Abstract

Optical traps have shown to be a flexible and powerful tool for 3D manipulations on the microscale. However, when it comes to sensitive measurements of particle displacements and forces thorough calibration procedures are required, which can be already demanding for trapped spheres. For asymmetric structures, with more complicated shapes, such as helical bacteria, novel calibration schemes need to be established. The paper describes different methods of how to extract various calibration parameters of a tiny helical bacterium, which is trapped and tracked in shape by scanning line optical tweezers. Tiny phase differences of the light scattered at each slope of the bacterium are measured by back focal plane interferometry, providing precise and high bandwidth information about fast deformations of the bacterium. A simplified theoretical model to estimate the optical forces on a chain like structure is presented. The methods presented here should be of interest to people that investigate optical trapping and tracking of asymmetric particles.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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  1. F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. G. Carmon, P. Kumar, and M. Feingold, “Optical tweezers assisted imaging of the Z-ring in Escherichia coli: measuring its radial width,” New J. Phys. 16(1), 013043 (2014).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  13. S. Trachtenberg and R. Gilad, “A bacterial linear motor: cellular and molecular organization of the contractile cytoskeleton of the helical bacterium Spiroplasma melliferum BC3,” Mol. Microbiol. 41(4), 827–848 (2001).
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    [Crossref]
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    [Crossref]
  20. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
    [Crossref] [PubMed]
  21. 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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    [Crossref]

2014 (2)

M. Grießhammer and A. Rohrbach, “5D-Tracking of a nanorod in a focused laser beam - a theoretical concept,” Opt. Express 22(5), 6114–6132 (2014).
[Crossref] [PubMed]

G. Carmon, P. Kumar, and M. Feingold, “Optical tweezers assisted imaging of the Z-ring in Escherichia coli: measuring its radial width,” New J. Phys. 16(1), 013043 (2014).
[Crossref]

2013 (1)

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

2012 (5)

B. Tränkle, M. Speidel, and A. Rohrbach, “Interaction dynamics of two colloids in a single optical potential,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021401 (2012).
[Crossref] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical Conveyors: A Class of Active Tractor Beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

M. Koch and A. Rohrbach, “Object-adapted optical trapping and shape-tracking of energy-switching helical bacteria,” Nat. Photonics 6(10), 680–686 (2012).
[Crossref]

L. Friedrich and A. Rohrbach, “Tuning the detection sensitivity: a model for axial backfocal plane interferometric tracking,” Opt. Lett. 37(11), 2109–2111 (2012).
[Crossref] [PubMed]

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

2011 (2)

2009 (1)

2007 (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]

2005 (1)

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, “Control of relative radiation pressure in optical traps: Application to phagocytic membrane binding studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 061927 (2005).
[Crossref] [PubMed]

2004 (3)

R. Nambiar, A. Gajraj, and J. C. Meiners, “All-optical constant-force laser tweezers,” Biophys. J. 87(3), 1972–1980 (2004).
[Crossref] [PubMed]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004).
[Crossref]

M. Brunner, J. Dobnikar, H. H. von Grünberg, and C. Bechinger, “Direct measurement of three-body interactions amongst charged colloids,” Phys. Rev. Lett. 92(7), 078301 (2004).
[Crossref] [PubMed]

2001 (1)

S. Trachtenberg and R. Gilad, “A bacterial linear motor: cellular and molecular organization of the contractile cytoskeleton of the helical bacterium Spiroplasma melliferum BC3,” Mol. Microbiol. 41(4), 827–848 (2001).
[Crossref] [PubMed]

1999 (2)

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]

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82(21), 4352–4355 (1999).
[Crossref]

1995 (2)

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic Forcing of a Brownian Particle,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5239–5250 (1995).
[Crossref] [PubMed]

L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, and A. J. Libchaber, “Optical thermal ratchet,” Phys. Rev. Lett. 74(9), 1504–1507 (1995).
[Crossref] [PubMed]

1994 (1)

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

Bechinger, C.

M. Brunner, J. Dobnikar, H. H. von Grünberg, and C. Bechinger, “Direct measurement of three-body interactions amongst charged colloids,” Phys. Rev. Lett. 92(7), 078301 (2004).
[Crossref] [PubMed]

Block, S. M.

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

Bourdieu, L. S.

L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, and A. J. Libchaber, “Optical thermal ratchet,” Phys. Rev. Lett. 74(9), 1504–1507 (1995).
[Crossref] [PubMed]

Bowman, R.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Branczyk, A. M.

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]

Brunner, M.

M. Brunner, J. Dobnikar, H. H. von Grünberg, and C. Bechinger, “Direct measurement of three-body interactions amongst charged colloids,” Phys. Rev. Lett. 92(7), 078301 (2004).
[Crossref] [PubMed]

Campos, C. P.

Carberry, D. M.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Carmon, G.

G. Carmon, P. Kumar, and M. Feingold, “Optical tweezers assisted imaging of the Z-ring in Escherichia coli: measuring its radial width,” New J. Phys. 16(1), 013043 (2014).
[Crossref]

Crocker, J. C.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82(21), 4352–4355 (1999).
[Crossref]

Demergis, V.

Dinsmore, A. D.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82(21), 4352–4355 (1999).
[Crossref]

Dobnikar, J.

M. Brunner, J. Dobnikar, H. H. von Grünberg, and C. Bechinger, “Direct measurement of three-body interactions amongst charged colloids,” Phys. Rev. Lett. 92(7), 078301 (2004).
[Crossref] [PubMed]

Faucheux, L. P.

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic Forcing of a Brownian Particle,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5239–5250 (1995).
[Crossref] [PubMed]

L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, and A. J. Libchaber, “Optical thermal ratchet,” Phys. Rev. Lett. 74(9), 1504–1507 (1995).
[Crossref] [PubMed]

Feingold, M.

G. Carmon, P. Kumar, and M. Feingold, “Optical tweezers assisted imaging of the Z-ring in Escherichia coli: measuring its radial width,” New J. Phys. 16(1), 013043 (2014).
[Crossref]

Florin, E. L.

V. Demergis and E. L. Florin, “High precision and continuous optical transport using a standing wave optical line trap,” Opt. Express 19(21), 20833–20848 (2011).
[Crossref] [PubMed]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004).
[Crossref]

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]

Friedrich, L.

Gajraj, A.

R. Nambiar, A. Gajraj, and J. C. Meiners, “All-optical constant-force laser tweezers,” Biophys. J. 87(3), 1972–1980 (2004).
[Crossref] [PubMed]

Gao, Q.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Gibson, G. M.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Gilad, R.

S. Trachtenberg and R. Gilad, “A bacterial linear motor: cellular and molecular organization of the contractile cytoskeleton of the helical bacterium Spiroplasma melliferum BC3,” Mol. Microbiol. 41(4), 827–848 (2001).
[Crossref] [PubMed]

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Optical Conveyors: A Class of Active Tractor Beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

Grießhammer, M.

Grieve, J. A.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Griffiths, G.

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, “Control of relative radiation pressure in optical traps: Application to phagocytic membrane binding studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 061927 (2005).
[Crossref] [PubMed]

Hanna, S.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Heckenberg, N. R.

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]

Hörber, J. K. H.

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]

Jagadish, C.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Kaplan, P. D.

L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, and A. J. Libchaber, “Optical thermal ratchet,” Phys. Rev. Lett. 74(9), 1504–1507 (1995).
[Crossref] [PubMed]

Knöner, G.

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]

Koch, M.

M. Koch and A. Rohrbach, “Object-adapted optical trapping and shape-tracking of energy-switching helical bacteria,” Nat. Photonics 6(10), 680–686 (2012).
[Crossref]

Kress, H.

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, “Control of relative radiation pressure in optical traps: Application to phagocytic membrane binding studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 061927 (2005).
[Crossref] [PubMed]

Kumar, P.

G. Carmon, P. Kumar, and M. Feingold, “Optical tweezers assisted imaging of the Z-ring in Escherichia coli: measuring its radial width,” New J. Phys. 16(1), 013043 (2014).
[Crossref]

Lee, W. M.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Libchaber, A.

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic Forcing of a Brownian Particle,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5239–5250 (1995).
[Crossref] [PubMed]

Libchaber, A. J.

L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, and A. J. Libchaber, “Optical thermal ratchet,” Phys. Rev. Lett. 74(9), 1504–1507 (1995).
[Crossref] [PubMed]

Loke, V. L. Y.

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]

Mahamdeh, M.

Matteo, J. A.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82(21), 4352–4355 (1999).
[Crossref]

McGloin, D.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Meiners, J. C.

R. Nambiar, A. Gajraj, and J. C. Meiners, “All-optical constant-force laser tweezers,” Biophys. J. 87(3), 1972–1980 (2004).
[Crossref] [PubMed]

Miles, M. J.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Nambiar, R.

R. Nambiar, A. Gajraj, and J. C. Meiners, “All-optical constant-force laser tweezers,” Biophys. J. 87(3), 1972–1980 (2004).
[Crossref] [PubMed]

Neumayer, D.

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004).
[Crossref]

Nieminen, T. A.

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]

Padgett, M. J.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Phillips, D. B.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Pralle, A.

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]

Prummer, M.

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]

Rarity, J. G.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Reece, P. J.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Rohrbach, A.

M. Grießhammer and A. Rohrbach, “5D-Tracking of a nanorod in a focused laser beam - a theoretical concept,” Opt. Express 22(5), 6114–6132 (2014).
[Crossref] [PubMed]

L. Friedrich and A. Rohrbach, “Tuning the detection sensitivity: a model for axial backfocal plane interferometric tracking,” Opt. Lett. 37(11), 2109–2111 (2012).
[Crossref] [PubMed]

M. Koch and A. Rohrbach, “Object-adapted optical trapping and shape-tracking of energy-switching helical bacteria,” Nat. Photonics 6(10), 680–686 (2012).
[Crossref]

B. Tränkle, M. Speidel, and A. Rohrbach, “Interaction dynamics of two colloids in a single optical potential,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021401 (2012).
[Crossref] [PubMed]

M. Speidel, L. Friedrich, and A. Rohrbach, “Interferometric 3D tracking of several particles in a scanning laser focus,” Opt. Express 17(2), 1003–1015 (2009).
[Crossref] [PubMed]

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, “Control of relative radiation pressure in optical traps: Application to phagocytic membrane binding studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 061927 (2005).
[Crossref] [PubMed]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004).
[Crossref]

Rubinsztein-Dunlop, H.

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]

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, “Optical Conveyors: A Class of Active Tractor Beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

Schäffer, E.

Simpson, S. H.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[Crossref]

Speidel, M.

B. Tränkle, M. Speidel, and A. Rohrbach, “Interaction dynamics of two colloids in a single optical potential,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021401 (2012).
[Crossref] [PubMed]

M. Speidel, L. Friedrich, and A. Rohrbach, “Interferometric 3D tracking of several particles in a scanning laser focus,” Opt. Express 17(2), 1003–1015 (2009).
[Crossref] [PubMed]

Stelzer, E. H. K.

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, “Control of relative radiation pressure in optical traps: Application to phagocytic membrane binding studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 061927 (2005).
[Crossref] [PubMed]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004).
[Crossref]

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]

Stilgoe, A. B.

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]

Stolovitzky, G.

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic Forcing of a Brownian Particle,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5239–5250 (1995).
[Crossref] [PubMed]

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]

Tan, H. H.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Tischer, C.

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004).
[Crossref]

Toe, W. J.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Trachtenberg, S.

S. Trachtenberg and R. Gilad, “A bacterial linear motor: cellular and molecular organization of the contractile cytoskeleton of the helical bacterium Spiroplasma melliferum BC3,” Mol. Microbiol. 41(4), 827–848 (2001).
[Crossref] [PubMed]

Tränkle, B.

B. Tränkle, M. Speidel, and A. Rohrbach, “Interaction dynamics of two colloids in a single optical potential,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021401 (2012).
[Crossref] [PubMed]

von Grünberg, H. H.

M. Brunner, J. Dobnikar, H. H. von Grünberg, and C. Bechinger, “Direct measurement of three-body interactions amongst charged colloids,” Phys. Rev. Lett. 92(7), 078301 (2004).
[Crossref] [PubMed]

Wang, F.

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Yodh, A. G.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82(21), 4352–4355 (1999).
[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]

Biophys. J. (1)

R. Nambiar, A. Gajraj, and J. C. Meiners, “All-optical constant-force laser tweezers,” Biophys. J. 87(3), 1972–1980 (2004).
[Crossref] [PubMed]

Europhys. Lett. (1)

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99(5), 58004 (2012).
[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]

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).
[Crossref] [PubMed]

Mol. Microbiol. (1)

S. Trachtenberg and R. Gilad, “A bacterial linear motor: cellular and molecular organization of the contractile cytoskeleton of the helical bacterium Spiroplasma melliferum BC3,” Mol. Microbiol. 41(4), 827–848 (2001).
[Crossref] [PubMed]

Nano Lett. (1)

F. Wang, W. J. Toe, W. M. Lee, D. McGloin, Q. Gao, H. H. Tan, C. Jagadish, and P. J. Reece, “Resolving Stable Axial Trapping Points of Nanowires in an Optical Tweezers Using Photoluminescence Mapping,” Nano Lett. 13(3), 1185–1191 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

M. Koch and A. Rohrbach, “Object-adapted optical trapping and shape-tracking of energy-switching helical bacteria,” Nat. Photonics 6(10), 680–686 (2012).
[Crossref]

New J. Phys. (1)

G. Carmon, P. Kumar, and M. Feingold, “Optical tweezers assisted imaging of the Z-ring in Escherichia coli: measuring its radial width,” New J. Phys. 16(1), 013043 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, “Control of relative radiation pressure in optical traps: Application to phagocytic membrane binding studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 061927 (2005).
[Crossref] [PubMed]

B. Tränkle, M. Speidel, and A. Rohrbach, “Interaction dynamics of two colloids in a single optical potential,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021401 (2012).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

L. P. Faucheux, G. Stolovitzky, and A. Libchaber, “Periodic Forcing of a Brownian Particle,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5239–5250 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

M. Brunner, J. Dobnikar, H. H. von Grünberg, and C. Bechinger, “Direct measurement of three-body interactions amongst charged colloids,” Phys. Rev. Lett. 92(7), 078301 (2004).
[Crossref] [PubMed]

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82(21), 4352–4355 (1999).
[Crossref]

D. B. Ruffner and D. G. Grier, “Optical Conveyors: A Class of Active Tractor Beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, and A. J. Libchaber, “Optical thermal ratchet,” Phys. Rev. Lett. 74(9), 1504–1507 (1995).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004).
[Crossref]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley, 1991).

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Figures (10)

Fig. 1
Fig. 1 Setup scheme for time multiplexed optical trapping and tracking. A 1064 nm laser passes an acousto optic deflector (AOD). The different diffraction orders are used for two independently steerable optical traps. Interference of light scattered at a trapped object with the unscattered light is analyzed by two quadrant photo diodes (QPDs). For further details see main text. A Köhler-illumination from the top is used to image the focal plane on a CCD with the aid of lens L7. Right inset: Brightfield image of a trapped bacterium with the optical line trap indicated by a red ellipse (reproduced from [14]). Scale bar: 1 µm. Left inset: (a) Axial signal from QPD2. (b) Different trap positions forming the time shared optical potential. A projection of the helical cell is shown in green together with the cell tube diameter d, the helical pitch p and the overall cell diameter D + d. (c) Distribution of incident intensity along the line trap. (d) Illustration of the coordinate system and vector definitions (reproduced from [14]).
Fig. 2
Fig. 2 Pearl model and principal of force generation. (a) The helical bacterium with center of mass position b is modeled as a chain of pearls at position a = b + c(x), where c(x) describes the slopes of the helix. The position of the laser focus is r L . (b)-(d) Illustration of the three steps to calculate the total force of the laterally sweeping focus on the whole bacterium.
Fig. 3
Fig. 3 Calculated force profiles (F) prls (r L ) on a helical structure. The laser focus is scanned along the position r L and is modulated in intensity over the width σT = 4 µm. The helical structure is centered at b = 0. (a), (b) Force profiles of F x p r l s in x-y and x-z direction. Force amplitudes are for Figs. (a) and (b) ± 0.9 a.u. (arbitrary units). (c) Line scans as indicated in (a). (d), (e) Force profiles of F y p r l s in the x-y and x-z plane. Force amplitudes are for Fig. (d) −1.3/1.3 a.u. and Fig. (e) −0.4/0.4 a.u.. (f) Line scans as indicated in (d). (g), (h) Force profiles of F z p r l s in the x-y and y-z plane. Force amplitudes are for Fig. (g) −0.015/0.015 a.u. and Fig. (h) −0.36/0.36 a.u. (i) Line scans as indicated in (g). Color scales range from negative (blue to positive (red) values.
Fig. 4
Fig. 4 Calculated force profiles (F) opt (b). (a)–(c) Simulated force profiles for the center of mass position b of the bacterium inside a line trap for all three directions. (d)–(f) Line scans as indicated in Figs. (a)–(c). The green lines illustrate the linear force dependence for small displacements from the trap center. Numbers on the abscissae are in µm. (Reproduced from supplementary information of [14])
Fig. 5
Fig. 5 Calculated optical potentials V opt (b). (a)–(c) Simulated potential profiles for the center of mass position b of the bacterium inside a line trap for all three directions. (d)–(f) Line scans (solid) as indicated in figures (a)-(c) and parabolic fits (dashed). Numbers on the abscissae are in µm. (Reproduced from supplementary information of [14])
Fig. 6
Fig. 6 Measured QPD signals from the helical bacterium. (a) y- and z- signals (according to Eq. (10)) over time (bottom axis) and corresponding position inside the line trap (top axis). (b) Kymographs of y-signal. The red lines show the edges of the cell. (c) Kymographs of z-signal. (d) Slightly smoothed slope amplitudes ay(xL), az(xL) obtained from a) after calibration. The rectangular offset function of the axial (z) signal has been removed.
Fig. 7
Fig. 7 Detector calibration at a freely diffusing cell. (a) Calibration schematic. The trap direction is suddenly changed by 90°, therefore performing a ‘calibration scan’ perpendicular to the long axis of the cell. (b) QPD signal Sy of the calibration scan showing the unique (blue fit) and linear (green line) detection region with gradient gy. (c) Temporal behavior of gy for five different calibration scans (indicated by different colors).
Fig. 8
Fig. 8 Trap calibration for a helical structure. (a) Position trajectory of the cell’s left and right edge (LE and RE) (b) and (c) Trajectory of the cell’s center of mass position (CMP) in y- and z- direction. (d) – (f) Histograms (Hist) of corresponding position data with error bars indicating the standard deviation 1 / N . Gaussian fits in blue. (g) – (i) Autocorrelations (AC) of corresponding position data and fit of exponential decay (y axis log scaled).
Fig. 9
Fig. 9 Sedimentation experiment to estimate the tracking range. (a) The bacterium is trapped far away from the cover slip (blue rectangle) in the focal plane (grey rectangle) of the TL. (b) The cover slip is moved towards the cell until they touch. (c) The cover slip is moved further thus pushing the cell out of the trap. (d) Maximum value per line scan of axial QPD signal Sz at every piezo position.
Fig. 10
Fig. 10 Analysis of tracking signals from focal averaging. (a) Illustration of focal averaging due to the extended helical structure with diameter D inside a point focus. (b) Meander scan scheme, comparable to multiple subsequent calibrations scans. (c) Simulated meander scan of a helical structure with indicated calibration scans by method M1 and M2. (d) Ratio qy = D/Dy’ of the actual cell diameter D and the apparent diameter Dy’ retrieved from the simulation for p = 900 nm. Dashed lines indicate experimentally obtained q values. The grey shaded area represents the Gaussian distribution of D from [13]. (e) Subsequent experimental meander scans with a length of 3 µm each. (f) Positions of the signal minima (min pos) of every line scan and sinusoidal fits. (g) Power spectral density (PSD) of minpos clearly showing the frequency of the meander scan (f = 0.33 µm−1) and the helix itself (f = (0.94 ± 1.2) µm−1, grey box). (h) Results for the frequency fit value and allowed frequency band (grey box, same as in h). (i) Diameter Dy’ after filtering for allowed values. Error bars represent the standard deviation of a single value. The mean diameter and its standard deviation are indicated (light red box).

Equations (13)

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F ( r L , a ) = F g r a d ( r L , a ) + F s c a t ( r L , a ) = P ( r L ) 1 4 Re { α ε } | E i ( r r L ) + E s ( r r L , a ) | 2 s ( r - a ) d 3 r P ( r L ) α n 2 c ( I i ) ( r r L ) s ( r - a ) d 3 r
I ( r , r L ) = I 0 r ( e ( x x L Δ x ) 2 e ( y y L Δ y ) 2 e ( z z L Δ z ) 2 )
c ( x ) = ( x , R H cos ( k H x ) , R H sin ( k H x ) )
F p r l ( r L , a ( x ) ) α n 2 c P ( r L ) ( I ) ( r r L ) δ ( r a ( x ) ) d 3 r α n 2 c P ( r L ) ( I ) ( a ( x ) r L ) = α n 2 c P ( r L ) ( I ) ( x + b x x L R H cos ( k H x ) + b y y L R H sin ( k H x ) + b z z L )
F p r l s ( x L , b ) n = N / 2 N / 2 F p r l ( x L , b + c ( x L + n d ) ) 1 d x L Δ x x L + Δ x F p r l ( x L , b + c ( x ) ) d x
F o p t ( b ) = 2 T s 0 T s / 2 F p r l s ( v L t , b ) d t = ( κ x e b x , κ y e b y , κ z e b z ) = κ e f f b
V o p t ( b ) = b F o p t ( r ) d r 1 2 κ x e b x 2 + 1 2 κ y e b y 2 + 1 2 κ z e b z 2
S ^ n r a w ( c ) = P ( t ) A n ( | E ˜ i ( k ) | 2 + | E ˜ s ( k , c ) | 2 + 2 Re { E ˜ i ( k ) E ˜ s * ( k , c ) ) } ) d 2 k 2 A A n Δ φ s ( k , c ) d 2 k + S o f f , n ( t )
Re { E ˜ i E ˜ s * ( c ) } 1 2 | E ˜ i + E ˜ s ( c ) | 2 1 2 | E ˜ i | 2 = | E ˜ i | | E ˜ s * ( c ) | Re { exp ( i φ s i φ i ( c ) ) } A sin ( Δ φ s ( c ) ) A Δ φ s ( c )
S ( c ( x L ) ) ~ ( k x x L + k y R H cos ( k H x L ) a k z R H sin ( k H x L ) ) H d 2 k ( g x x L , g y R H cos ( k H x L ) / q y , g z R H sin ( k H x L ) / q z )
κ y = k B T g y 2 σ y ' 2 q y 2 γ y = τ y κ y
γ y = γ z κ z = γ y τ z g z = q z σ z ' κ z k B T
κ x e = k B T σ x 2 γ x = τ x κ x

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