Abstract

Imaging and tracking three-dimensional (3D) nanoscale organizations and functions of live cells is essential for biological research but it remains challenging. Among different 3D super-resolution techniques, 3D structured illumination microscopy (SIM) has the intrinsic advantages for live-cell studies; it is based on wide-field imaging and does not require high light intensities or special fluorescent dyes to double 3D resolution. However, the 3D SIM system has developed relatively slowly, especially in live imaging. Here, we report a more flexible 3D SIM system based on two galvanometer sets conveniently controlling the structured illumination pattern’s period and orientation, which is able to study dynamics of live whole cells with high speed. We demonstrate our microscope’s capabilities with strong optical sectioning and lateral, axial, and volume temporal resolution of 104 nm, 320 nm and 4 s, respectively. We do this by imaging nanoparticle and microtubule organizations and mitochondria evolution. These characteristics enable our galvanometer-based 3D SIM system to broaden the accessible imaging content of SIM-family microscopes and further facilitate their applications in life sciences.

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

Full Article  |  PDF Article
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    [Crossref] [PubMed]
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2019 (1)

L. Schermelleh, A. Ferrand, T. Huser, C. Eggeling, M. Sauer, O. Biehlmaier, and G. P. C. Drummen, “Super-resolution microscopy demystified,” Nat. Cell Biol. 21(1), 72–84 (2019).
[Crossref] [PubMed]

2018 (9)

J. Tønnesen, V. V. G. K. Inavalli, and U. V. Nägerl, “Super-resolution imaging of the extracellular space in living brain tissue,” Cell 172(5), 1108–1121 (2018).
[Crossref] [PubMed]

Y. M. Sigal, R. Zhou, and X. Zhuang, “Visualizing and discovering cellular structures with super-resolution microscopy,” Science 361(6405), 880–887 (2018).
[Crossref] [PubMed]

W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
[Crossref]

Y. Wu and H. Shroff, “Faster, sharper, and deeper: structured illumination microscopy for biological imaging,” Nat. Methods 15(12), 1011–1019 (2018).
[Crossref] [PubMed]

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
[Crossref] [PubMed]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

A. Classen, J. von Zanthier, and G. S. Agarwal, “Analysis of super-resolution via 3D structured illumination intensity correlation microscopy,” Opt. Express 26(21), 27492–27503 (2018).
[Crossref] [PubMed]

2017 (7)

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117(23), 13890–13908 (2017).
[Crossref] [PubMed]

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

H. Blom and J. Widengren, “Stimulated emission depletion microscopy,” Chem. Rev. 117(11), 7377–7427 (2017).
[Crossref] [PubMed]

M. Sauer and M. Heilemann, “Single-molecule localization microscopy in eukaryotes,” Chem. Rev. 117(11), 7478–7509 (2017).
[Crossref] [PubMed]

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
[Crossref] [PubMed]

S. J. Sahl, S. W. Hell, and S. Jakobs, “Fluorescence nanoscopy in cell biology,” Nat. Rev. Mol. Cell Biol. 18(11), 685–701 (2017).
[Crossref] [PubMed]

2016 (2)

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
[Crossref] [PubMed]

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

2015 (2)

G. Ball, J. Demmerle, R. Kaufmann, I. Davis, I. M. Dobbie, and L. Schermelleh, “SIMcheck: a toolbox for successful super-resolution structured illumination microscopy,” Sci. Rep. 5(1), 15915 (2015).
[Crossref] [PubMed]

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

2013 (1)

2011 (1)

L. Shao, P. Kner, E. H. Rego, and M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
[Crossref] [PubMed]

2009 (1)

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

2008 (1)

M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

2005 (1)

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

2000 (1)

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

Agard, D. A.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Agarwal, G. S.

Allgeyer, E. S.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
[Crossref] [PubMed]

Baddeley, D.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
[Crossref] [PubMed]

Baird, M. A.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Ball, G.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

G. Ball, J. Demmerle, R. Kaufmann, I. Davis, I. M. Dobbie, and L. Schermelleh, “SIMcheck: a toolbox for successful super-resolution structured illumination microscopy,” Sci. Rep. 5(1), 15915 (2015).
[Crossref] [PubMed]

Beach, J. R.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Betzig, E.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Bewersdorf, J.

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
[Crossref] [PubMed]

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
[Crossref] [PubMed]

Biehlmaier, O.

L. Schermelleh, A. Ferrand, T. Huser, C. Eggeling, M. Sauer, O. Biehlmaier, and G. P. C. Drummen, “Super-resolution microscopy demystified,” Nat. Cell Biol. 21(1), 72–84 (2019).
[Crossref] [PubMed]

Blackstone, C.

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

Blom, H.

H. Blom and J. Widengren, “Stimulated emission depletion microscopy,” Chem. Rev. 117(11), 7377–7427 (2017).
[Crossref] [PubMed]

Bottanelli, F.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
[Crossref] [PubMed]

Cande, W. Z.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Cao, R.

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
[Crossref] [PubMed]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Carlton, P. M.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Chang, B.-J.

Chen, B.-C.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Chen, L.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Chen, Y.

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
[Crossref] [PubMed]

W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
[Crossref]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Chiang, S.-Y.

Chou, L.-J.

Classen, A.

Davidson, M. W.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Davis, I.

G. Ball, J. Demmerle, R. Kaufmann, I. Davis, I. M. Dobbie, and L. Schermelleh, “SIMcheck: a toolbox for successful super-resolution structured illumination microscopy,” Sci. Rep. 5(1), 15915 (2015).
[Crossref] [PubMed]

Demmerle, J.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

G. Ball, J. Demmerle, R. Kaufmann, I. Davis, I. M. Dobbie, and L. Schermelleh, “SIMcheck: a toolbox for successful super-resolution structured illumination microscopy,” Sci. Rep. 5(1), 15915 (2015).
[Crossref] [PubMed]

Dobbie, I. M.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

G. Ball, J. Demmerle, R. Kaufmann, I. Davis, I. M. Dobbie, and L. Schermelleh, “SIMcheck: a toolbox for successful super-resolution structured illumination microscopy,” Sci. Rep. 5(1), 15915 (2015).
[Crossref] [PubMed]

Drummen, G. P. C.

L. Schermelleh, A. Ferrand, T. Huser, C. Eggeling, M. Sauer, O. Biehlmaier, and G. P. C. Drummen, “Super-resolution microscopy demystified,” Nat. Cell Biol. 21(1), 72–84 (2019).
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Eggeling, C.

L. Schermelleh, A. Ferrand, T. Huser, C. Eggeling, M. Sauer, O. Biehlmaier, and G. P. C. Drummen, “Super-resolution microscopy demystified,” Nat. Cell Biol. 21(1), 72–84 (2019).
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Erdmann, R. S.

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
[Crossref] [PubMed]

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
[Crossref] [PubMed]

Fan, J.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
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Ferrand, A.

L. Schermelleh, A. Ferrand, T. Huser, C. Eggeling, M. Sauer, O. Biehlmaier, and G. P. C. Drummen, “Super-resolution microscopy demystified,” Nat. Cell Biol. 21(1), 72–84 (2019).
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M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
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P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
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Guo, Y.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
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Gustafsson, M. G.

L. Shao, P. Kner, E. H. Rego, and M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
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P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
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M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
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M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005).
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M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
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Hammer, J. A.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Harvey, K.

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

Heilemann, M.

M. Sauer and M. Heilemann, “Single-molecule localization microscopy in eukaryotes,” Chem. Rev. 117(11), 7478–7509 (2017).
[Crossref] [PubMed]

Heintzmann, R.

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117(23), 13890–13908 (2017).
[Crossref] [PubMed]

Hell, S. W.

S. J. Sahl, S. W. Hell, and S. Jakobs, “Fluorescence nanoscopy in cell biology,” Nat. Rev. Mol. Cell Biol. 18(11), 685–701 (2017).
[Crossref] [PubMed]

Hess, H. F.

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

Hu, J.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

Huang, H.-C.

Huang, X.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Huang, Y.

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Huser, T.

L. Schermelleh, A. Ferrand, T. Huser, C. Eggeling, M. Sauer, O. Biehlmaier, and G. P. C. Drummen, “Super-resolution microscopy demystified,” Nat. Cell Biol. 21(1), 72–84 (2019).
[Crossref] [PubMed]

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117(23), 13890–13908 (2017).
[Crossref] [PubMed]

Inavalli, V. V. G. K.

J. Tønnesen, V. V. G. K. Inavalli, and U. V. Nägerl, “Super-resolution imaging of the extracellular space in living brain tissue,” Cell 172(5), 1108–1121 (2018).
[Crossref] [PubMed]

Innocent, C.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

Jakobs, S.

S. J. Sahl, S. W. Hell, and S. Jakobs, “Fluorescence nanoscopy in cell biology,” Nat. Rev. Mol. Cell Biol. 18(11), 685–701 (2017).
[Crossref] [PubMed]

Jin, L.

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Kamiya, M.

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
[Crossref] [PubMed]

Kaufmann, R.

G. Ball, J. Demmerle, R. Kaufmann, I. Davis, I. M. Dobbie, and L. Schermelleh, “SIMcheck: a toolbox for successful super-resolution structured illumination microscopy,” Sci. Rep. 5(1), 15915 (2015).
[Crossref] [PubMed]

Kiehart, D. P.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

Kirchhausen, T.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Kner, P.

L. Shao, P. Kner, E. H. Rego, and M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
[Crossref] [PubMed]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Kromann, E. B.

F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
[Crossref] [PubMed]

Kuang, C.

W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
[Crossref]

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
[Crossref] [PubMed]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Lal, A.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Legant, W. R.

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

Li, D.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Li, L.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Lin, Y.

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
[Crossref] [PubMed]

Liu, C.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

Liu, H.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Liu, J.-J.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

Liu, W.

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
[Crossref] [PubMed]

W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
[Crossref]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Liu, X.

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
[Crossref] [PubMed]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
[Crossref]

Liu, Y.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Mao, H.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Markaki, Y.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

Matsuda, A.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

McNellis, B.

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
[Crossref] [PubMed]

Milkie, D. E.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Miron, E.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

Moerner, W. E.

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Moore, R. P.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

Moses, B.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Müller, M.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

Nägerl, U. V.

J. Tønnesen, V. V. G. K. Inavalli, and U. V. Nägerl, “Super-resolution imaging of the extracellular space in living brain tissue,” Cell 172(5), 1108–1121 (2018).
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Nixon-Abell, J.

J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
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J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
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W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
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D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
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J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
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L. Shao, P. Kner, E. H. Rego, and M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
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H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
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H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
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M. Sauer and M. Heilemann, “Single-molecule localization microscopy in eukaryotes,” Chem. Rev. 117(11), 7478–7509 (2017).
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H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
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F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
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M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
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D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
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L. Shao, P. Kner, E. H. Rego, and M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
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M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
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A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
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Y. Wu and H. Shroff, “Faster, sharper, and deeper: structured illumination microscopy for biological imaging,” Nat. Methods 15(12), 1011–1019 (2018).
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Y. M. Sigal, R. Zhou, and X. Zhuang, “Visualizing and discovering cellular structures with super-resolution microscopy,” Science 361(6405), 880–887 (2018).
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F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
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H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
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Tønnesen, J.

J. Tønnesen, V. V. G. K. Inavalli, and U. V. Nägerl, “Super-resolution imaging of the extracellular space in living brain tissue,” Cell 172(5), 1108–1121 (2018).
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Toomre, D.

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
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F. Bottanelli, E. B. Kromann, E. S. Allgeyer, R. S. Erdmann, S. Wood Baguley, G. Sirinakis, A. Schepartz, D. Baddeley, D. K. Toomre, J. E. Rothman, and J. Bewersdorf, “Two-colour live-cell nanoscale imaging of intracellular targets,” Nat. Commun. 7(1), 10778 (2016).
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W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
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Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
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H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
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H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
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von Diezmann, A.

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
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Wang, C. J.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
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Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
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X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
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J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
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H. Blom and J. Widengren, “Stimulated emission depletion microscopy,” Chem. Rev. 117(11), 7377–7427 (2017).
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Wu, R.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
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X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
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Y. Wu and H. Shroff, “Faster, sharper, and deeper: structured illumination microscopy for biological imaging,” Nat. Methods 15(12), 1011–1019 (2018).
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X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
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J. Nixon-Abell, C. J. Obara, A. V. Weigel, D. Li, W. R. Legant, C. S. Xu, H. A. Pasolli, K. Harvey, H. F. Hess, E. Betzig, C. Blackstone, and J. Lippincott-Schwartz, “Increased spatiotemporal resolution reveals highly dynamic dense tubular matrices in the peripheral ER,” Science 354(6311), aaf3928 (2016).
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D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
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Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
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Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
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Zhang, M.

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
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D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
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Zhang, S.

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

Zhang, X.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Zhang, Y.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

H. Takakura, Y. Zhang, R. S. Erdmann, A. D. Thompson, Y. Lin, B. McNellis, F. Rivera-Molina, S. N. Uno, M. Kamiya, Y. Urano, J. E. Rothman, J. Bewersdorf, A. Schepartz, and D. Toomre, “Long time-lapse nanoscopy with spontaneously blinking membrane probes,” Nat. Biotechnol. 35(8), 773–780 (2017).
[Crossref] [PubMed]

Zhang, Y.-H.

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
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Zhang, Z.

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
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Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
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Zheng, C.

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Zhou, R.

Y. M. Sigal, R. Zhou, and X. Zhuang, “Visualizing and discovering cellular structures with super-resolution microscopy,” Science 361(6405), 880–887 (2018).
[Crossref] [PubMed]

Zhu, D.

W. Liu, K. C. Toussaint, C. Okoro, D. Zhu, Y. Chen, C. Kuang, and X. Liu, “Breaking the axial diffraction limit: a guide to axial super-resolution fluorescence microscopy,” Laser Photonics Rev. 12(8), 1700333 (2018).
[Crossref]

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
[Crossref] [PubMed]

Y. Chen, W. Liu, Z. Zhang, C. Zheng, Y. Huang, R. Cao, D. Zhu, L. Xu, M. Zhang, Y.-H. Zhang, J. Fan, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Multi-color live-cell super-resolution volume imaging with multi-angle interference microscopy,” Nat. Commun. 9(1), 4818 (2018).
[Crossref] [PubMed]

Zhuang, X.

Y. M. Sigal, R. Zhou, and X. Zhuang, “Visualizing and discovering cellular structures with super-resolution microscopy,” Science 361(6405), 880–887 (2018).
[Crossref] [PubMed]

Biophys. J. (1)

M. G. Gustafsson, L. Shao, P. M. Carlton, C. J. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Cell (2)

Y. Guo, D. Li, S. Zhang, Y. Yang, J.-J. Liu, X. Wang, C. Liu, D. E. Milkie, R. P. Moore, U. S. Tulu, D. P. Kiehart, J. Hu, J. Lippincott-Schwartz, E. Betzig, and D. Li, “Visualizing intracellular organelle and cytoskeletal interactions at nanoscale resolution on millisecond timescales,” Cell 175(5), 1430–1442 (2018).
[Crossref] [PubMed]

J. Tønnesen, V. V. G. K. Inavalli, and U. V. Nägerl, “Super-resolution imaging of the extracellular space in living brain tissue,” Cell 172(5), 1108–1121 (2018).
[Crossref] [PubMed]

Chem. Rev. (4)

M. Sauer and M. Heilemann, “Single-molecule localization microscopy in eukaryotes,” Chem. Rev. 117(11), 7478–7509 (2017).
[Crossref] [PubMed]

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

H. Blom and J. Widengren, “Stimulated emission depletion microscopy,” Chem. Rev. 117(11), 7377–7427 (2017).
[Crossref] [PubMed]

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117(23), 13890–13908 (2017).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

Y. Chen, R. Cao, W. Liu, D. Zhu, Z. Zhang, C. Kuang, and X. Liu, “Widefield and total internal reflection fluorescent structured illumination microscopy with scanning galvo mirrors,” J. Biomed. Opt. 23(4), 1–9 (2018).
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Nat. Biotechnol. (2)

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Figures (6)

Fig. 1
Fig. 1 The diagram of 3D SIM setup. (a) Experimental setup. PMSF, polarization maintaining single-mode fiber; BC, beam collimator; M1–M4, reflecting mirror; HWP1–HWP3, half-wave plate; PBS1, PBS2, polarized beam splitter; PZT1, PZT2, piezoelectric stage; GM1, GM2, scanning galvanometer; SL1, SL2, scanning lens; PR1, PR2, polarization rotator; L1-L4, lens; QWP, quarter-wave plate; DM, dichroic mirror; BFP, back focal plane; TL, tube lens. (b) The polarizations of the three incident light beams for three pattern orientations at the BFP of the objective lens. The three beams are always maintained at the same azimuthal linear polarization, which ensures the highest possible modulation contrast of the structured illumination pattern. (c) x-z slice of the 3D structured illumination pattern (top), showing both lateral and axial periodic structure, and corresponding frequency components of the pattern in Fourier domain.
Fig. 2
Fig. 2 Overview of the principle and working flow of 3D SIM reconstruction. After the SIM system initialization, the raw image data is obtained at each axial plane with five pattern phases and three angles spaced by 60°. The “SIMcheck” method is then used to evaluate the data and provide the feedback to adjust the experimental parameters. If passed, the reconstruction is performed mainly in the Fourier domain. The final reconstructed result will further provide the feedback for the experiment acquisition and data processing.
Fig. 3
Fig. 3 Experimental results of 100 nm fluorescent nanoparticles. (a) Wide-filed image of deconvolution and (b) super-resolution image with 3D SIM, illustrating the improvement of lateral resolution. The bottom-right images in (a) and (b) are the corresponding axial slices of the blue-boxed regions, illustrating the improvement of axial resolution and the removal of out-of-focus background. The green arrowheads indicate the lateral differentiation of two adjacent nanoparticles from axial view. (c) Lateral intensity profiles of the nanoparticles in (a) (gray line) and (b) (orange line). The measurement was performed for 20 particles. (d) Lateral intensity profiles of the orange dotted lines in (a) (gray line) and (b) (orange line). (e) Axial intensity profiles of the yellow dotted lines in the bottom-right images in (a) (gray line) and (b) (orange line). Scale bars, 1 μm in (a, b) and 300 nm in the bottom-right images in (a, b).
Fig. 4
Fig. 4 Experimental results of mitochondria in a bovine pulmonary artery endothelial cell stained with MitoTracker Red. (a) Each line contains five linearly independent raw images at each pattern orientation with equidistant phase, the corresponding frequency distribution and the extended OTF. (b) “SIMcheck” results of the channel intensity profile, modulation contrast-to-noise ratio (MCN) and raw Fourier projection of the raw data shown in (a). (c) Wide-filed image of deconvolution (left) and super-resolution image with 3D SIM (right). The bottom-left images are the OTF before (left) and after reconstruction (right), illustrating the extension of the frequency support. (d) Intensity profiles of the orange dotted lines in (c). Scale bars, 10 μm in (a) and 5 μm in (c).
Fig. 5
Fig. 5 Experimental results of microtubules in a U2OS cell stained with Alexa Fluor 488. (a, b) Wide-filed image of deconvolution (left) and super-resolution image with 3D SIM (right) at axial positions of z = 1.25 μm and 2 μm, respectively, illustrating the improvement of 3D resolution and optical sectioning capacity. (c, d) Axial slices cut through the yellow and orange dashed lines in (a). Scale bars, 4 μm in (a, b) and 2 μm in (c, d).
Fig. 6
Fig. 6 Live-cell experimental results of mitochondria in a U2OS cell stained with Atto 647N. (a, c) Super-resolution image with 3D SIM at axial positions of z = 0.8 μm and z = 1.92 μm, respectively. The bottom-right of (a) is the corresponding wide-filed image of deconvolution. (b, d) Time lapse 3D SIM image sequences of the blue boxed regions in (a) and (c), showing mitochondria movement and fusion (orange arrowheads) and fission event (yellow arrowheads). Scale bars, 5 μm in (a, c), 10 μm in the bottom-right image in (a), and 1 μm in (b, d).

Equations (3)

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{ E 1 = A 1 e i( k x x+ k y y+ φ 1 )+i( k z z) E 2 = A 2 e i(kz+ φ 2 ) E 3 = A 3 e i( k x x+ k y y)+i( k z z)
I=( E 1 + E 2 + E 3 )( E 1 + E 2 + E 3 ) = A 1 2 + A 2 2 + A 3 2 m=0 + A 1 A 3 e i(2 k x x+2 k y y+ φ 1 ) m=2 + A 3 A 1 e i(2 k x x+2 k y y+ φ 1 ) m=2 + e i( k x x+ k y y) ( A 1 A 2 e i( k z zkz+ φ 1 φ 2 ) + A 2 A 3 e i(kz k z z+ φ 2 ) ) m=1 + e i( k x x+ k y y) ( A 2 A 1 e i(kz k z z+ φ 2 φ 1 ) + A 3 A 2 e i( k z zkz φ 2 ) ) m=1
I=( E 1 + E 2 + E 3 )( E 1 + E 2 + E 3 ) = A 1 2 + A 2 2 + A 3 2 m=0 + A 1 A 3 e i(2 k x x+2 k y y+ 2π 5 ) m=2 + A 3 A 1 e i(2 k x x+2 k y y+ 2π 5 ) m=2 + e i( k x x+ k y y+ π 5 ) ( A 1 A 2 e i( k z zkz) + A 2 A 3 e i(kz k z z) ) m=1 + e i( k x x+ k y y+ π 5 ) ( A 2 A 1 e i(kz k z z) + A 3 A 2 e i( k z zkz) ) m=1

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