Abstract

Despite the tremendous success of force-measuring optical traps in recent years, the calibration methods most commonly used in the field have been plagued with difficulties and limitations. Force sensing based on direct measurement of light momentum changes stands out among these as an exception. Especially significant is this method’s potential for working within living cells, with non-spherical particles or with non-Gaussian beams. However, so far, the technique has only been implemented in counter-propagating dual-beam traps, which are difficult to align and integrate with other microscopy techniques. Here, we show the feasibility of a single-beam gradient-trap system working with a force detection technique based on this same principle.

© 2010 OSA

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2010 (1)

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-So̸rensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010), http://rsi.aip.org/rsinak/v81/i1/p015103_s1 .
[CrossRef] [PubMed]

2009 (2)

P. A. Sims and X. S. Xie, “Probing dynein and kinesin stepping with mechanical manipulation in a living cell,” ChemPhysChem 10(9-10), 1511–1516 (2009), http://www3.interscience.wiley.com/journal/122440825/abstract .
[CrossRef] [PubMed]

F. Czerwinski, A. C. Richardson, and L. B. Oddershede, “Quantifying noise in optical tweezers by allan variance,” Opt. Express 17(15), 13255–13269 (2009), http://www.opticsinfobase.org/VJBO/abstract.cfm?URI=oe-17-15-13255 .
[CrossRef] [PubMed]

2007 (3)

M. Fischer and K. Berg-Sorensen, “Calibration of trapping force and response function of optical tweezers in viscoelastic media,” J. Opt. A, Pure Appl. Opt. 9(8), S239–S250 (2007), http://iopscience.iop.org/1464-4258/9/8/S18/pdf?ejredirect=.iopscience .
[CrossRef]

M. Capitanio, D. Maggi, F. Vanzi, and F. S. Pavone, “FIONA in the trap: the advantages of combining optical tweezers and fluorescence,” J. Opt. A, Pure Appl. Opt. 9(8), S157–S163 (2007), http://iopscience.iop.org/1464-4258/9/8/S07/?ejredirect=.iopscience .
[CrossRef]

D. C. Appleyard, K. Y. Vandermeulen, H. Lee, and M. J. Lang, “Optical trapping for undergraduates,” Am. J. Phys. 75(1), 5–14 (2007), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000075000001000005000001&idtype=cvips&gifs=yes .
[CrossRef]

2006 (4)

J. P. Rickgauer, D. N. Fuller, and D. E. Smith, “DNA as a metrology standard for length and force measurements with optical tweezers,” Biophys. J. 91(11), 4253–4257 (2006), http://www.cell.com/biophysj/retrieve/pii/S0006349506721397 .
[CrossRef] [PubMed]

S. F. Tolić-No̸rrelykke, 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(10), 103101 (2006), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000077000010103101000001&idtype=cvips&gifs=yes .
[CrossRef]

F. Merenda, G. Boer, J. Rohner, G. Delacrétaz, and R.-P. Salathé, “Escape trajectories of single-beam optically trapped micro-particles in a transverse fluid flow,” Opt. Express 14(4), 1685–1699 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-4-1685 .
[CrossRef] [PubMed]

P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, “Interferometric tracking of optically trapped probes behind structured surfaces: A phase correction method,” Appl. Opt. 45(28), 7309–7315 (2006), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-45-28-7309 .
[CrossRef] [PubMed]

2005 (1)

2004 (4)

M. Yanai, J. P. Butler, T. Suzuki, H. Sasaki, and H. Higuchi, “Regional rheological differences in locomoting neutrophils,” Am. J. Physiol. Cell Physiol. 287(3), C603–C611 (2004), http://ajpcell.physiology.org/cgi/content/abstract/287/3/C603 .
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical “cogwheel” tweezers,” Opt. Express 12(17), 4129–4135 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-17-4129 .
[CrossRef] [PubMed]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000075000003000594000001&idtype=cvips&gifs=yes .
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000075000009002787000001&idtype=cvips&gifs=yes .
[CrossRef]

2003 (4)

M. J. Lang and S. M. Block, “Resource Letter: LBOT-1: Laser-based optical tweezers,” Am. J. Phys. 71(3), 201–215 (2003), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000071000003000201000001&idtype=cvips&gifs=yes .
[CrossRef] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003), http://www.nature.com/nphoton/journal/vsample/nsample/full/nature01935.html .
[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), http://jap.aip.org/japiau/v93/i6/p3167_s1 .
[CrossRef]

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]

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), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000073000006002308000001&idtype=cvips&gifs=yes .
[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), http://iopscience.iop.org/0953-8984/14/33/314/?ejredirect=.iopscience .
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JAPIAU000091000008005474000001&idtype=cvips&gifs=yes .
[CrossRef]

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(4), 1687–1696 (2002), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000073000004001687000001&idtype=cvips&gifs=yes .
[CrossRef]

2001 (1)

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight ϕ29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001), http://www.nature.com/nature/journal/v413/n6857/abs/413748a0.html .
[CrossRef] [PubMed]

2000 (1)

S. C. Kuo and J. L. McGrath, “Steps and fluctuations of Listeria monocytogenes during actin-based motility,” Nature 407(6807), 1026–1029 (2000), http://www.nature.com/nature/journal/v407/n6807/abs/4071026a0.html .
[CrossRef] [PubMed]

1998 (2)

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998), http://www.springerlink.com/content/6x7wx7l2fqrfrhn5 .
[CrossRef]

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (1998), http://www.opticsinfobase.org/DirectPDFAccess/7463924C-BDB9-137E-CFB95A10D3C1858A_36510.pdf?da=1&id=36510&seq=0 .
[CrossRef]

1996 (3)

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), http://www.sciencemag.org/cgi/content/abstract/271/5250/795 .
[CrossRef] [PubMed]

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), http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=577338&tag=1 .
[CrossRef]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[CrossRef]

1994 (1)

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), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000065000009002762000001&idtype=cvips&gifs=yes .
[CrossRef]

1993 (3)

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), http://www.nature.com/nature/journal/v365/n6448/abs/365721a0.html .
[CrossRef] [PubMed]

L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. 18(19), 1678–1680 (1993), http://www.opticsinfobase.org/DirectPDFAccess/74525E7B-BDB9-137E-C5E24E3A219D736D_11961.pdf?da=1&id=11961&seq=0 .
[CrossRef] [PubMed]

C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40(8), 1631–1651 (1993), http://www.informaworld.com/smpp/content~db=all~content=a713823939 .
[CrossRef]

1992 (1)

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), http://www.cell.com/biophysj/retrieve/pii/S000634959281860X .
[CrossRef] [PubMed]

1990 (2)

W. Denk and W. W. Webb, “Optical measurement of picometer displacements of transparent microscopic objects,” Appl. Opt. 29(16), 2382–2391 (1990), http://www.opticsinfobase.org/DirectPDFAccess/7459B57C-BDB9-137E-CF84DFA116D13FB7_38312.pdf?da=1&id=38312&seq=0 .
[CrossRef] [PubMed]

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348(6299), 346–348 (1990), http://www.nature.com/nature/journal/v348/n6299/abs/348346a0.html .
[CrossRef] [PubMed]

1986 (1)

1971 (1)

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970), http://prola.aps.org/abstract/PRL/v24/i4/p156_1 .
[CrossRef]

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M. Yanai, J. P. Butler, T. Suzuki, H. Sasaki, and H. Higuchi, “Regional rheological differences in locomoting neutrophils,” Am. J. Physiol. Cell Physiol. 287(3), C603–C611 (2004), http://ajpcell.physiology.org/cgi/content/abstract/287/3/C603 .
[CrossRef] [PubMed]

Schäffer, E.

S. F. Tolić-No̸rrelykke, 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(10), 103101 (2006), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000077000010103101000001&idtype=cvips&gifs=yes .
[CrossRef]

Schliwa, M.

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348(6299), 346–348 (1990), http://www.nature.com/nature/journal/v348/n6299/abs/348346a0.html .
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F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (1998), http://www.opticsinfobase.org/DirectPDFAccess/7463924C-BDB9-137E-CFB95A10D3C1858A_36510.pdf?da=1&id=36510&seq=0 .
[CrossRef]

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), http://www.nature.com/nature/journal/v365/n6448/abs/365721a0.html .
[CrossRef] [PubMed]

Schnapp, B. J.

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), http://www.nature.com/nature/journal/v365/n6448/abs/365721a0.html .
[CrossRef] [PubMed]

Schütze, K.

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348(6299), 346–348 (1990), http://www.nature.com/nature/journal/v348/n6299/abs/348346a0.html .
[CrossRef] [PubMed]

Seitz, P. C.

Sheppard, C. J. R.

C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40(8), 1631–1651 (1993), http://www.informaworld.com/smpp/content~db=all~content=a713823939 .
[CrossRef]

Sims, P. A.

P. A. Sims and X. S. Xie, “Probing dynein and kinesin stepping with mechanical manipulation in a living cell,” ChemPhysChem 10(9-10), 1511–1516 (2009), http://www3.interscience.wiley.com/journal/122440825/abstract .
[CrossRef] [PubMed]

Smith, D. E.

J. P. Rickgauer, D. N. Fuller, and D. E. Smith, “DNA as a metrology standard for length and force measurements with optical tweezers,” Biophys. J. 91(11), 4253–4257 (2006), http://www.cell.com/biophysj/retrieve/pii/S0006349506721397 .
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Smith, S. B.

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]

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight ϕ29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001), http://www.nature.com/nature/journal/v413/n6857/abs/413748a0.html .
[CrossRef] [PubMed]

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), http://www.sciencemag.org/cgi/content/abstract/271/5250/795 .
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P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, “Interferometric tracking of optically trapped probes behind structured surfaces: A phase correction method,” Appl. Opt. 45(28), 7309–7315 (2006), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-45-28-7309 .
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E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998), http://www.springerlink.com/content/6x7wx7l2fqrfrhn5 .
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Suzuki, T.

M. Yanai, J. P. Butler, T. Suzuki, H. Sasaki, and H. Higuchi, “Regional rheological differences in locomoting neutrophils,” Am. J. Physiol. Cell Physiol. 287(3), C603–C611 (2004), http://ajpcell.physiology.org/cgi/content/abstract/287/3/C603 .
[CrossRef] [PubMed]

Svoboda, K.

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), http://www.nature.com/nature/journal/v365/n6448/abs/365721a0.html .
[CrossRef] [PubMed]

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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), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000065000009002762000001&idtype=cvips&gifs=yes .
[CrossRef]

Tans, S. J.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight ϕ29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001), http://www.nature.com/nature/journal/v413/n6857/abs/413748a0.html .
[CrossRef] [PubMed]

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S. F. Tolić-No̸rrelykke, 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(10), 103101 (2006), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK000077000010103101000001&idtype=cvips&gifs=yes .
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D. C. Appleyard, K. Y. Vandermeulen, H. Lee, and M. J. Lang, “Optical trapping for undergraduates,” Am. J. Phys. 75(1), 5–14 (2007), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000075000001000005000001&idtype=cvips&gifs=yes .
[CrossRef]

Vanzi, F.

M. Capitanio, D. Maggi, F. Vanzi, and F. S. Pavone, “FIONA in the trap: the advantages of combining optical tweezers and fluorescence,” J. Opt. A, Pure Appl. Opt. 9(8), S157–S163 (2007), http://iopscience.iop.org/1464-4258/9/8/S07/?ejredirect=.iopscience .
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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), http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=577338&tag=1 .
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von Bieren, K.

Webb, W. W.

Xie, X. S.

P. A. Sims and X. S. Xie, “Probing dynein and kinesin stepping with mechanical manipulation in a living cell,” ChemPhysChem 10(9-10), 1511–1516 (2009), http://www3.interscience.wiley.com/journal/122440825/abstract .
[CrossRef] [PubMed]

Yanai, M.

M. Yanai, J. P. Butler, T. Suzuki, H. Sasaki, and H. Higuchi, “Regional rheological differences in locomoting neutrophils,” Am. J. Physiol. Cell Physiol. 287(3), C603–C611 (2004), http://ajpcell.physiology.org/cgi/content/abstract/287/3/C603 .
[CrossRef] [PubMed]

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M. J. Lang and S. M. Block, “Resource Letter: LBOT-1: Laser-based optical tweezers,” Am. J. Phys. 71(3), 201–215 (2003), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000071000003000201000001&idtype=cvips&gifs=yes .
[CrossRef] [PubMed]

D. C. Appleyard, K. Y. Vandermeulen, H. Lee, and M. J. Lang, “Optical trapping for undergraduates,” Am. J. Phys. 75(1), 5–14 (2007), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000075000001000005000001&idtype=cvips&gifs=yes .
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Am. J. Physiol. Cell Physiol. (1)

M. Yanai, J. P. Butler, T. Suzuki, H. Sasaki, and H. Higuchi, “Regional rheological differences in locomoting neutrophils,” Am. J. Physiol. Cell Physiol. 287(3), C603–C611 (2004), http://ajpcell.physiology.org/cgi/content/abstract/287/3/C603 .
[CrossRef] [PubMed]

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Appl. Phys., A Mater. Sci. Process. (1)

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998), http://www.springerlink.com/content/6x7wx7l2fqrfrhn5 .
[CrossRef]

Biophys. J. (2)

J. P. Rickgauer, D. N. Fuller, and D. E. Smith, “DNA as a metrology standard for length and force measurements with optical tweezers,” Biophys. J. 91(11), 4253–4257 (2006), http://www.cell.com/biophysj/retrieve/pii/S0006349506721397 .
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[CrossRef] [PubMed]

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), http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=577338&tag=1 .
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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), http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JAPIAU000091000008005474000001&idtype=cvips&gifs=yes .
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C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40(8), 1631–1651 (1993), http://www.informaworld.com/smpp/content~db=all~content=a713823939 .
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

M. Fischer and K. Berg-Sorensen, “Calibration of trapping force and response function of optical tweezers in viscoelastic media,” J. Opt. A, Pure Appl. Opt. 9(8), S239–S250 (2007), http://iopscience.iop.org/1464-4258/9/8/S18/pdf?ejredirect=.iopscience .
[CrossRef]

M. Capitanio, D. Maggi, F. Vanzi, and F. S. Pavone, “FIONA in the trap: the advantages of combining optical tweezers and fluorescence,” J. Opt. A, Pure Appl. Opt. 9(8), S157–S163 (2007), http://iopscience.iop.org/1464-4258/9/8/S07/?ejredirect=.iopscience .
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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), http://iopscience.iop.org/0953-8984/14/33/314/?ejredirect=.iopscience .
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Methods Enzymol. (1)

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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S. C. Kuo and J. L. McGrath, “Steps and fluctuations of Listeria monocytogenes during actin-based motility,” Nature 407(6807), 1026–1029 (2000), http://www.nature.com/nature/journal/v407/n6807/abs/4071026a0.html .
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[CrossRef] [PubMed]

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight ϕ29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001), http://www.nature.com/nature/journal/v413/n6857/abs/413748a0.html .
[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), http://www.nature.com/nature/journal/v365/n6448/abs/365721a0.html .
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Supplementary Material (1)

» Media 1: MPG (3746 KB)     

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Figures (6)

Fig. 1
Fig. 1

Layout of the system: optical design. The optical train of an inverted microscope (Nikon, Eclipse TE-2000E) was used to both observe the samples and generate the optical traps. The force detection apparatus consists of a condenser lens, which collects the light from the trap, and a relay lens that simultaneously projects the light pattern at the back focal plane (BFP) of the condenser onto a position sensing detector (PSD) and a CCD camera. The latter was used to observe the structure and properties of the patterns projected onto the PSD.

Fig. 2
Fig. 2

(a) Image of the x-component of the electric field when a 1064-nm laser beam is focused by a 1.3-NA lens and is scattered by a 1-µm polystyrene sphere suspended in water. Light travels from left to right (Media 1). (b) Intensity distribution of light scattered by the bead. The results for three different positions of the trap are presented: centered with the bead, at half of the radius and at the edge of the bead. The forward-scattered light is contained in the region between −90° and 90°, as indicated on the plot by the shaded area. The amount of light in this region was computed for each curve.

Fig. 3
Fig. 3

(a) The field after the diffraction grating is composed of a discrete set of plane waves with amplitude (U)(kx,ky) and with the angle given by Eq. (5). Each of the waves is focused on a different position at the BFP of the condenser. (b) The focusing positions, r, depend strongly on the condition that the lens follows, that is, on the shape of the principal surface S. Adapted from Sheppard et al. [43]. (c) CCD image of the light pattern at the BFP of the condenser. The bright disk surrounding the spots corresponds to the light scattered within the grating substrate, which generates a disk at the BFP with an associated numerical aperture of 1.4. (d) Plotting of the positions of the spots in the plane as a function of G(θ), according to different conditions. The linear fitting at low angles provides the calibration of the plane.

Fig. 4
Fig. 4

Layout of the optical system between the spatial light modulator and the PSD (or CCD). The different elements at the conjugated planes of the PSD are indicated with solid arrows, and are visible with the CCD when the trapping laser passes through them. The correction hologram of the SLM, the phase plate of the objective, the annulus of the condenser and the aperture diaphragm of the microscope are shown.

Fig. 5
Fig. 5

(a) CCD image of the light pattern at the BFP of the condenser when a 1.2-NA objective focuses in a sample chamber filled with water. (b) If a particle interacts with the beam, the light changes its propagation direction. When this particle remains close to the microscope slide, the light within a cone of semi-angle α, very close to 90°, refracts within the capture angle of a high numerical aperture condenser (see text), which then collects all the forward-scattered light, since the acceptance angle, θ, of the lens is larger than the angle, β, of the refracted beam. (c) A 3-µm bead close to the upper surface of the chamber is trapped with the same objective.

Fig. 6
Fig. 6

(a) Temporal modulation of the hydrodynamic force applied to the trapped microspheres. (b) PSD signal obtained when dragging the bead with the fluid. (c) Comparison of the previous variables for different experimental conditions.

Equations (7)

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

u ( x 0 , y 0 , z ) = U ( k x , k y ) e i k r d k x d k y
r = f ' n sin θ = f ' p 0 p r = f ' k 0 k r
S x = ψ x R D I ( x , y ) d x d y
F x = p x ( x , y ) I ( x , y ) E dxdy = 1 f ' c x I ( x , y ) d x d y = R D ψ f ' c S x α S x
sin θ m = k r m k = 2 m π f 0 k
r m = f ' G ( θ m ) = f ' n sin θ m = f ' k 0 k r m = m λ φ f '
θ β n o i l sin θ n o i l sin β = n m sin α ~ n m N A c o n d e n s e r n m

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