Abstract

A technique is proposed for determination of the three-dimensional orientation of the transition dipoles of single molecules by use of polarization-sensitive detection of fluorescence through a high-N.A.  objective. Molecular orientation can be determined uniquely and rapidly based on the counts from three detectors that are sensitive to different polarizations of light.

© 2001 Optical Society of America

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References

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  1. T. Basché, W. E. Moerner, M. Orrit, and U. Wild, eds., Single Molecule Optical Detection, Imaging and Spectroscopy (Verlag-Chemie, Weinheim, Germany, 1997).
  2. W. E. Moerner and M. Orrit, Science 283, 1670 (1999).
    [CrossRef] [PubMed]
  3. S. Weiss, Science 283, 1676 (1999).
    [CrossRef] [PubMed]
  4. E. Betzig and R. J. Chichester, Science 262, 1422 (1993).
    [CrossRef] [PubMed]
  5. D. A. Higgins, D. A. Vanden Bout, J. Kerimo, and P. F. Barbara, J. Phys. Chem. 100, 13794 (1996).
  6. T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
    [CrossRef] [PubMed]
  7. A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. van Hulst, J. Phys. Chem. A 101, 7318 (1997).
  8. T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
    [CrossRef]
  9. R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
    [CrossRef]
  10. A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 3053 (1999).
  11. A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 11237 (1999).
  12. T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 103, 6839 (1999).
  13. D. Axelrod, Biophys. J. 26, 557 (1979).
    [CrossRef] [PubMed]
  14. P. R. Callis, Annu. Rev. Phys. Chem. 48, 271 (1997).
  15. L. Novotny, E. J. Sanchez, and X. S. Xie, Ultramicroscopy 71, 21 (1998).
    [CrossRef]

1999 (5)

W. E. Moerner and M. Orrit, Science 283, 1670 (1999).
[CrossRef] [PubMed]

S. Weiss, Science 283, 1676 (1999).
[CrossRef] [PubMed]

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 3053 (1999).

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 11237 (1999).

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 103, 6839 (1999).

1998 (3)

T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
[CrossRef]

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

L. Novotny, E. J. Sanchez, and X. S. Xie, Ultramicroscopy 71, 21 (1998).
[CrossRef]

1997 (2)

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. van Hulst, J. Phys. Chem. A 101, 7318 (1997).

P. R. Callis, Annu. Rev. Phys. Chem. 48, 271 (1997).

1996 (2)

D. A. Higgins, D. A. Vanden Bout, J. Kerimo, and P. F. Barbara, J. Phys. Chem. 100, 13794 (1996).

T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

1993 (1)

E. Betzig and R. J. Chichester, Science 262, 1422 (1993).
[CrossRef] [PubMed]

1979 (1)

D. Axelrod, Biophys. J. 26, 557 (1979).
[CrossRef] [PubMed]

Axelrod, D.

D. Axelrod, Biophys. J. 26, 557 (1979).
[CrossRef] [PubMed]

Barbara, P. F.

D. A. Higgins, D. A. Vanden Bout, J. Kerimo, and P. F. Barbara, J. Phys. Chem. 100, 13794 (1996).

Bartko, A. P.

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 11237 (1999).

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 3053 (1999).

Betzig, E.

E. Betzig and R. J. Chichester, Science 262, 1422 (1993).
[CrossRef] [PubMed]

Callis, P. R.

P. R. Callis, Annu. Rev. Phys. Chem. 48, 271 (1997).

Chemla, D. S.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 103, 6839 (1999).

T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
[CrossRef]

T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

Chichester, R. J.

E. Betzig and R. J. Chichester, Science 262, 1422 (1993).
[CrossRef] [PubMed]

Dickson, R. M.

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 11237 (1999).

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 3053 (1999).

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

Enderle, Th.

T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
[CrossRef]

T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

Garcia-Parajo, M. F.

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. van Hulst, J. Phys. Chem. A 101, 7318 (1997).

Glass, J.

T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
[CrossRef]

Ha, T.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 103, 6839 (1999).

T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
[CrossRef]

T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

Higgins, D. A.

D. A. Higgins, D. A. Vanden Bout, J. Kerimo, and P. F. Barbara, J. Phys. Chem. 100, 13794 (1996).

Kerimo, J.

D. A. Higgins, D. A. Vanden Bout, J. Kerimo, and P. F. Barbara, J. Phys. Chem. 100, 13794 (1996).

Laurence, T. A.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 103, 6839 (1999).

Moerner, W. E.

W. E. Moerner and M. Orrit, Science 283, 1670 (1999).
[CrossRef] [PubMed]

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

Norris, D. J.

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

Novotny, L.

L. Novotny, E. J. Sanchez, and X. S. Xie, Ultramicroscopy 71, 21 (1998).
[CrossRef]

Orrit, M.

W. E. Moerner and M. Orrit, Science 283, 1670 (1999).
[CrossRef] [PubMed]

Ruiter, A. G. T.

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. van Hulst, J. Phys. Chem. A 101, 7318 (1997).

Sanchez, E. J.

L. Novotny, E. J. Sanchez, and X. S. Xie, Ultramicroscopy 71, 21 (1998).
[CrossRef]

Selvin, P. R.

T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

van Hulst, N. F.

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. van Hulst, J. Phys. Chem. A 101, 7318 (1997).

Vanden Bout, D. A.

D. A. Higgins, D. A. Vanden Bout, J. Kerimo, and P. F. Barbara, J. Phys. Chem. 100, 13794 (1996).

Veerman, J. A.

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. van Hulst, J. Phys. Chem. A 101, 7318 (1997).

Weiss, S.

S. Weiss, Science 283, 1676 (1999).
[CrossRef] [PubMed]

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 103, 6839 (1999).

T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
[CrossRef]

T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

Xie, X. S.

L. Novotny, E. J. Sanchez, and X. S. Xie, Ultramicroscopy 71, 21 (1998).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

P. R. Callis, Annu. Rev. Phys. Chem. 48, 271 (1997).

Biophys. J. (1)

D. Axelrod, Biophys. J. 26, 557 (1979).
[CrossRef] [PubMed]

J. Phys. Chem. (1)

D. A. Higgins, D. A. Vanden Bout, J. Kerimo, and P. F. Barbara, J. Phys. Chem. 100, 13794 (1996).

J. Phys. Chem. A (1)

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. van Hulst, J. Phys. Chem. A 101, 7318 (1997).

J. Phys. Chem. B (3)

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 3053 (1999).

A. P. Bartko and R. M. Dickson, J. Phys. Chem. B 103, 11237 (1999).

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 103, 6839 (1999).

Phys. Rev. Lett. (3)

T. Ha, J. Glass, Th. Enderle, D. S. Chemla, and S. Weiss, Phys. Rev. Lett. 80, 2093 (1998).
[CrossRef]

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

T. Ha, Th. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

Science (3)

W. E. Moerner and M. Orrit, Science 283, 1670 (1999).
[CrossRef] [PubMed]

S. Weiss, Science 283, 1676 (1999).
[CrossRef] [PubMed]

E. Betzig and R. J. Chichester, Science 262, 1422 (1993).
[CrossRef] [PubMed]

Ultramicroscopy (1)

L. Novotny, E. J. Sanchez, and X. S. Xie, Ultramicroscopy 71, 21 (1998).
[CrossRef]

Other (1)

T. Basché, W. E. Moerner, M. Orrit, and U. Wild, eds., Single Molecule Optical Detection, Imaging and Spectroscopy (Verlag-Chemie, Weinheim, Germany, 1997).

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Figures (2)

Fig. 1
Fig. 1

Light from a fluorescing molecule is collected and collimated by a polarization-preserving, infinity-corrected objective. The collection angle, α, is given by sin-1 N.A./n, where n is the index of refraction of the medium. If the molecular transition dipole is in the x,y plane, the polarization of the fluorescence is predominantly along the axis of the transition dipole and varies little across the collimated beam. If the transition dipole points along the z axis, the polarization vector is directed radially at every point in the collimated beam, leading to no net polarization. These effects serve as the basis for determining the three-dimensional orientation of a single molecule.

Fig. 2
Fig. 2

Intensity that would be seen at a detector looking at light polarized along the x axis as a function of molecular angles Θ and Φ.

Equations (16)

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

η=[cos2θ+sin2θsin2φsinΘcosΦ-sinθcosθcosφcosΘ-sin2θsinφcosφsinΘsinΦ-sin2θsinφcosφsinΘcosΦ-sinθcosθsinφcosΘ+sin2θ cos2φ+cos2θsinΘsinΦ-sinθcosθcosφsinΘcosΦ+sin2θcosΘ-sinθcosθsinφsinΘsinΦ],
R˜=[cosθ cos2φ+sin2φcosθ-1sinφcosφ-sinθcosφcosθ-1sinφcosφcosθ sin2φ+cos2φ-sinθsinφsinθcosφsinθsinφcosθ].
E0θ,φ,Θ,Φ/Etott,t+τ=cosθ cos2φ+sin2φ×sinΘcosΦ-sinθcosφcosΘ+cosθ-1×sinφcosφsinΘsinΦ,
E45θ,φ,Θ,Φ/Etott,t+τ=1/2cosθ cos2φ+ sin2φ+cosθ-1sinφcosφsinΘcosΦ-sinφ+cosφsinθcosΘ+cosθ-1sinφcosφ+cosθ sin2φ+cos2φsinΘsinΦ,
E90θ,φ,Θ,Φ/Etott,t+τ=cosθ-1sinφcosφ×sinΘcosΦ-sinθsinφcosΘ+cosθ sin2φ+ cos2φsinΘsinΦ,
E135θ,φ,Θ,Φ/Etott,t+τ=-1/2cosθ cos2φ+sin2φ-cosθ-1sinφcosφsinΘcosΦ+sinφ-cosφsinθcosΘ+cosθ-1sinφcosφ-cosθ sin2φ-cos2φsinΘsinΦ,
I0Θ,Φ=Itott,t+τA+B sin2Θ+C sin2Θcos2Φ,
I45Θ,Φ=Itott,t+τA+B sin2Θ+C sin2Θsin2Φ,
I90Θ,Φ=Itott,t+τA+B sin2Θ-C sin2Θcos2Φ,
I135Θ,Φ=Itott,t+τA+B sin2Θ-Csin2Θsin2Φ.
A=16-14cosα+112cos3α,
B=18cosα-18cos3α,
C=748-116cosα-116cos2α-148cos3α.
Φ=12tan-1I45Θ,Φ-I0Θ,Φ+I90Θ,Φ2/I0Θ,Φ-I90Θ,Φ2,
Itott,t+τ=12A1-BCcos2ΦI0+1+BCcos2ΦI90,
Θ=sin-1I0Θ,Φ-I90Θ,Φ2Itott,t+τCcos2Φ1/2.

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