Abstract

Stochastic Optical Fluctuation Imaging (SOFI) is a super-resolution fluorescence microscopy technique which allows to enhance the spatial resolution of an image by evaluating the temporal fluctuations of blinking fluorescent emitters. SOFI is not based on the identification and localization of single molecules such as in the widely used Photoactivation Localization Microsopy (PALM) or Stochastic Optical Reconstruction Microscopy (STORM), but computes a superresolved image via temporal cumulants from a recorded movie. A technical challenge hereby is that, when directly applying the SOFI algorithm to a movie of raw images, the pixel size of the final SOFI image is the same as that of the original images, which becomes problematic when the final SOFI resolution is much smaller than this value. In the past, sophisticated cross-correlation schemes have been used for tackling this problem. Here, we present an alternative, exact, straightforward, and simple solution using an interpolation scheme based on Fourier transforms. We exemplify the method on simulated and experimental data.

© 2015 Optical Society of America

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2015 (2)

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

2014 (2)

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[Crossref] [PubMed]

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

2013 (1)

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

2012 (3)

T. Dertinger, J. Xu, O. ForoutanNaini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Nat. Acad. Sci. USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

2011 (1)

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Expr. 2, 810–813 (2011).
[Crossref]

2010 (2)

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution optical fluctuation imaging with organic dyes,” Ang. Chem. Int. Ed. 49, 9441–9443 (2010).
[Crossref]

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

2009 (1)

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

2006 (2)

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, 793–795 (2006).
[Crossref] [PubMed]

2004 (1)

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

2003 (1)

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Expr. 11, 3583–3591 (2003).
[Crossref]

1999 (1)

1994 (1)

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793–795 (2006).
[Crossref] [PubMed]

Berclaz, C.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

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

Bocchio, N. L.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

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]

Brown, J. T.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Calver, A. R.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Chen, X.

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

Cho, S.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Choi, M. C.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Collingridge, G. L.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[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. Expr. 18, 18875–18885 (2010).
[Crossref]

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

Couve, A.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Davidson, M. 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]

Davies, C. H.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Dedecker, P.

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Nat. Acad. Sci. USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

Dellagiacoma, C.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Expr. 2, 810–813 (2011).
[Crossref]

Dertinger, T.

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Nat. Acad. Sci. USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

T. Dertinger, J. Xu, O. ForoutanNaini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

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

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution optical fluctuation imaging with organic dyes,” Ang. Chem. Int. Ed. 49, 9441–9443 (2010).
[Crossref]

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

Dubikovskaya, E. A.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Enderlein, J.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

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

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

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Expr. 11, 3583–3591 (2003).
[Crossref]

J. Enderlein, Advanced Fluorescence Microscopy, in Comprehensive Biomedical Physics vol. 4, A. Brahme, ed. (Elsevier, 2014), pp. 111–151.

Fairfax, B.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

ForoutanNaini, O.

T. Dertinger, J. Xu, O. ForoutanNaini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

Ganesan, P.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Geissbuehler, S.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Expr. 2, 810–813 (2011).
[Crossref]

Gisou van der Goot, F.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Godinat, A.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Gregor, I.

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Expr. 11, 3583–3591 (2003).
[Crossref]

Heilemann, M.

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution optical fluctuation imaging with organic dyes,” Ang. Chem. Int. Ed. 49, 9441–9443 (2010).
[Crossref]

Hell, S. W.

Heo, W. D.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[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]

Hoogendoorn, E.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[Crossref] [PubMed]

Huang, N.

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

Huss, A.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Ihee, H.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Ingaramo, M.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[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. Nat. Acad. Sci. USA 106, 22287–22292 (2009).
[Crossref] [PubMed]

Jakobs, S.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Jang, J.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Jensen, N. A.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Jourdain, S.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Kim, M. W.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Klar, T. A.

Lasser, T.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Expr. 2, 810–813 (2011).
[Crossref]

Lee, H.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Leutenegger, M.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

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]

Medhurst, A. D.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Mo, G. C. H.

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Nat. Acad. Sci. USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

Moss, S. J.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Nation, J. H. L.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[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, 1642–1645 (2006).
[Crossref] [PubMed]

Pangalos, M. N.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Park, Y.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

Patterson, G. H.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[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]

Patting, M.

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Expr. 11, 3583–3591 (2003).
[Crossref]

Peng, J.

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Postma, M.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[Crossref] [PubMed]

Randall, A. D.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Restituito, S.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793–795 (2006).
[Crossref] [PubMed]

Sandoz, P. A.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Sauer, M.

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution optical fluctuation imaging with organic dyes,” Ang. Chem. Int. Ed. 49, 9441–9443 (2010).
[Crossref]

Shan, C.

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

Sharipov, A.

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Sheardown, S. A.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Shroff, H.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[Crossref] [PubMed]

Song, C.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[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]

Spencer, J. P.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Sun, Y.

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Teng, J.

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

Thuault, S. J.

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Topps, S

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Vogel, R.

T. Dertinger, J. Xu, O. ForoutanNaini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

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

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution optical fluctuation imaging with organic dyes,” Ang. Chem. Int. Ed. 49, 9441–9443 (2010).
[Crossref]

Wahl, M.

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Expr. 11, 3583–3591 (2003).
[Crossref]

Wang, H.

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

Weiss, S.

T. Dertinger, J. Xu, O. ForoutanNaini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

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

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution optical fluctuation imaging with organic dyes,” Ang. Chem. Int. Ed. 49, 9441–9443 (2010).
[Crossref]

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

Wichmann, J.

Xi, P.

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Xu, J.

T. Dertinger, J. Xu, O. ForoutanNaini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

Xu, P.

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Yoon, T.-Y.

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
[Crossref]

York, A. G.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[Crossref] [PubMed]

Zeng, Z.

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Zhang, H.

Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
[Crossref] [PubMed]

Zhang, J.

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Nat. Acad. Sci. USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

Zhang, M.

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Zhang, X.

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793–795 (2006).
[Crossref] [PubMed]

ACS Nano (1)

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a Reversibly Switchable Fluorescent Protein for Super-Resolution Optical Fluctuation Imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Ang. Chem. Int. Ed. (1)

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution optical fluctuation imaging with organic dyes,” Ang. Chem. Int. Ed. 49, 9441–9443 (2010).
[Crossref]

Biochem. Pharmacol. (1)

S. J. Thuault, J. T. Brown, S. A. Sheardown, S. Jourdain, B. Fairfax, J. P. Spencer, S. Restituito, J. H. L. Nation, S Topps, A. D. Medhurst, A. D. Randall, A. Couve, S. J. Moss, G. L. Collingridge, M. N. Pangalos, C. H. Davies, and A. R. Calver, “The GABAB2 subunit is critical for the tracking and function of native GABAB receptors,” Biochem. Pharmacol. 68, 1655–1666 (2004).
[Crossref] [PubMed]

Biomed. Opt. Expr. (1)

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Expr. 2, 810–813 (2011).
[Crossref]

ChemPhysChem (1)

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths,” ChemPhysChem 15, 794–800 (2014).
[Crossref] [PubMed]

Nature Commun. (1)

S. Geissbuehler, A. Sharipov, A. Godinat, N. L. Bocchio, P. A. Sandoz, A. Huss, N. A. Jensen, S. Jakobs, J. Enderlein, F. Gisou van der Goot, E. A. Dubikovskaya, T. Lasser, and M. Leutenegger, “Live-cell multiplane three-dimensional super-resolution optical fluctuation imaging,” Nature Commun. 5, 5830 (2014).
[Crossref]

Nature Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793–795 (2006).
[Crossref] [PubMed]

Opt. Expr. (2)

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Expr. 11, 3583–3591 (2003).
[Crossref]

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

Opt. Lett. (2)

Opt. Nanoscopy (2)

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

T. Dertinger, J. Xu, O. ForoutanNaini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

Proc. Nat. Acad. Sci. USA (2)

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. USA 106, 22287–22292 (2009).
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P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Nat. Acad. Sci. USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

Sci. Rep. (2)

S. Cho, J. Jang, C. Song, H. Lee, P. Ganesan, T.-Y. Yoon, M. W. Kim, M. C. Choi, H. Ihee, W. D. Heo, and Y. Park, “Simple super-resolution live-cell imaging based on diffusion-assisted Förster resonance energy transfer,” Sci. Rep. 3, 1208 (2013).
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Z. Zeng, X. Chen, H. Wang, N. Huang, C. Shan, H. Zhang, J. Teng, and P. Xi, “Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging,” Sci. Rep. 5, 8359 (2015).
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Science (1)

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]

Other (2)

J. Enderlein, Advanced Fluorescence Microscopy, in Comprehensive Biomedical Physics vol. 4, A. Brahme, ed. (Elsevier, 2014), pp. 111–151.

M. Leutenegger, Balanced SOFI toolbox, http://documents.epfl.ch/users/l/le/leuteneg/www/BalancedSOFI/index.html

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Figures (6)

Fig. 1
Fig. 1 Hierarchical SOFI algorithm: For each window w with Nw frames multiple cumulant images are computed in a hierarchical way, where the time resolution is coarsened by factor 2 in each level. The sum of the cumulants of all levels approximates the integral over τ of C n w with exponentially growing bin size.
Fig. 2
Fig. 2 Algorithm of Fourier interpolation: Each frame (example: single emitter represented by an airy disc) is first Fourier-transformed. For sufficiently small detector pixel sizes, the Fourier transform is zero on the borders due to finite support of the OTF. The Fourier transform can thus be padded with zeros without changing the frequency information, here separated by a dashed white line from the original Fourier transform. Transforming back into real space gives an artifact-free image with more pixels, where each “virtual” pixel corresponds to a smaller area than that of the original detector pixels.
Fig. 3
Fig. 3 Example of periodic padding of an image for preventing boundary artifacts upon Fourier upsampling: Instead of Fouier-upsampling the original image, one first extends the image with mirror symmetric half-copies to obtain a larger and continuously periodic image (periodic padding), which is then Fourier-upsampled, and then cropped back to the original size. The comparison between both results (unpadded Fourier upsampling, right bottom, versus padded Fourier upsampling, right top) clearly shows that the padding procedure leads to a perfectly artifact-free upsampling of the original image.
Fig. 4
Fig. 4 Comparison between fSOFI and interpolation of SOFI image using a simulation of two close emitters. a) Average of movie. b) 4th order SOFI image. c) Linear interpolation of b. d) 4th order fSOFI image. The coarseness of the pixel grid prevents standard SOFI to resolve the emitters. In contrast to interpolation, the fSOFI image captures true information and correctly resolves the emitters.
Fig. 5
Fig. 5 Two examples from a simulated SOFI experiment illustrating the presented Fourier interpolation in combination with SOFI. Top panels: 10 emitters in a ring. Bottom panels: Two emitters with sub-pixel shift (1.75 px, 0.25 px). a) Time average of all frames. b) 4th order SOFI. c) 4th order SOFI from 4x-super-sampled frames. d) Raw 4th order cross-correlation SOFI. It is easy to see that the Fourier interpolation improves image quality and exposes the sub-pixel positioning of the emitters without producing artifacts visible in the raw cross-correlation approach.
Fig. 6
Fig. 6 Fourier interpolation on a images of blinking quantum dots. Rat hippocampal neuron with neurotransmitter receptor subunit GABABR1 immunostained with commercial quantum dots QD525 (Invitrogen). The raw stack of images contains 3000 frames recorded at 20 Hz frame rate. Fluorescence was excited at 401 nm wavelength and about 20 W/cm2 using an laser (Cube401, 100 mW, Coherent). The microscope used was a commercial epi-fluorescence microscope (IX-71, Olympus) equipped with an 1.4 oil-immersion objective (UPlanSApo, Olympus), and an emCCD (DU-897-CS0-BV, Andor). Magnification was chosen in such a way that the effective pixel size of the recorded images was 100 nm. Fluorescent light was filtered from the excitation light using a dichroic beam splitter (FF444/520/590, Semrock). (a) Time average of original images. (b) 2nd order SOFI. (c) 2nd order SOFI with 3x Fourier interpolation. The last two images show the raw 2nd cross-correlation SOFI (d) and the artifact corrected image (e) calculated using publicly available software [20].

Equations (9)

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F ( r , t ) = j = 1 N U ( r r j ) ε j s j ( t )
C 2 [ s j ( t ) , s k ( t + τ ) ] δ s j ( t ) δ s k ( t + τ ) = δ j k ε j 2 f 2 ( τ )
C 2 [ F ( r , t ) , F ( r , t + τ ) ] = j , k = 1 N U ( r r j ) U ( r r k ) ε j ε k δ s j ( t ) δ s k ( t + τ ) = j = 1 N U 2 ( r r j ) ε j 2 f 2 ( τ )
S 2 ( r ) = ( d τ f 2 ( τ ) ) j = 1 N U 2 ( r r j ) ε j 2
C 2 ( 1 ) ( r ) = C 2 [ F ( r , t ) , F ( r , t + 1 ) ] .
F ( 2 ) ( r , t / 2 ) = F ( r , t ) + F ( r , t + 1 ) .
C 2 ( 2 ) ( r ) = C 2 [ F ( 2 ) ( r , t ) , F ( 2 ) ( r , t + 1 ) ] .
S 2 ( r ) = k C 2 ( k ) ( r ) .
d new = ( N 1 ) / 2 ( N 1 ) / 2 + Δ d

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