Abstract

Super-resolution optical fluctuation imaging (SOFI) offers a simple and affordable alternative to other super-resolution (SR) imaging techniques. The theoretical resolution enhancement of SOFI scales linearly with the order of cumulants, while the imaging conditions exhibit less photo-toxicity to the living samples as compared to other SR methods. High order SOFI could, therefore, be a method of choice for dynamic live cell imaging. However, due to the cusp-artifacts and dynamic range expansion of pixel intensities, this promise has not been materialized as of yet. Here we investigated and compared high order moments vs. high order cumulant SOFI reconstructions. We demonstrate that even-order moments reconstructions are intrinsically free of cusp artifacts, allowing for a subsequent deconvolution operation to be performed, hence enhancing the resolution even further. High order moments reconstruction performance was examined for various (simulated) conditions and applied to (experimental) imaging of QD labeled microtubules in fixed cells, and actin stress fiber dynamics in live cells.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (2)

B. Han, R. Zhou, C. Xia, and X. Zhuang, “Structural organization of the actin-spectrin-based membrane skeleton in dendrites and soma of neurons,” Proc. Natl. Acad. Sci. U.S.A. 114(32), E6678–E6685 (2017).
[Crossref] [PubMed]

T. Chaigne, B. Arnal, S. Vilov, E. Bossy, and O. Katz, “Super-resolution photoacoustic imaging via flow-induced absorption fluctuations,” Optica 4(11), 1397–1404 (2017).
[Crossref]

2016 (6)

A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
[Crossref] [PubMed]

M. Wojcik, S. Kohler, A. F. Dernburg, and K. Xu, “Super-resolution microscopy reveals the three-dimensional organization of meiotic chromosome axes in intact C. elegans tissue,” Mol. Biol. Cell 27, E4734 (2016).

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

X. Chen, W. Zong, R. Li, Z. Zeng, J. Zhao, P. Xi, L. Chen, and Y. Sun, “Two-photon light-sheet nanoscopy by fluorescence fluctuation correlation analysis,” Nanoscale 8(19), 9982–9987 (2016).
[Crossref] [PubMed]

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

N. Gustafsson, S. Culley, G. Ashdown, D. M. Owen, P. M. Pereira, and R. Henriques, “Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations,” Nat. Commun. 7(1), 12471 (2016).
[Crossref] [PubMed]

2015 (7)

C. Sánchez-Huertas and J. Lüders, “The augmin connection in the geometry of microtubule networks,” Curr. Biol. 25(7), R294–R299 (2015).
[Crossref] [PubMed]

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
[Crossref] [PubMed]

M. Kim, C. Park, C. Rodriguez, Y. Park, and Y.-H. Cho, “Superresolution imaging with optical fluctuation using speckle patterns illumination,” Sci. Rep. 5(1), 16525 (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(3), 2659–2667 (2015).
[Crossref] [PubMed]

X. Chen, Z. Zeng, H. Wang, and P. Xi, “Three-dimensional multimodal sub-diffraction imaging with spinning-disk confocal microscopy using blinking/fluctuating probes,” Nano Res. 8(7), 2251–2260 (2015).
[Crossref]

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

S. C. Stein, A. Huss, D. Hähnel, I. Gregor, and J. Enderlein, “Fourier interpolation stochastic optical fluctuation imaging,” Opt. Express 23(12), 16154–16163 (2015).
[Crossref] [PubMed]

2014 (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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

2013 (5)

T. Dertinger, A. Pallaoro, G. Braun, S. Ly, T. A. Laurence, and S. Weiss, “Advances in superresolution optical fluctuation imaging (SOFI),” Q. Rev. Biophys. 46(2), 210–221 (2013).
[Crossref] [PubMed]

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(1), 1208 (2013).
[Crossref] [PubMed]

K. Xu, G. Zhong, and X. Zhuang, “Actin, Spectrin, and Associated Proteins Form a Periodic Cytoskeletal Structure in Axons,” Science 339(6118), 452–456 (2013).
[Crossref] [PubMed]

Y. Doksani, J. Y. Wu, T. de Lange, and X. Zhuang, “Super-resolution fluorescence imaging of telomeres reveals TRF2-dependent T-loop formation,” Cell 155(2), 345–356 (2013).
[Crossref] [PubMed]

K. Xu, G. Zhong, and X. Zhuang, “Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons,” Science 339(6118), 452–456 (2013).
[Crossref] [PubMed]

2012 (3)

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

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(1), 4 (2012).
[Crossref]

P. Dedecker, G. C. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Natl. Acad. Sci. U.S.A. 109(27), 10909–10914 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (3)

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, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution Optical Fluctuation Imaging with Organic Dyes,” Angew. Chem. Int. Ed. Engl. 49(49), 9441–9443 (2010).
[Crossref] [PubMed]

A. Dani, B. Huang, J. Bergan, C. Dulac, and X. Zhuang, “Superresolution imaging of chemical synapses in the brain,” Neuron 68(5), 843–856 (2010).
[Crossref] [PubMed]

2009 (1)

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]

2006 (2)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[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]

2005 (1)

H. Moradkhani, K. L. Hsu, H. Gupta, and S. Sorooshian, “Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter,” Water Resour. Res. 41(5), 1(2005).
[Crossref]

2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(Pt 2), 82–87 (2000).
[Crossref] [PubMed]

1995 (1)

1994 (1)

1981 (1)

D. Axelrod, “Cell-Substrate Contacts Illuminated by Total Internal Reflection Fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

1959 (1)

V. Leonov and A. N. Shiryaev, “On a method of calculation of semi-invariants,” Theory Probab. Appl. 4(3), 319–329 (1959).
[Crossref]

1956 (1)

E. J. Ambrose, “A surface contact microscope for the study of cell movements,” Nature 178(4543), 1194 (1956).
[Crossref] [PubMed]

1881 (1)

E. Abbe, “VII. On the Estimation of Aperture in the Microscope,” Journal of the Royal Microscopical Society 1(3), 388–423 (1881).
[Crossref]

Abbe, E.

E. Abbe, “VII. On the Estimation of Aperture in the Microscope,” Journal of the Royal Microscopical Society 1(3), 388–423 (1881).
[Crossref]

Ambrose, E. J.

E. J. Ambrose, “A surface contact microscope for the study of cell movements,” Nature 178(4543), 1194 (1956).
[Crossref] [PubMed]

Arnal, B.

Ashdown, G.

N. Gustafsson, S. Culley, G. Ashdown, D. M. Owen, P. M. Pereira, and R. Henriques, “Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations,” Nat. Commun. 7(1), 12471 (2016).
[Crossref] [PubMed]

Avendaño, M. S.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Axelrod, D.

D. Axelrod, “Cell-Substrate Contacts Illuminated by Total Internal Reflection Fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

Bantignies, F.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[Crossref] [PubMed]

Battle, C.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

Beliveau, B. J.

A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
[Crossref] [PubMed]

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Berclaz, C.

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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,” Nat. Commun. 5(1), 5830 (2014).
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A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
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B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
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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).
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Braun, G.

T. Dertinger, A. Pallaoro, G. Braun, S. Ly, T. A. Laurence, and S. Weiss, “Advances in superresolution optical fluctuation imaging (SOFI),” Q. Rev. Biophys. 46(2), 210–221 (2013).
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L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
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Chen, L.

X. Chen, W. Zong, R. Li, Z. Zeng, J. Zhao, P. Xi, L. Chen, and Y. Sun, “Two-photon light-sheet nanoscopy by fluorescence fluctuation correlation analysis,” Nanoscale 8(19), 9982–9987 (2016).
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X. Chen, Z. Zeng, H. Wang, and P. Xi, “Three-dimensional multimodal sub-diffraction imaging with spinning-disk confocal microscopy using blinking/fluctuating probes,” Nano Res. 8(7), 2251–2260 (2015).
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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(3), 2659–2667 (2015).
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A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
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Chizhik, A. M.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
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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(1), 1208 (2013).
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M. Kim, C. Park, C. Rodriguez, Y. Park, and Y.-H. Cho, “Superresolution imaging with optical fluctuation using speckle patterns illumination,” Sci. Rep. 5(1), 16525 (2015).
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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(1), 1208 (2013).
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B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
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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).
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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).
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Culley, S.

N. Gustafsson, S. Culley, G. Ashdown, D. M. Owen, P. M. Pereira, and R. Henriques, “Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations,” Nat. Commun. 7(1), 12471 (2016).
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A. Dani, B. Huang, J. Bergan, C. Dulac, and X. Zhuang, “Superresolution imaging of chemical synapses in the brain,” Neuron 68(5), 843–856 (2010).
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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(5793), 1642–1645 (2006).
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Y. Doksani, J. Y. Wu, T. de Lange, and X. Zhuang, “Super-resolution fluorescence imaging of telomeres reveals TRF2-dependent T-loop formation,” Cell 155(2), 345–356 (2013).
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Dedecker, P.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
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P. Dedecker, G. C. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Natl. Acad. Sci. U.S.A. 109(27), 10909–10914 (2012).
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Dekaliuk, M. O.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
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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(1), 4 (2012).
[Crossref]

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Express 2(3), 408–420 (2011).
[Crossref] [PubMed]

Demchenko, A. P.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
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Dernburg, A. F.

M. Wojcik, S. Kohler, A. F. Dernburg, and K. Xu, “Super-resolution microscopy reveals the three-dimensional organization of meiotic chromosome axes in intact C. elegans tissue,” Mol. Biol. Cell 27, E4734 (2016).

Dertinger, T.

T. Dertinger, A. Pallaoro, G. Braun, S. Ly, T. A. Laurence, and S. Weiss, “Advances in superresolution optical fluctuation imaging (SOFI),” Q. Rev. Biophys. 46(2), 210–221 (2013).
[Crossref] [PubMed]

P. Dedecker, G. C. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Natl. Acad. Sci. U.S.A. 109(27), 10909–10914 (2012).
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T. Dertinger, J. Xu, O. F. Naini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1(2), 2 (2012).
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T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution Optical Fluctuation Imaging with Organic Dyes,” Angew. Chem. Int. Ed. Engl. 49(49), 9441–9443 (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]

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]

Deschout, H.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

Doksani, Y.

Y. Doksani, J. Y. Wu, T. de Lange, and X. Zhuang, “Super-resolution fluorescence imaging of telomeres reveals TRF2-dependent T-loop formation,” Cell 155(2), 345–356 (2013).
[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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

Dulac, C.

A. Dani, B. Huang, J. Bergan, C. Dulac, and X. Zhuang, “Superresolution imaging of chemical synapses in the brain,” Neuron 68(5), 843–856 (2010).
[Crossref] [PubMed]

Enderlein, J.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

S. C. Stein, A. Huss, D. Hähnel, I. Gregor, and J. Enderlein, “Fourier interpolation stochastic optical fluctuation imaging,” Opt. Express 23(12), 16154–16163 (2015).
[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,” Nat. Commun. 5(1), 5830 (2014).
[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]

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]

Erceg, J.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Feletti, L.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

Fonseka, C. Y.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Fudenberg, G.

A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
[Crossref] [PubMed]

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(1), 1208 (2013).
[Crossref] [PubMed]

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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

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(1), 4 (2012).
[Crossref]

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Express 2(3), 408–420 (2011).
[Crossref] [PubMed]

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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

Gregor, I.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

S. C. Stein, A. Huss, D. Hähnel, I. Gregor, and J. Enderlein, “Fourier interpolation stochastic optical fluctuation imaging,” Opt. Express 23(12), 16154–16163 (2015).
[Crossref] [PubMed]

Gupta, H.

H. Moradkhani, K. L. Hsu, H. Gupta, and S. Sorooshian, “Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter,” Water Resour. Res. 41(5), 1(2005).
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Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(Pt 2), 82–87 (2000).
[Crossref] [PubMed]

Gustafsson, N.

N. Gustafsson, S. Culley, G. Ashdown, D. M. Owen, P. M. Pereira, and R. Henriques, “Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations,” Nat. Commun. 7(1), 12471 (2016).
[Crossref] [PubMed]

Hähnel, D.

Han, B.

B. Han, R. Zhou, C. Xia, and X. Zhuang, “Structural organization of the actin-spectrin-based membrane skeleton in dendrites and soma of neurons,” Proc. Natl. Acad. Sci. U.S.A. 114(32), E6678–E6685 (2017).
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Hannan, M. A.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Heilemann, M.

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution Optical Fluctuation Imaging with Organic Dyes,” Angew. Chem. Int. Ed. Engl. 49(49), 9441–9443 (2010).
[Crossref] [PubMed]

Hell, S. W.

Henriques, R.

N. Gustafsson, S. Culley, G. Ashdown, D. M. Owen, P. M. Pereira, and R. Henriques, “Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations,” Nat. Commun. 7(1), 12471 (2016).
[Crossref] [PubMed]

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(1), 1208 (2013).
[Crossref] [PubMed]

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

Higgins, D. A.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
[Crossref] [PubMed]

Hoang, H. G.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Hofkens, J.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

Hsu, K. L.

H. Moradkhani, K. L. Hsu, H. Gupta, and S. Sorooshian, “Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter,” Water Resour. Res. 41(5), 1(2005).
[Crossref]

Huang, B.

A. Dani, B. Huang, J. Bergan, C. Dulac, and X. Zhuang, “Superresolution imaging of chemical synapses in the brain,” Neuron 68(5), 843–856 (2010).
[Crossref] [PubMed]

Huss, A.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

S. C. Stein, A. Huss, D. Hähnel, I. Gregor, and J. Enderlein, “Fourier interpolation stochastic optical fluctuation imaging,” Opt. Express 23(12), 16154–16163 (2015).
[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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

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(1), 1208 (2013).
[Crossref] [PubMed]

Imakaev, M.

A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
[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).
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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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

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(1), 1208 (2013).
[Crossref] [PubMed]

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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

Joyce, E. F.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Jungmann, R.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Katz, O.

Kim, M.

M. Kim, C. Park, C. Rodriguez, Y. Park, and Y.-H. Cho, “Superresolution imaging with optical fluctuation using speckle patterns illumination,” Sci. Rep. 5(1), 16525 (2015).
[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(1), 1208 (2013).
[Crossref] [PubMed]

Kim-Kiselak, C.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Kirkeminde, A. W.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
[Crossref] [PubMed]

Kisley, L.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
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Kohler, S.

M. Wojcik, S. Kohler, A. F. Dernburg, and K. Xu, “Super-resolution microscopy reveals the three-dimensional organization of meiotic chromosome axes in intact C. elegans tissue,” Mol. Biol. Cell 27, E4734 (2016).

Landes, C. F.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
[Crossref] [PubMed]

Lasser, T.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

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(1), 4 (2012).
[Crossref]

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Express 2(3), 408–420 (2011).
[Crossref] [PubMed]

Laurence, T. A.

T. Dertinger, A. Pallaoro, G. Braun, S. Ly, T. A. Laurence, and S. Weiss, “Advances in superresolution optical fluctuation imaging (SOFI),” Q. Rev. Biophys. 46(2), 210–221 (2013).
[Crossref] [PubMed]

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(1), 1208 (2013).
[Crossref] [PubMed]

Lee, J. T.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Leonov, V.

V. Leonov and A. N. Shiryaev, “On a method of calculation of semi-invariants,” Theory Probab. Appl. 4(3), 319–329 (1959).
[Crossref]

Leutenegger, M.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

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(1), 4 (2012).
[Crossref]

Li, R.

X. Chen, W. Zong, R. Li, Z. Zeng, J. Zhao, P. Xi, L. Chen, and Y. Sun, “Two-photon light-sheet nanoscopy by fluorescence fluctuation correlation analysis,” Nanoscale 8(19), 9982–9987 (2016).
[Crossref] [PubMed]

Li, W.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[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.

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]

Lüders, J.

C. Sánchez-Huertas and J. Lüders, “The augmin connection in the geometry of microtubule networks,” Curr. Biol. 25(7), R294–R299 (2015).
[Crossref] [PubMed]

Lukes, T.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

Ly, S.

T. Dertinger, A. Pallaoro, G. Braun, S. Ly, T. A. Laurence, and S. Weiss, “Advances in superresolution optical fluctuation imaging (SOFI),” Q. Rev. Biophys. 46(2), 210–221 (2013).
[Crossref] [PubMed]

McCole, R. B.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Mirny, L. A.

A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
[Crossref] [PubMed]

Mo, G. C.

P. Dedecker, G. C. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Natl. Acad. Sci. U.S.A. 109(27), 10909–10914 (2012).
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Moffitt, J. R.

A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
[Crossref] [PubMed]

Moradkhani, H.

H. Moradkhani, K. L. Hsu, H. Gupta, and S. Sorooshian, “Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter,” Water Resour. Res. 41(5), 1(2005).
[Crossref]

Naini, O. F.

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

Owen, D. M.

N. Gustafsson, S. Culley, G. Ashdown, D. M. Owen, P. M. Pereira, and R. Henriques, “Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations,” Nat. Commun. 7(1), 12471 (2016).
[Crossref] [PubMed]

Pallaoro, A.

T. Dertinger, A. Pallaoro, G. Braun, S. Ly, T. A. Laurence, and S. Weiss, “Advances in superresolution optical fluctuation imaging (SOFI),” Q. Rev. Biophys. 46(2), 210–221 (2013).
[Crossref] [PubMed]

Park, C.

M. Kim, C. Park, C. Rodriguez, Y. Park, and Y.-H. Cho, “Superresolution imaging with optical fluctuation using speckle patterns illumination,” Sci. Rep. 5(1), 16525 (2015).
[Crossref] [PubMed]

Park, Y.

M. Kim, C. Park, C. Rodriguez, Y. Park, and Y.-H. Cho, “Superresolution imaging with optical fluctuation using speckle patterns illumination,” Sci. Rep. 5(1), 16525 (2015).
[Crossref] [PubMed]

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(1), 1208 (2013).
[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]

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(3), 2659–2667 (2015).
[Crossref] [PubMed]

Pereira, P. M.

N. Gustafsson, S. Culley, G. Ashdown, D. M. Owen, P. M. Pereira, and R. Henriques, “Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations,” Nat. Commun. 7(1), 12471 (2016).
[Crossref] [PubMed]

Platen, M.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

Radenovic, A.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

Rodriguez, C.

M. Kim, C. Park, C. Rodriguez, Y. Park, and Y.-H. Cho, “Superresolution imaging with optical fluctuation using speckle patterns illumination,” Sci. Rep. 5(1), 16525 (2015).
[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), 793–795 (2006).
[Crossref] [PubMed]

Sánchez-Huertas, C.

C. Sánchez-Huertas and J. Lüders, “The augmin connection in the geometry of microtubule networks,” Curr. Biol. 25(7), R294–R299 (2015).
[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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

Sauer, M.

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution Optical Fluctuation Imaging with Organic Dyes,” Angew. Chem. Int. Ed. Engl. 49(49), 9441–9443 (2010).
[Crossref] [PubMed]

Schaap, I. A.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

Schmidt, C. F.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

Sharipov, A.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[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,” Nat. Commun. 5(1), 5830 (2014).
[Crossref] [PubMed]

Shih, W. M.

B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
[Crossref] [PubMed]

Shiryaev, A. N.

V. Leonov and A. N. Shiryaev, “On a method of calculation of semi-invariants,” Theory Probab. Appl. 4(3), 319–329 (1959).
[Crossref]

Shuang, B.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
[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(1), 1208 (2013).
[Crossref] [PubMed]

Sorooshian, S.

H. Moradkhani, K. L. Hsu, H. Gupta, and S. Sorooshian, “Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter,” Water Resour. Res. 41(5), 1(2005).
[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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Stein, S.

A. M. Chizhik, S. Stein, M. O. Dekaliuk, C. Battle, W. Li, A. Huss, M. Platen, I. A. Schaap, I. Gregor, A. P. Demchenko, C. F. Schmidt, J. Enderlein, and A. I. Chizhik, “Super-resolution optical fluctuation bio-imaging with dual-color carbon nanodots,” Nano Lett. 16(1), 237–242 (2016).
[Crossref] [PubMed]

Stein, S. C.

Sun, Y.

X. Chen, W. Zong, R. Li, Z. Zeng, J. Zhao, P. Xi, L. Chen, and Y. Sun, “Two-photon light-sheet nanoscopy by fluorescence fluctuation correlation analysis,” Nanoscale 8(19), 9982–9987 (2016).
[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(3), 2659–2667 (2015).
[Crossref] [PubMed]

Szlag, D.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

Tauzin, L. J.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
[Crossref] [PubMed]

Vandenberg, W.

H. Deschout, T. Lukes, A. Sharipov, D. Szlag, L. Feletti, W. Vandenberg, P. Dedecker, J. Hofkens, M. Leutenegger, T. Lasser, and A. Radenovic, “Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions,” Nat. Commun. 7(1), 13693 (2016).
[Crossref] [PubMed]

Vilov, S.

Vogel, R.

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

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution Optical Fluctuation Imaging with Organic Dyes,” Angew. Chem. Int. Ed. Engl. 49(49), 9441–9443 (2010).
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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).
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Wang, H.

X. Chen, Z. Zeng, H. Wang, and P. Xi, “Three-dimensional multimodal sub-diffraction imaging with spinning-disk confocal microscopy using blinking/fluctuating probes,” Nano Res. 8(7), 2251–2260 (2015).
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Wang, S.

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Weiss, S.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
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T. Dertinger, A. Pallaoro, G. Braun, S. Ly, T. A. Laurence, and S. Weiss, “Advances in superresolution optical fluctuation imaging (SOFI),” Q. Rev. Biophys. 46(2), 210–221 (2013).
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T. Dertinger, J. Xu, O. F. Naini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1(2), 2 (2012).
[Crossref] [PubMed]

T. Dertinger, M. Heilemann, R. Vogel, M. Sauer, and S. Weiss, “Superresolution Optical Fluctuation Imaging with Organic Dyes,” Angew. Chem. Int. Ed. Engl. 49(49), 9441–9443 (2010).
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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).
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Wichmann, J.

Wojcik, M.

M. Wojcik, S. Kohler, A. F. Dernburg, and K. Xu, “Super-resolution microscopy reveals the three-dimensional organization of meiotic chromosome axes in intact C. elegans tissue,” Mol. Biol. Cell 27, E4734 (2016).

Wu, C. T.

A. N. Boettiger, B. Bintu, J. R. Moffitt, S. Wang, B. J. Beliveau, G. Fudenberg, M. Imakaev, L. A. Mirny, C. T. Wu, and X. Zhuang, “Super-resolution imaging reveals distinct chromatin folding for different epigenetic states,” Nature 529(7586), 418–422 (2016).
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B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
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Wu, J. Y.

Y. Doksani, J. Y. Wu, T. de Lange, and X. Zhuang, “Super-resolution fluorescence imaging of telomeres reveals TRF2-dependent T-loop formation,” Cell 155(2), 345–356 (2013).
[Crossref] [PubMed]

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X. Chen, W. Zong, R. Li, Z. Zeng, J. Zhao, P. Xi, L. Chen, and Y. Sun, “Two-photon light-sheet nanoscopy by fluorescence fluctuation correlation analysis,” Nanoscale 8(19), 9982–9987 (2016).
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X. Chen, Z. Zeng, H. Wang, and P. Xi, “Three-dimensional multimodal sub-diffraction imaging with spinning-disk confocal microscopy using blinking/fluctuating probes,” Nano Res. 8(7), 2251–2260 (2015).
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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(3), 2659–2667 (2015).
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T. Dertinger, J. Xu, O. F. Naini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1(2), 2 (2012).
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M. Wojcik, S. Kohler, A. F. Dernburg, and K. Xu, “Super-resolution microscopy reveals the three-dimensional organization of meiotic chromosome axes in intact C. elegans tissue,” Mol. Biol. Cell 27, E4734 (2016).

K. Xu, G. Zhong, and X. Zhuang, “Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons,” Science 339(6118), 452–456 (2013).
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K. Xu, G. Zhong, and X. Zhuang, “Actin, Spectrin, and Associated Proteins Form a Periodic Cytoskeletal Structure in Axons,” Science 339(6118), 452–456 (2013).
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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(3), 2659–2667 (2015).
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Yi, X.

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
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B. J. Beliveau, A. N. Boettiger, M. S. Avendaño, R. Jungmann, R. B. McCole, E. F. Joyce, C. Kim-Kiselak, F. Bantignies, C. Y. Fonseka, J. Erceg, M. A. Hannan, H. G. Hoang, D. Colognori, J. T. Lee, W. M. Shih, P. Yin, X. Zhuang, and C. T. Wu, “Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes,” Nat. Commun. 6(1), 7147 (2015).
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X. Chen, W. Zong, R. Li, Z. Zeng, J. Zhao, P. Xi, L. Chen, and Y. Sun, “Two-photon light-sheet nanoscopy by fluorescence fluctuation correlation analysis,” Nanoscale 8(19), 9982–9987 (2016).
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Zhong, G.

K. Xu, G. Zhong, and X. Zhuang, “Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons,” Science 339(6118), 452–456 (2013).
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Zhou, R.

B. Han, R. Zhou, C. Xia, and X. Zhuang, “Structural organization of the actin-spectrin-based membrane skeleton in dendrites and soma of neurons,” Proc. Natl. Acad. Sci. U.S.A. 114(32), E6678–E6685 (2017).
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Zhuang, X.

B. Han, R. Zhou, C. Xia, and X. Zhuang, “Structural organization of the actin-spectrin-based membrane skeleton in dendrites and soma of neurons,” Proc. Natl. Acad. Sci. U.S.A. 114(32), E6678–E6685 (2017).
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X. Chen, W. Zong, R. Li, Z. Zeng, J. Zhao, P. Xi, L. Chen, and Y. Sun, “Two-photon light-sheet nanoscopy by fluorescence fluctuation correlation analysis,” Nanoscale 8(19), 9982–9987 (2016).
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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(3), 2659–2667 (2015).
[Crossref] [PubMed]

L. Kisley, R. Brunetti, L. J. Tauzin, B. Shuang, X. Yi, A. W. Kirkeminde, D. A. Higgins, S. Weiss, and C. F. Landes, “Characterization of porous materials by fluorescence correlation spectroscopy super-resolution optical fluctuation imaging,” ACS Nano 9(9), 9158–9166 (2015).
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Supplementary Material (13)

NameDescription
» Code 1       SR_Simu3D
» Code 2       SOFI2.0
» Dataset 1       3D filaments with 100 focal plane acquisition
» Dataset 2       live cell imaging of fluorescence protein fused ß-Actin
» Dataset 3       simulation of random filaments with different conditions
» Visualization 1       Visualization 1
» Visualization 2       Visualization 2
» Visualization 3       Visualization 3
» Visualization 4       Visualization 4
» Visualization 5       Visualization 5
» Visualization 6       Visualization 6
» Visualization 7       Visualization 7
» Visualization 8       Visualization 8

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Figures (7)

Fig. 1
Fig. 1 Calculation of 5thth order joint-cumulants. A set of five elements is shown in (a), where the elements are the fluctuation profiles of five pixels. Repeating pixels are allowed. For example, if element A and B are repeating pixels, we have r 1 = r n . Simplified notations for the five elements are {δFA, δFB, δFC, δFD, δFE} respectively. (b) demonstrates all possible partitions of a set of five elements, and how each partition contributes a term to the summation series (as the product of f1 and f2) to yield the joint-cumulant. Note that all the partitions that contain a part of size 1 are equal to 0, because δ F 1 (t) t =0. The graphical demonstration of partitions is inspired by the work by Tilman Piesk [43].
Fig. 2
Fig. 2 Moments and cumulants as a function of the ‘on time ratio’ ρ. (a) shows different moments as a function of ρ and denoted as Mn(ρ), and (b) shows different cumulants as a function of ρ and denoted as Wn(ρ). In both notations, n represents the order.
Fig. 3
Fig. 3 Moments reconstruction of simulated data for 3 near-by blinking fluorophores. (a) shows the photophysical parameters used in the blinking simulation of the three emitters. (b) shows the ground truth location of the three emitters. Other parameters used for the simulations: emission wavelength of 520nm, numerical aperture of NA = 1.4, frame integration time of 2 ms. The pixel size was set to be small (17.78 nm) to avoid artifacts due to binning. (c) shows the comparison between the prediction (Pred.) and reconstruction (Recon.) of the 6th order moment. (d) shows the average image (Ave.) and moments of the simulated movie (M2 to M7). Scale bars: 160 nm.
Fig. 4
Fig. 4 Comparison of high-order moments reconstruction with high-order bSOFI and SRRF reconstructions on simulated filaments. A simulated data set consisting of filaments in a 3D space was generated with: 50 emitters per 1 um labeling density along the line, 10 nm cross-section thickness with a Gaussian profile, 520 nm emission wavelength, 1.4NA and 90x magnification and a grid of 125 × 125 pixels with a pixel size of 1.6 x 1.6 um2. The Gibson Lanni’s PSF model was used in the simulations. Small field of views are cropped with different feature densities for comparison. (a) Sparse filaments. All methods yield satisfactory results. While M6-ldrc exhibits some grids artifacts, SRRF emphasizes thin features with oscillatory intensities and bSOFI exhibits granular and discontinuous features. (b) Dense filaments. Compared to the ground truth image, M6-ldrc exhibits the most faithful representation, while SRRF-TRA omits filaments (circled area for example). bSOFI exhibits discontinues filaments and features at locations that have no ground-truth signal (boxed area for example). (c) and (d) shows the ground truth for (a) and (b) as labeled in the image respectively. Scale bars: 640 nm.
Fig. 5
Fig. 5 Comparison of high-order moments reconstruction with high-order SRRF reconstruction for 3D sectioning performance. 3D sectioning results of ldrc-M6 and SRRF on simulated data are shown for a small field-of-view (2.15 μm × 2.15 μm). The full field-of-view results during a continuous scan of of the focal plane is provided in SI Movie 1. (a) shows the ground truth image of the simulated filaments projected onto x-y plane. Emitters are represented by 3D delta functions convolved with a 3D Gaussian with FWHM = 86.27 nm for the purpose of display. The color scale represents the z coordinate of the emitters. (b) x-z scan corresponding to the dashed line in (a), where 4 filaments are penetrating through the plane (a fifth filament (yellow) is missing at this plane because the sparse, stochastic labeling algorithm did not place an emitter at the corresponding (x, y, z) coordinate. (c) A z-direction cross section of the first (green) filament for ground-truth and ldrc-M6 and SRRF reconstructions.
Fig. 6
Fig. 6 High-order moments reconstruction of experimental data (fixed cells). α-tubulin filaments in fixed Hela cells were labeled with QD800. 1000 frames were acquired with 30 ms integration per frame and processed. (a) shows the average image (b) shows the ldrc-M6 results from the full field-of-view. Three zoom-in panels in (a) are shown in panel (c) as FOV1, FOV2 and FOV3 respectively, for single frame, average image, and results from ldrc-M6, SRRF and bSOFI respectively. The displayed SRRF result is optimized among options of TRA and TRAC of different orders. bSOFI exhibit discontinuities, SRRF provides higher resolution details but with distortions (blue arrows) and extra features which could be perceived as extra filaments with perpendicular branching angle to the robustly visualized microtubules. However, the microtubule branching angles are most commonly distributed within a range of 20 o to 60 o with average of 40° [48], the perpendicular branching displayed in the SRRF could be an artifact. The ldrc-M6 image is similar to the average image but with less background and improved resolution. Scale bars: 800 nm.
Fig. 7
Fig. 7 High-order moments reconstruction of experimental data (live cells). Hela cells were transfected with plasmid encoding (a) Skylan-S fused to β-Actin and (b) Dronpa-C12 fused to β-Actin. Live cells were imaged with 30 ms frame integration. 200 frames of the movie were processed per block. For each panel, the top row shows the full field-of-view, the middle row shows a zoom-in region (green box in the Average image), and the bottom row shows the further zoom-in region (green and blue boxes in the middle row image with or without a triangle marker at the left bottom corner). Each column shows results for the reconstruction method labeled at the top. We can see that while SRRF exhibit excellent performance on highlighting small features (green arrows), but at the cost of introducing shadow artifacts (along and under the green dashed lines) along the sides of bright filaments, and extra feature that could be artifacts (blue arrows). The displayed SRRF result is optimized among options of TRA and TRAC of different orders. Scale bars: 8 μm.

Equations (13)

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F( r ,t)= k=1 N k b k (t) U( r r k ),
b k (t)={ 1 when the emitter is in the ''on'' state 0 when the emitter is in the ''off'' state ,
G n ( r 1 , r 2 ,.... r n ; τ 1 , τ 2 ,..., τ n )= δF( r 1 ,t+ τ 1 )δF( r 2 ,t+ τ 2 )...δF( r n ,t+ τ n ) t .
G n (δ F 1 ,δ F 2 ,....,δ F n )= δ F 1 δ F 2 ....δ F n t .
C n (I)= all partition of set {δ F i | i[1,n]} I 1 I 2 ... I σ ={δ F i | i[1,n]} (1) q1 (q1)!G( I 1 ) G( I 2 )....G( I q ).
C n ( r 1 , r 2 ,..., r n ; τ 1 , τ 2 ,..., τ n ) = W n ( r 1 , r 2 ,..., r n ) k=1 N k n C n (δ b k (t+ τ 1 ),δ b k (t+ τ 2 ),...,δ b k (t+ τ n )) U n ( r gs r k ) with: W( r 1 , r 2 ,..., r n )= i[1,n] J[1,n] i<j U( r i r j n ) ; r gs = 1 n ( r 1 + r 2 +..+ r n ) ,
U( r )=exp( r x 2 + r y 2 2 ω xy 2 r z 2 2 ω z 2 ).
M n (ρ)= (1ρ) n ρ+ (ρ) n (1ρ).
M n ( r ;τ=0)= all partition of set {δ F i | i[1,n]} I 1 I 2 ... I σ ={δ F i | i[1,n]} C s 1 ( r ,τ=0) ... C s σ ( r ,τ=0),
M n ( r ;τ=0) = all partition of set {1,2,...,n} I 1 I 2 ... I σ ={1,2,...,n} C s 1 ( r ,τ=0) ... C s σ ( r ,τ=0) = all partition of set {1,2,...,n} I 1 I 2 ... I σ ={1,2,...,n} [ k 1 =1 N ... k σ =1 N ( p=1 σ k p s p )( p=1 σ C s p (δ b k p (t)) ) U n ( r r m )W({ s p , r k p }) ]
r m = 1 n p=1 σ S p r k p ,
M 1 n ( r ;τ=0)= all partition of set {1,2,...,n} I 1 I 2 ... I σ ={1,2,...,n} [ k=1 N ( p=1 σ k s p ) ( p=1 σ C s p (δ b k (t)) ) U n ( r r m ) ] ,
M 1 n ( r ;τ=0)= k=1 N k n U n ( r r m ) M n (δ b k (t)).

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