Abstract

With recent developments in microscopy, such as stimulated emission depletion (STED) microscopy, far-field imaging at resolutions better than the diffraction limit is now a commercially available technique. Here, we show that, in the special case of a diffusive regime, the noise-limited resolution of STED imaging is independent of the saturation intensity of the fluorescent label. Thermal motion limits the signal integration time, which, for a given excited-state lifetime, limits the total number of photons available for detection.

© 2012 OSA

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  1. B. Huang, S. Jones, B. Brandenburg, and X. Zhuang, “Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution,” Nat. Methods 5, 1047–1052 (2008).
    [CrossRef] [PubMed]
  2. B. Hein, K. Willig, and S. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. USA 105, 14271–14276 (2008).
    [CrossRef] [PubMed]
  3. E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
    [CrossRef]
  4. B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16, 4154–4162 (2008).
    [CrossRef] [PubMed]
  5. M. Leutenegger, C. Eggeling, and S. W. Hell, “Analytical description of STED microscopy performance,” Opt. Express 18, 26417–26429 (2010).
    [CrossRef] [PubMed]
  6. M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
    [CrossRef] [PubMed]
  7. V. Beskrovnyy and M. Kolobov, “Quantum limits of super-resolution in reconstruction of optical objects,” Phys. Rev. A 71, 043802 (2005).
    [CrossRef]
  8. Y. Y. Hui, C.-L. Cheng, and H.-C. Chang, “Nanodiamonds for optical bioimaging,” J. Phys. D 43, 374021 (2010).
    [CrossRef]
  9. D. Wildanger, J. Maze, and S. Hell, “Diffraction unlimited all-optical recording of electron spin resonances,” Phys. Rev. Lett. 107, 017601 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. A. Caspi, R. Granek, and M. Elbaum, “Diffusion and directed motion in cellular transport,” Phys. Rev. E 66, 011916 (2002).
    [CrossRef]
  12. J. T. Verdeyen, Laser Electronics, 3rd ed. (Prentice Hall, New Jersey, 1995).
  13. M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells,” Biophys. J. 87, 3518–3524 (2004).
    [CrossRef] [PubMed]
  14. L. Nugent-Glandorf and T. T. Perkins, “Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection,” Opt. Lett. 29, 2611–2613 (2004).
    [CrossRef] [PubMed]

2011 (1)

D. Wildanger, J. Maze, and S. Hell, “Diffraction unlimited all-optical recording of electron spin resonances,” Phys. Rev. Lett. 107, 017601 (2011).
[CrossRef] [PubMed]

2010 (2)

2009 (1)

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

2008 (3)

B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16, 4154–4162 (2008).
[CrossRef] [PubMed]

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

B. Hein, K. Willig, and S. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. USA 105, 14271–14276 (2008).
[CrossRef] [PubMed]

2005 (1)

V. Beskrovnyy and M. Kolobov, “Quantum limits of super-resolution in reconstruction of optical objects,” Phys. Rev. A 71, 043802 (2005).
[CrossRef]

2004 (2)

M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells,” Biophys. J. 87, 3518–3524 (2004).
[CrossRef] [PubMed]

L. Nugent-Glandorf and T. T. Perkins, “Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection,” Opt. Lett. 29, 2611–2613 (2004).
[CrossRef] [PubMed]

2002 (1)

A. Caspi, R. Granek, and M. Elbaum, “Diffusion and directed motion in cellular transport,” Phys. Rev. E 66, 011916 (2002).
[CrossRef]

2000 (2)

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
[CrossRef] [PubMed]

A. Caspi, R. Granek, and M. Elbaum, “Enhanced diffusion in active intracellular transport,” Phys. Rev. Lett. 85, 5655–5658 (2000).
[CrossRef]

Beskrovnyy, V.

V. Beskrovnyy and M. Kolobov, “Quantum limits of super-resolution in reconstruction of optical objects,” Phys. Rev. A 71, 043802 (2005).
[CrossRef]

Brandenburg, B.

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

Caspi, A.

A. Caspi, R. Granek, and M. Elbaum, “Diffusion and directed motion in cellular transport,” Phys. Rev. E 66, 011916 (2002).
[CrossRef]

A. Caspi, R. Granek, and M. Elbaum, “Enhanced diffusion in active intracellular transport,” Phys. Rev. Lett. 85, 5655–5658 (2000).
[CrossRef]

Chang, H.-C.

Y. Y. Hui, C.-L. Cheng, and H.-C. Chang, “Nanodiamonds for optical bioimaging,” J. Phys. D 43, 374021 (2010).
[CrossRef]

Cheng, C.-L.

Y. Y. Hui, C.-L. Cheng, and H.-C. Chang, “Nanodiamonds for optical bioimaging,” J. Phys. D 43, 374021 (2010).
[CrossRef]

Eggeling, C.

M. Leutenegger, C. Eggeling, and S. W. Hell, “Analytical description of STED microscopy performance,” Opt. Express 18, 26417–26429 (2010).
[CrossRef] [PubMed]

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Elbaum, M.

A. Caspi, R. Granek, and M. Elbaum, “Diffusion and directed motion in cellular transport,” Phys. Rev. E 66, 011916 (2002).
[CrossRef]

A. Caspi, R. Granek, and M. Elbaum, “Enhanced diffusion in active intracellular transport,” Phys. Rev. Lett. 85, 5655–5658 (2000).
[CrossRef]

Elsner, M.

M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells,” Biophys. J. 87, 3518–3524 (2004).
[CrossRef] [PubMed]

Fabre, C.

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
[CrossRef] [PubMed]

Granek, R.

A. Caspi, R. Granek, and M. Elbaum, “Diffusion and directed motion in cellular transport,” Phys. Rev. E 66, 011916 (2002).
[CrossRef]

A. Caspi, R. Granek, and M. Elbaum, “Enhanced diffusion in active intracellular transport,” Phys. Rev. Lett. 85, 5655–5658 (2000).
[CrossRef]

Han, K. Y.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Harke, B.

Hein, B.

B. Hein, K. Willig, and S. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. USA 105, 14271–14276 (2008).
[CrossRef] [PubMed]

Hell, S.

D. Wildanger, J. Maze, and S. Hell, “Diffraction unlimited all-optical recording of electron spin resonances,” Phys. Rev. Lett. 107, 017601 (2011).
[CrossRef] [PubMed]

B. Hein, K. Willig, and S. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. USA 105, 14271–14276 (2008).
[CrossRef] [PubMed]

Hell, S. W.

Huang, B.

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

Hui, Y. Y.

Y. Y. Hui, C.-L. Cheng, and H.-C. Chang, “Nanodiamonds for optical bioimaging,” J. Phys. D 43, 374021 (2010).
[CrossRef]

Irvine, S. E.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Jones, S.

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

Kartberg, F.

M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells,” Biophys. J. 87, 3518–3524 (2004).
[CrossRef] [PubMed]

Keller, J.

Kolobov, M.

V. Beskrovnyy and M. Kolobov, “Quantum limits of super-resolution in reconstruction of optical objects,” Phys. Rev. A 71, 043802 (2005).
[CrossRef]

Kolobov, M. I.

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
[CrossRef] [PubMed]

Leutenegger, M.

Maze, J.

D. Wildanger, J. Maze, and S. Hell, “Diffraction unlimited all-optical recording of electron spin resonances,” Phys. Rev. Lett. 107, 017601 (2011).
[CrossRef] [PubMed]

Nilsson, T.

M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells,” Biophys. J. 87, 3518–3524 (2004).
[CrossRef] [PubMed]

Nugent-Glandorf, L.

Perkins, T. T.

Rittweger, E.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Schönle, A.

Ullal, C. K.

Verdeyen, J. T.

J. T. Verdeyen, Laser Electronics, 3rd ed. (Prentice Hall, New Jersey, 1995).

Weiss, M.

M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells,” Biophys. J. 87, 3518–3524 (2004).
[CrossRef] [PubMed]

Westphal, V.

Wildanger, D.

D. Wildanger, J. Maze, and S. Hell, “Diffraction unlimited all-optical recording of electron spin resonances,” Phys. Rev. Lett. 107, 017601 (2011).
[CrossRef] [PubMed]

Willig, K.

B. Hein, K. Willig, and S. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. USA 105, 14271–14276 (2008).
[CrossRef] [PubMed]

Zhuang, X.

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

Biophys. J. (1)

M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells,” Biophys. J. 87, 3518–3524 (2004).
[CrossRef] [PubMed]

J. Phys. D (1)

Y. Y. Hui, C.-L. Cheng, and H.-C. Chang, “Nanodiamonds for optical bioimaging,” J. Phys. D 43, 374021 (2010).
[CrossRef]

Nat. Methods (1)

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

Nat. Photonics (1)

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

V. Beskrovnyy and M. Kolobov, “Quantum limits of super-resolution in reconstruction of optical objects,” Phys. Rev. A 71, 043802 (2005).
[CrossRef]

Phys. Rev. E (1)

A. Caspi, R. Granek, and M. Elbaum, “Diffusion and directed motion in cellular transport,” Phys. Rev. E 66, 011916 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
[CrossRef] [PubMed]

D. Wildanger, J. Maze, and S. Hell, “Diffraction unlimited all-optical recording of electron spin resonances,” Phys. Rev. Lett. 107, 017601 (2011).
[CrossRef] [PubMed]

A. Caspi, R. Granek, and M. Elbaum, “Enhanced diffusion in active intracellular transport,” Phys. Rev. Lett. 85, 5655–5658 (2000).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

B. Hein, K. Willig, and S. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. USA 105, 14271–14276 (2008).
[CrossRef] [PubMed]

Other (1)

J. T. Verdeyen, Laser Electronics, 3rd ed. (Prentice Hall, New Jersey, 1995).

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Figures (2)

Fig. 1
Fig. 1

Signal-to-noise ratio (red) and lateral resolution (blue) as a function of STED laser intensity. Note that when the STED laser intensity falls below that of Is, the stimulated emission rate becomes negligible and the resolution is given by the diffraction-limit.

Fig. 2
Fig. 2

Diffusion-limited signal acquisition time (red) and resulting STED resolution (blue) as a function of α. The yellow shaded region is the diffusion regime that is of biological relevance.

Equations (10)

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

V = V 0 I s 3 2 I 3 2
Φ p = ρ e V τ c
R = 0 t i i r m s d t
i = e Θ Φ p
R = Θ ρ e V t τ c
δ r = D t α
R = Θ ρ e V d r 2 α D 1 α τ c
d r s = 1 2 2 α 1 3 α + 2 [ τ c π Θ ρ e ] α 3 α + 2 D 1 3 α + 2
I s = 8 π π h c n 2 λ 3 τ e , j τ e 2
d r s 1 2 2 α 1 3 α + 2 [ 8 π n 2 h c Θ ρ e λ 3 I s ] α 3 α + 2 D 1 3 α + 2

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