Abstract

The resolution of Single Molecule Localization Microscopy (SML) is dependent on the width of the Point Spread Function (PSF) and the number of photons collected. However, biological samples tend to degrade the shape of the PSF due to the heterogeneity of the index of refraction. In addition, there are aberrations caused by imperfections in the optical components and alignment, and the refractive index mismatch between the coverslip and the sample, all of which directly reduce the accuracy of SML. Adaptive Optics (AO) can play a critical role in compensating for aberrations in order to increase the resolution. However the stochastic nature of single molecule emission presents a challenge for wavefront optimization because the large fluctuations in photon emission do not permit many traditional optimization techniques to be used. Here we present an approach that optimizes the wavefront during SML acquisition by combining an intensity independent merit function with a Genetic algorithm (GA) to optimize the PSF despite the fluctuating intensity. We demonstrate the use of AO with GA in tissue culture cells and through ~50µm of tissue in the Drosophila Central Nervous System (CNS) to achieve a 4-fold increase in the localization precision.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]

2015 (3)

B. Thomas, A. Wolstenholme, S. N. Chaudhari, E. T. Kipreos, and P. Kner, “Enhanced resolution through thick tissue with structured illumination and adaptive optics,” J. Biomed. Opt. 20(2), 026006 (2015).
[Crossref] [PubMed]

J. Xu, K. F. Tehrani, and P. Kner, “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” ACS Nano 9(3), 2917–2925 (2015).
[Crossref] [PubMed]

D. Burke, B. Patton, F. Huang, J. Bewersdorf, and M. J. Booth, “Adaptive optics correction of specimen-induced aberrations in single-molecule switching microscopy,” Optica 2, 177–185 (2015).

2014 (4)

J. Antonello, T. van Werkhoven, M. Verhaegen, H. H. Truong, C. U. Keller, and H. C. Gerritsen, “Optimization-based wavefront sensorless adaptive optics for multiphoton microscopy,” J. Opt. Soc. Am. A 31(6), 1337–1347 (2014).
[Crossref] [PubMed]

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” J. Opt. 16(12), 125704 (2014).
[Crossref]

B. R. Patton, D. Burke, and M. J. Booth, “Adaptive optics from microscopy to nanoscopy,” Proc. SPIE 8948, 894802 (2014).

K. Deb and D. Deb, “Analysing mutation schemes for real-parameter genetic algorithms,” Int. J. Artif. Intell. Soft Comput. 4(1), 59280 (2014).
[Crossref]

2013 (3)

N. Banterle, K. H. Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super-resolution microscopy,” J. Struct. Biol. 183(3), 363–367 (2013).
[Crossref] [PubMed]

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
[Crossref] [PubMed]

X. Tao, A. Norton, M. Kissel, O. Azucena, and J. Kubby, “Adaptive optical two-photon microscopy using autofluorescent guide stars,” Opt. Lett. 38(23), 5075–5078 (2013).
[Crossref] [PubMed]

2012 (4)

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express 20(5), 4840–4849 (2012).
[Crossref] [PubMed]

I. Izeddin, M. El Beheiry, J. Andilla, D. Ciepielewski, X. Darzacq, and M. Dahan, “PSF shaping using adaptive optics for three-dimensional single-molecule super-resolution imaging and tracking,” Opt. Express 20(5), 4957–4967 (2012).
[Crossref] [PubMed]

F.-A. Fortin, F.-M. D. Rainville, M.-A. Gardner, M. Parizeau, and C. Gagné, “DEAP: Evolutionary Algorithms Made Easy,” J. Mach. Learn. Res. 13, 2171–2175 (2012).

J. Ries, C. Kaplan, E. Platonova, H. Eghlidi, and H. Ewers, “A simple, versatile method for GFP-based super-resolution microscopy via nanobodies,” Nat. Methods 9(6), 582–584 (2012).
[Crossref] [PubMed]

2011 (4)

F. Cella Zanacchi, Z. Lavagnino, M. Perrone Donnorso, A. Del Bue, L. Furia, M. Faretta, and A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8(12), 1047–1049 (2011).
[Crossref] [PubMed]

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8(12), 1027–1036 (2011).
[Crossref] [PubMed]

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]

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

2010 (3)

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

P. Kner, L. Winoto, D. A. Agard, and J. W. Sedat, “Closed loop adaptive optics for microscopy without a wavefront sensor,” Proc SPIE Int Soc Opt Eng 7570, 757006 (2010).
[Crossref] [PubMed]

O. Azucena, J. Crest, J. Cao, W. Sullivan, P. Kner, D. Gavel, D. Dillon, S. Olivier, and J. Kubby, “Wavefront aberration measurements and corrections through thick tissue using fluorescent microsphere reference beacons,” Opt. Express 18(16), 17521–17532 (2010).
[Crossref] [PubMed]

2009 (2)

D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34(16), 2495–2497 (2009).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-Resolution Imaging with Small Organic Fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

2008 (4)

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
[Crossref] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
[Crossref] [PubMed]

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, “Adaptive optics for structured illumination microscopy,” Opt. Express 16(13), 9290–9305 (2008).
[Crossref] [PubMed]

2007 (4)

M. J. Booth, “Wavefront sensorless adaptive optics for large aberrations,” Opt. Lett. 32(1), 5–7 (2007).
[Crossref] [PubMed]

D. Debarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express 15(13), 8176–8190 (2007).
[Crossref] [PubMed]

M. J. Booth, D. Débarre, and T. Wilson, “Image-based wavefront sensorless adaptive optics,” Proc. SPIE 6711, 671102 (2007).
[Crossref]

M. J. Booth, “Adaptive optics in microscopy,” Philos Transact A Math Phys, Eng. Sci. 365, 2829–2843 (2007).

2006 (5)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[Crossref] [PubMed]

M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. 263(2), 147–151 (2006).
[Crossref]

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)

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67(1), 36–44 (2005).
[Crossref] [PubMed]

2004 (3)

M. Schwertner, M. J. Booth, M. A. A. Neil, and T. Wilson, “Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry,” J. Microsc. 213(1), 11–19 (2004).
[Crossref] [PubMed]

M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc. 215(3), 271–280 (2004).
[Crossref] [PubMed]

M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (4)

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. 206(1), 65–71 (2002).
[Crossref] [PubMed]

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[Crossref] [PubMed]

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise Nanometer Localization Analysis for Individual Fluorescent Probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

2001 (1)

P. Shen and H. N. Cai, “Drosophila neuropeptide F mediates integration of chemosensory stimulation and conditioning of the nervous system by food,” J. Neurobiol. 47(1), 16–25 (2001).
[Crossref] [PubMed]

2000 (1)

1998 (1)

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192(2), 90–98 (1998).
[Crossref]

1993 (1)

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

1983 (1)

1978 (1)

K. Weber, P. C. Rathke, and M. Osborn, “Cytoplasmic microtubular images in glutaraldehyde-fixed tissue culture cells by electron microscopy and by immunofluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 75(4), 1820–1824 (1978).
[Crossref] [PubMed]

Agard, D. A.

P. Kner, L. Winoto, D. A. Agard, and J. W. Sedat, “Closed loop adaptive optics for microscopy without a wavefront sensor,” Proc SPIE Int Soc Opt Eng 7570, 757006 (2010).
[Crossref] [PubMed]

Agarwal, S.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Albert, O.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. 206(1), 65–71 (2002).
[Crossref] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, “Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy,” Opt. Lett. 25(1), 52–54 (2000).
[Crossref] [PubMed]

Andilla, J.

Antonello, J.

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G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8(12), 1027–1036 (2011).
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H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
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A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
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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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B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
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B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
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M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
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J. Ries, C. Kaplan, E. Platonova, H. Eghlidi, and H. Ewers, “A simple, versatile method for GFP-based super-resolution microscopy via nanobodies,” Nat. Methods 9(6), 582–584 (2012).
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M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. 263(2), 147–151 (2006).
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Kipreos, E. T.

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Kner, P.

B. Thomas, A. Wolstenholme, S. N. Chaudhari, E. T. Kipreos, and P. Kner, “Enhanced resolution through thick tissue with structured illumination and adaptive optics,” J. Biomed. Opt. 20(2), 026006 (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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N. Banterle, K. H. Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super-resolution microscopy,” J. Struct. Biol. 183(3), 363–367 (2013).
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R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
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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).
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K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
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Mukherjee, A.

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M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[Crossref] [PubMed]

Neil, M. A. A.

M. Schwertner, M. J. Booth, M. A. A. Neil, and T. Wilson, “Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry,” J. Microsc. 213(1), 11–19 (2004).
[Crossref] [PubMed]

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192(2), 90–98 (1998).
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R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
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Patterson, B. A.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67(1), 36–44 (2005).
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Patterson, G. H.

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

Patton, B. R.

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F. Cella Zanacchi, Z. Lavagnino, M. Perrone Donnorso, A. Del Bue, L. Furia, M. Faretta, and A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8(12), 1047–1049 (2011).
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Platonova, E.

J. Ries, C. Kaplan, E. Platonova, H. Eghlidi, and H. Ewers, “A simple, versatile method for GFP-based super-resolution microscopy via nanobodies,” Nat. Methods 9(6), 582–584 (2012).
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A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67(1), 36–44 (2005).
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K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Puig, D. L.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
[Crossref] [PubMed]

Rainville, F.-M. D.

F.-A. Fortin, F.-M. D. Rainville, M.-A. Gardner, M. Parizeau, and C. Gagné, “DEAP: Evolutionary Algorithms Made Easy,” J. Mach. Learn. Res. 13, 2171–2175 (2012).

Rathke, P. C.

K. Weber, P. C. Rathke, and M. Osborn, “Cytoplasmic microtubular images in glutaraldehyde-fixed tissue culture cells by electron microscopy and by immunofluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 75(4), 1820–1824 (1978).
[Crossref] [PubMed]

Rego, E. H.

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]

Reiner, G.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

Rieger, B.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
[Crossref] [PubMed]

Ries, J.

J. Ries, C. Kaplan, E. Platonova, H. Eghlidi, and H. Ewers, “A simple, versatile method for GFP-based super-resolution microscopy via nanobodies,” Nat. Methods 9(6), 582–584 (2012).
[Crossref] [PubMed]

Rueckel, M.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[Crossref] [PubMed]

Rust, M. J.

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

Sauer, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-Resolution Imaging with Small Organic Fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

Schüttpelz, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Schwertner, M.

M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. 263(2), 147–151 (2006).
[Crossref]

M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc. 215(3), 271–280 (2004).
[Crossref] [PubMed]

M. Schwertner, M. J. Booth, M. A. A. Neil, and T. Wilson, “Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry,” J. Microsc. 213(1), 11–19 (2004).
[Crossref] [PubMed]

M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004).
[Crossref] [PubMed]

Sedat, J. W.

P. Kner, L. Winoto, D. A. Agard, and J. W. Sedat, “Closed loop adaptive optics for microscopy without a wavefront sensor,” Proc SPIE Int Soc Opt Eng 7570, 757006 (2010).
[Crossref] [PubMed]

Shao, L.

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]

Shen, P.

P. Shen and H. N. Cai, “Drosophila neuropeptide F mediates integration of chemosensory stimulation and conditioning of the nervous system by food,” J. Neurobiol. 47(1), 16–25 (2001).
[Crossref] [PubMed]

Sherman, L.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. 206(1), 65–71 (2002).
[Crossref] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, “Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy,” Opt. Lett. 25(1), 52–54 (2000).
[Crossref] [PubMed]

Shroff, H.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

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]

Srinivas, S.

Stallinga, S.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
[Crossref] [PubMed]

Stelzer, E. H. K.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

Sullivan, W.

Tanaka, T.

M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. 263(2), 147–151 (2006).
[Crossref]

Tao, X.

Tehrani, K. F.

J. Xu, K. F. Tehrani, and P. Kner, “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” ACS Nano 9(3), 2917–2925 (2015).
[Crossref] [PubMed]

Thomas, B.

B. Thomas, A. Wolstenholme, S. N. Chaudhari, E. T. Kipreos, and P. Kner, “Enhanced resolution through thick tissue with structured illumination and adaptive optics,” J. Biomed. Opt. 20(2), 026006 (2015).
[Crossref] [PubMed]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise Nanometer Localization Analysis for Individual Fluorescent Probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Truong, H. H.

Tscherepanow, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Valentine, G. J.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67(1), 36–44 (2005).
[Crossref] [PubMed]

Van De Linde, S.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-Resolution Imaging with Small Organic Fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

van Werkhoven, T.

Vaughan, J. C.

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8(12), 1027–1036 (2011).
[Crossref] [PubMed]

Vaziri, A.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Vdovin, G.

Verhaegen, M.

Watanabe, T.

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise Nanometer Localization Analysis for Individual Fluorescent Probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Weber, K.

K. Weber, P. C. Rathke, and M. Osborn, “Cytoplasmic microtubular images in glutaraldehyde-fixed tissue culture cells by electron microscopy and by immunofluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 75(4), 1820–1824 (1978).
[Crossref] [PubMed]

Wilson, T.

D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34(16), 2495–2497 (2009).
[Crossref] [PubMed]

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, “Adaptive optics for structured illumination microscopy,” Opt. Express 16(13), 9290–9305 (2008).
[Crossref] [PubMed]

D. Debarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express 15(13), 8176–8190 (2007).
[Crossref] [PubMed]

M. J. Booth, D. Débarre, and T. Wilson, “Image-based wavefront sensorless adaptive optics,” Proc. SPIE 6711, 671102 (2007).
[Crossref]

M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. 263(2), 147–151 (2006).
[Crossref]

M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc. 215(3), 271–280 (2004).
[Crossref] [PubMed]

M. Schwertner, M. J. Booth, M. A. A. Neil, and T. Wilson, “Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry,” J. Microsc. 213(1), 11–19 (2004).
[Crossref] [PubMed]

M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004).
[Crossref] [PubMed]

M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[Crossref] [PubMed]

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192(2), 90–98 (1998).
[Crossref]

Winoto, L.

P. Kner, L. Winoto, D. A. Agard, and J. W. Sedat, “Closed loop adaptive optics for microscopy without a wavefront sensor,” Proc SPIE Int Soc Opt Eng 7570, 757006 (2010).
[Crossref] [PubMed]

Wolstenholme, A.

B. Thomas, A. Wolstenholme, S. N. Chaudhari, E. T. Kipreos, and P. Kner, “Enhanced resolution through thick tissue with structured illumination and adaptive optics,” J. Biomed. Opt. 20(2), 026006 (2015).
[Crossref] [PubMed]

Wolter, S.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Wright, A. J.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67(1), 36–44 (2005).
[Crossref] [PubMed]

Xu, J.

J. Xu, K. F. Tehrani, and P. Kner, “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” ACS Nano 9(3), 2917–2925 (2015).
[Crossref] [PubMed]

Ye, J. Y.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. 206(1), 65–71 (2002).
[Crossref] [PubMed]

York, A. G.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Zhang, X.

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” J. Opt. 16(12), 125704 (2014).
[Crossref]

Zhuang, X.

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8(12), 1027–1036 (2011).
[Crossref] [PubMed]

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
[Crossref] [PubMed]

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
[Crossref] [PubMed]

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

ACS Nano (1)

J. Xu, K. F. Tehrani, and P. Kner, “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” ACS Nano 9(3), 2917–2925 (2015).
[Crossref] [PubMed]

Angew. Chem. Int. Ed. Engl. (1)

M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-Resolution Imaging with Small Organic Fluorophores,” Angew. Chem. Int. Ed. Engl. 48(37), 6903–6908 (2009).
[Crossref] [PubMed]

Biophys. J. (2)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise Nanometer Localization Analysis for Individual Fluorescent Probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

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]

IEEE Trans. Evol. Comput. (1)

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Int. J. Artif. Intell. Soft Comput. (1)

K. Deb and D. Deb, “Analysing mutation schemes for real-parameter genetic algorithms,” Int. J. Artif. Intell. Soft Comput. 4(1), 59280 (2014).
[Crossref]

J. Biomed. Opt. (1)

B. Thomas, A. Wolstenholme, S. N. Chaudhari, E. T. Kipreos, and P. Kner, “Enhanced resolution through thick tissue with structured illumination and adaptive optics,” J. Biomed. Opt. 20(2), 026006 (2015).
[Crossref] [PubMed]

J. Mach. Learn. Res. (1)

F.-A. Fortin, F.-M. D. Rainville, M.-A. Gardner, M. Parizeau, and C. Gagné, “DEAP: Evolutionary Algorithms Made Easy,” J. Mach. Learn. Res. 13, 2171–2175 (2012).

J. Microsc. (6)

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. 206(1), 65–71 (2002).
[Crossref] [PubMed]

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192(2), 90–98 (1998).
[Crossref]

M. Schwertner, M. J. Booth, M. A. A. Neil, and T. Wilson, “Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry,” J. Microsc. 213(1), 11–19 (2004).
[Crossref] [PubMed]

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc. 215(3), 271–280 (2004).
[Crossref] [PubMed]

J. Neurobiol. (1)

P. Shen and H. N. Cai, “Drosophila neuropeptide F mediates integration of chemosensory stimulation and conditioning of the nervous system by food,” J. Neurobiol. 47(1), 16–25 (2001).
[Crossref] [PubMed]

J. Opt. (1)

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” J. Opt. 16(12), 125704 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Struct. Biol. (1)

N. Banterle, K. H. Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super-resolution microscopy,” J. Struct. Biol. 183(3), 363–367 (2013).
[Crossref] [PubMed]

Microsc. Res. Tech. (1)

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67(1), 36–44 (2005).
[Crossref] [PubMed]

Nat. Methods (10)

F. Cella Zanacchi, Z. Lavagnino, M. Perrone Donnorso, A. Del Bue, L. Furia, M. Faretta, and A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8(12), 1047–1049 (2011).
[Crossref] [PubMed]

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
[Crossref] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

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

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8(12), 1027–1036 (2011).
[Crossref] [PubMed]

J. Ries, C. Kaplan, E. Platonova, H. Eghlidi, and H. Ewers, “A simple, versatile method for GFP-based super-resolution microscopy via nanobodies,” Nat. Methods 9(6), 582–584 (2012).
[Crossref] [PubMed]

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10(6), 557–562 (2013).
[Crossref] [PubMed]

B. Huang, S. A. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5(12), 1047–1052 (2008).
[Crossref] [PubMed]

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]

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. 263(2), 147–151 (2006).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

Optica (1)

Philos Transact A Math Phys, Eng. Sci. (1)

M. J. Booth, “Adaptive optics in microscopy,” Philos Transact A Math Phys, Eng. Sci. 365, 2829–2843 (2007).

Proc SPIE Int Soc Opt Eng (1)

P. Kner, L. Winoto, D. A. Agard, and J. W. Sedat, “Closed loop adaptive optics for microscopy without a wavefront sensor,” Proc SPIE Int Soc Opt Eng 7570, 757006 (2010).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (3)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[Crossref] [PubMed]

M. J. Booth, M. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[Crossref] [PubMed]

K. Weber, P. C. Rathke, and M. Osborn, “Cytoplasmic microtubular images in glutaraldehyde-fixed tissue culture cells by electron microscopy and by immunofluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 75(4), 1820–1824 (1978).
[Crossref] [PubMed]

Proc. SPIE (2)

B. R. Patton, D. Burke, and M. J. Booth, “Adaptive optics from microscopy to nanoscopy,” Proc. SPIE 8948, 894802 (2014).

M. J. Booth, D. Débarre, and T. Wilson, “Image-based wavefront sensorless adaptive optics,” Proc. SPIE 6711, 671102 (2007).
[Crossref]

Science (1)

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

Other (5)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York, 1998).

J. W. Goodman, Statistical Optics (Wiley Interscience, New York, 1985).

J. C. Wyant, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, R. R. Shannon, and J. C. Wyant, eds. (Academic Press, 1992), pp. 28–39.

J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection (Complex Adaptive Systems) (Bradford, 1998).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, Boston, Massachusetts, 1996).

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Figures (8)

Fig. 1
Fig. 1

(a) Block diagram of the Genetic Algorithm. Different values of mutation and cross over ratios affect the number of generations the algorithm requires to converge to an optimized steady state. (b) Graphical presentation of the Genetic algorithm. Several Zernike modes (genes) comprise an individual wavefront. A population of individual wavefronts is generated and evaluated. A new generation is then generated through the mutation and crossover processes. (c) shows the generation number when the algorithm has converged to 90% of its final value for different settings. In T1 to T4, the mutation ratio is kept constant at 0.1 and the cross over ratio is increased from 0.2 to 0.8. In T5-T7, the cross over ratio is kept constant at 0.8, and the mutation ratio is increased from 0.2 to 0.6.

Fig. 2
Fig. 2

(a-b) Maximum intensity of STORM data sets with corrected wavefront using Quantum Dot blueing and Alexa dye blinking respectively, with their corresponding histograms shown in (c-d). (e-h) Simulations of 10 blinking molecules on a circle for 1000 frames. The average intensity of each molecule follows an exponential distribution. The value of the FM metric (arbitrary unit a.u.) and maximum intensity (photons) for each frame are shown for average photon counts of 100, 500, 1000, 5000 respectively. (i) In each frame a Zernike mode amplitude is varied from –10 to 10 radians, and the maximum image intensity (left axis, black) and the FM (right axis, blue) are measured. (The Zernike modes correspond to the following aberrations: 3 – defocus; 4, 5 – astigmatism; 6, 7 – coma; 8 – spherical aberration; 9, 10 – trefoil.).

Fig. 3
Fig. 3

Simulations of STORM with the Genetic Algorithm. A STORM data set was generated without aberration. One raw frame is shown in (a), and the reconstructed image is shown in (b). 1824 points were localized. (c) Reconstruction of a STORM data set with 0.8 radians rms wavefront error. 941 points were localized with lower accuracy than the previous case. The GA was applied to a STORM simulation with a random induced aberration consisting of Zernike modes 3 to 15 with an RMS wavefront aberration of 0.9. A graph of the FM (arbitrary units, a.u.) and Maximum Intensity (photons) versus Generation is shown in (d). (e) The first frame of the data set without correction. (f) A corrected frame from the 50th generation. (g) The reconstructed image from the last 10,000 frames (after convergence). Scale bars are 250nm.

Fig. 4
Fig. 4

Simulation of the effect of defocus on the resolution. (a-f) show reconstructions of simulated stacks with 0.2, 0.6, 0.8, 1.0, 1.2, and 1.4 radians RMS wavefront error respectively. (g) shows the resolution of each simulation calculated using Fourier ring correlation analysis. Scale bars are 250nm.

Fig. 5
Fig. 5

(a-c) Genetic Algorithm corrects aberrations induced by the optical components. PSF of a 200nm fluorescent microsphere is shown before and after correction in (a) and (b) respectively. The bar diagram of corrected Zernike modes is shown in (c). The scale bars are 1µm. (d-f) Aberrations induced by C. elegans worm. Images of before and after correction, and the bar diagram of corrected Zernike modes are shown in (d), (e), and (f) respectively. Scale bars are 5µm.

Fig. 6
Fig. 6

Real time wavefront correction using AO-STORM on the microtubules under the nucleus of a hepG2 cell. (a) widefield image before correction. (b) STORM image reconstructed from the frames after the algorithm reached an optimized steady state. (c) Bar diagram of the aberrations removed. Scalebars are (a) 5µm, (b) 2µm.

Fig. 7
Fig. 7

STORM image without AO correction on the Drosophila CNS. (a) widefield image of a bouton in the Ventral Nervous Cord. (b) The corresponding STORM image. Only 1359 fluorophores could be localized. Scalebars are 2µm.

Fig. 8
Fig. 8

Real time wavefront correction using AO-STORM on the Drosophila CNS. (a) widefield image of a soma in a Drosophila brain lobe. The ROI indicates the area where the FM was evaluated. (b) Reconstructed STORM image from frames after the algorithm reached an optimized steady state. (c) Bar diagram of the aberrations removed. Scalebars are (a) 2µm, (b) 1µm.

Equations (8)

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d=a+mtr×(bc)
mt r n = mt r max 1+exp( C[ t n t c ] )
t n = i=nm n1 ( g i 1 m j=nm n1 g j ) ( y i 1 m j=nm n1 y j ) i=nm n1 ( g i 1 m j=nm n1 g j )
FM= μ,v ( 1G( μ,ν ) )| I( μ,ν ) | circ( λ 2NA μ 2 + ν 2 ) μ,v | I( μ,ν ) | circ( λ 2NA μ 2 + ν 2 )
G( μ,ν )=exp( μ 2 + ν 2 2 σ 2 )
Δx s N
b 2 = (1p)N A/d x 2
Δx s N 1 p + 4 π sdx(1p) p 2 A

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