Abstract

We investigate the influence of an additional scatterer on the tracking signal of an optically trapped particle. The three-dimensional particle position is recorded interferometrically with nanometer precision by using a quadrant photodiode in the back focal plane of a detection lens. A phase disturbance underneath the sample leads to incorrect position signals. The resulting interaction potential and forces are therefore erroneous as well. We present a procedure to correct for the disturbance by measuring its interferometric signal. We prove the applicability of our phase correction approach by generating a defined displacement of the trapped probe.

© 2006 Optical Society of America

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  1. G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
    [CrossRef] [PubMed]
  2. B.-W. Yang and H.-P. D. Shieh, "Interlayer cross talk in dual-layer read-only optical disks," Appl. Opt. 38, 333-338 (1999).
    [CrossRef]
  3. F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, 2004).
  4. M. Feierabend, M. Rückel, and W. Denk, "Coherence-gated wave-front sensing in strongly scattering samples," Opt. Lett. 29, 2255-2257 (2004).
    [CrossRef] [PubMed]
  5. C. J. R. Sheppard, M. Roy, and M. D. Sharma, "Image formation in low-coherence and confocal interference microscopes," Appl. Opt. 43, 1493-502 (2004).
    [CrossRef] [PubMed]
  6. M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. U.S.A. 102, 13,081-13,086 (2005).
    [CrossRef]
  7. C. Bustamante, Z. Bryant, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423-427 (2003).
    [CrossRef] [PubMed]
  8. 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]
  9. L. P. Ghislain and W. W. Webb, "Scanning-force microscope based on an optical trap," Opt. Lett. 18, 1678-1680 (1993).
    [CrossRef] [PubMed]
  10. H. Hertz, L. Malmqvist, L. Rosengren, and K. Ljungberg, "Optically trapped nonlinear particles as probes for scanning near-field optical microscopy," Ultramicroscopy 57, 309-312 (1995).
    [CrossRef]
  11. S. Kawata, Y. Inouye, and T. Sugiura, "Near-field scanning optical microscope with a laser trapped probe," Jpn. J. Appl. Phys. 33, L1725-L1727 (1994).
    [CrossRef]
  12. E. L. Florin, A. Pralle, J. K. Hörber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-11 (1997).
    [CrossRef] [PubMed]
  13. G. M. Whitesides, J. K. Kriebel, and J. C. Love, "Molecular engineering of surfaces using self-assembled monolayers," Sci. Prog. 88, 17-48 (2005).
    [CrossRef] [PubMed]
  14. J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
    [CrossRef] [PubMed]
  15. 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 71, 061927 (2005).
    [CrossRef]
  16. A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
    [CrossRef] [PubMed]
  17. N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).
  18. 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, 2197-2210 (2004).
    [CrossRef]
  19. A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
    [CrossRef] [PubMed]
  20. 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, 411-413 (2003).
    [CrossRef] [PubMed]
  21. A. Jonás, P. Zemánek, and E.-L. Florin, "Single-beam trapping in front of reflective surfaces," Opt. Lett. 26, 1466-1468 (2001).
    [CrossRef]
  22. K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  23. A. Rohrbach and E. H. K. Stelzer, "Optical trapping of dielectric particles in arbitrary fields," J. Opt. Soc. Am. A 18, 839-853 (2001).
    [CrossRef]

2005

G. M. Whitesides, J. K. Kriebel, and J. C. Love, "Molecular engineering of surfaces using self-assembled monolayers," Sci. Prog. 88, 17-48 (2005).
[CrossRef] [PubMed]

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[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 71, 061927 (2005).
[CrossRef]

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. U.S.A. 102, 13,081-13,086 (2005).
[CrossRef]

2004

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

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, 2197-2210 (2004).
[CrossRef]

C. J. R. Sheppard, M. Roy, and M. D. Sharma, "Image formation in low-coherence and confocal interference microscopes," Appl. Opt. 43, 1493-502 (2004).
[CrossRef] [PubMed]

M. Feierabend, M. Rückel, and W. Denk, "Coherence-gated wave-front sensing in strongly scattering samples," Opt. Lett. 29, 2255-2257 (2004).
[CrossRef] [PubMed]

2003

2001

2000

A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
[CrossRef] [PubMed]

1999

A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
[CrossRef] [PubMed]

B.-W. Yang and H.-P. D. Shieh, "Interlayer cross talk in dual-layer read-only optical disks," Appl. Opt. 38, 333-338 (1999).
[CrossRef]

1998

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]

1997

E. L. Florin, A. Pralle, J. K. Hörber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-11 (1997).
[CrossRef] [PubMed]

1995

H. Hertz, L. Malmqvist, L. Rosengren, and K. Ljungberg, "Optically trapped nonlinear particles as probes for scanning near-field optical microscopy," Ultramicroscopy 57, 309-312 (1995).
[CrossRef]

1994

S. Kawata, Y. Inouye, and T. Sugiura, "Near-field scanning optical microscope with a laser trapped probe," Jpn. J. Appl. Phys. 33, L1725-L1727 (1994).
[CrossRef]

1993

1986

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Albrecht, K.

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[CrossRef] [PubMed]

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]

Altmann, S. M.

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

Becker, N. B.

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

Binnig, G.

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Block, S. M.

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

Bryant, Z.

C. Bustamante, Z. Bryant, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423-427 (2003).
[CrossRef] [PubMed]

Bustamante, C.

C. Bustamante, Z. Bryant, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423-427 (2003).
[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]

Denk, W.

Feierabend, M.

Florin, E. L.

A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
[CrossRef] [PubMed]

A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, J. K. Hörber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-11 (1997).
[CrossRef] [PubMed]

Florin, E.-L.

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, 2197-2210 (2004).
[CrossRef]

A. Jonás, P. Zemánek, and E.-L. Florin, "Single-beam trapping in front of reflective surfaces," Opt. Lett. 26, 1466-1468 (2001).
[CrossRef]

Gasteier, P.

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[CrossRef] [PubMed]

Gerber, C.

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Ghislain, L. P.

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]

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 71, 061927 (2005).
[CrossRef]

Groll, J.

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. U.S.A. 102, 13,081-13,086 (2005).
[CrossRef]

Hertz, H.

H. Hertz, L. Malmqvist, L. Rosengren, and K. Ljungberg, "Optically trapped nonlinear particles as probes for scanning near-field optical microscopy," Ultramicroscopy 57, 309-312 (1995).
[CrossRef]

Hörber, J. K.

A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
[CrossRef] [PubMed]

A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, J. K. Hörber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-11 (1997).
[CrossRef] [PubMed]

Hörber, J. K. H.

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

Inouye, Y.

S. Kawata, Y. Inouye, and T. Sugiura, "Near-field scanning optical microscope with a laser trapped probe," Jpn. J. Appl. Phys. 33, L1725-L1727 (1994).
[CrossRef]

Jonás, A.

Kawata, S.

S. Kawata, Y. Inouye, and T. Sugiura, "Near-field scanning optical microscope with a laser trapped probe," Jpn. J. Appl. Phys. 33, L1725-L1727 (1994).
[CrossRef]

Keller, P.

A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
[CrossRef] [PubMed]

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 71, 061927 (2005).
[CrossRef]

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, 411-413 (2003).
[CrossRef] [PubMed]

Kriebel, J. K.

G. M. Whitesides, J. K. Kriebel, and J. C. Love, "Molecular engineering of surfaces using self-assembled monolayers," Sci. Prog. 88, 17-48 (2005).
[CrossRef] [PubMed]

Ljungberg, K.

H. Hertz, L. Malmqvist, L. Rosengren, and K. Ljungberg, "Optically trapped nonlinear particles as probes for scanning near-field optical microscopy," Ultramicroscopy 57, 309-312 (1995).
[CrossRef]

Love, J. C.

G. M. Whitesides, J. K. Kriebel, and J. C. Love, "Molecular engineering of surfaces using self-assembled monolayers," Sci. Prog. 88, 17-48 (2005).
[CrossRef] [PubMed]

Malmqvist, L.

H. Hertz, L. Malmqvist, L. Rosengren, and K. Ljungberg, "Optically trapped nonlinear particles as probes for scanning near-field optical microscopy," Ultramicroscopy 57, 309-312 (1995).
[CrossRef]

Moeller, M.

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[CrossRef] [PubMed]

Neuman, K. C.

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

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, 2197-2210 (2004).
[CrossRef]

Pralle, A.

A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
[CrossRef] [PubMed]

A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, J. K. Hörber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-11 (1997).
[CrossRef] [PubMed]

Prummer, M.

A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
[CrossRef] [PubMed]

Quate, C. F.

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Riethmueller, S.

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[CrossRef] [PubMed]

Roddier, F.

F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, 2004).

Rohrbach, A.

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

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 71, 061927 (2005).
[CrossRef]

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, 2197-2210 (2004).
[CrossRef]

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, 411-413 (2003).
[CrossRef] [PubMed]

A. Rohrbach and E. H. K. Stelzer, "Optical trapping of dielectric particles in arbitrary fields," J. Opt. Soc. Am. A 18, 839-853 (2001).
[CrossRef]

Rosengren, L.

H. Hertz, L. Malmqvist, L. Rosengren, and K. Ljungberg, "Optically trapped nonlinear particles as probes for scanning near-field optical microscopy," Ultramicroscopy 57, 309-312 (1995).
[CrossRef]

Roy, M.

Rückel, M.

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]

Scholz, T.

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

Sharma, M. D.

Sheppard, C. J. R.

Shieh, H.-P. D.

Simons, K.

A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
[CrossRef] [PubMed]

Smith, S. B.

C. Bustamante, Z. Bryant, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423-427 (2003).
[CrossRef] [PubMed]

Stelzer, E. H.

A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, J. K. Hörber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-11 (1997).
[CrossRef] [PubMed]

Stelzer, E. H. K.

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

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 71, 061927 (2005).
[CrossRef]

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, 2197-2210 (2004).
[CrossRef]

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, 411-413 (2003).
[CrossRef] [PubMed]

A. Rohrbach and E. H. K. Stelzer, "Optical trapping of dielectric particles in arbitrary fields," J. Opt. Soc. Am. A 18, 839-853 (2001).
[CrossRef]

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]

Sugiura, T.

S. Kawata, Y. Inouye, and T. Sugiura, "Near-field scanning optical microscope with a laser trapped probe," Jpn. J. Appl. Phys. 33, L1725-L1727 (1994).
[CrossRef]

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, 2197-2210 (2004).
[CrossRef]

Webb, W. W.

Whitesides, G. M.

G. M. Whitesides, J. K. Kriebel, and J. C. Love, "Molecular engineering of surfaces using self-assembled monolayers," Sci. Prog. 88, 17-48 (2005).
[CrossRef] [PubMed]

Yang, B.-W.

Zemánek, P.

Ziener, U.

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[CrossRef] [PubMed]

Appl. Opt.

Biophys. 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]

ChemBioChem

J. Groll, K. Albrecht, P. Gasteier, S. Riethmueller, U. Ziener, and M. Moeller, "Nanostructured ordering of fluorescent markers and single proteins on substrates," ChemBioChem 6, 1782-7 (2005).
[CrossRef] [PubMed]

J. Cell Biol.

A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. Hörber, "Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells," J. Cell Biol. 148, 997-1008 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Struct. Biol.

E. L. Florin, A. Pralle, J. K. Hörber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-11 (1997).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys.

S. Kawata, Y. Inouye, and T. Sugiura, "Near-field scanning optical microscope with a laser trapped probe," Jpn. J. Appl. Phys. 33, L1725-L1727 (1994).
[CrossRef]

Microsc. Res. Tech.

A. Pralle, M. Prummer, E. L. Florin, E. H. Stelzer, and J. K. Hörber, "Three- dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-86 (1999).
[CrossRef] [PubMed]

Nature

C. Bustamante, Z. Bryant, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423-427 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. E

N. B. Becker, S. M. Altmann, T. Scholz, J. K. H. Hörber, E. H. K. Stelzer, and A. Rohrbach, "Three-dimensional bead position histograms reveal single-molecule nanomechanics," Phys. Rev. E 71, 021907 (2005).

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 71, 061927 (2005).
[CrossRef]

Phys. Rev. Lett.

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. U.S.A. 102, 13,081-13,086 (2005).
[CrossRef]

Rev. Sci. Instrum.

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, 2197-2210 (2004).
[CrossRef]

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

Sci. Prog.

G. M. Whitesides, J. K. Kriebel, and J. C. Love, "Molecular engineering of surfaces using self-assembled monolayers," Sci. Prog. 88, 17-48 (2005).
[CrossRef] [PubMed]

Ultramicroscopy

H. Hertz, L. Malmqvist, L. Rosengren, and K. Ljungberg, "Optically trapped nonlinear particles as probes for scanning near-field optical microscopy," Ultramicroscopy 57, 309-312 (1995).
[CrossRef]

Other

F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, 2004).

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Figures (6)

Fig. 1
Fig. 1

(Color online) Ligand coated spherical bead is placed near a receptor-coated surface with an optical trap. The surface structure, e.g., gold dots or a cell, disturbs the phase of the trapping laser.

Fig. 2
Fig. 2

(Color online) Detector signals S x and S z with and without trapped probe. The sample on the coverslip is a D = 400   nm silica sphere, the trapped probe is a D = 535   nm polystyrene sphere. The second column shows the lateral signal S x . The third and fourth columns show the axial signal S z at a distance h = 300   nm and h = 1100   nm of the laser focus to the surface. Top row, lateral and axial detector signals of the sample on the coverslip at two different heights h; middle row, corresponding detector signals formed by both the sample and the trapped probe; bottom row, linescans from the graphs above.

Fig. 3
Fig. 3

(Color online) Deviation from the center position due to surface effects plotted against the distance to the surface h. The contribution of the surface to the signal Δ S surf   z ( h ) increases linear close to the surface ( < D pr / 2 = r pr ) .

Fig. 4
Fig. 4

(Color online) Probe (in red) is rolled over the spherical surface structure (in blue) by the optical trap. (a) Measured traces of a D = 535   nm polystyrene sphere scanned over a D = 400   nm silica sphere. (b) Corrected particle traces. The colored and numbered traces represent the probe's center position at different heights above the surface.

Fig. 5
Fig. 5

(Color online) Probe (in red) is rolled over the spherical surface structure (in blue) by the optical trap. (a) Measured traces of a D = 356   nm polystyrene sphere scanned over a D = 400   nm silica sphere. (b) Corrected particle traces. The colored and numbered traces represent the probe's center position at different heights above the surface.

Fig. 6
Fig. 6

Corrected position traces in different heights for a trapped D = 535   nm polystyrene particle scanned over a D = 400   nm silica particle. Height h above the coverslip (a) 600   nm , (b) 500   nm , (c) 400   nm , (d) 300   nm . With decreasing height, the position of the trapped particle reveals the underlying structure.

Equations (192)

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W trap ( b )
b 0
i W trap
[ b i ( t ) ]
κ i
[ b i ( t ) b 0 i ]
Δ b i ( t ) = b i ( t ) b 0 i
i = x , y , z ; i = / ( x i )
κ i
τ i
τ i = γ / κ i
τ i
W ext
W tot
b ( t )
p ( b )
W tot ( b ) = k b T ln ( p ( b ) / p 0 ) = W trap ( b ) + W ext ( b ) .
p 0
p ( b )
k b
i W ext ( b ) = i [ W tot ( b ) W trap ( b ) ]
E in
E pr
I pr
Φ in ( k x , k y ) Φ pr ( k x , k y , b pr )
Φ pr ( k x , k y , b pr )
b pr
k x
k y
k = ( k x 2 + k y 2 ) 1 / 2
k x
k y
b pr
I pr ( k x , k y , b pr ) = | E in ( k x , k y ) + E pr ( k x , k y , b pr ) | 2
= | E in | 2 + | E pr | 2 + | E in | | E pr | × cos ( Φ in Φ pr ) .
A n
n = 1 , 2 , 3 , 4
S n ( b ) = A n I ( k x , k y , b ) Θ ( k 0 NA det k ) d k x d k y .
I = I pr
NA det
b z
S n
S ( b ) = ( S x , S y , S z ) = ( S 1 S 2 + S 3 S 4 ) , ( S 1 + S 2 S 3 S 4 ) , ( S 1 + S 2 + S 3 + S 4 ) S 0 .
S 0
S ( b ) = g ^ b + const
Δ b = b b 0
g ^
g ^
g i i
( b x , b y , b z )
S x
S y
S z
S off = S ( b = 0 )
Δ S surf   i ( h )
S i ( b i ) g i i ( Δ b i + b 0 i ) + S off   i + Δ S surf   i ( h ) .
Δ b i
Δ b i = g ii 1 [ S i g i i b 0 i S off   i Δ S surf   i ( h ) ]
Δ b i
I ( k x , k y , b )
b sa
I sa ( k x , k y , b sa ) = | E in | 2 + | E sa | 2 + | E in | | E sa | × cos ( Φ in Φ sa ) .
S x
S z
D sa = 400   nm
b pr
b sa
E in
E sa
I tot
k x
k y
b sa
I tot ( k x , k y , b sa , b pr ) = | E tot ( k x , k y , b sa , b pr ) | 2 = | E in ( k x , k y ) + E sa ( k x , k y , b s a ) + E pr ( k x , k y , b sa , b pr ) | 2 = | E in | 2 + | E sa | 2 + | E pr | 2 + | E in | | E sa | cos ( Φ in Φ sa ) + | E in | | E pr | cos ( Φ in Φ pr ) + | E sa | | E pr | cos ( Φ sa Φ pr ) .
E pr = E pr ( b pr , b sa )
Φ pr = Φ pr ( b sa , b pr )
Φ pr = Φ pr ( b pr )
r pr = 267   nm
E sa
h > D sa + r pr
h = 1100   nm
I sa ( k x , k y , b sa )
I tot ( k x , k y , b sa , b pr )
I diff = I tot I sa = | E pr | 2 + | E in | | E pr | cos ( Φ in Φ pr )
+ | E sa | | E pr | cos ( Φ sa Φ pr ) ,
E pr = E pr ( b pr , b sa )
E pr
b sa
E pr ( b pr , b sa ) E pr ( b pr )
Φ pr Φ pr
E sa
| E sa | | E pr | cos ( Φ sa Φ pr ) | E in | 2 , | E sa | | E pr | cos ( Φ sa Φ pr ) | E pr | 2 .
I pr I tot I sa + | E in | 2 .
b pr
S pr ( b pr ) S 0 S diff ( b pr ) = S tot ( b pr ) S sa ( b pr ) .
S tot ( b pr )
S tot ( b pr )
Δ S surf
Δ S surf   z ( h ) =
S pr   z ( b z ) S off   z
Δ S surf   z ( h )
Δ S surf ( h ) = 0
Δ S surf ( h )
Δ S surf ( h )
S tot ( b pr )
S tot ( b pr ) = S tot ( b pr ) Δ S surf ( h ) = g ^ tot ( Δ b + b 0 ) + S off   tot .
Δ b
Δ b
S sa ( b pr ) = g ^ sa ( Δ b + b 0 ) + S off   sa ,
g ^ pr g ^ diff = g ^ tot g ^ sa
S off   diff = S off   tot S off   sa
Δ b
Δ b = g ^ diff 1 [ S diff ( b pr ) S off   diff ] b 0 .
g ^ diff 1 S off   diff
b 0
S sa ( b 0 )
S sa ( b pr )
Δ b ,
n = 0
Δ b 0 = 0
S diff ( b 0 + Δ b n + 1 )
S diff ( Δ b n + 1 + b 0 ) = S tot ( b pr ) S sa ( Δ b n + b 0 ) .
Δ b n + 1
Δ b n + 1 = g ^ diff 1 [ S diff ( Δ b n + 1 + b 0 ) ] .
Δ b n + 1
Δ b
n < 1 0
Δ b n
Δ b ,
Δ b n Δ b
D sa = 400 nm
n pr = 1.43
λ =589   nm
D pr = 356
535   nm
λ 0 = 1064   nm
100 150   nm
Δ b z ( Δ b x , y
κ x , y κ z )
R = ( D pr + D sa ) / 2
Δ b z = [ R 2 ( b 0 x b sa   x ) 2 ] 1 / 2 + D pr / 2 , Δ b z 0.
T = 10   s
h 10   μm
g i i
b 0
S x
h = 1100   nm
( h = 300   nm )
Δ b ( t ) + b 0
D pr = 535   nm
100   nm
T = 100   ms
f = 1   kHz
Δ b z = 200   nm
1 4   ( Δ b = 0 )
d ( 535   nm + 400   nm ) / 2 = 467   nm
Δ b
D pr = 356   nm
Δ b z 800   nm
| E |
Q sca
| E | r ( Q sca ) 1 / 2
Q sca   sa = 0.018
n pr = 1.57
Q sca   pr = 0.22
D = 535   nm
Q sca   pr = 0.08
D = 356   nm
| E pr | 2 / ( | E sa | | E pr | )
cos ( Φ sa Φ pr ) = 1
D = 535   nm
D = 356   nm
S x
S z
D = 400   nm
D = 535   nm
S x
S z
h = 300   nm
h = 1100   nm
Δ S surf   z ( h )
( < D pr / 2 = r pr )
D = 535   nm
D = 400   nm
D = 356   nm
D = 400   nm
D = 535   nm
D = 400   nm
600   nm
500   nm
400   nm
300   nm

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