fig. 6
Fig. 6 Simulation showing the transition from low acceleration, low Qesc region to high acceleration, high Qesc region, for 4.5 μm and 10 μm diameter polystyrene spheres trapped in water by a 1064 nm laser beam focussed by a numerical aperture NA = 0.8 objective. The curves for different trapping powers do not overlap, and this non-overlap is larger for larger particles. This results in variations in Qesc even if all measurements are in the low (or high) Qesc regime.
Fig. 7
Fig. 7 Comparison of simulated (circles, ○) and experimental (crosses, ×) escape force (Qesc) for a) 4.5μm and b) 10μm diameter polystyrene particles in methyl cellulose solution with viscosities of 1 cP, 3 cP and 7 cP.
Fig. 8
Fig. 8 Effect of weight and buoyancy on escape trajectories and forces for 10 μm diameter polystyrene spheres trapped in water by a 5 mW 1064 nm laser beam focussed by a numerical aperture NA = 0.8 objective. Three cases are shown: an upward-propagating trap where the weight opposes the axial scattering force, a downward-propagating trap where the weight acts in the same direction as the axial scattering force, and a trap with zero weight and buoyancy. As the power increases, the zero axial force surface will approach this zero weight and buoyancy case. (a) Zero axial force surfaces. These are the trajectories for escape with very low accelerations. For very high accelerations, the trajectories will be straight horizontal lines, with heights depending on the weight and buoyancy. (b) Radial force for very low accelerations. (c) Radial force for very high accelerations.

Equations (5)

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

F = n Q c P ,
F esc = n Q esc c P .
f flow = Γ v = 6 π η r v ,
f esc = Γ V = 6 π η r V = 6 π η r t a ,
x i + 1 = x i + Γ 1 ( f flow ( t i ) + f o ( x i ) + f w + f b ) Δ t ,

Metrics