Abstract

Axial and lateral optical-trapping forces on polystyrene and glass microbeads are measured as a function of sphere size and axial trapping position inside a specimen chamber containing water. A strong decrease of the light forces with increasing distance of the trapping position from the coverslip of the chamber is found. It is shown that beyond a certain maximal distance the trapping efficiency decreases substantially but trapping becomes possible in different, axial positions. We consider these effects to be accounted for by spherical aberration of the focused laser beam.

© 1995 Optical Society of America

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  1. 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] [PubMed]
  2. A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
    [CrossRef]
  3. 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]
  4. K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap II: Mie scatterers,” Optik 90, 57–60 (1992).
  5. J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
    [CrossRef]
  6. K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers,” Optik 89, 174–180 (1992).
  7. 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]
  8. A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
    [CrossRef]
  9. S. C. Kuo, M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
    [CrossRef] [PubMed]
  10. K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
    [CrossRef]
  11. J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature (London) 368, 113–119 (1994).
    [CrossRef]
  12. 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]
  13. H. Felgner, “Die LaserPinzette: Charakterisierung und Eichung der Lichtkräfte einer optischen Einstrahl-Falle im Lichtmikroskop,” M.S. thesis (Technische Universität München, Garching, Germany, 1993).
  14. C. W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik (Akademische Verlagsgesellschaft, Leipzig, 1927).
  15. J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics, 2nd ed. (Nordhoff, Groningen, 1973).
  16. K. Svoboda, S. M. Block, “Biological applications of optical forces,” Ann. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  18. H. E. Keller, “Objective lenses for confocal microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Plenum, New York, 1990), pp. 77–86.
    [CrossRef]
  19. C. J. R. Sheppard, M. Gu, K. Brain, H. Zhou, “Influence of spherical aberration on axial imaging of confocal reflection microscopy,” Appl. Opt. 33, 616–624 (1994).
    [CrossRef] [PubMed]

1994 (4)

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

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

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]

C. J. R. Sheppard, M. Gu, K. Brain, H. Zhou, “Influence of spherical aberration on axial imaging of confocal reflection microscopy,” Appl. Opt. 33, 616–624 (1994).
[CrossRef] [PubMed]

1993 (3)

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]

S. C. Kuo, 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, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

1992 (3)

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]

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap II: Mie scatterers,” Optik 90, 57–60 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers,” Optik 89, 174–180 (1992).

1990 (1)

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

1989 (1)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

1987 (1)

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef]

1986 (1)

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

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

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef]

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] [PubMed]

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

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.

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

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Brain, K.

Brakenhoff, G. J.

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap II: Mie scatterers,” Optik 90, 57–60 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers,” Optik 89, 174–180 (1992).

Brenner, H.

J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics, 2nd ed. (Nordhoff, Groningen, 1973).

Chu, S.

Dziedzic, J. M.

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

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef]

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] [PubMed]

Euteneuer, U.

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

Felgner, H.

H. Felgner, “Die LaserPinzette: Charakterisierung und Eichung der Lichtkräfte einer optischen Einstrahl-Falle im Lichtmikroskop,” M.S. thesis (Technische Universität München, Garching, Germany, 1993).

Finer, J. T.

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

Gu, M.

Happel, J.

J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics, 2nd ed. (Nordhoff, Groningen, 1973).

Keller, H. E.

H. E. Keller, “Objective lenses for confocal microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Plenum, New York, 1990), pp. 77–86.
[CrossRef]

Kuo, S. C.

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

Oseen, C. W.

C. W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik (Akademische Verlagsgesellschaft, Leipzig, 1927).

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Schliwa, M.

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

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Schütze, K.

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

Sheetz, M. P.

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

Sheppard, C. J. R.

Simmons, R. M.

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

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

Svoboda, K.

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

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Visscher, K.

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers,” Optik 89, 174–180 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap II: Mie scatterers,” Optik 90, 57–60 (1992).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

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]

Yamane, T.

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef]

Zhou, H.

Ann. Rev. Biophys. Biomol. Struct. (1)

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

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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. (1)

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]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Nature (London) (4)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

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

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

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef]

Opt. Lett. (1)

Optik (2)

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers,” Optik 89, 174–180 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap II: Mie scatterers,” Optik 90, 57–60 (1992).

Science (1)

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

Other (5)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

H. E. Keller, “Objective lenses for confocal microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Plenum, New York, 1990), pp. 77–86.
[CrossRef]

H. Felgner, “Die LaserPinzette: Charakterisierung und Eichung der Lichtkräfte einer optischen Einstrahl-Falle im Lichtmikroskop,” M.S. thesis (Technische Universität München, Garching, Germany, 1993).

C. W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik (Akademische Verlagsgesellschaft, Leipzig, 1927).

J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics, 2nd ed. (Nordhoff, Groningen, 1973).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the optical tweezers setup: m’s, mirrors; p’s, polarizing beam-splitter cubes; be, beam expander; dm, dichroic mirror; obj, objective. The dichroic mirror is used to reflect the infrared laser beam into the microscope objective and to transmit the image to the CCD camera. The camera is connected to an image-processing board, video recorder, and monitor. The motorized stage is driven by computer control.

Fig. 2
Fig. 2

Cut through the specimen chamber. Shown is a microsphere trapped in the focus of the laser beam. The whole sandwich, consisting of a microscope slide, suspending medium, and cover glass, can be translated along all three axes relative to the spatially fixed objective and trapped object with a stepping motor-driven microscope stage. The laser beam is depicted in a geometric optics model as being focused to an infinitely small spot at the trapping region. According to electromagnetic theory the beam is thought to exhibit a diffraction-limited beam waist of approximately λ/2. The immersion oil has roughly the same refractive index as the coverslip (optical matching), introducing no refraction at the boundary to the glass.

Fig. 3
Fig. 3

Maximal axial trapping efficiency (escape force) on glass beads as a function of their diameter d in water. A bead was trapped and moved to a distance of T = 9 μm from the coverslip, and then the laser power was reduced until the bead fell out of the trap. The acting force was estimated from the gravitational minus the buoyant force and corrected by an additional term 2kT/d to account for thermal forces. This procedure was repeated five times for each bead. The diameters were determined optically by comparison with a micrometer scale.

Fig. 4
Fig. 4

Maximal axial trapping efficiency on polystyrene and glass beads in water. The measurements were performed as described in Fig. 3 except that the beads were brought to different distances T from the coverslip before the laser power was reduced.

Fig. 5
Fig. 5

Maximal lateral trapping efficiency on the polystyrene beads of diameter d = 1.020 ± 0.004 μm in 60% glycerol. A bead was trapped and moved relative to the surrounding medium until it fell out. The measurement was repeated 30 times for every distance T from the coverslip. Glycerol was used to increase the viscosity. In that way sedimentation rates and acceleration distances are decreased, which facilitates experimentation.

Tables (1)

Tables Icon

Table 1 Axial and Lateral Trapping Efficiencies as a Function of Bead Diameter d

Equations (6)

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

F ax = π 6 ( ρ s - ρ m ) d 3 g ,
F ax = D z z = 2 k T d .
F la = 3 π η d v k ,
k = 1 + 9 d 32 ( 1 T - 1 H - T ) ,
k = 1 1 - 9 32 ( d T ) + 1 64 ( d T ) 3 - 45 4096 ( d T ) 4 - 1 512 ( d T ) 5 .
F = n m Q P c .

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