Abstract

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

© 2012 OSA

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2011 (5)

J. Mas, A. Farré, C. López-Quesada, X. Fernández, E. Martín-Badosa, and M. Montes-Usategui, “Measuring stall forces in vivo with optical tweezers through light momentum changes,” Proc. SPIE 8097, 809726, 809726-10 (2011).
[CrossRef]

I. Verdeny, A.-S. Fontaine, A. Farré, M. Montes-Usategui, and E. Martín-Badosa, “Heating effects on NG108 cells induced by laser trapping,” Proc. SPIE 8097, 809724, 809724-12 (2011).
[CrossRef]

M. Jahnel, M. Behrndt, A. Jannasch, E. Schäffer, and S. W. Grill, “Measuring the complete force field of an optical trap,” Opt. Lett. 36(7), 1260–1262 (2011).
[CrossRef] [PubMed]

M. Mahamdeh, C. P. Campos, and E. Schäffer, “Under-filling trapping objectives optimizes the use of the available laser power in optical tweezers,” Opt. Express 19(12), 11759–11768 (2011).
[CrossRef] [PubMed]

T. Godazgar, R. Shokri, and S. N. S. Reihani, “Potential mapping of optical tweezers,” Opt. Lett. 36(16), 3284–3286 (2011).
[CrossRef] [PubMed]

2010 (3)

A. Farré and M. Montes-Usategui, “A force detection technique for single-beam optical traps based on direct measurement of light momentum changes,” Opt. Express 18(11), 11955–11968 (2010).
[CrossRef] [PubMed]

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17(12), 1422–1430 (2010).
[CrossRef] [PubMed]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[CrossRef]

2009 (1)

M. P. Landry, P. M. McCall, Z. Qi, and Y. R. Chemla, “Characterization of photoactivated singlet oxygen damage in single-molecule optical trap experiments,” Biophys. J. 97(8), 2128–2136 (2009).
[CrossRef] [PubMed]

2008 (1)

S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum. 79(10), 106101 (2008).
[CrossRef] [PubMed]

2007 (3)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9(8), S196–S203 (2007).
[CrossRef]

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2(12), 3226–3238 (2007).
[CrossRef] [PubMed]

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23(7), 3654–3665 (2007).
[CrossRef] [PubMed]

2006 (2)

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[CrossRef] [PubMed]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45(18), 4263–4269 (2006).
[CrossRef] [PubMed]

2004 (3)

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

I.-M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159(3), 225–240 (2004).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef] [PubMed]

2003 (4)

S. P. Gross, “Application of optical traps in vivo,” Methods Enzymol. 361, 162–174 (2003).
[CrossRef] [PubMed]

S. B. Smith, Y. Cui, and C. Bustamante, “Optical-trap force transducer that operates by direct measurement of light momentum,” Methods Enzymol. 361, 134–162 (2003).
[CrossRef] [PubMed]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, “Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture,” Opt. Lett. 28(6), 411–413 (2003).
[CrossRef] [PubMed]

K. Berg-Sørensen, L. Oddershede, E.-L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93(6), 3167–3176 (2003).
[CrossRef]

2002 (4)

W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73(6), 2308–2316 (2002).
[CrossRef]

P. Bartlett and S. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14(33), 7757–7768 (2002).
[CrossRef]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[CrossRef] [PubMed]

A. Rohrbach and E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002).
[CrossRef]

2001 (1)

1999 (2)

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, “Characterization of photodamage to Escherichia coli in optical traps,” Biophys. J. 77(5), 2856–2863 (1999).
[CrossRef] [PubMed]

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[CrossRef] [PubMed]

1998 (1)

1996 (2)

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[CrossRef] [PubMed]

1994 (4)

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65(9), 2762–2768 (1994).
[CrossRef]

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368(6467), 113–119 (1994).
[CrossRef] [PubMed]

K. Svoboda and S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77(5), 773–784 (1994).
[CrossRef] [PubMed]

1993 (6)

S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260(5105), 232–234 (1993).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993).
[CrossRef]

L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. 18(19), 1678–1680 (1993).
[CrossRef] [PubMed]

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[CrossRef]

C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40(8), 1631–1651 (1993).
[CrossRef]

1992 (2)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

S. Kamimura and R. Kamiya, “High-frequency vibration in flagellar axonemes with amplitudes reflecting the size of tubulin,” J. Cell Biol. 116(6), 1443–1454 (1992).
[CrossRef] [PubMed]

1990 (1)

1986 (1)

1977 (1)

1971 (1)

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[CrossRef]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Asbury, C. L.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

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(5), 288–290 (1986).
[CrossRef] [PubMed]

Bartlett, P.

P. Bartlett and S. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14(33), 7757–7768 (2002).
[CrossRef]

Behrndt, M.

Bergman, K.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, “Characterization of photodamage to Escherichia coli in optical traps,” Biophys. J. 77(5), 2856–2863 (1999).
[CrossRef] [PubMed]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

I.-M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159(3), 225–240 (2004).
[CrossRef]

K. Berg-Sørensen, L. Oddershede, E.-L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93(6), 3167–3176 (2003).
[CrossRef]

Berns, M. W.

W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef] [PubMed]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[CrossRef] [PubMed]

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, “Characterization of photodamage to Escherichia coli in optical traps,” Biophys. J. 77(5), 2856–2863 (1999).
[CrossRef] [PubMed]

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J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17(12), 1422–1430 (2010).
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J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17(12), 1422–1430 (2010).
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J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17(12), 1422–1430 (2010).
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K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, “Characterization of photodamage to Escherichia coli in optical traps,” Biophys. J. 77(5), 2856–2863 (1999).
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T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9(8), S196–S203 (2007).
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J. Mas, A. Farré, C. López-Quesada, X. Fernández, E. Martín-Badosa, and M. Montes-Usategui, “Measuring stall forces in vivo with optical tweezers through light momentum changes,” Proc. SPIE 8097, 809726, 809726-10 (2011).
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Maia Neto, P. A.

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W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2(12), 3226–3238 (2007).
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J. Mas, A. Farré, C. López-Quesada, X. Fernández, E. Martín-Badosa, and M. Montes-Usategui, “Measuring stall forces in vivo with optical tweezers through light momentum changes,” Proc. SPIE 8097, 809726, 809726-10 (2011).
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J. Mas, A. Farré, C. López-Quesada, X. Fernández, E. Martín-Badosa, and M. Montes-Usategui, “Measuring stall forces in vivo with optical tweezers through light momentum changes,” Proc. SPIE 8097, 809726, 809726-10 (2011).
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T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
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M. P. Landry, P. M. McCall, Z. Qi, and Y. R. Chemla, “Characterization of photoactivated singlet oxygen damage in single-molecule optical trap experiments,” Biophys. J. 97(8), 2128–2136 (2009).
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Metzger, N. K.

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2(12), 3226–3238 (2007).
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J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
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J. Mas, A. Farré, C. López-Quesada, X. Fernández, E. Martín-Badosa, and M. Montes-Usategui, “Measuring stall forces in vivo with optical tweezers through light momentum changes,” Proc. SPIE 8097, 809726, 809726-10 (2011).
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E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23(7), 3654–3665 (2007).
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K. Berg-Sørensen, L. Oddershede, E.-L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93(6), 3167–3176 (2003).
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K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
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T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9(8), S196–S203 (2007).
[CrossRef]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[CrossRef] [PubMed]

K. Svoboda and S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77(5), 773–784 (1994).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[CrossRef] [PubMed]

Switz, N. A.

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65(9), 2762–2768 (1994).
[CrossRef]

Tolic-Nørrelykke, I.-M.

I.-M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159(3), 225–240 (2004).
[CrossRef]

Verdeny, I.

I. Verdeny, A.-S. Fontaine, A. Farré, M. Montes-Usategui, and E. Martín-Badosa, “Heating effects on NG108 cells induced by laser trapping,” Proc. SPIE 8097, 809724, 809724-12 (2011).
[CrossRef]

Viana, N. B.

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

Volpe, G.

S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum. 79(10), 106101 (2008).
[CrossRef] [PubMed]

von Bieren, K.

Webb, W. W.

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[CrossRef]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Wright, W. H.

W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993).
[CrossRef]

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

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[CrossRef] [PubMed]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993).
[CrossRef]

Biophys. J. (4)

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[CrossRef] [PubMed]

M. P. Landry, P. M. McCall, Z. Qi, and Y. R. Chemla, “Characterization of photoactivated singlet oxygen damage in single-molecule optical trap experiments,” Biophys. J. 97(8), 2128–2136 (2009).
[CrossRef] [PubMed]

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, “Characterization of photodamage to Escherichia coli in optical traps,” Biophys. J. 77(5), 2856–2863 (1999).
[CrossRef] [PubMed]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

Cell (1)

K. Svoboda and S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell 77(5), 773–784 (1994).
[CrossRef] [PubMed]

Comput. Phys. Commun. (1)

I.-M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159(3), 225–240 (2004).
[CrossRef]

IEEE J. Sel. Top. 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. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

J. Appl. Phys. (2)

A. Rohrbach and E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002).
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K. Berg-Sørensen, L. Oddershede, E.-L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys. 93(6), 3167–3176 (2003).
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J. Cell Biol. (1)

S. Kamimura and R. Kamiya, “High-frequency vibration in flagellar axonemes with amplitudes reflecting the size of tubulin,” J. Cell Biol. 116(6), 1443–1454 (1992).
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J. Microsc. (1)

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
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J. Mod. Opt. (1)

C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40(8), 1631–1651 (1993).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9(8), S196–S203 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. Condens. Matter (1)

P. Bartlett and S. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14(33), 7757–7768 (2002).
[CrossRef]

Langmuir (1)

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23(7), 3654–3665 (2007).
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Methods Enzymol. (2)

S. P. Gross, “Application of optical traps in vivo,” Methods Enzymol. 361, 162–174 (2003).
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S. B. Smith, Y. Cui, and C. Bustamante, “Optical-trap force transducer that operates by direct measurement of light momentum,” Methods Enzymol. 361, 134–162 (2003).
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Microsc. Res. Tech. (1)

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
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Nat. Photonics (1)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[CrossRef]

Nat. Protoc. (1)

W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc. 2(12), 3226–3238 (2007).
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Nat. Struct. Mol. Biol. (1)

J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol. 17(12), 1422–1430 (2010).
[CrossRef] [PubMed]

Nature (2)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368(6467), 113–119 (1994).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (6)

Proc. Natl. Acad. Sci. U.S.A. (1)

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[CrossRef]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Proc. SPIE (2)

J. Mas, A. Farré, C. López-Quesada, X. Fernández, E. Martín-Badosa, and M. Montes-Usategui, “Measuring stall forces in vivo with optical tweezers through light momentum changes,” Proc. SPIE 8097, 809726, 809726-10 (2011).
[CrossRef]

I. Verdeny, A.-S. Fontaine, A. Farré, M. Montes-Usategui, and E. Martín-Badosa, “Heating effects on NG108 cells induced by laser trapping,” Proc. SPIE 8097, 809724, 809724-12 (2011).
[CrossRef]

Rev. Sci. Instrum. (5)

S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum. 79(10), 106101 (2008).
[CrossRef] [PubMed]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef] [PubMed]

W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73(6), 2308–2316 (2002).
[CrossRef]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65(9), 2762–2768 (1994).
[CrossRef]

Science (2)

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[CrossRef] [PubMed]

S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260(5105), 232–234 (1993).
[CrossRef] [PubMed]

Other (3)

S. B. Smith, “Stretch transitions observed in single biopolymer molecules (DNA or protein) using laser tweezers,” Doctoral Thesis, University of Twente, The Netherlands (1998).

See Table 1 in: A. Wozniak, “Characterizing quantitative measurements of force and displacement with optical tweezers on the NanotrackerTM,” JPK Instruments Technical Report, http://www.jpk.com/optical-tweezers.233.en.html ; the product of stiffness and parameter β changes by a factor of more than two, for polystyrene beads between 100 nm and 4260 nm (similarly for silica beads, Table 2). Also, in Table 1 and Fig. 5 in: A. Buosciolo, G. Pesce, and A. Sasso, “New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers,” Opt. Commun. 230, 375–368 (2004), a factor of two or more is observed between the values of κ·β obtained for different positions of the trap. Finally, Fig. 9 in: M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002), shows a product factor κ·β that apparently changes more than sevenfold for beads between 500 and 5000 nm in size (position detection is through DIC interferometry).

T. Otaki, “Condenser lens system for use in a microscope,” US Patent no. 5657166 (1997).

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