Abstract

We propose and analyze a method for isotropic resolution in far-field fluorescence nanoscopy based on switching and mathematically localizing individual emitters. Under typical imaging conditions, the coherent detection of fluorescence light through two opposing high angle lenses strongly improves the 3D-resolution down to 5–10nm in all directions. Furthermore, we give a detailed analysis of the resolution of this and other single molecule switching based approaches using the Fisher information matrix. We verify the results by Monte-Carlo simulations of the imaging process and by applying a simple maximum-likelihood estimator for position determination.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  42. H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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2008 (5)

B. Harke, C. Ullal, J. Keller, and S. W. Hell, "Three-dimensional nanoscopy of colloidal crystals," Nano. Lett. 8, 1309-1313 (2008).
[CrossRef] [PubMed]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef] [PubMed]

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

2007 (6)

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, "Multicolor super-resolution imaging with photo-switchable fluorescent probes," Science 317, 1749-1752 (2007).
[CrossRef] [PubMed]

S. W. Hell, "Far-field optical nanoscopy," Science 316, 1153-1158 (2007).
[CrossRef] [PubMed]

2006 (4)

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nature Methods 3, 793-796 (2006).
[CrossRef] [PubMed]

S. T. Hess, T. P. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescent photoactivation localization microscopy (FPALM)," Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

2005 (5)

M. Hofmann, C. Eggeling, S. Jakobs, and S.W. Hell, "Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins," Proc. Natl. Acad. Sci. USA 102, 565-569 (2005).
[CrossRef]

A. d. Dekker, S. v. Art, A. v. Bos, and D. v. Dyck, "Maximum likelihood estimation of structure parameters from high resolution electron microscopy images : A theoretical framework," Ultramicroscopy 104, 83-106 (2005).
[CrossRef]

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94,143,903 (2005).
[CrossRef]

F. Aguet, D. V. D. Ville, and M. Unser, "A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles," Opt. Express 13,10503-10522 (2005).
[CrossRef] [PubMed]

2004 (3)

A. Egner, S. Verrier, A. Goroshkov, H.-D. Sling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004).
[CrossRef]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (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 (2)

A. G. Basden, C. A. Haniff, and C. D. Mackay, "Photon counting strategies with low-light-level CCDs," Monthly Notices RAS 345(3), 985-991 (2003).
[CrossRef]

S. W. Hell, "Toward fluorescence nanoscopy," Nat. Biotechnol. 21, 1347-1355 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Dyba and S. W. Hell, "Focal spots of size ⌊ /23 open up far-field fluorescence microscopy at 33 nm axial resolution," Phys. Rev. Lett. 88, 163, 901 (2002).
[CrossRef]

A. Egner, S. Jakobs, and S. W. Hell, "Fast 100-nm resolution 3D-microscope reveals structural plasticity of mitochondria in live yeast," Proc. Natl. Acad. Sci. USA 99, 3370-3375 (2002).
[CrossRef] [PubMed]

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 (2)

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

M. Nagorni and S. W. Hell, "Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts," J. Opt. Soc. Am. A 18, 36-48 (2001).
[CrossRef]

1999 (1)

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

1994 (3)

1992 (1)

1986 (1)

1983 (1)

1959 (1)

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

1945 (1)

C. Rao, "Information and the accuracy attainable in the estimation of statistical parameters," Bull. Calcutta Math. Soc. 37, 81-89 (1945).

1925 (1)

R. A. Fisher, "Theory of statistical estimation," Proc. Cambridge Philos. Soc. 22, 700-725 (1925).
[CrossRef]

1873 (1)

E. Abbe, "Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung," Arch. f. Mikr. Anat. 9, 413-420 (1873).
[CrossRef]

Abbe, E.

E. Abbe, "Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung," Arch. f. Mikr. Anat. 9, 413-420 (1873).
[CrossRef]

Agard, D. A.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Aguet, F.

Andrei, M. A.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Andresen, M.

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

Art, S. v.

A. d. Dekker, S. v. Art, A. v. Bos, and D. v. Dyck, "Maximum likelihood estimation of structure parameters from high resolution electron microscopy images : A theoretical framework," Ultramicroscopy 104, 83-106 (2005).
[CrossRef]

Basden, A. G.

A. G. Basden, C. A. Haniff, and C. D. Mackay, "Photon counting strategies with low-light-level CCDs," Monthly Notices RAS 345(3), 985-991 (2003).
[CrossRef]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, "Multicolor super-resolution imaging with photo-switchable fluorescent probes," Science 317, 1749-1752 (2007).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nature Methods 3, 793-796 (2006).
[CrossRef] [PubMed]

Belov, V.

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

Belov, V. N.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

Bennett, B.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Betzig, E.

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Bewersdorf, J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
[CrossRef] [PubMed]

Bock, H.

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Bos, A. v.

A. d. Dekker, S. v. Art, A. v. Bos, and D. v. Dyck, "Maximum likelihood estimation of structure parameters from high resolution electron microscopy images : A theoretical framework," Ultramicroscopy 104, 83-106 (2005).
[CrossRef]

Bossi, M.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

Boyarskiy, V. P.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

Cheezum, M. K.

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

Cremer, C.

Davidson, M. W.

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Dekker, A. d.

A. d. Dekker, S. v. Art, A. v. Bos, and D. v. Dyck, "Maximum likelihood estimation of structure parameters from high resolution electron microscopy images : A theoretical framework," Ultramicroscopy 104, 83-106 (2005).
[CrossRef]

Dempsey, G. T.

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, "Multicolor super-resolution imaging with photo-switchable fluorescent probes," Science 317, 1749-1752 (2007).
[CrossRef] [PubMed]

Dieck, S. T.

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

Donnert, G.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Dyba, M.

M. Dyba and S. W. Hell, "Focal spots of size ⌊ /23 open up far-field fluorescence microscopy at 33 nm axial resolution," Phys. Rev. Lett. 88, 163, 901 (2002).
[CrossRef]

Dyck, D. v.

A. d. Dekker, S. v. Art, A. v. Bos, and D. v. Dyck, "Maximum likelihood estimation of structure parameters from high resolution electron microscopy images : A theoretical framework," Ultramicroscopy 104, 83-106 (2005).
[CrossRef]

Eggeling, C.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

M. Hofmann, C. Eggeling, S. Jakobs, and S.W. Hell, "Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins," Proc. Natl. Acad. Sci. USA 102, 565-569 (2005).
[CrossRef]

Egner, A.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

A. Egner, S. Verrier, A. Goroshkov, H.-D. Sling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004).
[CrossRef]

A. Egner, S. Jakobs, and S. W. Hell, "Fast 100-nm resolution 3D-microscope reveals structural plasticity of mitochondria in live yeast," Proc. Natl. Acad. Sci. USA 99, 3370-3375 (2002).
[CrossRef] [PubMed]

Elbaum, M.

Engelhardt, J.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
[CrossRef] [PubMed]

F¨olling, J.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
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R. A. Fisher, "Theory of statistical estimation," Proc. Cambridge Philos. Soc. 22, 700-725 (1925).
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H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

Galbraith, J. A.

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
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Geisler, C.

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
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A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
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Gillette, J.

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
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Girirajan, T. P.

S. T. Hess, T. P. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescent photoactivation localization microscopy (FPALM)," Biophys. J. 91, 4258-4272 (2006).
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Goroshkov, A.

A. Egner, S. Verrier, A. Goroshkov, H.-D. Sling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004).
[CrossRef]

Gould, T. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
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Gugel, H.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
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Guilford, W. H.

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

Gundelfinger, E. D.

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
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M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
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A. G. Basden, C. A. Haniff, and C. D. Mackay, "Photon counting strategies with low-light-level CCDs," Monthly Notices RAS 345(3), 985-991 (2003).
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Harke, B.

B. Harke, C. Ullal, J. Keller, and S. W. Hell, "Three-dimensional nanoscopy of colloidal crystals," Nano. Lett. 8, 1309-1313 (2008).
[CrossRef] [PubMed]

Hell, S.

Hell, S. W.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

B. Harke, C. Ullal, J. Keller, and S. W. Hell, "Three-dimensional nanoscopy of colloidal crystals," Nano. Lett. 8, 1309-1313 (2008).
[CrossRef] [PubMed]

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
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S. W. Hell, "Far-field optical nanoscopy," Science 316, 1153-1158 (2007).
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A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
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V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94,143,903 (2005).
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H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
[CrossRef] [PubMed]

A. Egner, S. Verrier, A. Goroshkov, H.-D. Sling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004).
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S. W. Hell, "Toward fluorescence nanoscopy," Nat. Biotechnol. 21, 1347-1355 (2003).
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M. Dyba and S. W. Hell, "Focal spots of size ⌊ /23 open up far-field fluorescence microscopy at 33 nm axial resolution," Phys. Rev. Lett. 88, 163, 901 (2002).
[CrossRef]

A. Egner, S. Jakobs, and S. W. Hell, "Fast 100-nm resolution 3D-microscope reveals structural plasticity of mitochondria in live yeast," Proc. Natl. Acad. Sci. USA 99, 3370-3375 (2002).
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M. Nagorni and S. W. Hell, "Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts," J. Opt. Soc. Am. A 18, 36-48 (2001).
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S. W. Hell and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission: stimulated emission depletion microscopy," Opt. Lett. 19, 780-782 (1994).
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S. W. Hell, E. H. K. Stelzer, S. Lindek, and C. Cremer, "Confocal microscopy with enhanced detection aperture: type B 4Pi-confocal microscopy," Opt. Lett. 19, 222-224 (1994).
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Hell, S.W.

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

M. Hofmann, C. Eggeling, S. Jakobs, and S.W. Hell, "Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins," Proc. Natl. Acad. Sci. USA 102, 565-569 (2005).
[CrossRef]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Hess, S. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

S. T. Hess, T. P. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescent photoactivation localization microscopy (FPALM)," Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

Hofmann, M.

M. Hofmann, C. Eggeling, S. Jakobs, and S.W. Hell, "Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins," Proc. Natl. Acad. Sci. USA 102, 565-569 (2005).
[CrossRef]

Huang, B.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, "Multicolor super-resolution imaging with photo-switchable fluorescent probes," Science 317, 1749-1752 (2007).
[CrossRef] [PubMed]

Jahn, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Jakobs, S.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

M. Hofmann, C. Eggeling, S. Jakobs, and S.W. Hell, "Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins," Proc. Natl. Acad. Sci. USA 102, 565-569 (2005).
[CrossRef]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
[CrossRef] [PubMed]

A. Egner, S. Jakobs, and S. W. Hell, "Fast 100-nm resolution 3D-microscope reveals structural plasticity of mitochondria in live yeast," Proc. Natl. Acad. Sci. USA 99, 3370-3375 (2002).
[CrossRef] [PubMed]

Juette, M. F.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
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H. P. Kao and A. Verkman, "Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position," Biophys. J. 67, 1291-1300 (1994).
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Keller, J.

B. Harke, C. Ullal, J. Keller, and S. W. Hell, "Three-dimensional nanoscopy of colloidal crystals," Nano. Lett. 8, 1309-1313 (2008).
[CrossRef] [PubMed]

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Khimich, D.

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

Kunetsky, R.

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

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]

Lessard, M. D.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Lindek, S.

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Lührmann, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Mackay, C. D.

A. G. Basden, C. A. Haniff, and C. D. Mackay, "Photon counting strategies with low-light-level CCDs," Monthly Notices RAS 345(3), 985-991 (2003).
[CrossRef]

Mason, M. D.

S. T. Hess, T. P. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescent photoactivation localization microscopy (FPALM)," Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

Medda, R.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Middendorff, C. v.

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

Mlodzianoski, M. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Moser, T.

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

Nagorni, M.

Nagpure, B. S.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Nouvian, R.

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

Nowakowski, J.

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]

Olenych, S.

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Pujol, R.

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

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]

Rao, C.

C. Rao, "Information and the accuracy attainable in the estimation of statistical parameters," Bull. Calcutta Math. Soc. 37, 81-89 (1945).

Richards, B.

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

Rizzoli, S. O.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nature Methods 3, 793-796 (2006).
[CrossRef] [PubMed]

Schmidt, R.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

Schönle, A.

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

Sedat, J. W.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Shroff, H.

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

Sling, H.-D.

A. Egner, S. Verrier, A. Goroshkov, H.-D. Sling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004).
[CrossRef]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Stelzer, E. H. K.

Stiel, A.

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

Storz, R.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
[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]

Ullal, C.

B. Harke, C. Ullal, J. Keller, and S. W. Hell, "Three-dimensional nanoscopy of colloidal crystals," Nano. Lett. 8, 1309-1313 (2008).
[CrossRef] [PubMed]

Unser, M.

Verkman, A.

H. P. Kao and A. Verkman, "Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position," Biophys. J. 67, 1291-1300 (1994).
[CrossRef] [PubMed]

Verrier, S.

A. Egner, S. Verrier, A. Goroshkov, H.-D. Sling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004).
[CrossRef]

Ville, D. V. D.

Walker, W. F.

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

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[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]

Wenzel, D.

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

Westphal, V.

V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94,143,903 (2005).
[CrossRef]

White, H.

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

Wichmann, J.

Winick, K.

Wolf, E.

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

Wurm, C. A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, "Multicolor super-resolution imaging with photo-switchable fluorescent probes," Science 317, 1749-1752 (2007).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nature Methods 3, 793-796 (2006).
[CrossRef] [PubMed]

Angew. Chem. Int. Ed. (1)

J. F¨olling, V. Belov, R. Kunetsky, R. Medda, A. Schönle, A. Egner, C. Eggeling, M. Bossi, and S. W. Hell, "Photochromic rhodamines provide nanoscopy with optical sectioning," Angew. Chem. Int. Ed. 46, 6266 - 6270 (2007).
[CrossRef]

Appl. Phys. B (1)

H. Bock, C. Geisler, C. A. Wurm, C. v. Middendorff, S. Jakobs, A. Schönle, A. Egner, S.W. Hell, and C. Eggeling, "Two-color far-field fluorescence nanoscopy based on photoswitchable emitters," Appl. Phys. B 88, 161-165 (2007).
[CrossRef]

Arch. f. Mikr. Anat. (1)

E. Abbe, "Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung," Arch. f. Mikr. Anat. 9, 413-420 (1873).
[CrossRef]

Biophys. J. (7)

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. Walker, and W. H. Guilford, "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]

H. P. Kao and A. Verkman, "Tracking of single fluorescent particles in three dimensions: Use of cylindrical optics to encode particle position," Biophys. J. 67, 1291-1300 (1994).
[CrossRef] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, "Cooperative 4Pi excitation and detection yields 7-fold sharper optical sections in live cell microscopy," Biophys. J. 87, 4146-4152 (2004).
[CrossRef] [PubMed]

S. T. Hess, T. P. Girirajan, and M. D. Mason, "Ultra-high resolution imaging by fluorescent photoactivation localization microscopy (FPALM)," Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

A. Egner, C. Geisler, C. v. Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. Stiel, S. Jakobs, C. Eggeling, A. Schönle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007).
[CrossRef] [PubMed]

Bull. Calcutta Math. Soc. (1)

C. Rao, "Information and the accuracy attainable in the estimation of statistical parameters," Bull. Calcutta Math. Soc. 37, 81-89 (1945).

J. Microsc. (1)

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Struct. Biol. (1)

A. Egner, S. Verrier, A. Goroshkov, H.-D. Sling, and S. W. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147(1), 70-76 (2004).
[CrossRef]

Monthly Notices RAS (1)

A. G. Basden, C. A. Haniff, and C. D. Mackay, "Photon counting strategies with low-light-level CCDs," Monthly Notices RAS 345(3), 985-991 (2003).
[CrossRef]

Nano. Lett. (2)

B. Harke, C. Ullal, J. Keller, and S. W. Hell, "Three-dimensional nanoscopy of colloidal crystals," Nano. Lett. 8, 1309-1313 (2008).
[CrossRef] [PubMed]

M. Bossi, J. F¨olling, V. N. Belov, V. P. Boyarskiy, R. Medda, A. Egner, C. Eggeling, A. Schönle, and S. W. Hell, "Multicolor far-field fluorescence nanoscopy through isolated detection of distinct molecular species," Nano. Lett. 8, 2463-2468 (2008).
[CrossRef] [PubMed]

Nat. Biotechnol. (1)

S. W. Hell, "Toward fluorescence nanoscopy," Nat. Biotechnol. 21, 1347-1355 (2003).
[CrossRef] [PubMed]

Nature (1)

D. Khimich, R. Nouvian, R. Pujol, S. T. Dieck, A. Egner, E. D. Gundelfinger, and T. Moser, "Hair cell synaptic ribbons are essential for synchronous auditory signalling," Nature 434(7035), 889-894 (2005).
[CrossRef]

Nature Methods (3)

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nature Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nature Methods 3, 793-796 (2006).
[CrossRef] [PubMed]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, "Spherical nanosized focal spot unravels the interior of cells," Nature Methods 5, 539 - 544 (2008).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94,143,903 (2005).
[CrossRef]

M. Dyba and S. W. Hell, "Focal spots of size ⌊ /23 open up far-field fluorescence microscopy at 33 nm axial resolution," Phys. Rev. Lett. 88, 163, 901 (2002).
[CrossRef]

Proc. Cambridge Philos. Soc. (1)

R. A. Fisher, "Theory of statistical estimation," Proc. Cambridge Philos. Soc. 22, 700-725 (1925).
[CrossRef]

Proc. Natl. Acad. Sci. USA (4)

A. Egner, S. Jakobs, and S. W. Hell, "Fast 100-nm resolution 3D-microscope reveals structural plasticity of mitochondria in live yeast," Proc. Natl. Acad. Sci. USA 99, 3370-3375 (2002).
[CrossRef] [PubMed]

M. Hofmann, C. Eggeling, S. Jakobs, and S.W. Hell, "Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins," Proc. Natl. Acad. Sci. USA 102, 565-569 (2005).
[CrossRef]

H. Shroff, C. G. Galbraith, J. A. Galbraith, H. White, J. Gillette, S. Olenych, M. W. Davidson, and E. Betzig "Dual-color superresolution imaging of genetically expressed probes within individual adhesion complexes," Proc. Natl. Acad. Sci. USA 104, 20308-20313 (2007).
[CrossRef] [PubMed]

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 440-445 (2006).
[CrossRef]

Proc. R. Soc. Lond. A (1)

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

Science (4)

S. W. Hell, "Far-field optical nanoscopy," Science 316, 1153-1158 (2007).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, "Multicolor super-resolution imaging with photo-switchable fluorescent probes," Science 317, 1749-1752 (2007).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging intracellular fluorescent proteins at nanometer resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Ultramicroscopy (1)

A. d. Dekker, S. v. Art, A. v. Bos, and D. v. Dyck, "Maximum likelihood estimation of structure parameters from high resolution electron microscopy images : A theoretical framework," Ultramicroscopy 104, 83-106 (2005).
[CrossRef]

Other (4)

D. R. Cox and D. V. Hinkley, Theoretical Statistics (Chapman and Hall, London, 1974).

H. Cramer, Mathematical Methods of Statistics (Princeton Univ. Press, Princeton, 1946).

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, Cambridge, 2002).

W. Heisenberg, The Physical Principles of Quantum Theory (Chicago Univ. Press, Chicago, 1930).

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Figures (9)

Fig. 1.
Fig. 1.

xz-cuts of the PSFs h (top row) for an unaberrated PSF (a), in the presence of an astigmatism (b) and detection in two axially offset channels in order to break the axial symmetry (c). The second row shows xz-cuts of the differential axial information content i zz , k while the third row shows the combined differential information content averaged over all polar angles i zz . Please note that for the astigmatism case h(x,y, z) and thus i kz (x,y, z) are not rotationally symmetric in the xy-plane. For example, the yz-cut would be the mirror image about the focal plane of the xz-cut shown here.

Fig. 2.
Fig. 2.

Radial Cramer-Rao bounds σ x , σ y (a) and axial bound σ z (b) for the aberrated detection scheme with different strengths S of the astigmatism. The graphs correspond to S=3 (1), 2 (2), 1.75 (3), 1.5 (4), 1.25 (5) and 1 (6). The bounds for ordinary wide-field detection (S=0) are plotted for comparison (red).

Fig. 3.
Fig. 3.

Radial Cramer-Rao bounds σ x , σ y (a) and axial bound σ z (b) for the defocused detection scheme with two or more channels with different focal planes (solid). The different graphs correspond to setups with 2, 4 and 6 channels as indicated by the numbers in the plot. Their focal planes were assumed to be evenly spaced with the highest and lowest one at z=±300nm. As before, the performance for wide-field detection in a single channel has been plotted for comparison (dotted).

Fig. 4.
Fig. 4.

Radial Cramer-Rao bounds σ x , σ y (a) and axial bound σ z (b) for the defocused detection scheme with two channels with their focal planes placed symmetrically about z=0 at varying distances of d=200nm (1), 400 nm (2) and 600 nm (3). Again the onefocus result (dotted) was plotted for comparison.

Fig. 5.
Fig. 5.

Schematic illustration of an interferometric 4-channel detection setup. The light is collected by two opposing objective lenses OL1 and OL2. A first beam splitter is used to combine the beams from the two objective lenses. The phase retardation φ a is used to control the relative phase of the two beams, e.g. in order to produce constructive interference in the focal spot in beam E 1 and destructive interference in E 2. By overlaying half their intensity at a second beam-splitter, two additional beams are produced. Their relative phase shifts can be offset relative to those of the first two channels using a second phase retardation φ b .

Fig. 6.
Fig. 6.

xz-cuts of the PSFs (top row) for wide-field detection (a) and the different channels of the interferometric setup (b). The second row shows the differential information content which is much higher for interferometric detection due to the steepened axial features of the PSF. Please note the change of scale as compared to Fig. 1. Using just one beam-splitter and combining the two resulting channels results in approximate axial symmetry and almost vanishing information content in the minima and maxima of the PSFs (second row). Only the combination of all four channels leads to almost uniformly high information content along the optic axis (bottom row).

Fig. 7.
Fig. 7.

Radial Cramer-Rao bounds σ x , σ y (a) and axial bound σ z (b) for the inter-ferometric detection scheme (blue) in comparison to the two-channel defocus setup (red) with two channels focused at z=±300nm and an astigmatism of strength S=3 (black). The Cramer-Rao bounds for interferometric detection using just one beam splitter and two channels is also shown (blue, dotted). As before we have plotted the bounds for wide-field detection in a single channel for comparison (red, dotted). As above, introducing more channels can lower radial precision due to a smaller signal-to-noise level.

Fig. 8.
Fig. 8.

Radial Cramer-Rao bounds σ x , σ y (a) and axial bound σ z (b) for the interferometric detection setup at different signal-to-noise levels b=1/500 (1), 1/32 (2), 1/8 (3) and 1/2 (4). The first graph (1) is based on the same signal-to-noise level that was used for all other calculations.

Fig. 9.
Fig. 9.

Monte-Carlo simulation of a maximum-likelihood estimator in a 3D single switching event based microscope using 4-channel interferometric detection. (a) Mean squared error of the axial position determined during 150 simulated localizations per individual axial value (grey) and corresponding Cramer-Rao bounds (blue). (b) Histogram plot of the errors showing no side maxima at any axial position which would indicate systematic false assignments.

Equations (23)

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h ijk ( r ) = h k ( x i x , y j y , z )
k d x d y h k ( r ) = 1 .
n ijk ( r ) = N ( h ijk ( r ) + b ) ,
p ( { N ijk } r ) = k ij f ( N ijk ; n ijk ( r ) )
f ( k ; λ ) = λ k exp ( λ ) k !
I qs ( r ) = [ q ln p ( o r ) ] [ s ln p ( o r ) ] p ( o r ) d o ,
I qs ( r ) = k ij N 2 [ q h ijk ( r ) ] [ s h ijk ( r ) ] n ijk ( r ) .
i q s , k ( r ) = [ q h k ( r ) ] [ s h k ( r ) ] [ h k ( r ) + b ] .
i q s ( r , z ) = k i q s , k ( r , φ , z ) d φ 2 π
I q q ( r ) = N I q ( z ) = N k i q q , k ( r ) d x d y .
σ q ( z ) 1 N I q ( z ) .
exp [ i S ρ 2 cos ( 2 ϕ ) ] .
E 1 = [ E a exp ( ι π 2 ) exp ( ι φ a ) + E b ] 2
E 2 = [ E a exp ( ι φ a ) + E b exp ( ι π 2 ) ] 2
E 3 = [ E 1 exp ( ι π 2 ) exp ( ι φ b ) + E 2 ] 2
E 4 = [ E 1 exp ( ι φ b ) + E 2 exp ( ι π 2 ) ] 2 .
E 3 = exp ( ι φ b 2 ) exp ( ι π 2 ) [ E a exp ( ι φ a ) cos ( [ π + φ b ] 2 ) + E b cos ( φ b 2 ) ]
E 4 = exp ( ι φ b 2 ) exp ( ι π 2 ) [ E a exp ( ι φ a ) cos ( φ b 2 ) + E b cos ( [ π φ b ] 2 ) ]
E 3 = exp ( ι π 4 ) [ E a exp ( ι φ a ) + E b ] 2
E 4 = exp ( ι π 4 ) [ E a exp ( ι φ a ) E b ] 2
E k = exp ( ι φ k ) [ E a exp ( ι [ φ a + Δ φ k ] ) + E b ] 2
I k ( r ) = E ( r ) + exp ( ι φ a ) exp ( ι Δ φ k ) M E ( Mr ) 2
M = ( 1 0 0 0 1 0 0 0 1 ) ,

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