Abstract

3D single-molecule localization microscopy relies on fitting the shape of point-spread-functions (PSFs) recorded on a wide-field detector. However, optical aberrations distort those shapes, which compromises the accuracy and precision of single-molecule localization microscopy. Here, we employ a computational phase retrieval based on a vectorial PSF model to quantify the spatial variance of optical aberrations in a two-channel ultrawide-field single-molecule localization microscope. The use of a spatially variant PSF model enables accurate and precise emitter localization in x-, y- and z-directions throughout the entire field of view.

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

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (5)

M. Mustafi and J. C. Weisshaar, “Simultaneous Binding of Multiple EF-Tu Copies to Translating Ribosomes in Live Escherichia coli,” MBio 9(1), e02143 (2018).
[Crossref] [PubMed]

J. M. Rocha, C. J. Richardson, M. Zhang, C. M. Darch, E. Cai, A. Diepold, and A. Gahlmann, “Single-molecule tracking in live Yersinia enterocolitica reveals distinct cytosolic complexes of injectisome subunits,” Integr. Biol. 10(9), 502–515 (2018).
[Crossref] [PubMed]

M. Siemons, C. N. Hulleman, R. O. Thorsen, C. S. Smith, and S. Stallinga, “High precision wavefront control in point spread function engineering for single emitter localization,” Opt. Express 26(7), 8397–8416 (2018).
[Crossref] [PubMed]

O. Zhang, J. Lu, T. Ding, and M. D. Lew, “Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function,” Appl. Phys. Lett. 113(3), 031103 (2018).
[Crossref] [PubMed]

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
[Crossref] [PubMed]

2017 (5)

P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25(7), 7945–7959 (2017).
[Crossref] [PubMed]

H. P. Babcock and X. Zhuang, “Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines,” Sci. Rep. 7(1), 552 (2017).
[Crossref] [PubMed]

Z. Zhao, B. Xin, L. Li, and Z. L. Huang, “High-power homogeneous illumination for super-resolution localization microscopy with large field-of-view,” Opt. Express 25(12), 13382–13395 (2017).
[Crossref] [PubMed]

A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (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 (4)

C. Smith, M. Huisman, M. Siemons, D. Grünwald, and S. Stallinga, “Simultaneous measurement of emission color and 3D position of single molecules,” Opt. Express 24(5), 4996–5013 (2016).
[Crossref] [PubMed]

Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref] [PubMed]

A. S. Backer, M. Y. Lee, and W. E. Moerner, “Enhanced DNA imaging using super-resolution microscopy and simultaneous single-molecule orientation measurements,” Optica 3(6), 659–666 (2016).
[Crossref] [PubMed]

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimised flat-field epi-illumination,” Nat. Photonics 10(11), 705–708 (2016).
[Crossref] [PubMed]

2015 (6)

A. Tahmasbi, E. S. Ward, and R. J. Ober, “Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy,” Opt. Express 23(6), 7630–7652 (2015).
[Crossref] [PubMed]

A. von Diezmann, M. Y. Lee, M. D. Lew, and W. E. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2(11), 985–993 (2015).
[Crossref] [PubMed]

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15(6), 4194–4199 (2015).
[Crossref] [PubMed]

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a Depth-Dependent Lateral Distortion in 3D Super-Resolution Imaging,” PLoS One 10(11), e0142949 (2015).
[Crossref] [PubMed]

P. Almada, S. Culley, and R. Henriques, “PALM and STORM: Into large fields and high-throughput microscopy with sCMOS detectors,” Methods 88, 109–121 (2015).
[Crossref] [PubMed]

P. Rubin-Delanchy, G. L. Burn, J. Griffié, D. J. Williamson, N. A. Heard, A. P. Cope, and D. M. Owen, “Bayesian cluster identification in single-molecule localization microscopy data,” Nat. Methods 12(11), 1072–1076 (2015).
[Crossref] [PubMed]

2014 (6)

A. Gahlmann and W. E. Moerner, “Exploring bacterial cell biology with single-molecule tracking and super-resolution imaging,” Nat. Rev. Microbiol. 12(1), 9–22 (2014).
[Crossref] [PubMed]

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic 3D Super-resolution Imaging with a Self-bending Point Spread Function,” Nat. Photonics 8, 302–306 (2014).
[Crossref] [PubMed]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
[Crossref] [PubMed]

A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118(28), 8313–8329 (2014).
[Crossref] [PubMed]

2013 (3)

G. Zheng, X. Ou, R. Horstmeyer, and C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013).
[Crossref] [PubMed]

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

2012 (4)

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

W. E. Moerner, “Microscopy beyond the diffraction limit using actively controlled single molecules,” J. Microsc. 246(3), 213–220 (2012).
[Crossref] [PubMed]

S. Stallinga and B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20(6), 5896–5921 (2012).
[Crossref] [PubMed]

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: a theoretical study,” J. Microsc. 247(2), 147–160 (2012).
[Crossref] [PubMed]

2011 (5)

M. Řeřábek, P. Patá, and K. Fliegel, “Enhancement of the accuracy of the astronomical measurements carried on the wide-field astronomical image data,” Proc. SPIE 8135, 81351M (2011).

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett. 11(1), 209–213 (2011).
[Crossref] [PubMed]

P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis,” Nat. Methods 8(11), 969–975 (2011).
[Crossref] [PubMed]

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36(2), 202–204 (2011).
[Crossref] [PubMed]

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
[Crossref]

2010 (1)

M. A. Thompson, M. D. Lew, M. Badieirostami, and W. E. Moerner, “Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function,” Nano Lett. 10(1), 211–218 (2010).
[Crossref] [PubMed]

2009 (2)

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[Crossref] [PubMed]

2008 (4)

S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
[Crossref] [PubMed]

M. Řeřábek and P. Patá, “The space variant PSF for deconvolution of wide-field astronomical images,” Proc. SPIE 7015, 70152G (2008).
[Crossref]

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]

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H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67(3), 1291–1300 (1994).
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1992 (1)

1965 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253, 358–379 (1959).

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M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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Almada, P.

P. Almada, S. Culley, and R. Henriques, “PALM and STORM: Into large fields and high-throughput microscopy with sCMOS detectors,” Methods 88, 109–121 (2015).
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Archetti, A.

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimised flat-field epi-illumination,” Nat. Photonics 10(11), 705–708 (2016).
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H. P. Babcock and X. Zhuang, “Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines,” Sci. Rep. 7(1), 552 (2017).
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Backer, A. S.

A. S. Backer, M. Y. Lee, and W. E. Moerner, “Enhanced DNA imaging using super-resolution microscopy and simultaneous single-molecule orientation measurements,” Optica 3(6), 659–666 (2016).
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Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
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Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15(6), 4194–4199 (2015).
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A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118(28), 8313–8329 (2014).
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Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
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M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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Backlund, M. P.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
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M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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Baddeley, D.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
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Badieirostami, M.

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36(2), 202–204 (2011).
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M. A. Thompson, M. D. Lew, M. Badieirostami, and W. E. Moerner, “Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function,” Nano Lett. 10(1), 211–218 (2010).
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Baird, M. A.

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Bates, M.

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
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B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
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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).
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S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
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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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Bewersdorf, J.

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Biteen, J. S.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
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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).
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Bowman, G. R.

J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
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Burn, G. L.

P. Rubin-Delanchy, G. L. Burn, J. Griffié, D. J. Williamson, N. A. Heard, A. P. Cope, and D. M. Owen, “Bayesian cluster identification in single-molecule localization microscopy data,” Nat. Methods 12(11), 1072–1076 (2015).
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Cai, E.

J. M. Rocha, C. J. Richardson, M. Zhang, C. M. Darch, E. Cai, A. Diepold, and A. Gahlmann, “Single-molecule tracking in live Yersinia enterocolitica reveals distinct cytosolic complexes of injectisome subunits,” Integr. Biol. 10(9), 502–515 (2018).
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Cannell, M. B.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
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L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a Depth-Dependent Lateral Distortion in 3D Super-Resolution Imaging,” PLoS One 10(11), e0142949 (2015).
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Chen, P.

A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (2017).
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Chen, T. Y.

A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (2017).
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Cope, A. P.

P. Rubin-Delanchy, G. L. Burn, J. Griffié, D. J. Williamson, N. A. Heard, A. P. Cope, and D. M. Owen, “Bayesian cluster identification in single-molecule localization microscopy data,” Nat. Methods 12(11), 1072–1076 (2015).
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Culley, S.

P. Almada, S. Culley, and R. Henriques, “PALM and STORM: Into large fields and high-throughput microscopy with sCMOS detectors,” Methods 88, 109–121 (2015).
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Darch, C. M.

J. M. Rocha, C. J. Richardson, M. Zhang, C. M. Darch, E. Cai, A. Diepold, and A. Gahlmann, “Single-molecule tracking in live Yersinia enterocolitica reveals distinct cytosolic complexes of injectisome subunits,” Integr. Biol. 10(9), 502–515 (2018).
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Davidson, M. W.

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[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).
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Deschamps, J.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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Diepold, A.

J. M. Rocha, C. J. Richardson, M. Zhang, C. M. Darch, E. Cai, A. Diepold, and A. Gahlmann, “Single-molecule tracking in live Yersinia enterocolitica reveals distinct cytosolic complexes of injectisome subunits,” Integr. Biol. 10(9), 502–515 (2018).
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Ding, T.

O. Zhang, J. Lu, T. Ding, and M. D. Lew, “Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function,” Appl. Phys. Lett. 113(3), 031103 (2018).
[Crossref] [PubMed]

Douglass, K. M.

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimised flat-field epi-illumination,” Nat. Photonics 10(11), 705–708 (2016).
[Crossref] [PubMed]

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a Depth-Dependent Lateral Distortion in 3D Super-Resolution Imaging,” PLoS One 10(11), e0142949 (2015).
[Crossref] [PubMed]

Duim, W. C.

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Eckart, M. R.

J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
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Ellenberg, J.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett. 11(1), 209–213 (2011).
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M. Řeřábek, P. Patá, and K. Fliegel, “Enhancement of the accuracy of the astronomical measurements carried on the wide-field astronomical image data,” Proc. SPIE 8135, 81351M (2011).

Gahlmann, A.

J. M. Rocha, C. J. Richardson, M. Zhang, C. M. Darch, E. Cai, A. Diepold, and A. Gahlmann, “Single-molecule tracking in live Yersinia enterocolitica reveals distinct cytosolic complexes of injectisome subunits,” Integr. Biol. 10(9), 502–515 (2018).
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A. Gahlmann and W. E. Moerner, “Exploring bacterial cell biology with single-molecule tracking and super-resolution imaging,” Nat. Rev. Microbiol. 12(1), 9–22 (2014).
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J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
[Crossref] [PubMed]

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Genova, L. A.

A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (2017).
[Crossref] [PubMed]

George Thompson, A. M.

A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (2017).
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Gibson, S. F.

Gillette, J. M.

S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
[Crossref] [PubMed]

Girirajan, T. P.

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

Griffié, J.

P. Rubin-Delanchy, G. L. Burn, J. Griffié, D. J. Williamson, N. A. Heard, A. P. Cope, and D. M. Owen, “Bayesian cluster identification in single-molecule localization microscopy data,” Nat. Methods 12(11), 1072–1076 (2015).
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Grover, G.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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Grünwald, D.

Hartwich, T. M.

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Heard, N. A.

P. Rubin-Delanchy, G. L. Burn, J. Griffié, D. J. Williamson, N. A. Heard, A. P. Cope, and D. M. Owen, “Bayesian cluster identification in single-molecule localization microscopy data,” Nat. Methods 12(11), 1072–1076 (2015).
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S. J. Sahl, S. W. Hell, and S. Jakobs, “Fluorescence nanoscopy in cell biology,” Nat. Rev. Mol. Cell Biol. 18(11), 685–701 (2017).
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J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett. 11(1), 209–213 (2011).
[Crossref] [PubMed]

Henriques, R.

P. Almada, S. Culley, and R. Henriques, “PALM and STORM: Into large fields and high-throughput microscopy with sCMOS detectors,” Methods 88, 109–121 (2015).
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Hess, H. F.

S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
[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]

Hess, S. T.

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

Hoess, P.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
[Crossref] [PubMed]

Holden, S. J.

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a Depth-Dependent Lateral Distortion in 3D Super-Resolution Imaging,” PLoS One 10(11), e0142949 (2015).
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Hoyer, P.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett. 11(1), 209–213 (2011).
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B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
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B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

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F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Huisman, M.

Hulleman, C. N.

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).
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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic 3D Super-resolution Imaging with a Self-bending Point Spread Function,” Nat. Photonics 8, 302–306 (2014).
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P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis,” Nat. Methods 8(11), 969–975 (2011).
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Jung, W.

A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (2017).
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H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67(3), 1291–1300 (1994).
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J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett. 11(1), 209–213 (2011).
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H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” in 2013 IEEE 10th International Symposium on Biomedical Imaging (IEEE, 2013), pp. 588–591.
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K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimised flat-field epi-illumination,” Nat. Photonics 10(11), 705–708 (2016).
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Lee, M. K.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
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Lee, M. Y.

Lee, S. F.

Lew, M. D.

O. Zhang, J. Lu, T. Ding, and M. D. Lew, “Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function,” Appl. Phys. Lett. 113(3), 031103 (2018).
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A. von Diezmann, M. Y. Lee, M. D. Lew, and W. E. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2(11), 985–993 (2015).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36(2), 202–204 (2011).
[Crossref] [PubMed]

M. A. Thompson, M. D. Lew, M. Badieirostami, and W. E. Moerner, “Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function,” Nano Lett. 10(1), 211–218 (2010).
[Crossref] [PubMed]

M. D. Lew, A. R. S. von Diezmann, and W. E. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protoc. Exch. (2013), doi:.
[Crossref]

Li, L.

Li, Y.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
[Crossref] [PubMed]

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F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

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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).
[Crossref] [PubMed]

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P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis,” Nat. Methods 8(11), 969–975 (2011).
[Crossref] [PubMed]

S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
[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]

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S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

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Long, J. J.

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Lord, S. J.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
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O. Zhang, J. Lu, T. Ding, and M. D. Lew, “Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function,” Appl. Phys. Lett. 113(3), 031103 (2018).
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K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimised flat-field epi-illumination,” Nat. Photonics 10(11), 705–708 (2016).
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L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a Depth-Dependent Lateral Distortion in 3D Super-Resolution Imaging,” PLoS One 10(11), e0142949 (2015).
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S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
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S. T. Hess, T. P. 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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Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (2017).
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P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25(7), 7945–7959 (2017).
[Crossref] [PubMed]

A. S. Backer, M. Y. Lee, and W. E. Moerner, “Enhanced DNA imaging using super-resolution microscopy and simultaneous single-molecule orientation measurements,” Optica 3(6), 659–666 (2016).
[Crossref] [PubMed]

Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref] [PubMed]

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15(6), 4194–4199 (2015).
[Crossref] [PubMed]

A. von Diezmann, M. Y. Lee, M. D. Lew, and W. E. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2(11), 985–993 (2015).
[Crossref] [PubMed]

J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
[Crossref] [PubMed]

A. S. Backer and W. E. Moerner, “Extending single-molecule microscopy using optical Fourier processing,” J. Phys. Chem. B 118(28), 8313–8329 (2014).
[Crossref] [PubMed]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

A. Gahlmann and W. E. Moerner, “Exploring bacterial cell biology with single-molecule tracking and super-resolution imaging,” Nat. Rev. Microbiol. 12(1), 9–22 (2014).
[Crossref] [PubMed]

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

W. E. Moerner, “Microscopy beyond the diffraction limit using actively controlled single molecules,” J. Microsc. 246(3), 213–220 (2012).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
[Crossref] [PubMed]

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36(2), 202–204 (2011).
[Crossref] [PubMed]

M. A. Thompson, M. D. Lew, M. Badieirostami, and W. E. Moerner, “Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function,” Nano Lett. 10(1), 211–218 (2010).
[Crossref] [PubMed]

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

M. D. Lew, A. R. S. von Diezmann, and W. E. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protoc. Exch. (2013), doi:.
[Crossref]

Mothes, W.

F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
[Crossref] [PubMed]

Mund, M.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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M. Mustafi and J. C. Weisshaar, “Simultaneous Binding of Multiple EF-Tu Copies to Translating Ribosomes in Live Escherichia coli,” MBio 9(1), e02143 (2018).
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F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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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).
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P. Rubin-Delanchy, G. L. Burn, J. Griffié, D. J. Williamson, N. A. Heard, A. P. Cope, and D. M. Owen, “Bayesian cluster identification in single-molecule localization microscopy data,” Nat. Methods 12(11), 1072–1076 (2015).
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Patá, P.

M. Řeřábek, P. Patá, and K. Fliegel, “Enhancement of the accuracy of the astronomical measurements carried on the wide-field astronomical image data,” Proc. SPIE 8135, 81351M (2011).

M. Řeřábek and P. Patá, “The space variant PSF for deconvolution of wide-field astronomical images,” Proc. SPIE 7015, 70152G (2008).
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S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
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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).
[Crossref] [PubMed]

Pavani, S. R.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

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Perez, A. M.

J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
[Crossref] [PubMed]

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Piestun, R.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
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S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
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J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
[Crossref] [PubMed]

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
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A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
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P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis,” Nat. Methods 8(11), 969–975 (2011).
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M. Řeřábek, P. Patá, and K. Fliegel, “Enhancement of the accuracy of the astronomical measurements carried on the wide-field astronomical image data,” Proc. SPIE 8135, 81351M (2011).

M. Řeřábek and P. Patá, “The space variant PSF for deconvolution of wide-field astronomical images,” Proc. SPIE 7015, 70152G (2008).
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J. M. Rocha, C. J. Richardson, M. Zhang, C. M. Darch, E. Cai, A. Diepold, and A. Gahlmann, “Single-molecule tracking in live Yersinia enterocolitica reveals distinct cytosolic complexes of injectisome subunits,” Integr. Biol. 10(9), 502–515 (2018).
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Ries, J.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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J. M. Rocha, C. J. Richardson, M. Zhang, C. M. Darch, E. Cai, A. Diepold, and A. Gahlmann, “Single-molecule tracking in live Yersinia enterocolitica reveals distinct cytosolic complexes of injectisome subunits,” Integr. Biol. 10(9), 502–515 (2018).
[Crossref] [PubMed]

Rubin-Delanchy, P.

P. Rubin-Delanchy, G. L. Burn, J. Griffié, D. J. Williamson, N. A. Heard, A. P. Cope, and D. M. Owen, “Bayesian cluster identification in single-molecule localization microscopy data,” Nat. Methods 12(11), 1072–1076 (2015).
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Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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S. J. Sahl, S. W. Hell, and S. Jakobs, “Fluorescence nanoscopy in cell biology,” Nat. Rev. Mol. Cell Biol. 18(11), 685–701 (2017).
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Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15(6), 4194–4199 (2015).
[Crossref] [PubMed]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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A. G. Santiago, T. Y. Chen, L. A. Genova, W. Jung, A. M. George Thompson, M. M. McEvoy, and P. Chen, “Adaptor protein mediates dynamic pump assembly for bacterial metal efflux,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6694–6699 (2017).
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Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3D single-molecule localization using experimental point spread functions,” Nat. Methods 15(5), 367–369 (2018).
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P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis,” Nat. Methods 8(11), 969–975 (2011).
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Shapiro, L.

J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
[Crossref] [PubMed]

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Shechtman, Y.

P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25(7), 7945–7959 (2017).
[Crossref] [PubMed]

Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref] [PubMed]

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15(6), 4194–4199 (2015).
[Crossref] [PubMed]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

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S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008).
[Crossref] [PubMed]

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K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimised flat-field epi-illumination,” Nat. Photonics 10(11), 705–708 (2016).
[Crossref] [PubMed]

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Skoko, D.

P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis,” Nat. Methods 8(11), 969–975 (2011).
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Small, A.

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
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Smith, C.

Smith, C. S.

Soeller, C.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
[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).
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Stahlheber, S.

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

Stallinga, S.

Staudt, T.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett. 11(1), 209–213 (2011).
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Tahmasbi, A.

Thompson, M. A.

M. A. Thompson, M. D. Lew, M. Badieirostami, and W. E. Moerner, “Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function,” Nano Lett. 10(1), 211–218 (2010).
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S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
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Toomre, D.

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Twieg, R. J.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

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F. Huang, T. M. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10(7), 653–658 (2013).
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H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” in 2013 IEEE 10th International Symposium on Biomedical Imaging (IEEE, 2013), pp. 588–591.
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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic 3D Super-resolution Imaging with a Self-bending Point Spread Function,” Nat. Photonics 8, 302–306 (2014).
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P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis,” Nat. Methods 8(11), 969–975 (2011).
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von Diezmann, A. R.

J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
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A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
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von Diezmann, A. R. S.

M. D. Lew, A. R. S. von Diezmann, and W. E. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protoc. Exch. (2013), doi:.
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Vonesch, C.

H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” in 2013 IEEE 10th International Symposium on Biomedical Imaging (IEEE, 2013), pp. 588–591.
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B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
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Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
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Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15(6), 4194–4199 (2015).
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M. Mustafi and J. C. Weisshaar, “Simultaneous Binding of Multiple EF-Tu Copies to Translating Ribosomes in Live Escherichia coli,” MBio 9(1), e02143 (2018).
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Zhao, Z.

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Zhuang, X.

H. P. Babcock and X. Zhuang, “Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines,” Sci. Rep. 7(1), 552 (2017).
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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic 3D Super-resolution Imaging with a Self-bending Point Spread Function,” Nat. Photonics 8, 302–306 (2014).
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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).
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Appl. Phys. Lett. (1)

O. Zhang, J. Lu, T. Ding, and M. D. Lew, “Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function,” Appl. Phys. Lett. 113(3), 031103 (2018).
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J. Microsc. (2)

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J. Opt. Soc. Am. (1)

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MBio (1)

M. Mustafi and J. C. Weisshaar, “Simultaneous Binding of Multiple EF-Tu Copies to Translating Ribosomes in Live Escherichia coli,” MBio 9(1), e02143 (2018).
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Methods (1)

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Nano Lett. (4)

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15(6), 4194–4199 (2015).
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J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett. 11(1), 209–213 (2011).
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M. A. Thompson, M. D. Lew, M. Badieirostami, and W. E. Moerner, “Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function,” Nano Lett. 10(1), 211–218 (2010).
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A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
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Nano Res. (1)

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
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Nat. Methods (7)

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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).
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Nat. Photonics (3)

Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic 3D Super-resolution Imaging with a Self-bending Point Spread Function,” Nat. Photonics 8, 302–306 (2014).
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Nat. Rev. Microbiol. (1)

A. Gahlmann and W. E. Moerner, “Exploring bacterial cell biology with single-molecule tracking and super-resolution imaging,” Nat. Rev. Microbiol. 12(1), 9–22 (2014).
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Nat. Rev. Mol. Cell Biol. (1)

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Opt. Express (8)

M. Siemons, C. N. Hulleman, R. O. Thorsen, C. S. Smith, and S. Stallinga, “High precision wavefront control in point spread function engineering for single emitter localization,” Opt. Express 26(7), 8397–8416 (2018).
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C. Smith, M. Huisman, M. Siemons, D. Grünwald, and S. Stallinga, “Simultaneous measurement of emission color and 3D position of single molecules,” Opt. Express 24(5), 4996–5013 (2016).
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S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
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Z. Zhao, B. Xin, L. Li, and Z. L. Huang, “High-power homogeneous illumination for super-resolution localization microscopy with large field-of-view,” Opt. Express 25(12), 13382–13395 (2017).
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S. Stallinga and B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20(6), 5896–5921 (2012).
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A. Tahmasbi, E. S. Ward, and R. J. Ober, “Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy,” Opt. Express 23(6), 7630–7652 (2015).
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P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25(7), 7945–7959 (2017).
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Opt. Lett. (1)

Optica (2)

Phys. Rev. Lett. (1)

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
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PLoS One (1)

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M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. U.S.A. 109(47), 19087–19092 (2012).
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J. L. Ptacin, A. Gahlmann, G. R. Bowman, A. M. Perez, A. R. von Diezmann, M. R. Eckart, W. E. Moerner, and L. Shapiro, “Bacterial scaffold directs pole-specific centromere segregation,” Proc. Natl. Acad. Sci. U.S.A. 111(19), E2046–E2055 (2014).
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Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253, 358–379 (1959).

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Sci. Rep. (1)

H. P. Babcock and X. Zhuang, “Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines,” Sci. Rep. 7(1), 552 (2017).
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Science (2)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[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]

Other (2)

H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” in 2013 IEEE 10th International Symposium on Biomedical Imaging (IEEE, 2013), pp. 588–591.
[Crossref]

M. D. Lew, A. R. S. von Diezmann, and W. E. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protoc. Exch. (2013), doi:.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic fluorescence emission paths of the microscope system. Two phase masks were placed in planes conjugate to the back focal plane of the objective lens (dashed lines) to generate the DHPSF, i.e. the Fourier plane of the imaging system. The inset shows the distance d of nominal focal plane relative to the refractive index boundary, as well as the emitter depth z in the refractive index mismatched medium. (The nominal focal plane is equal to the focal plane in absence of a refractive index boundary.) Positive values of d place the nominal focal plane below the refractive index boundary, whereas a negative distance d places the nominal focal plane into the refractive index mismatched medium. Emitter depths are parameterized by positive values of z, i.e. they are always localized above the refractive index boundary.
Fig. 2
Fig. 2 Spatially variant Zernike coefficients. a) Coefficients for Zernike polynomials j = 4,…, 15 at two different bead positions in the field of view (indicated by red arrows and the red dots in panel b). Insets: experimentally measured DHPSFs (left) and simulated DHPSFs (right) based on the estimated Zernike coefficients. b) Spatial variation of Zernike coefficients a4 (defocus). The amount of defocus aberration were estimated at N = 427 bead positions (blue dots and red dots) pooled from three separately acquired fields-of-view. The surface is a second-order polynomial fit to the experimentally determined defocus coefficients. The corresponding contour map is also shown. Scale bar: 20 µm. c) The coefficient residuals, defined as the vertical difference between the blue dots and the polynomial surface. No spatial dependence is evident. d) Mean (red circles) and standard deviation (error bars) of coefficient residuals for all Zernike modes considered.
Fig. 3
Fig. 3 a) Cross-validation of polynomial surface fitting. The first row shows contour surfaces of the defocus aberration coefficient a4 obtained after removing the beads acquired in one of three fields-of-view. The second row shows the difference contours relative to the full data set contour map shown in Fig. 2(b). Scale bars: 20 µm. Bb) Defocus aberration coefficient a4 contours in the other (green) channel of our microscope acquired using different laser intensities. The peak intensities are 23.5 W/cm2 amd 4 W/cm2 for high and low illumination intensity, respectively. The size of the excitation spot was 320 μm (1/e2 radius) in both cases. For this data set, the standard deviation of a4 residuals was 57 a.u. Scale bars: 20 µm. c) Effect of bead size on aberration coefficient estimation at a single position in the field of view. The difference between estimated and true coefficients are shown for different bead sizes (blue and red circles). Gray bars represent ± one standard deviation of the experimentally determined coefficient residuals [Fig. 2(d)] centered at zero. Among the Zernike modes considered here, only the defocus (j = 4) and primary spherical aberration (j = 11) exhibit strong coupling with emitter z-position. d) Effect of coefficient estimation on localization accuracy. Zernike coefficients were changed one at a time by the amount of one standard deviation of the corresponding residuals and the resulting DHPSFs were analysed using the original coefficients.
Fig. 4
Fig. 4 Aberration coefficient profiles in both color channels of our microscope. Top row: Aberration coefficient contour maps for a4 (defocus), a6 (vertical astigmatism) and a11 (primary spherical aberration) in the red channel. Bottom row: Corresponding contour maps in the green color channel. Scale bars: 20 µm.
Fig. 5
Fig. 5 a) Change in the distance d due to stage drift. The same bead was used as a constant z-position reference. b) top panel: z-position measurements for different fluorescent beads on a flat coverslip immobilized by agarose before (blue) and after (yellow) a 10 µm lateral shift. The first bead (black) is the reference bead fixed at z = 50 nm. The red dots represent mean values from 40 measurement and the error bars represent the standard deviations. Inset: the spatial distribution of localized beads before and after the lateral shift. Bottom panel: the difference between z-position measurements before and after the lateral shift. Beads with noticeable motion from frame to frame in x,y- and/or z-directions are colored red. c) distribution of standard deviations of individual bead position measurement in the x-, y- and z-dimensions. Red colored bars represent beads with localization precisions of more than 10 nm (arbitrarily chosen threshold). The mean precison here is calculated excluding these aforementioned beads. If those beads were not excluded, the mean precision is: σx = 5.3 nm, σy = 5.7 nm, and σz = 5.1 nm.
Fig. 6
Fig. 6 a) Top panel: z-positions of the same beads as measured in two separate color channels. The bead colored in black was used as a reference marker in both channels. Bottom panel: z-position differences for each bead shown in the top panel. b) The distribution of localized beads in the green channel across the field of view. c) z-position differences.
Fig. 7
Fig. 7 Comparison of double-Gaussian and the spatially variant vectorial PSF model. a) z-positions estimates of fluorescent beads immobilized on the coverslip obtained by using the double-Gaussian PSF model and a global lookup table. Inset: Scatterplot of bead x, y-positions with each bead colored according to its z-position. b) Same results as in panel A, except that simulated DHPSFs of isotropic emitters were used as inputs. The z-error is defined as the difference between estimated z-positions and the ground truth (50 nm). The nominal focal plane is coincident with the refractive index boundary (d = 0 nm). Inset in panels B-E: the projection of emitters in x, y-plane with beads colored according to their z-errors. c) The same simulation as in panel B, but processed with a double Gaussian model using many local look-up tables. d) The same simulation as in panel C, but the nominal focal plane was placed 500 nm above the refractive index boundary (d = −500 nm). e) The same simulation as in panel d (d = −500 nm, local lookup tables), but z-positions for DHPSF simulations were randomly chosen in the interval [0, 1000] nm. f) Accuracy and precision comparison of double Gaussian vs. spatially variant vectorial PSF model fitting. Both analytical models perform worse than the vectorial PSF model.

Equations (15)

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T s =1+ n 2 cos θ 2 n 1 cos θ 1 n 2 cos θ 2 + n 1 cos θ 1 = 2 n 2 cos θ 2 n 2 cos θ 2 + n 1 cos θ 1
T p =(1+ n 2 sec θ 2 n 1 sec θ 1 n 2 sec θ 2 + n 1 sec θ 1 )( cos θ 2 cos θ 1 )= 2 n 2 cos θ 2 n 2 cos θ 1 + n 1 cos θ 2
ρ max = NA n 1
μ =[ μ x μ y μ z ]=[ sinΘcosΦ sinΘsinΦ cosΘ ]
E x A = [ ( n 1 n 2 )( ( cos θ 1 cosθ 2 ) T s sin 2 φ+ T p cos 2 φ 1 ρ 2 ) sin2φ( n 1 n 2 )( ( cos θ 1 cos θ 2 ) T S T p 1 ρ 2 ) 2 ( n 1 n 2 ) 2 ( cos θ 1 cos θ 2 ) T P ρcosφ ] T [ μ x μ y μ z ]
E y A = [ sin2φ( n 1 n 2 )( ( cos θ 1 cosθ 2 ) T s T p 1 ρ 2 ) 2 ( n 1 n 2 )( T P sin 2 φ 1 ρ 2 +( cos θ 1 cosθ 2 ) T s cos 2 φ ) ( n 1 n 2 ) 2 ( cos θ 1 cos θ 2 ) T P ρsinφ ] T [ μ x μ y μ z ]
ψ depth = 2π n 2 z λ 1 ( n 1 n 2 ρ ) 2 ,
ψ d ={ 2π n 1 d λ 1 ρ 2 ,d>0 2π n 2 d λ 1 ρ 2 ,d<0 ,
ψ lateral = 2πNAM λ M 2 N A 2 ρ(xcosφ+ysinφ),
ψ= ψ depth + ψ d + ψ lateral
E x FP = E x A e iψ
E y FP = E y A e iψ
PSF= | F { P( u,v ) E x FP } | 2 + | F { P( u,v ) E y FP } | 2
PSF= | F { e iW(x,y;ρ,φ) P( u,v ) E x FP } | 2 + | F { e iW(x,y;ρ,φ) P( u,v ) E y FP } | 2
W(x,y;ρ,φ)= j=4 15 a ( x,y ) j Z j ( ρ,φ )

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