Abstract

The technique of determining the position of individual fluorescent molecules with nanometer resolution, called FIONA, has become an important tool for several biophysical applications such as studying motility mechanisms of motor proteins. The position determination is usually done by fitting a 2-D Gaussian (x-y vs. photon number) to the emission intensity distribution of the fluorescent molecule. However, the intensity distribution of an emitting molecule depends not only on its position in space, but also on its three-dimensional orientation. Here, we present an extensive numerical study of the achievable accuracy of position determination as a function of molecule orientation. We compare objectives with different numerical apertures and show that an effective pixel size of 100 nm or less per CCD pixel is required to obtain good positional accuracy. Nonetheless, orientation effects can still cause position errors for large anisotropy, as high as 10 nm for high numerical aperture objectives. However, position accuracy is significantly better (< 2.5 nm) when using objectives with a numerical aperture of 1.2. Of course, probes with lower anisotropy decrease the positional uncertainty.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Yildiz, and P. R. Selvin, "Fluorescence imaging with one nanometer accuracy, Application to molecular motors," Acc. Chem. Res. 38, 574-582 (2005).
    [CrossRef] [PubMed]
  2. A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
    [CrossRef] [PubMed]
  3. H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometre localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
    [CrossRef] [PubMed]
  4. G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).
  5. M. P. Gordon, T. Ha, and P. R. Selvin, "Single-molecule high-resolution imaging with photobleaching," Proc. Nat. Acad. Sci. USA 101, 6462-6465 (2004).
    [CrossRef] [PubMed]
  6. H. Balci, T. Ha, H. L. Sweeney, and P. R. Selvin, "Interhead distance measurements in Myosin VI via SHRImP support a simplified hand-over-hand model," Biophys. J. 89, 413-417 (2005).
    [CrossRef] [PubMed]
  7. B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
    [CrossRef]
  8. M. J. Saxton, and K. Jacobson, "Single-particle tracking: Applications to membrane dynamics," Ann Rev Biophys Biomol Struct 26, 373-399 (1997).
    [CrossRef]
  9. M. Speidel, A. Jonas, and E. L. Florin, "Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging," Opt. Lett. 28, 69-71 (2003).
    [CrossRef] [PubMed]
  10. R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002).
    [CrossRef] [PubMed]
  11. M. K. Cheezum, W. F. Guilford, and W. H. Walker, "Quantitative comparison of Algorithms for tracking single fluorescent particles," Biophys. J. 81, 2378-2388 (2001).
    [CrossRef] [PubMed]
  12. R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
    [CrossRef] [PubMed]
  13. A. P. Bartko, and R. M. Dickson, "Imaging three-dimensional singe molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
    [CrossRef]
  14. M. Böhmer, and J. Enderlein, "Orientation imaging of single molecules by wide-field epi-fluorescence microscopy," J. Opt. Soc. B 20, 554-559 (2003). In Eq. (11) of this publication, the factor i is erroneous and has to be replaced by -1. J.E. thanks Rolfe Petschek for finding this typo.
    [CrossRef]
  15. P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
    [CrossRef]
  16. J. Enderlein, "Theoretical study of detecting a dipole emitter through an objective with high numerical aperture," Opt. Lett. 25, 634-636 (2000).
    [CrossRef]
  17. J. Enderlein, and M. Böhmer, "Influence of interface-dipole interactions on the efficiency of fluorescence light collection near surfaces," Opt. Lett. 28, 941-943 (2003).
    [CrossRef] [PubMed]
  18. W. Lukosz, and R. E. Kunz, "Light emission by magnetic and electric dipoles close to a plane interface II. Radiation patterns of perpendicular oriented dipoles," J. Opt. Soc. Am. 67, 1615-1619 (1977).
    [CrossRef]
  19. W. Lukosz, "Light emission by magnetic and electric dipoles close to a plane interface III. Radiation patterns of dipoles with arbitrary orientation," J. Opt. Soc. Am. 69, 1495-1503 (1997).
    [CrossRef]
  20. W. Lukosz, "Light emission by multipole sources in thin layers. I. Radiation patterns of electric and magnetic dipoles," J. Opt. Soc. Am. 71, 744-54 (1981).
    [CrossRef]
  21. E. H. Hellen, and D. Axelrod, "Fluorescence emission at dielectric and metal-film interfaces," J. Opt. Soc. Am. B 4, 337-350 (1987).
    [CrossRef]
  22. J. D. JacksonClassical Electrodynamics (John Wiley, New York, 1975).
  23. M. Abramowitz, and I. A. Stegun, eds., Handbook of mathematical functions (Harry Deutsch, Thun and Frankfurt/Main, 1984).
  24. B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
    [CrossRef]
  25. J. Enderlein, T. Ruckstuhl, and S. Seeger, "Highly efficient optical detection of surface-generated fluorescence," Appl. Opt. 38, 724-732 (1999).
    [CrossRef]
  26. A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
    [CrossRef]
  27. S. W. Hell, and E. H. K. Stelzer, "Properties of a 4Pi-confocal fluorescence microscope," J. Opt. Soc. Am. A 9, 2159-2166 (1992).
    [CrossRef]
  28. S. W. Hell, and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission: stimulated emission depletion microscopy," Opt. Lett. 19, 780-782 (1994).
    [CrossRef] [PubMed]
  29. M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I/sup 5/M: 3D widefield light microscopy with better than 100 nm axial resolution," J Microsc. 195, 10-16 (1999).
    [CrossRef] [PubMed]

2005 (3)

A. Yildiz, and P. R. Selvin, "Fluorescence imaging with one nanometer accuracy, Application to molecular motors," Acc. Chem. Res. 38, 574-582 (2005).
[CrossRef] [PubMed]

H. Balci, T. Ha, H. L. Sweeney, and P. R. Selvin, "Interhead distance measurements in Myosin VI via SHRImP support a simplified hand-over-hand model," Biophys. J. 89, 413-417 (2005).
[CrossRef] [PubMed]

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

2004 (4)

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometre localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef] [PubMed]

G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).

M. P. Gordon, T. Ha, and P. R. Selvin, "Single-molecule high-resolution imaging with photobleaching," Proc. Nat. Acad. Sci. USA 101, 6462-6465 (2004).
[CrossRef] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

2003 (3)

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002).
[CrossRef] [PubMed]

2001 (1)

M. K. Cheezum, W. F. Guilford, and W. H. Walker, "Quantitative comparison of Algorithms for tracking single fluorescent particles," Biophys. J. 81, 2378-2388 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (3)

J. Enderlein, T. Ruckstuhl, and S. Seeger, "Highly efficient optical detection of surface-generated fluorescence," Appl. Opt. 38, 724-732 (1999).
[CrossRef]

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I/sup 5/M: 3D widefield light microscopy with better than 100 nm axial resolution," J Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

A. P. Bartko, and R. M. Dickson, "Imaging three-dimensional singe molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

1998 (2)

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

1997 (2)

W. Lukosz, "Light emission by magnetic and electric dipoles close to a plane interface III. Radiation patterns of dipoles with arbitrary orientation," J. Opt. Soc. Am. 69, 1495-1503 (1997).
[CrossRef]

M. J. Saxton, and K. Jacobson, "Single-particle tracking: Applications to membrane dynamics," Ann Rev Biophys Biomol Struct 26, 373-399 (1997).
[CrossRef]

1994 (1)

1992 (1)

1987 (1)

1981 (1)

1977 (1)

1959 (1)

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Agard, D. A.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I/sup 5/M: 3D widefield light microscopy with better than 100 nm axial resolution," J Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Axelrod, D.

Balci, H.

H. Balci, T. Ha, H. L. Sweeney, and P. R. Selvin, "Interhead distance measurements in Myosin VI via SHRImP support a simplified hand-over-hand model," Biophys. J. 89, 413-417 (2005).
[CrossRef] [PubMed]

Bartko, A. P.

A. P. Bartko, and R. M. Dickson, "Imaging three-dimensional singe molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

Böhmer, M.

Brakenhoff, G. J.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

Cheezum, M. K.

M. K. Cheezum, W. F. Guilford, and W. H. Walker, "Quantitative comparison of Algorithms for tracking single fluorescent particles," Biophys. J. 81, 2378-2388 (2001).
[CrossRef] [PubMed]

Dickson, R. M.

A. P. Bartko, and R. M. Dickson, "Imaging three-dimensional singe molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

Duff, S. R.

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometre localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef] [PubMed]

Enderlein, J.

Florin, E. L.

Forkey, J. N.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Goldman, Y. E.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Gordon, M. P.

M. P. Gordon, T. Ha, and P. R. Selvin, "Single-molecule high-resolution imaging with photobleaching," Proc. Nat. Acad. Sci. USA 101, 6462-6465 (2004).
[CrossRef] [PubMed]

Guilford, W. F.

M. K. Cheezum, W. F. Guilford, and W. H. Walker, "Quantitative comparison of Algorithms for tracking single fluorescent particles," Biophys. J. 81, 2378-2388 (2001).
[CrossRef] [PubMed]

Gustafsson, M. G.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I/sup 5/M: 3D widefield light microscopy with better than 100 nm axial resolution," J Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Ha, T.

H. Balci, T. Ha, H. L. Sweeney, and P. R. Selvin, "Interhead distance measurements in Myosin VI via SHRImP support a simplified hand-over-hand model," Biophys. J. 89, 413-417 (2005).
[CrossRef] [PubMed]

M. P. Gordon, T. Ha, and P. R. Selvin, "Single-molecule high-resolution imaging with photobleaching," Proc. Nat. Acad. Sci. USA 101, 6462-6465 (2004).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Hammer, J. A.

G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).

Hanson, G. T.

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometre localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef] [PubMed]

Hell, S. W.

Hellen, E. H.

Higdon, P. D.

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

Hofkens, J.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Jacobson, K.

M. J. Saxton, and K. Jacobson, "Single-particle tracking: Applications to membrane dynamics," Ann Rev Biophys Biomol Struct 26, 373-399 (1997).
[CrossRef]

Jonas, A.

Josemon, J.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Köhler, J.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

Kunz, R. E.

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002).
[CrossRef] [PubMed]

Lukosz, W.

McKinney, S. A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Melnikov, S.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Moussa, A.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Müllen, K.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Müller, M.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

Muls, B.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Ober, R. J.

R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

Park, H.

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometre localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef] [PubMed]

Ram, S.

R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

Richards, B.

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Ruckstuhl, T.

Sakamoto, T.

G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).

Saxton, M. J.

M. J. Saxton, and K. Jacobson, "Single-particle tracking: Applications to membrane dynamics," Ann Rev Biophys Biomol Struct 26, 373-399 (1997).
[CrossRef]

Schmidt, J.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

Sedat, J. W.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I/sup 5/M: 3D widefield light microscopy with better than 100 nm axial resolution," J Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Seeger, S.

Sellers, J. R.

G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).

Selvin, P. R.

A. Yildiz, and P. R. Selvin, "Fluorescence imaging with one nanometer accuracy, Application to molecular motors," Acc. Chem. Res. 38, 574-582 (2005).
[CrossRef] [PubMed]

H. Balci, T. Ha, H. L. Sweeney, and P. R. Selvin, "Interhead distance measurements in Myosin VI via SHRImP support a simplified hand-over-hand model," Biophys. J. 89, 413-417 (2005).
[CrossRef] [PubMed]

G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).

M. P. Gordon, T. Ha, and P. R. Selvin, "Single-molecule high-resolution imaging with photobleaching," Proc. Nat. Acad. Sci. USA 101, 6462-6465 (2004).
[CrossRef] [PubMed]

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometre localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Snyder, G. E.

G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).

Soumillion, J. P.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Speidel, M.

Stelzer, E. H. K.

Sweeney, H. L.

H. Balci, T. Ha, H. L. Sweeney, and P. R. Selvin, "Interhead distance measurements in Myosin VI via SHRImP support a simplified hand-over-hand model," Biophys. J. 89, 413-417 (2005).
[CrossRef] [PubMed]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002).
[CrossRef] [PubMed]

Török, P.

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

Uji-i, H.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

van Oijen, A. M.

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

Verheijen, W.

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

Walker, W. H.

M. K. Cheezum, W. F. Guilford, and W. H. Walker, "Quantitative comparison of Algorithms for tracking single fluorescent particles," Biophys. J. 81, 2378-2388 (2001).
[CrossRef] [PubMed]

Ward, E. S.

R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002).
[CrossRef] [PubMed]

Wichmann, J.

Wilson, T.

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

Wolf, E.

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Yildiz, A.

A. Yildiz, and P. R. Selvin, "Fluorescence imaging with one nanometer accuracy, Application to molecular motors," Acc. Chem. Res. 38, 574-582 (2005).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Acc. Chem. Res. (1)

A. Yildiz, and P. R. Selvin, "Fluorescence imaging with one nanometer accuracy, Application to molecular motors," Acc. Chem. Res. 38, 574-582 (2005).
[CrossRef] [PubMed]

Ann Rev Biophys Biomol Struct (1)

M. J. Saxton, and K. Jacobson, "Single-particle tracking: Applications to membrane dynamics," Ann Rev Biophys Biomol Struct 26, 373-399 (1997).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (5)

H. Balci, T. Ha, H. L. Sweeney, and P. R. Selvin, "Interhead distance measurements in Myosin VI via SHRImP support a simplified hand-over-hand model," Biophys. J. 89, 413-417 (2005).
[CrossRef] [PubMed]

G. E. Snyder, T. Sakamoto, J. A. Hammer, J. R. Sellers, and P. R. Selvin, "Nanometer localization of single green fluorescent proteins, Evidence that Myosin V walks and-over-hand via Telemark Configuration," Biophys. J. 87, 1776-1783 (2004).

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002).
[CrossRef] [PubMed]

M. K. Cheezum, W. F. Guilford, and W. H. Walker, "Quantitative comparison of Algorithms for tracking single fluorescent particles," Biophys. J. 81, 2378-2388 (2001).
[CrossRef] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

A. M. van Oijen, J. Köhler, J. Schmidt, M. Müller, and G. J. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

ChemPhysChem. (1)

B. Muls, H. Uji-i, S. Melnikov, A. Moussa, W. Verheijen, J. P. Soumillion, J. Josemon, K. Müllen, and J. Hofkens, "Direct measurement of the end-to-end distance of individual polyfluorene polymer chains," ChemPhysChem. 6, 2286-2294 (2005).
[CrossRef]

J Microsc. (1)

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I/sup 5/M: 3D widefield light microscopy with better than 100 nm axial resolution," J Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

J. Microsc. (1)

H. Park, G. T. Hanson, S. R. Duff, and P. R. Selvin, "Nanometre localization of single ReAsH molecules," J. Microsc. 216, 199-205 (2004).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

J. Opt. Soc. Am. (3)

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

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

J. Phys. Chem. B (1)

A. P. Bartko, and R. M. Dickson, "Imaging three-dimensional singe molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

Opt. Lett. (4)

Proc. Nat. Acad. Sci. USA (1)

M. P. Gordon, T. Ha, and P. R. Selvin, "Single-molecule high-resolution imaging with photobleaching," Proc. Nat. Acad. Sci. USA 101, 6462-6465 (2004).
[CrossRef] [PubMed]

Proc. Roy. Soc. London A (1)

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Science (1)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand, single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Other (3)

M. Böhmer, and J. Enderlein, "Orientation imaging of single molecules by wide-field epi-fluorescence microscopy," J. Opt. Soc. B 20, 554-559 (2003). In Eq. (11) of this publication, the factor i is erroneous and has to be replaced by -1. J.E. thanks Rolfe Petschek for finding this typo.
[CrossRef]

J. D. JacksonClassical Electrodynamics (John Wiley, New York, 1975).

M. Abramowitz, and I. A. Stegun, eds., Handbook of mathematical functions (Harry Deutsch, Thun and Frankfurt/Main, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Sketch of the connection between angles η and η’ upon imaging. The shown lens symbolizes the whole imaging optics, i.e. both the objective and any subsequent lens such as a tube lens.

Fig. 2.
Fig. 2.

Vectors and angles used in the calculation of the angular distribution of radiation and image formation.

Fig. 3.
Fig. 3.

Visualization of the angular distribution of radiation (ADR) and the resulting intensity distribution on the CCD for an inclined dipole emitter.

Fig. 4.
Fig. 4.

Ideal intensity distributions of molecules on the CCD for different dipole inclinations towards the sample surface as indicated by the arrows depicted above each image.

Fig. 5.
Fig. 5.

Calculated probability distributions of the differences between determined and true position of a molecule for three different inclination angles as indicated. It is assumed that a molecule is placed in water on top of a glass cover slide; imaging is done with a 1.4 N.A. objective onto a CCD chip with 50 nm effective pixel size, average photon number per image was 16000.

Fig. 6.
Fig. 6.

Mean square deviation σ of the position difference distributions for imaging with a 1.2, 1.4, 1.45 and 1.65 N.A. objective, using a CCD camera with 50 nm, 100 nm, and 200 nm effective pixel size. Every graph shows six curves for increasing signal strength; from top to bottom 500, 1000, 2000, 4000, 8000, and 16000 and infinity number of average photons per pattern.

Equations (8)

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

E η ψ = sin β [ e s E s ( η ) sin ( ψ α ) + e p E p ( η ) cos ( ψ + α ) ] + e p cos β E p ( η )
E p ( η ) = nw w m q n m T p , E p ( η ) = nw n m T p , E s = nw w m T s
{ E j B j } = 0 η max d η sin η cos η cos η { e j b j }
{ e x e y } = sin β 2 { J 0 cos α ( cos η E p E s ) J 2 cos ( 2 ϕ α ) ( cos η E p E s ) J 0 sin α ( cos η E p E s ) J 2 sin ( 2 ϕ α ) ( cos η E p + E s ) }
i cos β cos η J 1 { cos ϕ sin ϕ } E p
{ b x b y } = sin β 2 { J 0 sin α ( E p cos η E s ) + J 2 sin ( 2 ϕ α ) ( E p + cos η ' s ) J 0 cos α ( E p cos η E s ) J 2 cos ( 2 ϕ α ) ( E p + cos η E s ) }
i cos β J 1 E p { sin ϕ cos ϕ } .
S = ( c 8 π ) e z ( E × B * ) .

Metrics