Abstract

A systematic study of the influence of a glass-water interface on the on-axis trapping of micrometer-sized spherical objects by optical tweezers is presented. The ways in which the escape force and the trapping position, as well as the stiffness of the trap, depend on the focusing depth, the numerical aperture, and the degree of overfilling of the objective entrance pupil are investigated. It is concluded, among other things, that objectives with the highest numerical aperture and the use of large degrees of overfilling do not always provide the optimum trapping conditions at finite depths.

© 2003 Optical Society of America

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [CrossRef]
  3. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
    [CrossRef] [PubMed]
  4. M. P. Sheetz, Laser Tweezers in Cell Biology (Academic, New York, 1998).
  5. K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef] [PubMed]
  6. A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
    [CrossRef] [PubMed]
  7. L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
    [CrossRef]
  8. K. Svoboda, S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77, 773–784 (1994).
    [CrossRef] [PubMed]
  9. J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
    [CrossRef] [PubMed]
  10. J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
    [CrossRef] [PubMed]
  11. R. M. Simmons, J. T. Finer, S. Chu, J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
    [CrossRef] [PubMed]
  12. K. Visscher, S. P. Gross, 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]
  13. M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
    [CrossRef] [PubMed]
  14. M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276, 1122–1116 (1997).
    [CrossRef]
  15. Z.-P. Luo, K.-N. An, “Development and validation of a nanometer manipulation and measurement system for biomechanical testing of single macro-molecules,” J. Biomechan. 31, 1075–1079 (1998).
    [CrossRef]
  16. M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
    [CrossRef] [PubMed]
  17. M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
    [CrossRef]
  18. R. B. Dickinson, A. R. Clapp, S. E. Truesdail, “Direct measurement of long-range interaction forces between a single bacterium and a substrate using an optical trap,” in Handbook of Bacterial Adhesion, R. J. Friedman, ed. (Humana Press, Totowa, N.J., 2000), pp. 297–306.
    [CrossRef]
  19. 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]
  20. R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the traping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1922–1930 (1992).
    [CrossRef]
  21. T. C. B. Schut, G. Hesselink, B. G. Degrooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical-optics model for calculating the stability of optical traps,” Cytometry 16, 479–485 (1991).
    [CrossRef]
  22. W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
    [CrossRef]
  23. W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
    [CrossRef] [PubMed]
  24. M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
    [CrossRef]
  25. S. Nemoto, H. Togo, “Axial force acting on a dielectric sphere in a focused laser beam,” Appl. Opt. 37, 6386–6394 (1998).
    [CrossRef]
  26. P. C. Ke, M. Gu, “Characterization of trapping force on metallic Mie particles,” Appl. Opt. 38, 160–167 (1999).
    [CrossRef]
  27. R. C. Gauthier, A. Frangioudakis, “Theoretical investigation of the optical trapping properties of a micro-optic cubic glass structure,” Appl. Opt. 39, 3060–3070 (2000).
    [CrossRef]
  28. P. C. Ke, M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
    [CrossRef]
  29. T. Tlusty, A. Meller, B.-Z. Roy, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
    [CrossRef]
  30. P. A. Maia Neto, H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
    [CrossRef]
  31. D. A. White, “Vector finite element modeling of optical tweezers,” Comput. Phys. Commun. 128, 558–564 (2000).
    [CrossRef]
  32. Traditional aberration theory shows that spherical aberration is strongly dependent on the NA of an optical system. The longitudinal (also referred to as the axial) spherical aberration is proportional to NA2; whereas the spherical wave aberration is proportional to NA4. Optical tweezers, which utilize high-NA objectives to produce rays with large angles, are therefore particularly susceptible to this effect.
  33. There are also objectives that have provisions for adjustment of the spherical-aberration-free depth. However, such objectives are often costly and complicated and are therefore not common for optical tweezers applications. In addition, they contain a significant number of lenses, which also makes them less suitable for optical trapping.
  34. A. Rohrbach, E. H. K. Stelzer, “Trapping forces, force constants, and potential depths for dielectrical spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (2002).
    [CrossRef] [PubMed]
  35. X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
    [CrossRef]
  36. E. Fällman, O. Axner are preparing the following paper for publication: “Comparison of on-axis trapping of optical traps under the influence of spherical aberration by objectives that adhere to the sin and tan conditions.”
  37. E. Fällman, O. Axner are preparing the following paper for publication: “The influence of a cover glass surface on the trapping of spherical objects by optical tweezers—The off-axis case.”

2002

2000

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

R. C. Gauthier, A. Frangioudakis, “Theoretical investigation of the optical trapping properties of a micro-optic cubic glass structure,” Appl. Opt. 39, 3060–3070 (2000).
[CrossRef]

P. A. Maia Neto, H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[CrossRef]

D. A. White, “Vector finite element modeling of optical tweezers,” Comput. Phys. Commun. 128, 558–564 (2000).
[CrossRef]

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

1999

1998

P. C. Ke, M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

T. Tlusty, A. Meller, B.-Z. Roy, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

S. Nemoto, H. Togo, “Axial force acting on a dielectric sphere in a focused laser beam,” Appl. Opt. 37, 6386–6394 (1998).
[CrossRef]

Z.-P. Luo, K.-N. An, “Development and validation of a nanometer manipulation and measurement system for biomechanical testing of single macro-molecules,” J. Biomechan. 31, 1075–1079 (1998).
[CrossRef]

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

1997

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276, 1122–1116 (1997).
[CrossRef]

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

1996

R. M. Simmons, J. T. Finer, S. Chu, J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
[CrossRef] [PubMed]

K. Visscher, S. P. Gross, 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]

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

1995

J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
[CrossRef] [PubMed]

1994

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

K. Svoboda, S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77, 773–784 (1994).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

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

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

1993

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

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]

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the traping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1922–1930 (1992).
[CrossRef]

1991

T. C. B. Schut, G. Hesselink, B. G. Degrooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical-optics model for calculating the stability of optical traps,” Cytometry 16, 479–485 (1991).
[CrossRef]

1990

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
[CrossRef] [PubMed]

1986

1970

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

An, K.-N.

Z.-P. Luo, K.-N. An, “Development and validation of a nanometer manipulation and measurement system for biomechanical testing of single macro-molecules,” J. Biomechan. 31, 1075–1079 (1998).
[CrossRef]

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

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, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Axner, O.

E. Fällman, O. Axner are preparing the following paper for publication: “The influence of a cover glass surface on the trapping of spherical objects by optical tweezers—The off-axis case.”

E. Fällman, O. Axner are preparing the following paper for publication: “Comparison of on-axis trapping of optical traps under the influence of spherical aberration by objectives that adhere to the sin and tan conditions.”

Berns, M. W.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

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

K. Svoboda, S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77, 773–784 (1994).
[CrossRef] [PubMed]

Brevik, I.

Burns, J. E.

J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
[CrossRef] [PubMed]

Bustamante, C.

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276, 1122–1116 (1997).
[CrossRef]

Cheng, B. Y.

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

Choi, I. S.

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

Choi, S. K.

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

Chu, S.

R. M. Simmons, J. T. Finer, S. Chu, J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef]

Clapp, A. R.

R. B. Dickinson, A. R. Clapp, S. E. Truesdail, “Direct measurement of long-range interaction forces between a single bacterium and a substrate using an optical trap,” in Handbook of Bacterial Adhesion, R. J. Friedman, ed. (Humana Press, Totowa, N.J., 2000), pp. 297–306.
[CrossRef]

Degrooth, B. G.

T. C. B. Schut, G. Hesselink, B. G. Degrooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical-optics model for calculating the stability of optical traps,” Cytometry 16, 479–485 (1991).
[CrossRef]

Dickinson, R. B.

R. B. Dickinson, A. R. Clapp, S. E. Truesdail, “Direct measurement of long-range interaction forces between a single bacterium and a substrate using an optical trap,” in Handbook of Bacterial Adhesion, R. J. Friedman, ed. (Humana Press, Totowa, N.J., 2000), pp. 297–306.
[CrossRef]

Dziedzic, J. M.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef]

Euteneuer, U.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
[CrossRef] [PubMed]

Fällman, E.

E. Fällman, O. Axner are preparing the following paper for publication: “Comparison of on-axis trapping of optical traps under the influence of spherical aberration by objectives that adhere to the sin and tan conditions.”

E. Fällman, O. Axner are preparing the following paper for publication: “The influence of a cover glass surface on the trapping of spherical objects by optical tweezers—The off-axis case.”

Finer, J. T.

R. M. Simmons, J. T. Finer, S. Chu, 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, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

Frangioudakis, A.

Gan, X. S.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Gauthier, R. C.

Ghislain, L. P.

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

Granzier, H. L.

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276, 1122–1116 (1997).
[CrossRef]

Greve, J.

T. C. B. Schut, G. Hesselink, B. G. Degrooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical-optics model for calculating the stability of optical traps,” Cytometry 16, 479–485 (1991).
[CrossRef]

Gross, S. P.

K. Visscher, S. P. Gross, 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]

Gu, M.

P. C. Ke, M. Gu, “Characterization of trapping force on metallic Mie particles,” Appl. Opt. 38, 160–167 (1999).
[CrossRef]

P. C. Ke, M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Guo, H. L.

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

Gussgard, R.

Han, X. H.

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

Helmerson, K.

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

Hesselink, G.

T. C. B. Schut, G. Hesselink, B. G. Degrooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical-optics model for calculating the stability of optical traps,” Cytometry 16, 479–485 (1991).
[CrossRef]

Hong, Y.

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Jeff, G.

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Ke, P. C.

P. C. Ke, M. Gu, “Characterization of trapping force on metallic Mie particles,” Appl. Opt. 38, 160–167 (1999).
[CrossRef]

P. C. Ke, M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Kellermayer, M. S. Z.

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276, 1122–1116 (1997).
[CrossRef]

Kendrick-Jones, J.

J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
[CrossRef] [PubMed]

Kishore, R.

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

Li, Z. L.

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

Liang, M. N.

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

Lindmo, T.

Luo, Z.-P.

Z.-P. Luo, K.-N. An, “Development and validation of a nanometer manipulation and measurement system for biomechanical testing of single macro-molecules,” J. Biomechan. 31, 1075–1079 (1998).
[CrossRef]

Maia Neto, P. A.

P. A. Maia Neto, H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[CrossRef]

Mammen, M.

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

Meller, A.

T. Tlusty, A. Meller, B.-Z. Roy, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Metallo, S. J.

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

Molloy, J. E.

J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
[CrossRef] [PubMed]

Nemoto, S.

Nussenzveig, H. M.

P. A. Maia Neto, H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[CrossRef]

Phillips, W. D.

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

Prentiss, M.

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

Robert, L.

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Rohrbach, A.

Roy, B.-Z.

T. Tlusty, A. Meller, B.-Z. Roy, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Schliwa, M.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
[CrossRef] [PubMed]

Schmith, S. P.

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

Schnitzer, M. J.

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Schut, T. C. B.

T. C. B. Schut, G. Hesselink, B. G. Degrooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical-optics model for calculating the stability of optical traps,” Cytometry 16, 479–485 (1991).
[CrossRef]

Schutze, K.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
[CrossRef] [PubMed]

Sheetz, M. P.

M. P. Sheetz, Laser Tweezers in Cell Biology (Academic, New York, 1998).

Simmons, R. M.

R. M. Simmons, J. T. Finer, S. Chu, 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, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

Smith, S. B.

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276, 1122–1116 (1997).
[CrossRef]

Sonek, G. J.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Spudich, J. A.

R. M. Simmons, J. T. Finer, S. Chu, 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, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

Stelzer, E. H. K.

Svoboda, K.

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

K. Svoboda, S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77, 773–784 (1994).
[CrossRef] [PubMed]

Switz, N. A.

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

Tlusty, T.

T. Tlusty, A. Meller, B.-Z. Roy, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Togo, H.

Tregear, R. T.

J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
[CrossRef] [PubMed]

Truesdail, S. E.

R. B. Dickinson, A. R. Clapp, S. E. Truesdail, “Direct measurement of long-range interaction forces between a single bacterium and a substrate using an optical trap,” in Handbook of Bacterial Adhesion, R. J. Friedman, ed. (Humana Press, Totowa, N.J., 2000), pp. 297–306.
[CrossRef]

Visscher, K.

K. Visscher, S. P. Gross, 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]

Wang, M. D.

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Webb, W. W.

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

White, D. A.

D. A. White, “Vector finite element modeling of optical tweezers,” Comput. Phys. Commun. 128, 558–564 (2000).
[CrossRef]

White, D. C. S.

J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
[CrossRef] [PubMed]

Whitesides, G. M.

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

Wright, W. H.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Yao, X. C.

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

Zhang, D. Z.

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

Annu. Rev. Biophys. Biomol. Struct.

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

Appl. Opt.

Appl. Phys. Lett.

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Biophys. J.

R. M. Simmons, J. T. Finer, S. Chu, J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996).
[CrossRef] [PubMed]

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]

Cell

K. Svoboda, S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77, 773–784 (1994).
[CrossRef] [PubMed]

Chem. Biol.

M. Mammen, K. Helmerson, R. Kishore, S. K. Choi, W. D. Phillips, G. M. Whitesides, “Optically controlled collisions of biological objects to evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chem. Biol. 3, 757–763 (1996).
[CrossRef] [PubMed]

Chin. Phys.

X. C. Yao, Z. L. Li, H. L. Guo, B. Y. Cheng, X. H. Han, D. Z. Zhang, “Effect of spherical aberration introduced by water solution on trapping force,” Chin. Phys. 9, 824–826 (2000).
[CrossRef]

Comput. Phys. Commun.

D. A. White, “Vector finite element modeling of optical tweezers,” Comput. Phys. Commun. 128, 558–564 (2000).
[CrossRef]

Cytometry

T. C. B. Schut, G. Hesselink, B. G. Degrooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical-optics model for calculating the stability of optical traps,” Cytometry 16, 479–485 (1991).
[CrossRef]

Europhys. Lett.

P. A. Maia Neto, H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Visscher, S. P. Gross, 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]

J. Biomechan.

Z.-P. Luo, K.-N. An, “Development and validation of a nanometer manipulation and measurement system for biomechanical testing of single macro-molecules,” J. Biomechan. 31, 1075–1079 (1998).
[CrossRef]

J. Mod. Opt.

P. C. Ke, M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White, “Movement and force produced by a single myosin head,” Nature 378, 209–212 (1995).
[CrossRef] [PubMed]

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

T. Tlusty, A. Meller, B.-Z. Roy, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Proc. Natl. Acad. Sci. USA

M. N. Liang, S. P. Schmith, S. J. Metallo, I. S. Choi, M. Prentiss, G. M. Whitesides, “Measuring the forces involved in polyvalent adhesion of urophatogenic Escherichia coli to mannose-presenting surfaces,” Proc. Natl. Acad. Sci. USA 97, 13,092–13,096 (2000).
[CrossRef]

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

L. P. Ghislain, N. A. Switz, W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994).
[CrossRef]

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Science

M. D. Wang, M. J. Schnitzer, Y. Hong, L. Robert, G. Jeff, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276, 1122–1116 (1997).
[CrossRef]

Other

R. B. Dickinson, A. R. Clapp, S. E. Truesdail, “Direct measurement of long-range interaction forces between a single bacterium and a substrate using an optical trap,” in Handbook of Bacterial Adhesion, R. J. Friedman, ed. (Humana Press, Totowa, N.J., 2000), pp. 297–306.
[CrossRef]

M. P. Sheetz, Laser Tweezers in Cell Biology (Academic, New York, 1998).

Traditional aberration theory shows that spherical aberration is strongly dependent on the NA of an optical system. The longitudinal (also referred to as the axial) spherical aberration is proportional to NA2; whereas the spherical wave aberration is proportional to NA4. Optical tweezers, which utilize high-NA objectives to produce rays with large angles, are therefore particularly susceptible to this effect.

There are also objectives that have provisions for adjustment of the spherical-aberration-free depth. However, such objectives are often costly and complicated and are therefore not common for optical tweezers applications. In addition, they contain a significant number of lenses, which also makes them less suitable for optical trapping.

E. Fällman, O. Axner are preparing the following paper for publication: “Comparison of on-axis trapping of optical traps under the influence of spherical aberration by objectives that adhere to the sin and tan conditions.”

E. Fällman, O. Axner are preparing the following paper for publication: “The influence of a cover glass surface on the trapping of spherical objects by optical tweezers—The off-axis case.”

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration of the propagation of light in an optical tweezers system including a glass-water interface. (a) Unrefracted ray fan (originating from a system with a homogeneous index of refraction in which n = n g = n o ) overlaid upon a refracted ray fan experiencing spherical aberration (corresponding to a situation in which the object is placed in water, i.e., n = n w < n g ). (b) Schematic showing how the angle of an incident ray and a bead is found. See text for definitions. The incoming ray is marked Ray.

Fig. 2
Fig. 2

Total restoring force Q as a function of bead position z b given in units of the bead radius r b . (a), (c) Situation for an objective with a NA of 1.0; (b), (d) objective with a NA of 1.35. (a) (b) Laser beam with a Gaussian intensity distribution with ς = 1; (c), (d) laser beam with a top-hat intensity distribution (technically a laser beam with ς = 100). Curves a, b, c, d, e, f, g, h, i, j, and k in each figure correspond to cover glass positions, z cg, of 0, -r b , -2r b , -3r b , -4r b , -5r b , -6r b , -7r b , -8r b , -9r b , and -10r b , respectively.

Fig. 3
Fig. 3

Escape forces as a function of position of cover glass z cg. In (a)–(d) the four uppermost curves (a–d, left axis) represent the escape force in the positive z direction, i.e., Q esc +, whereas the four lowermost curves (e–h, right axis) correspond to the escape force in the reverse direction, i.e., Q esc -. (a), (b), (c), (d) Degrees of overfilling of 0.67, 1.0, 1.5, and 100, respectively. The four curves in each set (a, b, c, and d and e, f, g, and h) correspond to NAs of 1.0, 1.2, 1.25, and 1.35, respectively.

Fig. 4
Fig. 4

Trapping position z t as a function of the position of the cover glass. (a), (b), (c), (d) Degrees of overfilling of 0.67, 1.0, 1.5, and 100, respectively. In (a)–(d) the four curves (a, b, c, and d) correspond to NAs 1.0, 1.2, 1.25, and 1.35, respectively.

Fig. 5
Fig. 5

Stiffness of the trap k at the trapping position as a function of cover glass position, z cg. Curves a and b correspond to an objective with a NA of 1; curves c and d represent an objective with a NA of 1.25; Curves e and f correspond to an objective with a NA of 1.35. Curves a, c, and e represent a degree of overfilling of 1.0; curves b, d, and f correspond to a top-hat intensity distribution (ς = 100).

Fig. 6
Fig. 6

Multiple reflections and transmissions of a ray entering a sphere at an angle θ. One part of the ray will be reflected at the first surface, PR. The transmitted ray will give rise to a multitude of (an infinite number of) refracted rays PTin T ext R, where T is the transmission coefficient and R is the reflection coefficient.

Tables (1)

Tables Icon

Table 1 Parameter Values for Parameterization of the Escape Force in the Positive z Direction According to Eqs. (5) and (6) for a Microscopic-Sized Bead Trapped in an Optical Trap by an Oil-Immersion Objective Adhering to the sine Condition, Fully Corrected for Spherical Aberrations at the Glass-Liquid Media Interface

Equations (17)

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

Iρ=I0 exp-2ρ2/ω02ρρp0ρ>ρp,
Fz=QznPc,
Qesc+=-minQz  z>zt.
Qesc-=-maxQz  z<zt,
Qesc+zcg, NA, σ=c0NA, ς11+c1NA, ςzcg+c2NA, ςzcg2,
ciNA, ς=ci00ci10ci20ci01ci11ci21ci02ci12ci22×1N.A.-1.2N.A.-1.22T1ς-1ς-2,
Δzpar=1-nwngzcg=0.13zcg,
Δzmarg=1-nwng1-NAnw21-NAng2 zcg for NAnwzcg for NAnw.
k=dFdz
Qs=1+R cos2θ-T2cos2θ-2r+R cos2θ1+R2+2R cos2r,
Qg=R sin2θ-T2sin2θ-2r+R cos2θ1+R2+2R cos2r,
nb sinr=nw sinθ,
η=ρρp.
sinθ=zb-Δzrbsinϕ,
Δz=zcg1-nwng1-η2NAnw21-η2NAng21/2.
sinϕ=NAnw η.
θ=arcsinzbrb-zcgrb1-nwng1-η2NAnw21-η2NAng21/2×NAnw η.

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