Abstract

Fluorescence phase-shifting interferometry (FPSI) is an optical technique that coherently combines the phase-shifted 4π steradian emission wavefronts of a single fluorescent emitter to obtain multiple interferograms from which the emitter axial displacement can be retrieved with high precision. Here, we study the axial displacement sensitivity in 4-step FPSI within the framework of maximum-likelihood (ML) phase estimation. Using Monte-Carlo simulations, we show that regardless of the method used to preprocess the measured interferograms, the variance of the ML estimate of the axial displacement approaches the Cramér-Rao lower bound and is closely limited from above by the variance of the classical 4-step phase shifting estimator. The difference between these lower and upper bounds depends on the interferogram visibility and signal-to-noise-ratio (SNR), with a percentage change of up to 29% that yields an absolute change of a few sub-nanometers to some nanometers for SNRs larger than ~5. Our results suggest that for these levels of SNR, the use of the computationally simpler classical 4-step phase shifting estimation can be adequate to accurately determine axial displacements in FPSI, as we also experimentally verified. FPSI interferograms with lower SNR but good visibility can benefit from the use of the ML estimator, provided that the spatiotemporal phase stability of the FPSI system is high.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (2)

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

S. Chen, C. Li, and Y. Zhu, “Sensitivity evaluation of quantitative phase imaging: a study of wavelength shifting interferometry,” Opt. Lett. 42(6), 1088–1091 (2017).
[Crossref] [PubMed]

2016 (1)

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[Crossref] [PubMed]

2015 (1)

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]

2014 (1)

2013 (1)

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 (1)

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012).
[Crossref] [PubMed]

2011 (1)

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

2010 (2)

M. F. Juette and J. Bewersdorf, “Three-dimensional tracking of single fluorescent particles with submillisecond temporal resolution,” Nano Lett. 10(11), 4657–4663 (2010).
[Crossref] [PubMed]

M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010).
[Crossref] [PubMed]

2009 (1)

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

2008 (4)

C. von Middendorff, A. Egner, C. Geisler, S. W. Hell, and A. Schönle, “Isotropic 3D Nanoscopy based on single emitter switching,” Opt. Express 16(25), 20774–20788 (2008).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95(12), 6025–6043 (2008).
[Crossref] [PubMed]

B. Nitzsche, F. Ruhnow, and S. Diez, “Quantum-dot-assisted characterization of microtubule rotations during cargo transport,” Nat. Nanotechnol. 3(9), 552–556 (2008).
[Crossref] [PubMed]

W. Supatto, S. E. Fraser, and J. Vermot, “An all-optical approach for probing microscopic flows in living embryos,” Biophys. J. 95(4), L29–L31 (2008).
[Crossref] [PubMed]

2007 (2)

H. Cang, C. S. Xu, D. Montiel, and H. Yang, “Guiding a confocal microscope by single fluorescent nanoparticles,” Opt. Lett. 32(18), 2729–2731 (2007).
[Crossref] [PubMed]

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7(7), 2043–2045 (2007).
[Crossref] [PubMed]

2006 (1)

T. Ragan, H. Huang, P. So, and E. Gratton, “3D particle tracking on a two-photon microscope,” J. Fluoresc. 16(3), 325–336 (2006).
[Crossref] [PubMed]

2005 (3)

V. Levi, Q. Ruan, and E. Gratton, “3-D particle tracking in a two-photon microscope: Application to the study of molecular dynamics in cells,” Biophys. J. 88(4), 2919–2928 (2005).
[Crossref] [PubMed]

L. S. Churchman, Z. Ökten, R. S. Rock, J. F. Dawson, and J. A. Spudich, “Single molecule high-resolution colocalization of Cy3 and Cy5 attached to macromolecules measures intramolecular distances through time,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1419–1423 (2005).
[Crossref] [PubMed]

F. Aguet, D. Van De Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13(26), 10503–10522 (2005).
[Crossref] [PubMed]

2004 (1)

D. Li, J. Xiong, A. Qu, and T. Xu, “Three-dimensional tracking of single secretory granules in live PC12 cells,” Biophys. J. 87(3), 1991–2001 (2004).
[Crossref] [PubMed]

2003 (2)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

M. Speidel, A. Jonás, and E. L. Florin, “Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging,” Opt. Lett. 28(2), 69–71 (2003).
[Crossref] [PubMed]

2001 (1)

1997 (1)

1996 (1)

R. M. Dickson, D. J. Norris, Y. L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274(5289), 966–968 (1996).
[Crossref] [PubMed]

1994 (1)

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).
[Crossref] [PubMed]

Aguet, F.

Allgeyer, E. S.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[Crossref] [PubMed]

Aquino, D.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Arbel, E.

Backer, A. S.

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]

Badieirostami, M.

M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Balci, H.

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7(7), 2043–2045 (2007).
[Crossref] [PubMed]

Barrett, H. H.

Bewersdorf, J.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[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]

M. F. Juette and J. Bewersdorf, “Three-dimensional tracking of single fluorescent particles with submillisecond temporal resolution,” Nano Lett. 10(11), 4657–4663 (2010).
[Crossref] [PubMed]

Bilenca, A.

Blehm, B. H.

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7(7), 2043–2045 (2007).
[Crossref] [PubMed]

Booth, M. J.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[Crossref] [PubMed]

Brown, P. O.

M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010).
[Crossref] [PubMed]

Cang, H.

Casolari, J. M.

M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010).
[Crossref] [PubMed]

Chao, J.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95(12), 6025–6043 (2008).
[Crossref] [PubMed]

Chen, S.

Churchman, L. S.

L. S. Churchman, Z. Ökten, R. S. Rock, J. F. Dawson, and J. A. Spudich, “Single molecule high-resolution colocalization of Cy3 and Cy5 attached to macromolecules measures intramolecular distances through time,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1419–1423 (2005).
[Crossref] [PubMed]

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]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Dawson, J. F.

L. S. Churchman, Z. Ökten, R. S. Rock, J. F. Dawson, and J. A. Spudich, “Single molecule high-resolution colocalization of Cy3 and Cy5 attached to macromolecules measures intramolecular distances through time,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1419–1423 (2005).
[Crossref] [PubMed]

Dickson, R. M.

R. M. Dickson, D. J. Norris, Y. L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274(5289), 966–968 (1996).
[Crossref] [PubMed]

Diez, S.

B. Nitzsche, F. Ruhnow, and S. Diez, “Quantum-dot-assisted characterization of microtubule rotations during cargo transport,” Nat. Nanotechnol. 3(9), 552–556 (2008).
[Crossref] [PubMed]

Dubois, A.

Duim, W. C.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[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]

Egner, A.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

C. von Middendorff, A. Egner, C. Geisler, S. W. Hell, and A. Schönle, “Isotropic 3D Nanoscopy based on single emitter switching,” Opt. Express 16(25), 20774–20788 (2008).
[Crossref] [PubMed]

Fetter, R. D.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Florin, E. L.

Forkey, J. N.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
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Galbraith, J. A.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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Geisler, C.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
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G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
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T. Ragan, H. Huang, P. So, and E. Gratton, “3D particle tracking on a two-photon microscope,” J. Fluoresc. 16(3), 325–336 (2006).
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V. Levi, Q. Ruan, and E. Gratton, “3-D particle tracking in a two-photon microscope: Application to the study of molecular dynamics in cells,” Biophys. J. 88(4), 2919–2928 (2005).
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A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
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Handel, M. A.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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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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Hell, S. W.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
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C. von Middendorff, A. Egner, C. Geisler, S. W. Hell, and A. Schönle, “Isotropic 3D Nanoscopy based on single emitter switching,” Opt. Express 16(25), 20774–20788 (2008).
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Hess, H. F.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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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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Huang, H.

T. Ragan, H. Huang, P. So, and E. Gratton, “3D particle tracking on a two-photon microscope,” J. Fluoresc. 16(3), 325–336 (2006).
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Irnov, I.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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Jacobs-Wagner, C.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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Jonás, A.

Juette, M. F.

M. F. Juette and J. Bewersdorf, “Three-dimensional tracking of single fluorescent particles with submillisecond temporal resolution,” Nano Lett. 10(11), 4657–4663 (2010).
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G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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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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Kim, D.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012).
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Kromann, E. B.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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Lang, T.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
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Lessard, M.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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Levi, V.

V. Levi, Q. Ruan, and E. Gratton, “3-D particle tracking in a two-photon microscope: Application to the study of molecular dynamics in cells,” Biophys. J. 88(4), 2919–2928 (2005).
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Li, C.

Li, D.

D. Li, J. Xiong, A. Qu, and T. Xu, “Three-dimensional tracking of single secretory granules in live PC12 cells,” Biophys. J. 87(3), 1991–2001 (2004).
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Lin, Y.

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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Lippincott-Schwartz, J.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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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).
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Lusk, C. P.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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Manley, S.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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McKinney, S. A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
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Middendorff, C. V.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
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Moerner, W. E.

A. von Diezmann, Y. Shechtman, and W. E. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
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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. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010).
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R. M. Dickson, D. J. Norris, Y. L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274(5289), 966–968 (1996).
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Montiel, D.

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]

Myers, J. R.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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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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Nitzsche, B.

B. Nitzsche, F. Ruhnow, and S. Diez, “Quantum-dot-assisted characterization of microtubule rotations during cargo transport,” Nat. Nanotechnol. 3(9), 552–556 (2008).
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Norris, D. J.

R. M. Dickson, D. J. Norris, Y. L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274(5289), 966–968 (1996).
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Ober, R. J.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012).
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S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95(12), 6025–6043 (2008).
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Okamura, Y.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
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Ökten, Z.

L. S. Churchman, Z. Ökten, R. S. Rock, J. F. Dawson, and J. A. Spudich, “Single molecule high-resolution colocalization of Cy3 and Cy5 attached to macromolecules measures intramolecular distances through time,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1419–1423 (2005).
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Phan, T.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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Prabhat, P.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95(12), 6025–6043 (2008).
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Praiz, A.

Qu, A.

D. Li, J. Xiong, A. Qu, and T. Xu, “Three-dimensional tracking of single secretory granules in live PC12 cells,” Biophys. J. 87(3), 1991–2001 (2004).
[Crossref] [PubMed]

Ragan, T.

T. Ragan, H. Huang, P. So, and E. Gratton, “3D particle tracking on a two-photon microscope,” J. Fluoresc. 16(3), 325–336 (2006).
[Crossref] [PubMed]

Ram, S.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95(12), 6025–6043 (2008).
[Crossref] [PubMed]

Rivera-Molina, F. E.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[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]

Rock, R. S.

L. S. Churchman, Z. Ökten, R. S. Rock, J. F. Dawson, and J. A. Spudich, “Single molecule high-resolution colocalization of Cy3 and Cy5 attached to macromolecules measures intramolecular distances through time,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1419–1423 (2005).
[Crossref] [PubMed]

Rogala, E. W.

Rothman, J. E.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[Crossref] [PubMed]

Ruan, Q.

V. Levi, Q. Ruan, and E. Gratton, “3-D particle tracking in a two-photon microscope: Application to the study of molecular dynamics in cells,” Biophys. J. 88(4), 2919–2928 (2005).
[Crossref] [PubMed]

Ruhnow, F.

B. Nitzsche, F. Ruhnow, and S. Diez, “Quantum-dot-assisted characterization of microtubule rotations during cargo transport,” Nat. Nanotechnol. 3(9), 552–556 (2008).
[Crossref] [PubMed]

Sahl, S. J.

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]

Schönle, A.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

C. von Middendorff, A. Egner, C. Geisler, S. W. Hell, and A. Schönle, “Isotropic 3D Nanoscopy based on single emitter switching,” Opt. Express 16(25), 20774–20788 (2008).
[Crossref] [PubMed]

Schroeder, L. K.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
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Selvin, P. R.

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7(7), 2043–2045 (2007).
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A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Shechtman, Y.

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

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]

Shtengel, G.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Sirinakis, G.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[Crossref] [PubMed]

So, P.

T. Ragan, H. Huang, P. So, and E. Gratton, “3D particle tracking on a two-photon microscope,” J. Fluoresc. 16(3), 325–336 (2006).
[Crossref] [PubMed]

Sougrat, R.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Speidel, M.

Spudich, J. A.

L. S. Churchman, Z. Ökten, R. S. Rock, J. F. Dawson, and J. A. Spudich, “Single molecule high-resolution colocalization of Cy3 and Cy5 attached to macromolecules measures intramolecular distances through time,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1419–1423 (2005).
[Crossref] [PubMed]

Supatto, W.

W. Supatto, S. E. Fraser, and J. Vermot, “An all-optical approach for probing microscopic flows in living embryos,” Biophys. J. 95(4), L29–L31 (2008).
[Crossref] [PubMed]

Thompson, M. A.

M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010).
[Crossref] [PubMed]

Toomre, D.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[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]

Toprak, E.

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7(7), 2043–2045 (2007).
[Crossref] [PubMed]

Tzeng, Y. L.

R. M. Dickson, D. J. Norris, Y. L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274(5289), 966–968 (1996).
[Crossref] [PubMed]

Uchil, P. D.

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]

Unser, M.

Van De Ville, D.

Verkman, A. S.

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).
[Crossref] [PubMed]

Vermot, J.

W. Supatto, S. E. Fraser, and J. Vermot, “An all-optical approach for probing microscopic flows in living embryos,” Biophys. J. 95(4), L29–L31 (2008).
[Crossref] [PubMed]

von Diezmann, A.

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

von Middendorff, C.

Ward, E. S.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95(12), 6025–6043 (2008).
[Crossref] [PubMed]

Waterman, C. M.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Weiss, L. E.

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]

Wurm, C. A.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Xiong, J.

D. Li, J. Xiong, A. Qu, and T. Xu, “Three-dimensional tracking of single secretory granules in live PC12 cells,” Biophys. J. 87(3), 1991–2001 (2004).
[Crossref] [PubMed]

Xu, C. S.

Xu, T.

D. Li, J. Xiong, A. Qu, and T. Xu, “Three-dimensional tracking of single secretory granules in live PC12 cells,” Biophys. J. 87(3), 1991–2001 (2004).
[Crossref] [PubMed]

Yang, H.

Yildiz, A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Zhang, Y.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[Crossref] [PubMed]

Zhu, Y.

Appl. Opt. (1)

Biophys. J. (6)

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).
[Crossref] [PubMed]

V. Levi, Q. Ruan, and E. Gratton, “3-D particle tracking in a two-photon microscope: Application to the study of molecular dynamics in cells,” Biophys. J. 88(4), 2919–2928 (2005).
[Crossref] [PubMed]

D. Li, J. Xiong, A. Qu, and T. Xu, “Three-dimensional tracking of single secretory granules in live PC12 cells,” Biophys. J. 87(3), 1991–2001 (2004).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95(12), 6025–6043 (2008).
[Crossref] [PubMed]

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012).
[Crossref] [PubMed]

W. Supatto, S. E. Fraser, and J. Vermot, “An all-optical approach for probing microscopic flows in living embryos,” Biophys. J. 95(4), L29–L31 (2008).
[Crossref] [PubMed]

Cell (1)

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166(4), 1028–1040 (2016).
[Crossref] [PubMed]

Chem. Rev. (1)

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

J. Fluoresc. (1)

T. Ragan, H. Huang, P. So, and E. Gratton, “3D particle tracking on a two-photon microscope,” J. Fluoresc. 16(3), 325–336 (2006).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Nano Lett. (3)

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]

M. F. Juette and J. Bewersdorf, “Three-dimensional tracking of single fluorescent particles with submillisecond temporal resolution,” Nano Lett. 10(11), 4657–4663 (2010).
[Crossref] [PubMed]

E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7(7), 2043–2045 (2007).
[Crossref] [PubMed]

Nat. Methods (2)

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]

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

B. Nitzsche, F. Ruhnow, and S. Diez, “Quantum-dot-assisted characterization of microtubule rotations during cargo transport,” Nat. Nanotechnol. 3(9), 552–556 (2008).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

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

M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010).
[Crossref] [PubMed]

L. S. Churchman, Z. Ökten, R. S. Rock, J. F. Dawson, and J. A. Spudich, “Single molecule high-resolution colocalization of Cy3 and Cy5 attached to macromolecules measures intramolecular distances through time,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1419–1423 (2005).
[Crossref] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

Science (2)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

R. M. Dickson, D. J. Norris, Y. L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274(5289), 966–968 (1996).
[Crossref] [PubMed]

Other (2)

V. Levi and E. Gratton, “Three-dimensional particle tracking in a laser scanning fluorescence microscope,” in Single Particle Tracking and Single Molecule Energy Transfer, C. Bräuchle, D. C. Lamb, and J. Michaelis, eds. (Wiley-VCH, 2010).

L. Holtzer and T. Schmidt, “The tracking of individual molecules in cells and tissues,” in Single Particle Tracking and Single Molecule Energy Transfer, C Bräuchle, DC Lamb, J Michaelis eds. (Wiley-VCH, Weinheim, 2010).

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Figures (5)

Fig. 1
Fig. 1 Fluorescence phase-shifting interferometry (FPSI). (a) Principle-of-operation. A fluorescent emitter located at (x0, y0, z0) is optically excited and its emitted fluorescence is self-interfered in a wide-aperture, two-beam interferometer that introduces multiple phase shifts δn between the two beams. The interferograms are then processed to retrieve (x0, y0, z0). The interferometer can be realized, for example, by a triangle interferometer with two-opposing objectives and a phase-shifting mirror as shown in the top inset (emitter, pink dot; lenses, light-blue ovals; mirrors, black thin lines; dichroic mirrors, gray thick lines; beam splitter, black thin-thick line; camera and emission filter, dotted line; excitation, dark gray line; emission, light gray line). (b) 4-step FPSI. Simulated interferograms with phase shifts of δn = /2, n = 0, 1, 2, 3. The simulation parameters used here were the same as in Fig. 2.
Fig. 2
Fig. 2 ML and classical z0−estimations from 4-step FPSI simulations over a DOF of ~λ/2. (a) Bias of the ML estimate using binary (top) and Gaussian (bottom) spatial weighting masks on the simulated interferograms. (b, c) Standard deviation (SD) of the ML and classical estimates using binary (b) and Gaussian (c) spatial weighting masks on the simulated interferograms. CRLB (black dashed line) and analytical SD of the classical estimator (gray dashed line) are also depicted. For the binary mask, the interferogram SNR and EV were 10.6 and 0.6, respectively, and for the Gaussian mask, SNR = 10.6 and EV = 0.67. The SNR is defined at z0 = 0 as ∫∫wI”ρdρdφ/{∫∫w2I'ρdρdφ + ∫∫w2σ2roρdρdφ}1/2, whereas the EV is expressed as ∫∫w2I”ρdρdφ/{∫∫w2I'ρdρdφ + ∫∫w2σ2roρdρdφ}. The simulations used an emission wavelength of λ = 520 nm, 4 readout/background noise photons per pixel, 1,000 detected photons per axial localization (or 250 dc signal photons per interferogram), 0.95 NA, × 100 objective lenses, and a 20 × 20 pixel array with 6.5 × 6.5 μm pixel size. 10,000 Monte-Carlo simulations were employed at each axial localization.
Fig. 3
Fig. 3 Dependence of the standard deviation of the ML (CRLB, solid line) and classical (classic upper bound, dashed line) estimators of z0 on the SNR and EV of simulated FPSI interferograms over a DOF of ~λ/2. (a, b) Standard deviation (SD) against z0 at a different number of readout/background noise photons per pixel using binary (a) and Gaussian (b) spatial weighting masks on the simulated interferograms. The interferograms had SNRs ranging from 5.7 to 12.7 with corresponding EVs varying from 0.17 to 0.86, respectively. (c, d) SD against z0 at a different number of detected photons per axial localization and readout/background noise photons per pixel maintained at a constant ratio of 1:250 of the photon yield using binary (c) and Gaussian (d) spatial weighting masks on the simulated interferograms. The interferograms had SNRs ranging from 5.7 to 12.7 with a constant EV of ~0.6.
Fig. 4
Fig. 4 ML and classical z0−estimations from 4-step FPSI simulations over a DOF of ~2λ. (a) Bias of the ML estimate using binary (top) and Gaussian (bottom) spatial weighting masks on the simulated interferograms. (b, c) Standard deviation (SD) of the ML and classical estimates using binary (b) and Gaussian (c) spatial weighting masks on the simulated interferograms. The CRLB (black dashed line) and the analytical SD of the classical estimator (gray dashed line) are also depicted. For the binary mask, the interferogram SNR and EV were 9.39 and 0.67, respectively, and for the Gaussian mask, SNR = 10.6 and EV = 0.67. The SNR and EV correspond here to those of the weighted inner section of the interferograms using the definitions in the legend of Fig. 2. The simulation parameters used were the same as in Fig. 2.
Fig. 5
Fig. 5 Experimental comparison between the ML and classical z0−estimations in 4-step FPSI. (a, b) Standard deviation (SD) of the ML and classical estimators against z0 over a DOF of ~λ/2 using binary (a) and Gaussian (b) spatial weighting masks on the measured interferograms. (c, d) SD of the ML and classical estimators against z0 over an extended DOF of ~1.25λ using binary (a) and Gaussian (b) spatial weighting masks on the measured interferograms. At each z0, 10 different beads were localized simultaneously in the field-of-view using 50 axial localizations per bead. The same 10 beads were used to measure the localization precision over the entire DOF. The analytical SDs of the classical estimator are also depicted (mean value, gray solid line; minimum and maximum values, gray dashed lines).

Equations (18)

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I n ( ρ,z| ρ 0 , z 0 )= I n shot ( ρ,z| ρ 0 , z 0 )+ n readout ( ρ ) I n shot ( ρ,z| ρ 0 , z 0 )~Ρ( I ¯ n shot ( ρ,z| ρ 0 , z 0 ) ) n readout ( ρ )~Ν( μ ro ( ρ ), σ ro 2 ( ρ ) ),
I ¯ n shot ( ρ,z| ρ 0 , z 0 )= I ( ρ ρ 0 s ,z z 0 s )+ I ( ρ ρ 0 s ,z z 0 s )cos[ Δϕ( ρ ρ 0 s ,z z 0 s )+ δ n ],
I n ( ρ,z| ρ 0 , z 0 )( μ ro ( ρ ) σ ro 2 ( ρ ) )~Ρ( I ¯ n shot ( ρ,z| ρ 0 , z 0 )+ σ ro 2 ( ρ ) ).
I n weighted ( z| z 0 )= 0 2π 0 w( ρ ) I n ( ρ,z| ρ 0 , z 0 )ρdρdφ ,
p( I n weighted ( z| z 0 )( μ ¯ ro σ ¯ ro 2 )=k )= 1 k! ( I ¯ n shot ( z| z 0 )+ σ ¯ ro 2 ) k exp[ ( I ¯ n shot ( z| z 0 )+ σ ¯ ro 2 ) ],
I ¯ n shot ( z| z 0 )= ρ A I ( ρ ρ 0 s ,z z 0 s )+ I ( ρ ρ 0 s ,z z 0 s )cos[ Δϕ( ρ ρ 0 s ,z z 0 s )+ δ n ]ρdρdφ = I ¯ ( z z 0 s )+ I ¯ ( z z 0 s )cos[ Δϕ ¯ ( z z 0 s )+ δ n ],
μ ¯ ro = ρ A μ ro ( ρ )ρdρdφ , σ ¯ ro 2 = ρ A σ ro 2 ( ρ )ρdρdφ .
p( I weighted ( z| z 0 )( μ ¯ ro σ ¯ ro 2 )=k )= n=0 3 1 k n ! ( I ¯ n shot ( z| z 0 )+ σ ¯ ro 2 ) k n exp[ ( I ¯ n shot ( z| z 0 )+ σ ¯ ro 2 ) ] ,
n=0 3 d I ¯ n shot ( z| z 0 ) d θ j ( I n weighted ( z| z 0 )( μ ¯ ro σ ¯ ro 2 ) I ¯ n shot ( z| z 0 )+ σ ¯ ro 2 1 ) =0, j=1,2,3,
I ¯ n shot ( z| z 0 )= ρ A w( ρ ){ I ( ρ ρ 0 s ,z z 0 s )+ I ( ρ ρ 0 s ,z z 0 s )cos[ Δϕ( ρ ρ 0 s ,z z 0 s )+ δ n ] }ρdρdφ = I ¯ ( z z 0 s )+ I ¯ ( z z 0 s )cos[ Δϕ ¯ ( z z 0 s )+ δ n ],
σ ¯ I n shot 2 + σ ¯ ro 2 = ρ A w 2 ( ρ ){ I ( ρ ρ 0 s ,z z 0 s )+ I ( ρ ρ 0 s ,z z 0 s )cos[ Δϕ( ρ ρ 0 s ,z z 0 s )+ δ n ] }ρdρdφ + ρ A w 2 ( ρ ) σ ro 2 ( ρ )ρdρdφ .
μ ¯ ro = ρ A w( ρ ) μ ro ( ρ )ρdρdφ .
p( I weighted ( z| z 0 ) μ ¯ ro =i )= n=0 3 1 2π( σ ¯ I n shot 2 + σ ¯ ro 2 ) exp[ ( i n I ¯ n shot ( z| z 0 ) ) 2 2( σ ¯ I n shot 2 + σ ¯ ro 2 ) ] ,
n=0 3 d I ¯ n shot ( z| z 0 ) d θ j ( I n weighted ( z| z 0 ) μ ¯ ro I ¯ n shot ( z| z 0 ) σ ¯ I n shot 2 + σ ¯ ro 2 ) =0, j=1,2,3,
σ Δϕ ¯ ^ ML 2 E { 2 Δϕ ¯ 2 log[ p( I weighted ( z| z 0 )( μ ¯ ro σ ¯ ro 2 ) ) ] } 1
σ Δϕ ¯ ^ ML 2 I ¯ 2 { [ ( I ¯ 0 shot + σ ¯ ro 2 ) 1 + ( I ¯ 2 shot + σ ¯ ro 2 ) 1 ] sin 2 ( Δϕ ¯ )+ [ ( I ¯ 1 shot + σ ¯ ro 2 ) 1 + ( I ¯ 3 shot + σ ¯ ro 2 ) 1 ] cos 2 ( Δϕ ¯ ) } 1 ,
Δϕ ¯ ^ C = tan 1 ( I 3 weighted ( z| z 0 ) I 1 weighted ( z| z 0 ) I 0 weighted ( z| z 0 ) I 2 weighted ( z| z 0 ) ).
σ Δϕ ¯ ^ C 2 n=0 3 σ I n weighted 2 ( Δϕ ¯ ^ C I n weighted | I ¯ n weighted ) 2 = 1 8 I ¯ 2 n=0 3 σ I n weighted 2

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