Abstract

We demonstrate a fast and direct calibration method for systems using a single laser for optical tweezers and particle position detection. The method takes direct advantage of back-focal-plane interferometry measuring not an absolute but a differential position, i.e. the position of the trapped particle relative to the center of the optical tweezers. Therefore, a fast step-wise motion of the optical tweezers yields the impulse response of the trapped particle. Calibration parameters such as the detector’s spatial and temporal response and the spring constant of the optical tweezers then follow readily from fitting the measured impulse response.

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References

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  1. K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer- resolution position sensing,” IEEE J. Quantum Electron. 2, 1066–1076 (1996).
    [Crossref]
  2. F. Gittes and C. Schmidt “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
    [Crossref]
  3. K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
    [Crossref] [PubMed]
  4. K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
    [Crossref] [PubMed]
  5. Y. R. Chemla, “Revealing the base pair stepping dynamics of nucleic acid motor proteins with optical traps,” Phys. Chem. Chem. Phys. 12, 3080–3095 (2010).
    [Crossref] [PubMed]
  6. S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
    [Crossref]
  7. M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
    [Crossref] [PubMed]
  8. K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
    [Crossref]
  9. K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93, 3167–3176 (2003).
    [Crossref]
  10. K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594–612 (2004).
    [Crossref]
  11. P. M. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, “tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers,” Comput. Phys. Commun. 175, 572–573 (2006).
    [Crossref]

2010 (1)

Y. R. Chemla, “Revealing the base pair stepping dynamics of nucleic acid motor proteins with optical traps,” Phys. Chem. Chem. Phys. 12, 3080–3095 (2010).
[Crossref] [PubMed]

2008 (1)

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref] [PubMed]

2006 (3)

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

P. M. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, “tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers,” Comput. Phys. Commun. 175, 572–573 (2006).
[Crossref]

2004 (1)

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

2003 (1)

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93, 3167–3176 (2003).
[Crossref]

1999 (1)

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

1998 (2)

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

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

1996 (1)

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer- resolution position sensing,” IEEE J. Quantum Electron. 2, 1066–1076 (1996).
[Crossref]

Allersma, M. W.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Berg-Sørensen, K.

P. M. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, “tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers,” Comput. Phys. Commun. 175, 572–573 (2006).
[Crossref]

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

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93, 3167–3176 (2003).
[Crossref]

Block, S. M.

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer- resolution position sensing,” IEEE J. Quantum Electron. 2, 1066–1076 (1996).
[Crossref]

Chemla, Y. R.

Y. R. Chemla, “Revealing the base pair stepping dynamics of nucleic acid motor proteins with optical traps,” Phys. Chem. Chem. Phys. 12, 3080–3095 (2010).
[Crossref] [PubMed]

deCastro, M. J.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Florin, E. L.

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93, 3167–3176 (2003).
[Crossref]

Flyvbjerg, H.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

P. M. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, “tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers,” Comput. Phys. Commun. 175, 572–573 (2006).
[Crossref]

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

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93, 3167–3176 (2003).
[Crossref]

Gittes, F.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

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

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer- resolution position sensing,” IEEE J. Quantum Electron. 2, 1066–1076 (1996).
[Crossref]

Hansen, P. M.

P. M. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, “tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers,” Comput. Phys. Commun. 175, 572–573 (2006).
[Crossref]

Howard, J.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

Jülicher, F.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

Nagy, A.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref] [PubMed]

Neuman, K. C.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref] [PubMed]

Oddershede, L. B.

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93, 3167–3176 (2003).
[Crossref]

Pavone, F. S.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

Peterman, E.

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

Schäffer, E.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

Schmidt, C.

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

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

Schmidt, C. F.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Schnitzer, M. J.

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

Stewart, R. J.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Stienen, G.

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

Tolic-Nørrelykke, I.

P. M. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, “tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers,” Comput. Phys. Commun. 175, 572–573 (2006).
[Crossref]

Tolic-Nørrelykke, S. F.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

van Mameren, J.

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

Vermeulen, K.

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

Visscher, K.

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer- resolution position sensing,” IEEE J. Quantum Electron. 2, 1066–1076 (1996).
[Crossref]

Wuite, G.

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

Biophys. J. (1)

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Comput. Phys. Commun. (1)

P. M. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, “tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers,” Comput. Phys. Commun. 175, 572–573 (2006).
[Crossref]

IEEE J. Quantum Electron. (1)

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer- resolution position sensing,” IEEE J. Quantum Electron. 2, 1066–1076 (1996).
[Crossref]

J. Appl. Phys. (1)

K. Berg-Sørensen, L. B. Oddershede, E. L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93, 3167–3176 (2003).
[Crossref]

Nat. Methods (1)

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref] [PubMed]

Nature (1)

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (1)

Y. R. Chemla, “Revealing the base pair stepping dynamics of nucleic acid motor proteins with optical traps,” Phys. Chem. Chem. Phys. 12, 3080–3095 (2010).
[Crossref] [PubMed]

Rev. Sci. Instrum. (3)

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg,“Calibration of optical tweezers with positional detection in the back focal plane” Rev. Sci. Instrum. 77, 103101–11 (2006).
[Crossref]

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

K. Vermeulen, J. van Mameren, G. Stienen, E. Peterman, G. Wuite, and C. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77, 013704 (2006).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Experimental set-up. Dashed lines represent the conjugated planes at the center of the AOD and on the QPD. A cover glass and a photodiode (PD) were used to probe the laser power before the objective in order to keep it constant via the feedback board. Focal lengths are (in mm) 175, 500, 50, 50, 300, 300 and 40 for L1 to 7.

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Fig. 2
Fig. 2

Computed displacement in dimensionless units of a trapped silica bead of diameter 1 μm. Displacement of 77 nm of the trap was repeated 100 times and QPD signal (blue circles) was averaged before being fitted by Eq. (3) (red line). The inset shows the whole acquired signal and the main graph shows a zoom of the second peak fitted with Eq. (3). The averages of the fitting parameters for the two peaks give a detector calibration of 0.515 pm−1, a cutoff frequency of the trap of 302 Hz, a fraction of instantaneous response of the QPD of α = 0.36, and a cutoff frequency for the QPD of 6341 Hz (indeed 100 times lower than the AOD bandwidth and 10 times lower than the sampling rate).

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Fig. 3
Fig. 3

Linearity of detector response. Blue circles represent the experimental data and the red line the fit of the linear region of the trap. Experimental data show a linear range of the detector response of ±150 nm with a slope of 0.324 ±2.10−3 nm−1 and an intersection with the vertical axis at 0.3 ±0.2 (dimensionless).

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Equations (3)

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X ( t ) = X 0 e − t / t b
g ( t ) = α δ ( t ) + ( 1 − α ) 1 t d e − t / t d
S ( t ) = ∫ 0 t X ( t ) g ( t − t ′ ) d t = X 0 α e − t / t b + X 0 ( 1 − α ) t b t b − t d ( e − t / t b − e − t / t d )

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