Abstract

We assess the performance of a CMOS camera for the measurement of particle position within optical tweezers and the associated autocorrelation function and power spectrum. Measurement of the displacement of the particle from the trap center can also be related to the applied force. By considering the Allan variance of these measurements, we show that such cameras are capable of reaching the thermal limits of nanometer and femtonewton accuracies, and hence are suitable for many of the applications that traditionally use quadrant photodiodes. As an example of a multi-particle measurement we show the hydrodynamic coupling between two particles.

© 2008 Optical Society of America

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  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. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
    [CrossRef]
  3. J.-C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended DNA molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
    [CrossRef] [PubMed]
  4. K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  5. M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
    [CrossRef] [PubMed]
  6. S. Keen, J. Leach, G. Gibson, and M. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A: Pure Appl. Opt. 9, S264-S266 (2007).
    [CrossRef]
  7. O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, "Optical tweezers with 2.5kHz bandwidth video detection for single-colloid electrophoresis," Rev. Sci. Instrum. 79, 023710 (2008).
    [CrossRef] [PubMed]
  8. D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
    [CrossRef]
  9. J. Leach, K. Wulff, G. Sinclair, P. Jordan, J. Courtial, L. Thomson, G. Gibson, K. Karunwi, J. Cooper, Z. J. Laczik, and M. Padgett, "Interactive approach to optical tweezers control," Appl. Opt. 45, 897-903 (2006).
    [CrossRef] [PubMed]
  10. G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
    [CrossRef]
  11. K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
    [CrossRef]
  12. J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," PNAS 103, 9006-9011 (2006).
    [CrossRef] [PubMed]
  13. M. Klein, M. Andersson, O. Axner, and E. F¨allman, "Dual-trap technique for reduction of low-frequency noise in force measuring optical tweezers," Appl. Opt. 46, 405-412 (2007).
    [CrossRef] [PubMed]
  14. M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instrum. 79, 043103 (2008).
    [CrossRef] [PubMed]
  15. J.-C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
    [CrossRef]
  16. C. D. Saunter, G. D. Love,M. Johns, and J. Holmes, "FGPA technology for high-speed, low-cost adaptive optics," vol. 6018 of 5th International Workshop on Adaptive Optics for Industry and Medicine (SPIE, 2005).
  17. R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
    [CrossRef]

2008

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, "Optical tweezers with 2.5kHz bandwidth video detection for single-colloid electrophoresis," Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instrum. 79, 043103 (2008).
[CrossRef] [PubMed]

2007

M. Klein, M. Andersson, O. Axner, and E. F¨allman, "Dual-trap technique for reduction of low-frequency noise in force measuring optical tweezers," Appl. Opt. 46, 405-412 (2007).
[CrossRef] [PubMed]

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

S. Keen, J. Leach, G. Gibson, and M. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A: Pure Appl. Opt. 9, S264-S266 (2007).
[CrossRef]

2006

M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
[CrossRef] [PubMed]

J. Leach, K. Wulff, G. Sinclair, P. Jordan, J. Courtial, L. Thomson, G. Gibson, K. Karunwi, J. Cooper, Z. J. Laczik, and M. Padgett, "Interactive approach to optical tweezers control," Appl. Opt. 45, 897-903 (2006).
[CrossRef] [PubMed]

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," PNAS 103, 9006-9011 (2006).
[CrossRef] [PubMed]

2004

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

2002

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

2000

J.-C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended DNA molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

1999

J.-C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

1986

1966

D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
[CrossRef]

Addas, K. M.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instrum. 79, 043103 (2008).
[CrossRef] [PubMed]

Allan, D. W.

D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
[CrossRef]

Andersson, M.

Ashkin, A.

Atakhorrami, M.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instrum. 79, 043103 (2008).
[CrossRef] [PubMed]

Axner, O.

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," PNAS 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Carberry, D. M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," PNAS 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Chu, S.

Cooper, J.

Courtial, J.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

J. Leach, K. Wulff, G. Sinclair, P. Jordan, J. Courtial, L. Thomson, G. Gibson, K. Karunwi, J. Cooper, Z. J. Laczik, and M. Padgett, "Interactive approach to optical tweezers control," Appl. Opt. 45, 897-903 (2006).
[CrossRef] [PubMed]

Di Leonardo, R.

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

Dziedzic, J. M.

F¨allman, E.

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Gibson, G.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

S. Keen, J. Leach, G. Gibson, and M. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A: Pure Appl. Opt. 9, S264-S266 (2007).
[CrossRef]

J. Leach, K. Wulff, G. Sinclair, P. Jordan, J. Courtial, L. Thomson, G. Gibson, K. Karunwi, J. Cooper, Z. J. Laczik, and M. Padgett, "Interactive approach to optical tweezers control," Appl. Opt. 45, 897-903 (2006).
[CrossRef] [PubMed]

Grier, D. G.

M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
[CrossRef] [PubMed]

Gutsche, C.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, "Optical tweezers with 2.5kHz bandwidth video detection for single-colloid electrophoresis," Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Izhaky, D.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," PNAS 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Jackson, J. C.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Jordan, P.

Karunwi, K.

Keen, S.

S. Keen, J. Leach, G. Gibson, and M. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A: Pure Appl. Opt. 9, S264-S266 (2007).
[CrossRef]

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

Keyser, U. F.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, "Optical tweezers with 2.5kHz bandwidth video detection for single-colloid electrophoresis," Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Klein, M.

Kremer, F.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, "Optical tweezers with 2.5kHz bandwidth video detection for single-colloid electrophoresis," Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Laczik, Z. J.

Leach, J.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

S. Keen, J. Leach, G. Gibson, and M. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A: Pure Appl. Opt. 9, S264-S266 (2007).
[CrossRef]

J. Leach, K. Wulff, G. Sinclair, P. Jordan, J. Courtial, L. Thomson, G. Gibson, K. Karunwi, J. Cooper, Z. J. Laczik, and M. Padgett, "Interactive approach to optical tweezers control," Appl. Opt. 45, 897-903 (2006).
[CrossRef] [PubMed]

Love, G. D.

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

Meiners, J.-C.

J.-C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended DNA molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

J.-C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

Miles, M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," PNAS 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Molloy, J. E.

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Neuman, K. C.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Otto, O.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, "Optical tweezers with 2.5kHz bandwidth video detection for single-colloid electrophoresis," Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Padgett, M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

S. Keen, J. Leach, G. Gibson, and M. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A: Pure Appl. Opt. 9, S264-S266 (2007).
[CrossRef]

J. Leach, K. Wulff, G. Sinclair, P. Jordan, J. Courtial, L. Thomson, G. Gibson, K. Karunwi, J. Cooper, Z. J. Laczik, and M. Padgett, "Interactive approach to optical tweezers control," Appl. Opt. 45, 897-903 (2006).
[CrossRef] [PubMed]

Padgett, M. J.

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Polin, M.

M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
[CrossRef] [PubMed]

Quake, S. R.

M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
[CrossRef] [PubMed]

J.-C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended DNA molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

J.-C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

Robert, D.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Ruocco, G.

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

Saunter, C. D.

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

Schmidt, C. F.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instrum. 79, 043103 (2008).
[CrossRef] [PubMed]

Sinclair, G.

Thomson, L.

Whyte, G.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Wulff, K.

Appl. Opt.

Contemp. Phys.

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, "Holographic assembly workstation for optical manipulation," J. Opt. A: Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

S. Keen, J. Leach, G. Gibson, and M. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A: Pure Appl. Opt. 9, S264-S266 (2007).
[CrossRef]

Opt. Lett.

Phys. Rev. E

R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, "Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring," Phys. Rev. E 76, 061402 (2007).
[CrossRef]

Phys. Rev. Lett.

J.-C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
[CrossRef] [PubMed]

J.-C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended DNA molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

PNAS

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," PNAS 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Proc. IEEE

D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE 54, 221-230 (1966).
[CrossRef]

Rev. Sci. Instrum.

M. Atakhorrami, K. M. Addas, and C. F. Schmidt, "Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk," Rev. Sci. Instrum. 79, 043103 (2008).
[CrossRef] [PubMed]

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, "Optical tweezers with 2.5kHz bandwidth video detection for single-colloid electrophoresis," Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Other

C. D. Saunter, G. D. Love,M. Johns, and J. Holmes, "FGPA technology for high-speed, low-cost adaptive optics," vol. 6018 of 5th International Workshop on Adaptive Optics for Industry and Medicine (SPIE, 2005).

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Figures (7)

Fig. 1.
Fig. 1.

The tweezers system is based around an inverted microscope. A titanium sapphire laser provides up to 1W @ 830nm, which is expanded to fill the aperture of an SLM. SLM control software allows the creation of multiple optical traps, coupled into the tweezers using a polarizing beamsplitter. The motion of trapped particles in the sample is analyzed using a CMOS camera.

Fig. 2.
Fig. 2.

Lateral displacement for a 2µm silica bead fixed to the coverslip and 2µm silica beads trapped with low and high laser power. Weak trap (7mW, κ=5.6E-6 N/m), strong trap (37mW, κ=2.3E-5 N/m).

Fig. 3.
Fig. 3.

Autocorrelation of position for a 2µm silica bead trapped with low and high laser power.

Fig. 4.
Fig. 4.

Power Spectra of position for a 2µm silica bead trapped with low and high laser power.

Fig. 5.
Fig. 5.

Stability of position measurements. Increasing the trap power results in a higher measurement precision. For the case of a single bead measurement, the optimum averaging time is in the range 1–10 seconds. The blue lines correspond to the single and differential measurements of two 2µm silica beads that were fixed to the microscope coverglass, having a separation comparable to the trapped beads. The thermal limit is estimated for the strongly trapped bead. Weak trap (7mW, κ=5.6E-6 N/m), strong trap (37mW, κ=2.3E-5 N/m).

Fig. 6.
Fig. 6.

Correlation graphs for two 2µm silica beads separated by 3µm. The traces were averaged over 30 sequential data sets, each consisting of 2 seconds continuous data.

Fig. 7.
Fig. 7.

Stability of force measurements. In contrast to the measurement of position, it is the weaker trap that results in a more precise measurement of force. As in the case of position measurement, the optimum measurement time is in the range 110 seconds. Weak trap (7mW, κ=5.6E-6 N/m), strong trap (37mW, κ=2.3E-5 N/m).

Equations (6)

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1 2 k B T = 1 2 κ x 2 .
f 0 = κ 2 π γ
σ x 2 ( τ ) = 1 2 ( x n + 1 x n ) 2
N Δ t 2 τ 0 = κ Δ t 2 γ
S E x = x 2 N 2 k B T γ κ 2 Δ t .
S E F = S E x κ 2 k B T γ Δ t .

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