Abstract

: Tracking of single fluorescent probes along the axial (depth) dimension is an important task in the biological and physical sciences. In this paper, we propose and analyze the use of fluorescence phase-shifting interferometry (FPSI) for axial single particle tracking (SPT) along 1 μm-depth (z) trajectories. FPSI is a photon-efficient, self-interference method that collects and coherently combines the 4π steradian emission wavefronts of a single fluorescent particle while introducing multiple phase shifts between the wavefronts to axially localize the particle with high precision over an extended depth-of-field. We employ vectorial imaging analysis and Monte-Carlo simulations of diffusive and directed motions to present a detailed comparative study of spatial and temporal FPSI for axial SPT based on simultaneous and time sequential collection of four phase-shifted interferograms using a single camera, respectively. The results of the numerical simulations show that for ≤0.105 μm2/s diffusion, spatial FPSI attains a maximal twofold improvement in the trajectory reconstruction precision at the expense of a fourfold reduced field-of-view compared to temporal FPSI. Furthermore, the analysis predicts that for sufficiently slow random linear motions, temporal FPSI is superior to spatial FPSI and achieves a smaller trajectory reconstruction error.

© 2014 Optical Society of America

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  2. L. S. Churchman, Z. Okten, 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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    [Crossref] [PubMed]
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2012 (1)

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. 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]

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]

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)

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]

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]

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]

2007 (3)

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]

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90(5), 053902 (2007).
[Crossref]

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]

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 (2)

L. S. Churchman, Z. Okten, 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]

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]

2004 (1)

D. D. Li, J. Xiong, A. L. 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]

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), 966–969 (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]

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]

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]

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]

Bewersdorf, J.

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]

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]

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]

Churchman, L. S.

L. S. Churchman, Z. Okten, 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.

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. Okten, 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), 966–969 (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]

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).
[Crossref] [PubMed]

Fraser, S. E.

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]

Galbraith, C. 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]

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).
[Crossref] [PubMed]

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).
[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]

Gillette, J. 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]

Goldman, Y. E.

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]

Gratton, E.

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]

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]

Ha, T.

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]

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).
[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]

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).
[Crossref] [PubMed]

Holtzer, L.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90(5), 053902 (2007).
[Crossref]

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).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Kaminski, T.

Kanchanawong, P.

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]

Kao, H. P.

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]

Königshoven, H. P.

Kubitscheck, U.

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).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Li, D. D.

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

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).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Meckel, T.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90(5), 053902 (2007).
[Crossref]

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).
[Crossref] [PubMed]

Moerner, W. E.

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]

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), 966–969 (1996).
[Crossref] [PubMed]

Montiel, D.

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).
[Crossref] [PubMed]

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), 966–969 (1996).
[Crossref] [PubMed]

Ober, R. 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]

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).
[Crossref] [PubMed]

Okten, Z.

L. S. Churchman, Z. Okten, 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]

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).
[Crossref] [PubMed]

Qu, A. L.

D. D. Li, J. Xiong, A. L. 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, 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]

Rock, R. S.

L. S. Churchman, Z. Okten, 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]

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]

Schmidt, T.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90(5), 053902 (2007).
[Crossref]

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]

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).
[Crossref] [PubMed]

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]

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]

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.

Spille, J. H.

Spudich, J. A.

L. S. Churchman, Z. Okten, 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]

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), 966–969 (1996).
[Crossref] [PubMed]

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 Middendorff, C.

Ward, E. S.

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]

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. D. Li, J. Xiong, A. L. 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. D. Li, J. Xiong, A. L. 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]

Appl. Phys. Lett. (1)

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90(5), 053902 (2007).
[Crossref]

Biophys. J. (5)

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]

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]

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]

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

Nano Lett. (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]

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 (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]

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 (2)

Opt. Lett. (2)

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

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]

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. Okten, 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]

Science (2)

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), 966–969 (1996).
[Crossref] [PubMed]

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]

Other (3)

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, D. C. Lamb, and J. Michaelis, eds. (Wiley-VCH, 2010).

P. R. T. Munro, “Application of numerical methods to high numerical aperture imaging,” PhD Thesis, University of London (2007).

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Figures (7)

Fig. 1
Fig. 1 Fluorescence phase-shifting interferometry (FPSI). (a) Schematics of FPSI based on a triangular two-opposing lenses interferometer referred to as a 4π interferometer. A single fluorescent emitter located at (0,0,ζ) with moment p is imaged and the phase-shifted intensity pattern Ik(ρ,ζ,p) is recorded on the detector array. (b) The imaged wavefront phase difference Δϕ (ρ, ζ, p) computed for various axial locations of a static dipole. The computation assumed emission wavelength of λ = 520 nm, collector lens of NA = 0.95, × 100, p = (1,0,0), and an ideal 4π interferometeric system using a four-step PSI algorithm with a single camera. (c) The angularly integrated imaged wavefront phase difference Δϕ (ρ, ζ, p) against the radial coordinate for different axial dipole positions ζ that result in linear phase differences Δϕl = 4πζ /λ. Solid and dashed lines represent positive and negative Δϕl values, respectively, where the different line colors stand for the magnitude of the various Δϕl values. The simulation parameters used here were the same as in (b).
Fig. 2
Fig. 2 The behavior of the integrated inner and outer imaged wavefront phase differences Δϕ i/o. (a) Dependence of Δϕ i/o on the linear wavefront phase difference Δϕl = 4πζ /λ that corresponds for a low-angle imaging scenario. (b) Δϕ oϕ i lookup curves of a static emitter located at (0, 0, ζ). The parameters used in these figures were the same as in Fig. 1(b).
Fig. 3
Fig. 3 Temporal and spatial FPSI using a four-step PSI algorithm on a single camera. (a) Temporal FPSI (tFPSI) employs a time-sequential collection of the four phase-shifted interferograms of multiple optically resolved emitters, whereas (b) spatial FPSI (sFPSI) uses a simultaneous interferogram collection, but at the expense of a smaller field-of-view compared to tFPSI with an identical sensor array.
Fig. 4
Fig. 4 Simulations of high precision, extended depth-of-field axial single particle tracking (SPT) of a Brownian emitter by FPSI. The parameters used in the simulations were as follows: emission wavelength of λ = 520 nm, 10 background noise photons/pixel, diffusion coefficient of D = 0.05 μm2/sec, collector lens with NA = 0.95, × 100, two-dimensional pixel array of 14 × 14 pixels with a 16 μm2 pixel size, and an emitted photon rate of 500 photons per camera integration time across a 4π solid angle where a 100 Hz acquisition frame rate was assumed. Also, M = 4 interferograms were averaged out to model the finite exposure time of the camera and the width σ2 of the inner/outer Gaussian-based spatial masks wi/o(ρ) was equal to the focused PSF width. (a) Spatial FPSI (sFPSI)-based SPT of a diffusive particle. The actual and reconstructed trajectories are shown in solid gray and dashed pink lines, respectively. (b) Temporal FPSI (tFPSI)-based SPT of a diffusive particle. The actual and reconstructed trajectories are shown in solid gray and dashed blue lines, respectively. (c) Histograms of the estimation error Δζ = ‾ζ − ζ of spatial and temporal FPSI-based SPT.‾ζ and ζ are the estimated and actual position of the particle, respectively. (d) sFPSI-based SPT corrected for Δζ2 mislocalizations. (e) tFPSI-based SPT corrected for Δζ2 mislocalizations. Actual and reconstructed trajectories following the correction for Δζ2 mislocalizations are shown in solid gray and dashed lines, respectively. (f) Histograms of the estimation error Δζ = ‾ζ−ζ of spatial and temporal FPSI-based SPT corrected for Δζ2-mislocalizations.
Fig. 5
Fig. 5 Simulated performance comparison curves (in terms of root mean square error) of spatial and temporal FPSI for axial SPT of diffusive particles with an emission rate of 500 (a) and 250 (b) photons per camera integration time (τcamera) across a 4π solid angle. The additional parameters employed in the simulations were the same as in Fig. 4.
Fig. 6
Fig. 6 Simulations of high precision, extended depth-of-field axial single particle tracking (SPT) of random linear motion by FPSI. The simulated emission photon rate used here was 250 photons per camera integration time. The additional simulation parameters were those employed in the simulations of Fig. 4. (a) tFPSI/improved tFPSI-based SPT of random linear motion. The actual trajectory is shown in solid gray line where the tFPSI and improved tFPSI reconstructed trajectories are shown in open blue and closed green circles, respectively. (b) Simulated performance comparison curves (in terms of root mean square error) of spatial / temporal / improved temporal FPSI for axial SPT of random liner motion.
Fig. 7
Fig. 7 Infinity-corrected high-angle imaging system. The schematics shows a dipole located on the optical axis at (0,0,0) and rays on the ϕ = ϕd = 0 meridional plane. f and fd represent the focal lengths of the collector and detector lenses, respectively. θ and θd are the polar angles of the diverging and converging rays, respectively. Positions in the focal region of the detector lens are defined by the vector (ρ, ζd) = (ρ cosφ, ρ sinφ, ζd).

Equations (11)

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E( ρ,ζ,p )= [ E l ( ρ,ζ,p ) ] l=x,y,z = [ A l ( ρ,ζ,p ) e i ϕ l ( ρ,ζ,p ) ]  l=x,y,z E( ρ,ζ,p, δ k )= [ E l ( ρ,ζ,p ) e i δ k ]  l=x,y,z = [ A l ( ρ,ζ,p ) e i[ ϕ l ( ρ,ζ,p ) δ k ] ] l=x,y,z
I k ( ρ,ζ,p )= | E( ρ,ζ,p )+E( ρ,ζ,p, δ k ) | 2 = I ( ρ,ζ,p )+ I ( ρ,ζ,p )cos[ Δϕ( ρ,ζ,p ) δ k ]
cos[ Δϕ( ρ,ζ,p ) ]= Re{ E( ρ,ζ,p,0 ) E * ( ρ,ζ,p ) } | E( ρ,ζ,p,0 ) || E( ρ,ζ,p ) |
I ¯ k i/o ( ζ,p )= 0 2π 0 I k ( ρ,ζ,p ) w i/o ( ρ )ρdρdφ = I ¯ k i/o ( ζ,p )+ I ¯ k i/o ( ζ,p )cos[ Δ ϕ i/o ( ζ,p ) δ k ]
w i ( ρ )= e ρ 2 2 σ 2 , w o ( ρ )= ρ 3 e ρ 2 2 σ 2
Δ ϕ i/o ( ζ,p )= tan 1 ( I ¯ 4 i/o I ¯ 2 i/o I ¯ 1 i/o I ¯ 3 i/o )
E( ρ,φ, ζ d )= i f d k 2π 0 2π 0 α d e( θ d , ϕ d ) e ikρsin θ d cos( ϕ d φ ) e ik ζ d cos θ d sin θ d d θ d d ϕ d
e( θ d , ϕ d )= cos θ d cosθ R 1 ( ϕ )L( θ d )L( θ )R( ϕ )p
R( ϕ )=( cosϕ sinϕ 0 sinϕ cosϕ 0 0 0 1 ), L( θ )=( cosθ 0 sinθ 0 1 0 sinθ 0 cosθ )
sinθ sin θ d = f d f =M
E( ρ,φ, ζ d M 2 ζ )

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