Abstract

Various types of non-uniform illumination can be used for resolution improvement in fluorescence microscopy. Here we study the differences between several types of incoherent illumination patterns, such as multi-spot, line and pseudo-random patterns. This requires an imaging setup and an image reconstruction algorithm that are flexible enough to incorporate any type of illumination pattern. We employ fluorescence microscope with structured illumination generated by a Digital Micro-mirror Device (DMD) and the pattern-illuminated Fourier Ptychography reconstruction algorithm (piFP) to this end. The piFP method is modified and improved by identifying the algorithm as steepest descent optimization of a least squares function. We find that illumination patterns with regular structure are superior to those with irregular structure in terms of resolution enhancement and noise level in the reconstructed images.

© 2015 Optical Society of America

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2015 (4)

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]

A. Jost, E. Tolstik, P. Feldmann, K. Wicker, A. Sentenac, and R. Heintzmann, “Optical sectioning and high resolution in single-slice Structured Illumination Microscopy by thick slice blind-SIM reconstruction,” PLoS One 10(7), e0132174 (2015).
[Crossref] [PubMed]

N. Chakrova, B. Rieger, and S. Stallinga, “Development of a DMD-based fluorescence microscope,” Proc. SPIE 9330, 933008 (2015).
[Crossref]

F. Ströhl and C. F. Kaminski, “A joint Richardson–Lucy deconvolution algorithm for the reconstruction of multifocal structured illumination microscopy data,” Methods Appl. Fluoresc. 3(1), 014002 (2015).
[Crossref]

2014 (2)

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy Deconvolution as a General Tool for Combining Images with Complementary Strengths,” ChemPhysChem 15(4), 794–800 (2014).
[Crossref] [PubMed]

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
[Crossref] [PubMed]

2013 (7)

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
[Crossref] [PubMed]

K. Wicker, O. Mandula, G. Best, R. Fiolka, and R. Heintzmann, “Phase optimisation for structured illumination microscopy,” Opt. Express 21(2), 2032–2049 (2013).
[Crossref] [PubMed]

C. H. Righolt, J. A. Slotman, I. T. Young, S. Mai, L. J. van Vliet, and S. Stallinga, “Image filtering in structured illumination microscopy using the Lukosz bound,” Opt. Express 21(21), 24431–24451 (2013).
[Crossref] [PubMed]

K. Wicker, “Non-iterative determination of pattern phase in structured illumination microscopy using auto-correlations in Fourier space,” Opt. Express 21(21), 24692–24701 (2013).
[Crossref] [PubMed]

R. Ayuk, H. Giovannini, A. Jost, E. Mudry, J. Girard, T. Mangeat, N. Sandeau, R. Heintzmann, K. Wicker, K. Belkebir, and A. Sentenac, “Structured illumination fluorescence microscopy with distorted excitations using a filtered blind-SIM algorithm,” Opt. Lett. 38(22), 4723–4726 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
[Crossref] [PubMed]

2012 (3)

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

P. Křížek, I. Raška, and G. M. Hagen, “Flexible structured illumination microscope with a programmable illumination array,” Opt. Express 20(22), 24585–24599 (2012).
[Crossref] [PubMed]

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

2011 (1)

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

2009 (1)

2008 (2)

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278 (2008).
[Crossref] [PubMed]

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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]

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

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

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

2005 (1)

2001 (2)

J. G. Walker, “Non-scanning confocal fluorescence microscopy using speckle illumination,” Opt. Commun. 189(4-6), 221–226 (2001).
[Crossref]

R. Heintzmann, Q. S. Hanley, D. Arndt-Jovin, and T. M. Jovin, “A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images,” J. Microsc. 204(2), 119–135 (2001).
[Crossref] [PubMed]

2000 (4)

M. G. Somekh, C. W. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97(13), 7232–7236 (2000).
[Crossref] [PubMed]

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]

G. E. Cragg and P. T. So, “Lateral resolution enhancement with standing evanescent waves,” Opt. Lett. 25(1), 46–48 (2000).
[Crossref] [PubMed]

1999 (2)

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
[Crossref]

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[Crossref] [PubMed]

1998 (1)

P. J. Verveer, Q. S. Hanley, P. W. Verbeek, L. J. v Vliet, and T. M. Jovin, “Theory of confocal fluorescence imaging in the programmable array microscope (PAM),” J. Microsc. 189(3), 192–198 (1998).
[Crossref]

1997 (1)

1994 (1)

Agard, D. A.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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]

Allain, M.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Arndt-Jovin, D.

R. Heintzmann, Q. S. Hanley, D. Arndt-Jovin, and T. M. Jovin, “A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images,” J. Microsc. 204(2), 119–135 (2001).
[Crossref] [PubMed]

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[Crossref] [PubMed]

Ayuk, R.

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]

Bates, M.

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

Belkebir, K.

R. Ayuk, H. Giovannini, A. Jost, E. Mudry, J. Girard, T. Mangeat, N. Sandeau, R. Heintzmann, K. Wicker, K. Belkebir, and A. Sentenac, “Structured illumination fluorescence microscopy with distorted excitations using a filtered blind-SIM algorithm,” Opt. Lett. 38(22), 4723–4726 (2013).
[Crossref] [PubMed]

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Best, G.

Betzig, E.

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]

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]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Cande, W. Z.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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]

Carlton, P. M.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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]

Chakrova, N.

N. Chakrova, B. Rieger, and S. Stallinga, “Development of a DMD-based fluorescence microscope,” Proc. SPIE 9330, 933008 (2015).
[Crossref]

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]

Chitnis, A. B.

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Choi, C.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
[Crossref] [PubMed]

Combs, C. A.

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Cragg, G. E.

Cremer, C.

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
[Crossref]

Dan, D.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
[Crossref] [PubMed]

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]

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]

Dong, S.

Feldmann, P.

A. Jost, E. Tolstik, P. Feldmann, K. Wicker, A. Sentenac, and R. Heintzmann, “Optical sectioning and high resolution in single-slice Structured Illumination Microscopy by thick slice blind-SIM reconstruction,” PLoS One 10(7), e0132174 (2015).
[Crossref] [PubMed]

Fienup, J. R.

Fiolka, R.

Fischer, R. S.

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
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J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97(13), 7232–7236 (2000).
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Gao, P.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
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Giovannini, H.

Girard, J.

R. Ayuk, H. Giovannini, A. Jost, E. Mudry, J. Girard, T. Mangeat, N. Sandeau, R. Heintzmann, K. Wicker, K. Belkebir, and A. Sentenac, “Structured illumination fluorescence microscopy with distorted excitations using a filtered blind-SIM algorithm,” Opt. Lett. 38(22), 4723–4726 (2013).
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E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
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S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
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M. G. Somekh, C. W. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

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M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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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Guo, K.

Gustafsson, M. G.

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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Gustafsson, M. G. L.

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

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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]

Hagen, G. M.

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]

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R. Heintzmann, Q. S. Hanley, D. Arndt-Jovin, and T. M. Jovin, “A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images,” J. Microsc. 204(2), 119–135 (2001).
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Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
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A. Jost, E. Tolstik, P. Feldmann, K. Wicker, A. Sentenac, and R. Heintzmann, “Optical sectioning and high resolution in single-slice Structured Illumination Microscopy by thick slice blind-SIM reconstruction,” PLoS One 10(7), e0132174 (2015).
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R. Heintzmann, Q. S. Hanley, D. Arndt-Jovin, and T. M. Jovin, “A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images,” J. Microsc. 204(2), 119–135 (2001).
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R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
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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]

Hess, S. T.

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

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M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy Deconvolution as a General Tool for Combining Images with Complementary Strengths,” ChemPhysChem 15(4), 794–800 (2014).
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G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy Deconvolution as a General Tool for Combining Images with Complementary Strengths,” ChemPhysChem 15(4), 794–800 (2014).
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Jang, J.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
[Crossref] [PubMed]

Jeong, K.-H.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
[Crossref] [PubMed]

Jost, A.

A. Jost, E. Tolstik, P. Feldmann, K. Wicker, A. Sentenac, and R. Heintzmann, “Optical sectioning and high resolution in single-slice Structured Illumination Microscopy by thick slice blind-SIM reconstruction,” PLoS One 10(7), e0132174 (2015).
[Crossref] [PubMed]

R. Ayuk, H. Giovannini, A. Jost, E. Mudry, J. Girard, T. Mangeat, N. Sandeau, R. Heintzmann, K. Wicker, K. Belkebir, and A. Sentenac, “Structured illumination fluorescence microscopy with distorted excitations using a filtered blind-SIM algorithm,” Opt. Lett. 38(22), 4723–4726 (2013).
[Crossref] [PubMed]

Jovin, T. M.

R. Heintzmann, Q. S. Hanley, D. Arndt-Jovin, and T. M. Jovin, “A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images,” J. Microsc. 204(2), 119–135 (2001).
[Crossref] [PubMed]

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[Crossref] [PubMed]

P. J. Verveer, Q. S. Hanley, P. W. Verbeek, L. J. v Vliet, and T. M. Jovin, “Theory of confocal fluorescence imaging in the programmable array microscope (PAM),” J. Microsc. 189(3), 192–198 (1998).
[Crossref]

Kaminski, C. F.

F. Ströhl and C. F. Kaminski, “A joint Richardson–Lucy deconvolution algorithm for the reconstruction of multifocal structured illumination microscopy data,” Methods Appl. Fluoresc. 3(1), 014002 (2015).
[Crossref]

Keum, D.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
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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]

Knapp, H. F.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97(13), 7232–7236 (2000).
[Crossref] [PubMed]

Kner, P.

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

Krause, A. W.

Krížek, P.

Le Moal, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Lei, M.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
[Crossref] [PubMed]

Li, D.

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]

Liang, M.

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]

Mai, S.

Mandula, O.

Mangeat, T.

Mason, M. D.

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

Mertz, J.

Milkie, D. E.

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]

Min, J.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
[Crossref] [PubMed]

Mione, M.

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[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]

Mudry, E.

R. Ayuk, H. Giovannini, A. Jost, E. Mudry, J. Girard, T. Mangeat, N. Sandeau, R. Heintzmann, K. Wicker, K. Belkebir, and A. Sentenac, “Structured illumination fluorescence microscopy with distorted excitations using a filtered blind-SIM algorithm,” Opt. Lett. 38(22), 4723–4726 (2013).
[Crossref] [PubMed]

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Nanda, P.

Nicoletti, C.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Nogare, D. D.

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (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]

Parekh, S. H.

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Pasham, M.

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]

Patterson, G. H.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy Deconvolution as a General Tool for Combining Images with Complementary Strengths,” ChemPhysChem 15(4), 794–800 (2014).
[Crossref] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Postma, M.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy Deconvolution as a General Tool for Combining Images with Complementary Strengths,” ChemPhysChem 15(4), 794–800 (2014).
[Crossref] [PubMed]

Qi, Y.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
[Crossref] [PubMed]

Raška, I.

Rego, E. H.

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

Rieger, B.

N. Chakrova, B. Rieger, and S. Stallinga, “Development of a DMD-based fluorescence microscope,” Proc. SPIE 9330, 933008 (2015).
[Crossref]

Righolt, C. H.

Rust, M. J.

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

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J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
[Crossref] [PubMed]

Sandeau, N.

Savatier, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Sedat, J. W.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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]

See, C. W.

M. G. Somekh, C. W. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

Sentenac, A.

A. Jost, E. Tolstik, P. Feldmann, K. Wicker, A. Sentenac, and R. Heintzmann, “Optical sectioning and high resolution in single-slice Structured Illumination Microscopy by thick slice blind-SIM reconstruction,” PLoS One 10(7), e0132174 (2015).
[Crossref] [PubMed]

R. Ayuk, H. Giovannini, A. Jost, E. Mudry, J. Girard, T. Mangeat, N. Sandeau, R. Heintzmann, K. Wicker, K. Belkebir, and A. Sentenac, “Structured illumination fluorescence microscopy with distorted excitations using a filtered blind-SIM algorithm,” Opt. Lett. 38(22), 4723–4726 (2013).
[Crossref] [PubMed]

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Shao, L.

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]

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

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. 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]

Shiradkar, R.

Shroff, H.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy Deconvolution as a General Tool for Combining Images with Complementary Strengths,” ChemPhysChem 15(4), 794–800 (2014).
[Crossref] [PubMed]

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Shroff, S. A.

Slotman, J. A.

So, P. T.

Somekh, M. G.

M. G. Somekh, C. W. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[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]

Stallinga, S.

Stehr, R. L.

Stemmer, A.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97(13), 7232–7236 (2000).
[Crossref] [PubMed]

Ströhl, F.

F. Ströhl and C. F. Kaminski, “A joint Richardson–Lucy deconvolution algorithm for the reconstruction of multifocal structured illumination microscopy data,” Methods Appl. Fluoresc. 3(1), 014002 (2015).
[Crossref]

Temprine, K.

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Tolstik, E.

A. Jost, E. Tolstik, P. Feldmann, K. Wicker, A. Sentenac, and R. Heintzmann, “Optical sectioning and high resolution in single-slice Structured Illumination Microscopy by thick slice blind-SIM reconstruction,” PLoS One 10(7), e0132174 (2015).
[Crossref] [PubMed]

v Vliet, L. J.

P. J. Verveer, Q. S. Hanley, P. W. Verbeek, L. J. v Vliet, and T. M. Jovin, “Theory of confocal fluorescence imaging in the programmable array microscope (PAM),” J. Microsc. 189(3), 192–198 (1998).
[Crossref]

van Vliet, L. J.

Ventalon, C.

Verbeek, P. W.

P. J. Verveer, Q. S. Hanley, P. W. Verbeek, L. J. v Vliet, and T. M. Jovin, “Theory of confocal fluorescence imaging in the programmable array microscope (PAM),” J. Microsc. 189(3), 192–198 (1998).
[Crossref]

Verveer, P. J.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
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Wang, W.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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Wichmann, J.

Wicker, K.

Williams, D. R.

Winterhalder, M.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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Xia, L.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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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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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3, 2075 (2013).
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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, “Richardson-Lucy Deconvolution as a General Tool for Combining Images with Complementary Strengths,” ChemPhysChem 15(4), 794–800 (2014).
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Zhang, M.

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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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination Super-resolution and optical sectioning microscopy,” Sci. Rep. 3, 1116 (2013).
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Figures (10)

Fig. 1
Fig. 1

(a) Simulated resolution target. Line group 4 has the pitch of λem/2NA, corresponding to the limit of the widefield imaging. (b)-(d) Examples of illumination patterns generated at the DMD: multi-spot (b), line (c) and pseudo-random (d) patterns.

Fig. 2
Fig. 2

Change of the MTF curves during the piFP iterations. Multi-spot illumination patterns with a pitch of 12 pixels, which corresponds to a spatial frequency cutoff of 1.7 times the widefield bandwidth 2NA/λ, were used to simulate the illumination of a line object. The MTF is calculated as the Fourier transform of the line profile at each iteration of the piFP reconstruction algorithm. The stopping iteration is highlighted in red. The vertical dashed line indicates the highest possible resolution improvement estimated from the pitch of the projected illumination patterns.

Fig. 3
Fig. 3

Comparison of the image quality for pseudo-random patterns with different sparsity. (a) Illustration of the stopping condition. The crossings of the curves with the horizontal dashed line indicate when the error reaches the noise level within 1%. (b) Lower fill factor results in higher SNR. Horizontal dashed line shows the SNR in a widefield image. Round markers indicate the final iteration according to our stopping criterion. (c) Lower fill factor results in smaller FWHM. The dashed lines show the FWHM in a widefield image and the best possible resolution λ/4NA

Fig. 4
Fig. 4

(a) In the case of pseudo-random illumination, the resolution of the reconstructed image improves with increasing number of illumination patterns N. We used 10 illumination patterns in (b) and 100 illumination patterns in (c). The sparsity of the patterns is kept constant (f = 10%).

Fig. 5
Fig. 5

Performance of the original piFP algorithm compared to the performance of the piFP algorithm with NR update rule for different types of illumination patterns. SNR (a) and FWHM (b) curves display the trade-off between the sharpness of the structures and the noise appearance in the reconstructed images. Application of the NR update rule leads to faster convergence, reduced SNR and improved FWHM. Round markers indicate the final iteration according to our stopping criterion. The SNR and FWHM values of the widefield and conventional SIM images are given for comparison.

Fig. 6
Fig. 6

Schematic view of the DMD-based fluorescence microscope. The beam of the 488 nm diode laser is despeckled and expanded in order to provide illumination of the DMD surface. The DMD patterns, demagnified by the 250:150 mm optical relay and by the objective lens, are projected onto the sample. The sCMOS camera detects fluorescence from the sample. One camera frame is taken for each illumination pattern [33].

Fig. 7
Fig. 7

Comparison of piFP reconstructions for different illumination patterns. The sample containing 100 nm diameter fluorescent microspheres was imaged using a 60 × /0.7 air objective. (a) Widefield image. The two neighboring beads shown in the zoom-in area are not resolved. (b) Widefield image deconvolved using the Richardson-Lucy algorithm shows slight resolution improvement. (c) piFP reconstruction for the multi-spot illumination patterns. The two neighboring beads are well resolved. (d) piFP reconstruction for the pseudo-random illumination patterns with fill factor f = 1%. The neighboring beads are separated, however, the relative intensities of the beads are not preserved. (e) piFP reconstruction for the pseudo-random illumination patterns with fill factor f = 10% shows weaker resolution improvement compared to the multi-spot patterns.

Fig. 8
Fig. 8

Comparison of piFP reconstructions for different illumination patterns. Images of the BPAE cells were acquired using a 60 × /0.7 air objective. (a) The sum of all acquired frames is given to demonstrate the uniformity of the illumination. (b) Widefield image. (c) Deconvolution of the widefield image using Richardson-Lucy algorithm. (d) piFP reconstruction for the multi-spot illumination patterns. (e) piFP reconstruction for the pseudo-random illumination patterns with fill factor f = 1% showing enhanced graininess. (f) piFP reconstruction for the pseudo-random illumination patterns with fill factor f = 10% showing pronounced low frequent noise structures. The profile plots along the highlighted yellow line only show three distinct filaments for the multi-spot reconstruction in (d).

Fig. 9
Fig. 9

The algorithms with and without the reconstruction of the illumination patterns produce comparable results. (a) piFP reconstruction using known illumination patterns reaches convergence in 7 iterations. Images show the reconstructed object and an example of the known illumination pattern. (b) piFP reconstruction with estimation of the illumination patterns reaches convergence within 9 iterations. Images show the reconstructed object and an example of the estimated illumination pattern. (c) An example of the actually measured image dn and the corresponding expected image µn in case the known illumination patterns are used.

Fig. 10
Fig. 10

Comparison of the expected (a) and reconstructed (b) patterns in case of pseudo-random illumination with fill-factor f = 10%. (c) The profile of the difference Pexp – Prec along the yellow line shown in (a) reveals good correspondence between the expected and reconstructed illumination patterns.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

μ n ( r i )= j=1 M h em ( r i r j )x( r j ) p n ( r j ) ,
p i n = j=1 M h ij ex q j n .
E= 1 2 n=1 N i=1 M ( d i n μ i n ) 2 ,
x i ' = x i + β x E x i ,
E x i = n=1 N j=1 M h ji em p i n ( d j n μ j n ) = n=1 N j=1 M h ji em p i n ( d j n k=1 M h jk em x k p k n ) .
y i n = p i n x i .
step 1: y i n = p i n x i
step 2: y ' i n = y i n + β y j=1 M h ji em ( d j n k=1 M h jk em y k n )
step 3: x i ' = x i + β x β y n=1 N p i n ( y ' i n p i n x i )
Y ' i n = Y i n + β y OT F * ( D i n Y i n OTF ),
p ' i n = p i n + β p E p i n = p i n + β p β y x i ( y ' i n p i n x i ).
L ij = 2 E x i x j = n=1 N k=1 M h ki em h kj em p i n p j n =( k=1 M h ki em h kj em )( l=1 M m=1 M h il ex h jm ex ( n=1 N q l n q m n ) )
n=1 N q i n =N q ,
n=1 N ( q i n ) 2 =N q 2 ,
n=1 N q l n q m n N( q 2 q 2 ) δ lm +N q 2
L ij =N( q 2 q 2 ) k=1 M h ki em h kj em l=1 M h il ex h jl ex +N q 2 k=1 M h ki em h kj em
x i '= x i 1 L ii E x i
L ii =N( q 2 q 2 ) k=1 M ( h ki em ) 2 l=1 M ( h li ex ) 2 +N q 2 k=1 M ( h ki em ) 2 .
K i em = k=1 M ( h ki em ) 2 = K em ,
K i ex = l=1 M ( h li ex ) 2 = K ex ,
L ii =N( q 2 q 2 ) K em K ex +N q 2 K em ,
NL= n=1 N i=1 M d i n .

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