Abstract

By exploiting the saturation of a reversible single photon transition, RESOLFT microscopy is capable of resolving three dimensional structures inside specimen with a resolution that is no longer limited by the wavelength of the light in use. The transition is driven by a spatially varying intensity distribution that features at least one isolated point, line or plane with zero intensity and the resolution achieved depends critically on the field distribution around these zeros. Based on a vectorial analysis of the image formation in a RESOLFT microscope, we develop a method to effectively search for optimal zero intensity point patterns under typical experimental conditions. Using this approach, we derived a spatial intensity distribution that optimizes the focal plane resolution. Moreover, we outline a general strategy that allows optimization of the resolution for a given experimental situation and present solutions for the most common cases in biological imaging.

©2007 Optical Society of America

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References

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  1. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. f. Mikr. Anat. 9,413–420 (1873).
    [Crossref]
  2. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248,73–76 (1990).
    [Crossref] [PubMed]
  3. L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17,1685–1694 (2000).
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  5. S. Hell, “Toward fluorescence nanoscopy,” Nature Biotechnol. 21,1347–1355 (2003).
    [Crossref]
  6. S. Hell, “Strategy for far-field optical imaging and writing without diffraction limit,” Phys. Lett. A 326,140–145 (2004).
    [Crossref]
  7. S. W. Hell, M. Dyba, and S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobio. 14(5),599–609 (2004).
    [Crossref]
  8. S. Hell and A. S., “Nanoscale resolution in Far-Field Fluorescence Microscopy,” in Science of Microscopy, P. Hawkes and J. Spence, eds. (Springer, 2006).
  9. S. Hell and A. S., “Nanoscopy: The Future of Optical Microscopy,” in Biomedical Optical Imaging, J. Fujimoto and D. Farkas, eds. (Oxford University Press, Oxford, 2006).
  10. M. Hofmann, C. Eggeling, S. Jakobs, and S. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102,17,565–17,569 (2005).
    [Crossref]
  11. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated emission depletion microscopy,” Opt. Lett. 19,780–782 (1994).
    [Crossref] [PubMed]
  12. S. W. Hell and M. Kroug, “Ground-state depletion fluorescence microscopy, a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60,495–497 (1995).
    [Crossref]
  13. V. Westphal and S. Hell, “Nanoscale Resolution in the Focal Plane of an Optical Microscope,” Phys. Rev. Lett. 94,143,903 (2005).
    [Crossref]
  14. G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
    [Crossref]
  15. R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - A concept for optical resolution improvement,” J. Opt. Soc. Am. A: Optics and Image Science, and Vision 19,1599–1609 (2002).
    [Crossref]
  16. T. Klar, E. Engel, and S. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066,613,1–9 (2001).
    [Crossref]
  17. P. Török and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12,3605–3617 (2004).
    [Crossref] [PubMed]
  18. N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4pi focusing of a radially polarized Laguerre-Gaussian beam,” Opt. Lett. 31,149–151 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253,358–379 (1959).
    [Crossref]
  21. W. J. Tango, “Circle Polynomials of Zernike and Their Application in Optics,” Appl. Phys. 13,327–332 (1977).
    [Crossref]
  22. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
    [Crossref]
  23. J. A. Nelder and R. Mead, “A Simplex-Method for Function Minimization,” Comput. J. 7,308–313 (1965).
  24. T. Klar and S. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett. 24,954–956 (1999).
    [Crossref]
  25. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7,77–87 (2000).
    [Crossref] [PubMed]

2006 (3)

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4pi focusing of a radially polarized Laguerre-Gaussian beam,” Opt. Lett. 31,149–151 (2006).
[Crossref] [PubMed]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis.” Nature 440,935 –939 (2006).
[Crossref] [PubMed]

2005 (2)

V. Westphal and S. Hell, “Nanoscale Resolution in the Focal Plane of an Optical Microscope,” Phys. Rev. Lett. 94,143,903 (2005).
[Crossref]

M. Hofmann, C. Eggeling, S. Jakobs, and S. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102,17,565–17,569 (2005).
[Crossref]

2004 (3)

S. Hell, “Strategy for far-field optical imaging and writing without diffraction limit,” Phys. Lett. A 326,140–145 (2004).
[Crossref]

S. W. Hell, M. Dyba, and S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobio. 14(5),599–609 (2004).
[Crossref]

P. Török and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12,3605–3617 (2004).
[Crossref] [PubMed]

2003 (1)

S. Hell, “Toward fluorescence nanoscopy,” Nature Biotechnol. 21,1347–1355 (2003).
[Crossref]

2002 (1)

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - A concept for optical resolution improvement,” J. Opt. Soc. Am. A: Optics and Image Science, and Vision 19,1599–1609 (2002).
[Crossref]

2001 (1)

T. Klar, E. Engel, and S. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066,613,1–9 (2001).
[Crossref]

2000 (2)

1999 (1)

1995 (1)

S. W. Hell and M. Kroug, “Ground-state depletion fluorescence microscopy, a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60,495–497 (1995).
[Crossref]

1994 (1)

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248,73–76 (1990).
[Crossref] [PubMed]

1977 (1)

W. J. Tango, “Circle Polynomials of Zernike and Their Application in Optics,” Appl. Phys. 13,327–332 (1977).
[Crossref]

1965 (1)

J. A. Nelder and R. Mead, “A Simplex-Method for Function Minimization,” Comput. J. 7,308–313 (1965).

1959 (1)

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

1953 (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
[Crossref]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. f. Mikr. Anat. 9,413–420 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. f. Mikr. Anat. 9,413–420 (1873).
[Crossref]

Andrei, M. A.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

Bokor, N.

Brown, T. G.

Cremer, C.

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - A concept for optical resolution improvement,” J. Opt. Soc. Am. A: Optics and Image Science, and Vision 19,1599–1609 (2002).
[Crossref]

Davidson, N.

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248,73–76 (1990).
[Crossref] [PubMed]

Donnert, G.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

Dyba, M.

S. W. Hell, M. Dyba, and S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobio. 14(5),599–609 (2004).
[Crossref]

Eggeling, C.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

M. Hofmann, C. Eggeling, S. Jakobs, and S. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102,17,565–17,569 (2005).
[Crossref]

Engel, E.

T. Klar, E. Engel, and S. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066,613,1–9 (2001).
[Crossref]

Harke, B.

A. Schönle, J. Keller, B. Harke, and S. Hell, “Diffraction Unlimited Far-Field Fluorescence Microscopy,” in Handbook of Biological Nonlinear Optical Microscopy, M. Masters and P. So, eds. (Oxford University Press, Oxford, 2007).

Heintzmann, R.

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - A concept for optical resolution improvement,” J. Opt. Soc. Am. A: Optics and Image Science, and Vision 19,1599–1609 (2002).
[Crossref]

Hell, S.

V. Westphal and S. Hell, “Nanoscale Resolution in the Focal Plane of an Optical Microscope,” Phys. Rev. Lett. 94,143,903 (2005).
[Crossref]

M. Hofmann, C. Eggeling, S. Jakobs, and S. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102,17,565–17,569 (2005).
[Crossref]

S. Hell, “Strategy for far-field optical imaging and writing without diffraction limit,” Phys. Lett. A 326,140–145 (2004).
[Crossref]

S. Hell, “Toward fluorescence nanoscopy,” Nature Biotechnol. 21,1347–1355 (2003).
[Crossref]

T. Klar, E. Engel, and S. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066,613,1–9 (2001).
[Crossref]

T. Klar and S. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett. 24,954–956 (1999).
[Crossref]

S. Hell and A. S., “Nanoscale resolution in Far-Field Fluorescence Microscopy,” in Science of Microscopy, P. Hawkes and J. Spence, eds. (Springer, 2006).

S. Hell and A. S., “Nanoscopy: The Future of Optical Microscopy,” in Biomedical Optical Imaging, J. Fujimoto and D. Farkas, eds. (Oxford University Press, Oxford, 2006).

A. Schönle, J. Keller, B. Harke, and S. Hell, “Diffraction Unlimited Far-Field Fluorescence Microscopy,” in Handbook of Biological Nonlinear Optical Microscopy, M. Masters and P. So, eds. (Oxford University Press, Oxford, 2007).

Hell, S. W.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis.” Nature 440,935 –939 (2006).
[Crossref] [PubMed]

S. W. Hell, M. Dyba, and S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobio. 14(5),599–609 (2004).
[Crossref]

S. W. Hell and M. Kroug, “Ground-state depletion fluorescence microscopy, a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60,495–497 (1995).
[Crossref]

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated emission depletion microscopy,” Opt. Lett. 19,780–782 (1994).
[Crossref] [PubMed]

Hofmann, M.

M. Hofmann, C. Eggeling, S. Jakobs, and S. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102,17,565–17,569 (2005).
[Crossref]

Jahn, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis.” Nature 440,935 –939 (2006).
[Crossref] [PubMed]

Jakobs, S.

M. Hofmann, C. Eggeling, S. Jakobs, and S. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102,17,565–17,569 (2005).
[Crossref]

S. W. Hell, M. Dyba, and S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobio. 14(5),599–609 (2004).
[Crossref]

Jovin, T. M.

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - A concept for optical resolution improvement,” J. Opt. Soc. Am. A: Optics and Image Science, and Vision 19,1599–1609 (2002).
[Crossref]

Keller, J.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

A. Schönle, J. Keller, B. Harke, and S. Hell, “Diffraction Unlimited Far-Field Fluorescence Microscopy,” in Handbook of Biological Nonlinear Optical Microscopy, M. Masters and P. So, eds. (Oxford University Press, Oxford, 2007).

Klar, T.

T. Klar, E. Engel, and S. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066,613,1–9 (2001).
[Crossref]

T. Klar and S. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett. 24,954–956 (1999).
[Crossref]

Kroug, M.

S. W. Hell and M. Kroug, “Ground-state depletion fluorescence microscopy, a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60,495–497 (1995).
[Crossref]

Lührmann, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

Mead, R.

J. A. Nelder and R. Mead, “A Simplex-Method for Function Minimization,” Comput. J. 7,308–313 (1965).

Medda, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

Mertz, J.

Metropolis, N.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
[Crossref]

Moreaux, L.

Munro, P. R. T.

Nelder, J. A.

J. A. Nelder and R. Mead, “A Simplex-Method for Function Minimization,” Comput. J. 7,308–313 (1965).

Richards, B.

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

Rizzoli, S. O.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis.” Nature 440,935 –939 (2006).
[Crossref] [PubMed]

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

Rosenbluth, A. W.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
[Crossref]

Rosenbluth, M. N.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
[Crossref]

S., A.

S. Hell and A. S., “Nanoscopy: The Future of Optical Microscopy,” in Biomedical Optical Imaging, J. Fujimoto and D. Farkas, eds. (Oxford University Press, Oxford, 2006).

S. Hell and A. S., “Nanoscale resolution in Far-Field Fluorescence Microscopy,” in Science of Microscopy, P. Hawkes and J. Spence, eds. (Springer, 2006).

Sandre, O.

Schönle, A.

A. Schönle, J. Keller, B. Harke, and S. Hell, “Diffraction Unlimited Far-Field Fluorescence Microscopy,” in Handbook of Biological Nonlinear Optical Microscopy, M. Masters and P. So, eds. (Oxford University Press, Oxford, 2007).

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248,73–76 (1990).
[Crossref] [PubMed]

Tango, W. J.

W. J. Tango, “Circle Polynomials of Zernike and Their Application in Optics,” Appl. Phys. 13,327–332 (1977).
[Crossref]

Teller, A. H.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
[Crossref]

Teller, E.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
[Crossref]

Török, P.

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248,73–76 (1990).
[Crossref] [PubMed]

Westphal, V.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis.” Nature 440,935 –939 (2006).
[Crossref] [PubMed]

V. Westphal and S. Hell, “Nanoscale Resolution in the Focal Plane of an Optical Microscope,” Phys. Rev. Lett. 94,143,903 (2005).
[Crossref]

Wichmann, J.

Willig, K. I.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis.” Nature 440,935 –939 (2006).
[Crossref] [PubMed]

Wolf, E.

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

Youngworth, K. S.

Appl. Phys. (1)

W. J. Tango, “Circle Polynomials of Zernike and Their Application in Optics,” Appl. Phys. 13,327–332 (1977).
[Crossref]

Appl. Phys. B (1)

S. W. Hell and M. Kroug, “Ground-state depletion fluorescence microscopy, a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60,495–497 (1995).
[Crossref]

Arch. f. Mikr. Anat. (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. f. Mikr. Anat. 9,413–420 (1873).
[Crossref]

Comput. J. (1)

J. A. Nelder and R. Mead, “A Simplex-Method for Function Minimization,” Comput. J. 7,308–313 (1965).

Curr. Opin. Neurobio. (1)

S. W. Hell, M. Dyba, and S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobio. 14(5),599–609 (2004).
[Crossref]

J. Chem. Phys. (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21,1087–1092 (1953).
[Crossref]

J. Opt. Soc. Am. A: Optics and Image Science, and Vision (1)

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - A concept for optical resolution improvement,” J. Opt. Soc. Am. A: Optics and Image Science, and Vision 19,1599–1609 (2002).
[Crossref]

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

Nature (1)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis.” Nature 440,935 –939 (2006).
[Crossref] [PubMed]

Nature Biotechnol. (1)

S. Hell, “Toward fluorescence nanoscopy,” Nature Biotechnol. 21,1347–1355 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Lett. A (1)

S. Hell, “Strategy for far-field optical imaging and writing without diffraction limit,” Phys. Lett. A 326,140–145 (2004).
[Crossref]

Phys. Rev. E (1)

T. Klar, E. Engel, and S. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066,613,1–9 (2001).
[Crossref]

Phys. Rev. Lett. (1)

V. Westphal and S. Hell, “Nanoscale Resolution in the Focal Plane of an Optical Microscope,” Phys. Rev. Lett. 94,143,903 (2005).
[Crossref]

Proc. Natl. Acad. Sci. USA (2)

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 103,11,440–11,445 (2006).
[Crossref]

M. Hofmann, C. Eggeling, S. Jakobs, and S. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102,17,565–17,569 (2005).
[Crossref]

Proc. R. Soc. Lond. A (1)

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

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248,73–76 (1990).
[Crossref] [PubMed]

Other (3)

A. Schönle, J. Keller, B. Harke, and S. Hell, “Diffraction Unlimited Far-Field Fluorescence Microscopy,” in Handbook of Biological Nonlinear Optical Microscopy, M. Masters and P. So, eds. (Oxford University Press, Oxford, 2007).

S. Hell and A. S., “Nanoscale resolution in Far-Field Fluorescence Microscopy,” in Science of Microscopy, P. Hawkes and J. Spence, eds. (Springer, 2006).

S. Hell and A. S., “Nanoscopy: The Future of Optical Microscopy,” in Biomedical Optical Imaging, J. Fujimoto and D. Farkas, eds. (Oxford University Press, Oxford, 2006).

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Figures (3)

Fig. 1.
Fig. 1. Schematic illustration of a point-scanning RESOLFT microscope. An excitation (Exc.) and inhibition (Inh.) light beam are combined with a dichroic mirror (DC) so that they can be focused onto the same spot. The inhibition beam is modulated by a phase and/or amplitude filter (F) so that its focal light distribution features a focal intensity zero and large contributions in its immediate vicinity. To this end, the filter creates an amplitude and phase distribution P(r,ϕ) which is imaged onto the back aperture of the objective lens.

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Fig. 2.
Fig. 2. Results for the limited field amplitude in the entrance pupil of the objective lens (condition A). In a), the points of interest used for the calculation of the FoM are shown schematically for linearly and circularly polarized light. The creation of optimized inhibition patterns for resolution increase in X, Y, Z, XY and 3D was investigated. In b), the results of the global optimization algorithm are shown as phase and amplitude distributions of the pupil function. In c), the idealized phase-only pupil functions are shown together with the optimal values of the parameters d and h. In d), sections of the corresponding inhibition patterns are shown. Only the intensity of the x-component is depicted. The number at the bottom right corner of each section reflects the maximal intensity relative to the intensity in the focus of an unmodified beam.

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Fig. 3.
Fig. 3. Results for limited focal power (condition B). In a), the results of the global optimization are shown for the Z and the XY pattern. The idealized phase and amplitude distributions are shown in b). Central intensity profiles through the pupil function are shown in c) in comparison with the results for condition (A) (denoted by B and A, respectively). In d), profiles of the inhibition beam’s intensity pattern along the z-axis for the Z pattern and along the x-axis for the XY pattern are shown (NA=1.2).

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Equations (23)

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h ( r′ , p ) = C ∣ E ex ∙ p ∣ 2 f ( ∣ E inh ∙ p ∣ 2 ) CEF ( p , r′ )
i ( R ) = ∫ h ( r′ , p ) ρ ( p , R − r′ ) d Ω d 3 r′
E inh ( r′ ) = ∫ cos ⁡ θ [ A x K ( θ , ϕ ) + A y MK ( θ , ϕ − π 2 ) ] exp ⁡ ( iknr′ cos ⁡ ε ) sin ⁡ θdθdϕ ,
K x = cos ⁡ θ + ( 1 − cos ⁡ θ ) sin ⁡ 2 ϕ
K y = ( cos ⁡ θ − 1 ) sin ⁡ ϕ cos ⁡ ϕ
K z = sin ⁡ θ cos ⁡ ϕ
A x = P ( r , ϕ )
A y = 0
A x = P ( r , ϕ ) 2
A y = iP ( r , ϕ ) 2
Z ˜ i ( r , ϕ ) = ( 2 n + 2 ) 1 2 Z n m ( r , ϕ ) [ π ( 1 + δ m 0 ) ]
P ( r , ϕ ) ≃ ∑ i = 1 N c i Z ˜ i ( r , ϕ ) , c i ∈ ℂ ,
E inh ( r′ ) [ P ] ≃ ∑ i = 1 N c i E inh ( r′ ) [ Z ˜ i ]
M li = E inh k ( r′ j ) [ Z ˜ i ]
S l = E inh k ( r′ j ) [ P ]
S = Mc
P 3 D ( r , ϕ ) = { 1 for r > d 2 − 1 else
P XY ( r , ϕ ) = exp ⁡ ( iϕ )
P XY ( r , ϕ ) = { 1 for r > h 2 ∧ ( x > 0 ∨ y < h 2 ) − 1 else
P X ( r , ϕ ) = { 1 for x < h 2 − 1 else
P Y ( r , ϕ ) = { 1 for ϕ > π − 1 else
P 3 D ( r , ϕ ) = { c α ( r α − r ) α for r < d − c β ( r − r β ) β for r ≥ d
P XY ( r , ϕ ) = ( ( α + 1 ) / π ) 1 2 r α

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