Abstract

A straightforward method to achieve super-resolution consists of taking an image sequence of stochastically blinking emitters using a standard wide-field fluorescence microscope. Densely packed single molecules can be distinguished sequentially in time using high-precision localization algorithms (e.g., PALM and STORM) or by analyzing the statistics of the temporal fluctuations (SOFI). In a face-to-face comparison of the two post-processing algorithms, we show that localization-based super-resolution can deliver higher resolution enhancements but imposes significant constraints on the blinking behavior of the probes, which limits its applicability for live-cell imaging. SOFI, on the other hand, works more consistently over different photo-switching kinetics and also delivers information about the specific blinking statistics. Its suitability for low SNR acquisition reveals SOFI's potential as a high-speed super-resolution imaging technique.

© 2011 OSA

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2010 (9)

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190(2), 165–175 (2010).
[Crossref] [PubMed]

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

T. M. Watanabe, S. Fukui, T. Jin, F. Fujii, and T. Yanagida, “Real-time nanoscopy by using blinking enhanced quantum dots,” Biophys. J. 99(7), L50–L52 (2010).
[Crossref] [PubMed]

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149(4), 260–266 (2010).
[Crossref] [PubMed]

C. M. Winterflood, T. Ruckstuhl, D. Verdes, and S. Seeger, “Nanometer axial resolution by three-dimensional supercritical angle fluorescence microscopy,” Phys. Rev. Lett. 105(10), 108103 (2010).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, R. Vogel, J. Enderlein, and S. Weiss, “Achieving increased resolution and more pixels with Superresolution Optical Fluctuation Imaging (SOFI),” Opt. Express 18(18), 18875–18885 (2010).
[Crossref] [PubMed]

I. Märki, N. L. Bocchio, S. Geissbuehler, F. Aguet, A. Bilenca, and T. Lasser, “Three-dimensional nano-localization of single fluorescent emitters,” Opt. Express 18(19), 20263–20272 (2010).
[Crossref] [PubMed]

2009 (7)

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

F. Aguet, S. Geissbühler, I. Märki, T. Lasser, and M. Unser, “Super-resolution orientation estimation and localization of fluorescent dipoles using 3-D steerable filters,” Opt. Express 17(8), 6829–6848 (2009).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-resolution imaging with small organic fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[Crossref] [PubMed]

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[Crossref] [PubMed]

2008 (2)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

2007 (1)

H. M. O’Hare, K. Johnsson, and A. Gautier, “Chemical probes shed light on protein function,” Curr. Opin. Struct. Biol. 17(4), 488–494 (2007).
[Crossref] [PubMed]

2006 (3)

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

2005 (1)

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005).
[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(5), 2775–2783 (2002).
[Crossref] [PubMed]

2001 (1)

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81(4), 2378–2388 (2001).
[Crossref] [PubMed]

1998 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IEEE 86(2), 447–457 (1998).
[Crossref]

1994 (1)

1991 (1)

J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications,” Proc. IEEE 79(3), 278–305 (1991).
[Crossref]

Aguet, F.

Banala, S.

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

Bates, M.

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Betzig, E.

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bilenca, A.

Biteen, J. S.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Bocchio, N.

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

Bocchio, N. L.

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(5793), 1642–1645 (2006).
[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(4), 2378–2388 (2001).
[Crossref] [PubMed]

Colyer, R.

T. Dertinger, R. Colyer, R. Vogel, J. Enderlein, and S. Weiss, “Achieving increased resolution and more pixels with Superresolution Optical Fluctuation Imaging (SOFI),” Opt. Express 18(18), 18875–18885 (2010).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Cornish, V. W.

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

Davidson, M.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

Davidson, M. W.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Dellagiacoma, C.

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

Dertinger, T.

T. Dertinger, R. Colyer, R. Vogel, J. Enderlein, and S. Weiss, “Achieving increased resolution and more pixels with Superresolution Optical Fluctuation Imaging (SOFI),” Opt. Express 18(18), 18875–18885 (2010).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Enderlein, J.

T. Dertinger, R. Colyer, R. Vogel, J. Enderlein, and S. Weiss, “Achieving increased resolution and more pixels with Superresolution Optical Fluctuation Imaging (SOFI),” Opt. Express 18(18), 18875–18885 (2010).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Fetter, R. D.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Fujii, F.

T. M. Watanabe, S. Fukui, T. Jin, F. Fujii, and T. Yanagida, “Real-time nanoscopy by using blinking enhanced quantum dots,” Biophys. J. 99(7), L50–L52 (2010).
[Crossref] [PubMed]

Fukui, S.

T. M. Watanabe, S. Fukui, T. Jin, F. Fujii, and T. Yanagida, “Real-time nanoscopy by using blinking enhanced quantum dots,” Biophys. J. 99(7), L50–L52 (2010).
[Crossref] [PubMed]

Galbraith, C. G.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Galbraith, J. A.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Gautier, A.

H. M. O’Hare, K. Johnsson, and A. Gautier, “Chemical probes shed light on protein function,” Curr. Opin. Struct. Biol. 17(4), 488–494 (2007).
[Crossref] [PubMed]

Geissbuehler, S.

Geissbühler, S.

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

F. Aguet, S. Geissbühler, I. Märki, T. Lasser, and M. Unser, “Super-resolution orientation estimation and localization of fluorescent dipoles using 3-D steerable filters,” Opt. Express 17(8), 6829–6848 (2009).
[Crossref] [PubMed]

Gillette, J. M.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Girirajan, T. P.

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

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(4), 2378–2388 (2001).
[Crossref] [PubMed]

Gustafsson, M. G.

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005).
[Crossref] [PubMed]

Heidbreder, M.

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

Heilemann, M.

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149(4), 260–266 (2010).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-resolution imaging with small organic fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

Heintzmann, R.

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190(2), 165–175 (2010).
[Crossref] [PubMed]

Hell, S. W.

Hess, H. F.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Hess, S. T.

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Huang, B.

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

Iyer, G.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Jin, T.

T. M. Watanabe, S. Fukui, T. Jin, F. Fujii, and T. Yanagida, “Real-time nanoscopy by using blinking enhanced quantum dots,” Biophys. J. 99(7), L50–L52 (2010).
[Crossref] [PubMed]

Johnsson, K.

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

H. M. O’Hare, K. Johnsson, and A. Gautier, “Chemical probes shed light on protein function,” Curr. Opin. Struct. Biol. 17(4), 488–494 (2007).
[Crossref] [PubMed]

Kanchanawong, P.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Kasper, R.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Lasser, T.

Leonhardt, H.

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190(2), 165–175 (2010).
[Crossref] [PubMed]

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Liu, N.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Lord, S. J.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Lukinavicius, G.

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

Manley, S.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Märki, I.

Mason, M. D.

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Mendel, J. M.

J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications,” Proc. IEEE 79(3), 278–305 (1991).
[Crossref]

Moerner, W. E.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Mukherjee, A.

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-resolution imaging with small organic fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

O’Hare, H. M.

H. M. O’Hare, K. Johnsson, and A. Gautier, “Chemical probes shed light on protein function,” Curr. Opin. Struct. Biol. 17(4), 488–494 (2007).
[Crossref] [PubMed]

Olenych, 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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Patterson, G.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Pavani, S. R.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Piestun, R.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Ruckstuhl, T.

C. M. Winterflood, T. Ruckstuhl, D. Verdes, and S. Seeger, “Nanometer axial resolution by three-dimensional supercritical angle fluorescence microscopy,” Phys. Rev. Lett. 105(10), 108103 (2010).
[Crossref] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Sauer, M.

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149(4), 260–266 (2010).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-resolution imaging with small organic fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

Schermelleh, L.

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190(2), 165–175 (2010).
[Crossref] [PubMed]

Schüttpelz, M.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

Seefeldt, B.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

Seeger, S.

C. M. Winterflood, T. Ruckstuhl, D. Verdes, and S. Seeger, “Nanometer axial resolution by three-dimensional supercritical angle fluorescence microscopy,” Phys. Rev. Lett. 105(10), 108103 (2010).
[Crossref] [PubMed]

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IEEE 86(2), 447–457 (1998).
[Crossref]

Sheetz, M. P.

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

Shtengel, G.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Sougrat, R.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Thompson, M. A.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[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(5), 2775–2783 (2002).
[Crossref] [PubMed]

Tinnefeld, P.

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

Twieg, R. J.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Unser, M.

van de Linde, S.

S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149(4), 260–266 (2010).
[Crossref] [PubMed]

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-resolution imaging with small organic fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

Verdes, D.

C. M. Winterflood, T. Ruckstuhl, D. Verdes, and S. Seeger, “Nanometer axial resolution by three-dimensional supercritical angle fluorescence microscopy,” Phys. Rev. Lett. 105(10), 108103 (2010).
[Crossref] [PubMed]

Vogel, R.

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(4), 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(5864), 810–813 (2008).
[Crossref] [PubMed]

Watanabe, T. M.

T. M. Watanabe, S. Fukui, T. Jin, F. Fujii, and T. Yanagida, “Real-time nanoscopy by using blinking enhanced quantum dots,” Biophys. J. 99(7), L50–L52 (2010).
[Crossref] [PubMed]

Waterman, C. M.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[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(5), 2775–2783 (2002).
[Crossref] [PubMed]

Weiss, S.

T. Dertinger, R. Colyer, R. Vogel, J. Enderlein, and S. Weiss, “Achieving increased resolution and more pixels with Superresolution Optical Fluctuation Imaging (SOFI),” Opt. Express 18(18), 18875–18885 (2010).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Wichmann, J.

Winterflood, C. M.

C. M. Winterflood, T. Ruckstuhl, D. Verdes, and S. Seeger, “Nanometer axial resolution by three-dimensional supercritical angle fluorescence microscopy,” Phys. Rev. Lett. 105(10), 108103 (2010).
[Crossref] [PubMed]

Wolter, S.

S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149(4), 260–266 (2010).
[Crossref] [PubMed]

Wombacher, R.

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

Yanagida, T.

T. M. Watanabe, S. Fukui, T. Jin, F. Fujii, and T. Yanagida, “Real-time nanoscopy by using blinking enhanced quantum dots,” Biophys. J. 99(7), L50–L52 (2010).
[Crossref] [PubMed]

Zhuang, X.

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Angew. Chem. Int. Ed. Engl. (2)

M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. 47(33), 6172–6176 (2008).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-resolution imaging with small organic fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

Annu. Rev. Biochem. (1)

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[Crossref] [PubMed]

Annu. Rev. Phys. Chem. (1)

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

Biophys. J. (4)

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

T. M. Watanabe, S. Fukui, T. Jin, F. Fujii, and T. Yanagida, “Real-time nanoscopy by using blinking enhanced quantum dots,” Biophys. J. 99(7), L50–L52 (2010).
[Crossref] [PubMed]

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81(4), 2378–2388 (2001).
[Crossref] [PubMed]

ChemBioChem (1)

C. Dellagiacoma, G. Lukinavičius, N. Bocchio, S. Banala, S. Geissbühler, I. Märki, K. Johnsson, and T. Lasser, “Targeted photoswitchable probe for nanoscopy of biological structures,” ChemBioChem 11(10), 1361–1363 (2010).
[Crossref] [PubMed]

Curr. Opin. Struct. Biol. (1)

H. M. O’Hare, K. Johnsson, and A. Gautier, “Chemical probes shed light on protein function,” Curr. Opin. Struct. Biol. 17(4), 488–494 (2007).
[Crossref] [PubMed]

J. Biotechnol. (1)

S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149(4), 260–266 (2010).
[Crossref] [PubMed]

J. Cell Biol. (1)

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190(2), 165–175 (2010).
[Crossref] [PubMed]

Nat. Methods (3)

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7(9), 717–719 (2010).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

C. M. Winterflood, T. Ruckstuhl, D. Verdes, and S. Seeger, “Nanometer axial resolution by three-dimensional supercritical angle fluorescence microscopy,” Phys. Rev. Lett. 105(10), 108103 (2010).
[Crossref] [PubMed]

Proc. IEEE (2)

C. E. Shannon, “Communication in the presence of noise,” Proc. IEEE 86(2), 447–457 (1998).
[Crossref]

J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications,” Proc. IEEE 79(3), 278–305 (1991).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (4)

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Science (2)

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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Figures (11)

Fig. 1.
Fig. 1.

The different steps of calculating cross-cumulant SOFI with Fourier reweighting (XC-SOFI-FRW), illustrated for the second order. Before the computation of crosscumulants, the mean is subtracted from the data. Using different combinations of crosscumulants between pixels gives rise to an inhomogeneous weight distribution (step 2), which needs to be corrected by a distance factor (step 3). The distance-factor correction also provides an estimation of the system's PSF. Fourier reweighting (FRW) enables the modification of the SOFI equivalent PSF to retrieve the microscope's PSF with an n-fold reduced size (step 4). Higher-order cumulants are computed using the exact formulation described in [21]. Scale bars: 200 nm.

Fig. 2.
Fig. 2.

Fourth-order cross-cumulant combinations for pixel i with or without repetitions. Different combinations within a neighborhood matrix of i can be used to generate 15 inter-pixels in between the original pixel matrix (ABCD). Combinations leading to the same inter-pixel are averaged. (a) All n-combinations within a 2×2 neighborhood (ABCD) starting with A and allowing for repetitions are computed. This scheme can be expanded easily to any order n. Due to the presence of autocumulants, this method does not suppress shot noise very well unless non-zero time lags are used. (b) The different combinations within a 4×4 neighborhood of pixel i can be used to generate inter-pixels in a circular arrangement (left). By excluding repetitions (autocumulants), shot noise is suppressed much better. For computational reasons, only combinations featuring the shortest sum of distances with respect to their corresponding inter-pixels are considered. By considering more combinations and averaging over the corresponding cross-cumulants, even more noise could be eliminated. Further simplification can be done by considering only combinations leading to the 15 inter-pixels within ABCD (right). This scheme is expandable until order 10. To go beyond this range, the size of the neighborhood has to be increased.

Fig. 3.
Fig. 3.

STORM-principle: The image sequence is processed frame by frame. For the localization, the images are segmented and each isolated diffraction pattern is fitted to a parameterized Gaussian PSF model (step 2). The determined single-molecule positions are combined in a composite image with a ten-fold finer sampling grid (step 3). Scale bars: 200 nm.

Fig. 4.
Fig. 4.

The visibility defined in Eq. (4) serves as a benchmark for comparing the different algorithms. The line profiles are obtained by projecting the images along the y direction. I max,1 and I max,2 are obtained by taking the mean intensity at the known positions of the lines (x 1 and x 2) and Imin is the mean intensity between 0.4(x 1+x 2) and 0.6(x 1+x 2). Scale bars: 500 nm.

Fig. 5.
Fig. 5.

Comparison of the visibility versus rate ratio. The best XC-SOFI is obtained by the SOFI order yielding the highest average relative visibility for a specific set of simulation parameters. σ denotes the average relative standard deviation. Fixed simulation parameters: k/f = 0.5, line separation: 0.6 Airy units, labeling density: 5/µm, 1000 frames, 50 realizations per point.

Fig. 6.
Fig. 6.

Visual comparison of SOFI and STORM reconstructions at different rate-ratios. (a) Target structure. (b) Summed TIRF. (c) XC-SOFI5 FRW, r = 0.6. (d) STORM, r = 0.6. (e) XC-SOFI4 FRW, r = 10. (f) STORM, r = 10. Scale bars: 200 nm.

Fig. 7.
Fig. 7.

Comparison of the visibility versus labeling density. The best XC-SOFI is obtained by the SOFI order yielding the highest average relative visibility for a specific set of simulation parameters. σ denotes the average relative standard deviation. Fixed simulation parameters: k/f = 0.5, r = 2, line separation: 0.6 Airy units, 1000 frames, 25 realizations per point.

Fig. 8.
Fig. 8.

Visual comparison of SOFI and STORM reconstructions at different labeling densities. Labeling density: (a–d) 3/µm, (e–h) 20/µm. (a,e) Target structure. (b,f) Summed TIRF. (c) XC-SOFI5 FRW. (g) XC-SOFI3 FRW. (d,h) STORM. Scale bars: 200 nm.

Fig. 9.
Fig. 9.

Comparison of the visibility versus pSNR. XC-SOFI has been computed using cross-cumulant combinations without repetitions. The best XC-SOFI is obtained by the SOFI order yielding the highest average relative visibility for a specific set of simulation parameters. σ denotes the average relative standard deviation. Fixed simulation parameters: k/f = 0.5, r = 6.7, line separation: 0.6 Airy units, labeling density: 5/µm, 2000 frames, 50 realizations per point.

Fig. 10.
Fig. 10.

Comparison of the visibility versus line separation distance. The best XC-SOFI is obtained by the SOFI order yielding the highest average relative visibility for a specific set of simulation parameters. σ denotes the average relative standard deviation. Fixed simulation parameters: k/f = 0.5, r = 6.7, labeling density: 5/µm, 2000 frames, 50 realizations per point.

Fig. 11.
Fig. 11.

Microtubule structures in human osteosarcoma cells: Experimental demonstration of resolution improvements for SOFI and STORM. Row 2 illustrates the effect of insufficient rate ratios at high labeling densities, which makes it impossible for STORM to resolve the two closely spaced microtubuli at the pointing arrow. Regions of well-separated structures are less problematic (row 3). Row 4 shows the transversal intensity distribution of a microtubule (white box in row 3) fitted to a Gaussian. The intensity distribution is averaged over a length of 400 nm along the structure. Scale bars: 2µm

Tables (1)

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Table 1. Limits of resolution in Airy units and the corresponding improvement factors with regards to wide-field TIRF

Equations (4)

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k = k on k off k on + k off ,
r = k off k on = τ off τ on .
v 0 = 0.5 I max , 1 I min I max , 1 + I min + 0.5 I max , 2 I min I max , 2 + I min
v = v 0 ( min { I max , 1 I 1 , I max , 2 I 2 } max { I max , 1 I 1 , I max , 2 I 2 } ) sign { v 0 } ,

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