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

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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 ,” Chem-PhysChem.   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 ,” Bio-phys. 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 (4)

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]

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

M. Speidel , A. Jonas , and E. L. Florin , “ Three-dimensional tracking of fluorescent nanoparticles with sub-nanometer precision by use of off-focus imaging ,” Opt. Lett.   28 , 69 – 71 ( 2003 ).
[CrossRef] [PubMed]

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]

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)

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]

J. Enderlein , T. Ruckstuhl , and S. Seeger , “ Highly efficient optical detection of surface-generated fluorescence ,” Appl. Opt.   38 , 724 – 732 ( 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)

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

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]

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.

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. 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]

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 handover-hand, ingle 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 handover-hand, ingle 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 handover-hand, ingle 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 ,” Bio-phys. 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 ,” Chem-PhysChem.   6 , 2286 – 2294 ( 2005 ).
[CrossRef]

Jackson, J. D.

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

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 ,” Chem-PhysChem.   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 handover-hand, ingle 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 ,” Chem-PhysChem.   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 ,” Chem-PhysChem.   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 ,” Chem-PhysChem.   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 ,” Chem-PhysChem.   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 ,” Bio-phys. 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 ,” Bio-phys. 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 ,” Bio-phys. 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 handover-hand, ingle 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 ,” Bio-phys. 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 ,” Chem-PhysChem.   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 ,” Chem-PhysChem.   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 ,” Chem-PhysChem.   6 , 2286 – 2294 ( 2005 ).
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A. Yildiz and P. R. Selvin , “ Fluorescence imaging with one nanometer accuracy, Application to molecular motors ,” Acc. Chem. Res.   38 , 574 – 582 ( 2005 ).
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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 ,” Bio-phys. J.   87 , 1776 – 1783 ( 2004 ).

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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 ).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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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 ,” Chem-PhysChem.   6 , 2286 – 2294 ( 2005 ).
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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 ).
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H. Park , G. T. Hanson , S. R. Duff , and P. R. Selvin , “ Nanometre localization of single ReAsH molecules ,” J. Microsc.   216 , 199 – 205 ( 2004 ).
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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 ).
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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 handover-hand, ingle fluorophore imaging with 1.5-nm localization ,” Science   300 , 2061 – 2065 ( 2003 ).
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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)

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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 * ) .

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