Abstract

We study the use of coherent counterpropagating interfering waves to increase threefold to sevenfold the optical bandwidth and the resolution of fluorescence microscopy along the optic axis. Systematic comparison of the point-spread function and the optical transfer function (OTF) for the standing-wave microscope (SWM), the incoherent illumination interference image interference microscope (I5M), and the 4Pi confocal microscope reveals essential differences among their resolution capabilities. It is shown that the OTF’s of these microscopes differ strongly in contiguity and amplitude within the enlarged range of transferred frequencies, and therefore they also differ in their ability to provide data from which interference artifacts can be removed. We demonstrate that for practical aperture angles the production of an interference pattern is insufficient for improving the axial resolution by the expected factor of 3–7. Conditions of the OTF for unambiguous improvement of axial resolution of arbitrary objects are fulfilled not at all in the SWM, partially in the I5M, and fully in the two-photon 4Pi confocal microscope.

© 2001 Optical Society of America

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  1. S. W. Hell, J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated emission depletion microscopy,” Opt. Lett. 19, 780–782 (1994).
    [CrossRef] [PubMed]
  2. T. A. Klar, S. Jakobs, M. Dyba, A. Egner, S. W. Hell, “Fluorescence microscopy with diffraction resolution limit broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000).
    [CrossRef]
  3. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1993).
  4. J. Pawley, Handbook of Biological Confocal Microscopy (Plenum, New York, 1995).
  5. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  6. F. Lanni, Applications of Fluorescence in the Biomedical Sciences, 1st ed. (Liss, New York, 1986).
  7. B. Bailey, D. L. Farkas, D. L. Taylor, F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature (London) 366, 44–48 (1993).
    [CrossRef]
  8. S. Hell, E. H. K. Stelzer, “Properties of a 4Pi-confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
    [CrossRef]
  9. S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with three-dimensional resolution in the 100 nm range,” J. Microsc. (Oxford) 185, 1–5 (1997).
    [CrossRef]
  10. M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “Sevenfold improvement of axial resolution in 3D widefield microscopy using two objective lenses,” in Three-Dimensional Microscopy: Image Acquisition and Processing II, T. Wilson, C. J. Cogswell, eds., Proc. SPIE2412, 147–156 (1995).
    [CrossRef]
  11. M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. (Oxford) 195, 10–16 (1999).
    [CrossRef]
  12. F. Lanni, B. Bailey, D. L. Farkas, D. L. Taylor, “Excitation field synthesis as a means for obtaining enhanced axial resolution in fluorescence microscopy,” Bioimaging 1, 187–192 (1994).
    [CrossRef]
  13. M. G. L. Gustafsson, “Extended resolution fluorescence microscopy,” Curr. Opin. Struct. Biol. 9, 627–634 (1999).
    [CrossRef] [PubMed]
  14. M. Gu, C. J. R. Sheppard, “Three-dimensional transfer functions in 4Pi confocal microscopes,” J. Opt. Soc. Am. A 11, 1619–1627 (1994).
    [CrossRef]
  15. V. Krishnamurthi, B. Bailey, F. Lanni, “Image processing in 3-D standing wave fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 18–25 (1996).
    [CrossRef]
  16. R. Freimann, S. Pentz, H. Hörler, “Development of a standing-wave fluorescence microscope with high nodal plane flatness,” J. Microsc. 187, 193–200 (1997).
    [CrossRef] [PubMed]
  17. M. Schrader, S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc. (Oxford) 183, 189–193 (1996).
  18. M. Nagorni, S. Hell, “4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150-nm resolution,” J. Struct. Bio. 123, 236–247 (1998).
    [CrossRef]
  19. K. Bahlmann, S. Jakobs, S. W. Hell, “4Pi-confocal microscopy of live cells,” Ultramicroscopy (to be published).
  20. S. W. Hell, “Increasing the resolution of far-field fluorescence light microscopy by point-spread-function engineering,” in Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York, 1997), Vol. 5, pp. 361–422.
  21. W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  22. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
    [CrossRef]
  23. K. Bahlmann, S. W. Hell, “Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses,” Appl. Opt. 39, 1653–1658 (2000).
    [CrossRef]
  24. S. W. Hell, E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
    [CrossRef]
  25. S. W. Hell, M. Schrader, P. E. Hänninen, E. Soini, “Resolving fluorescence beads at 100–200 distance with a two-photon 4Pi-microscope working in the near infrared,” Opt. Commun. 117, 20–24 (1995).
    [CrossRef]
  26. M. Schrader, K. Bahlmann, G. Giese, S. W. Hell, “4Pi-confocal imaging in fixed biological specimens,” Biophys. J. 75, 1659–1668 (1998).
    [CrossRef] [PubMed]
  27. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996), p. 142.
  28. M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, H. T. M. Van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. (Oxford) 157, 3–20 (1990).
    [CrossRef]
  29. S. W. Hell, M. Nagorni, “4Pi confocal microscopy with alternate interference,” Opt. Lett. 23, 1567–1569 (1998).
    [CrossRef]
  30. R. Heintzmann, C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 185–195 (1998).
    [CrossRef]
  31. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. (Oxford) 198, 82–87 (2000).
    [CrossRef]

2000

K. Bahlmann, S. W. Hell, “Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses,” Appl. Opt. 39, 1653–1658 (2000).
[CrossRef]

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, S. W. Hell, “Fluorescence microscopy with diffraction resolution limit broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000).
[CrossRef]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. (Oxford) 198, 82–87 (2000).
[CrossRef]

1999

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. (Oxford) 195, 10–16 (1999).
[CrossRef]

M. G. L. Gustafsson, “Extended resolution fluorescence microscopy,” Curr. Opin. Struct. Biol. 9, 627–634 (1999).
[CrossRef] [PubMed]

1998

S. W. Hell, M. Nagorni, “4Pi confocal microscopy with alternate interference,” Opt. Lett. 23, 1567–1569 (1998).
[CrossRef]

M. Schrader, K. Bahlmann, G. Giese, S. W. Hell, “4Pi-confocal imaging in fixed biological specimens,” Biophys. J. 75, 1659–1668 (1998).
[CrossRef] [PubMed]

M. Nagorni, S. Hell, “4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150-nm resolution,” J. Struct. Bio. 123, 236–247 (1998).
[CrossRef]

1997

R. Freimann, S. Pentz, H. Hörler, “Development of a standing-wave fluorescence microscope with high nodal plane flatness,” J. Microsc. 187, 193–200 (1997).
[CrossRef] [PubMed]

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with three-dimensional resolution in the 100 nm range,” J. Microsc. (Oxford) 185, 1–5 (1997).
[CrossRef]

1996

M. Schrader, S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc. (Oxford) 183, 189–193 (1996).

1995

S. W. Hell, M. Schrader, P. E. Hänninen, E. Soini, “Resolving fluorescence beads at 100–200 distance with a two-photon 4Pi-microscope working in the near infrared,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

1994

1993

B. Bailey, D. L. Farkas, D. L. Taylor, F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature (London) 366, 44–48 (1993).
[CrossRef]

1992

S. W. Hell, E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

S. Hell, E. H. K. Stelzer, “Properties of a 4Pi-confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
[CrossRef]

1990

M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, H. T. M. Van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. (Oxford) 157, 3–20 (1990).
[CrossRef]

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

1959

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

Agard, D. A.

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. (Oxford) 195, 10–16 (1999).
[CrossRef]

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “Sevenfold improvement of axial resolution in 3D widefield microscopy using two objective lenses,” in Three-Dimensional Microscopy: Image Acquisition and Processing II, T. Wilson, C. J. Cogswell, eds., Proc. SPIE2412, 147–156 (1995).
[CrossRef]

Bahlmann, K.

K. Bahlmann, S. W. Hell, “Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses,” Appl. Opt. 39, 1653–1658 (2000).
[CrossRef]

M. Schrader, K. Bahlmann, G. Giese, S. W. Hell, “4Pi-confocal imaging in fixed biological specimens,” Biophys. J. 75, 1659–1668 (1998).
[CrossRef] [PubMed]

K. Bahlmann, S. Jakobs, S. W. Hell, “4Pi-confocal microscopy of live cells,” Ultramicroscopy (to be published).

Bailey, B.

F. Lanni, B. Bailey, D. L. Farkas, D. L. Taylor, “Excitation field synthesis as a means for obtaining enhanced axial resolution in fluorescence microscopy,” Bioimaging 1, 187–192 (1994).
[CrossRef]

B. Bailey, D. L. Farkas, D. L. Taylor, F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature (London) 366, 44–48 (1993).
[CrossRef]

V. Krishnamurthi, B. Bailey, F. Lanni, “Image processing in 3-D standing wave fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 18–25 (1996).
[CrossRef]

Bertero, M.

M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, H. T. M. Van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. (Oxford) 157, 3–20 (1990).
[CrossRef]

Boccacci, P.

M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, H. T. M. Van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. (Oxford) 157, 3–20 (1990).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1993).

Brakenhoff, G. J.

M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, H. T. M. Van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. (Oxford) 157, 3–20 (1990).
[CrossRef]

Cremer, C.

R. Heintzmann, C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 185–195 (1998).
[CrossRef]

Denk, W.

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

Dyba, M.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, S. W. Hell, “Fluorescence microscopy with diffraction resolution limit broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000).
[CrossRef]

Egner, A.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, S. W. Hell, “Fluorescence microscopy with diffraction resolution limit broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000).
[CrossRef]

Farkas, D. L.

F. Lanni, B. Bailey, D. L. Farkas, D. L. Taylor, “Excitation field synthesis as a means for obtaining enhanced axial resolution in fluorescence microscopy,” Bioimaging 1, 187–192 (1994).
[CrossRef]

B. Bailey, D. L. Farkas, D. L. Taylor, F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature (London) 366, 44–48 (1993).
[CrossRef]

Freimann, R.

R. Freimann, S. Pentz, H. Hörler, “Development of a standing-wave fluorescence microscope with high nodal plane flatness,” J. Microsc. 187, 193–200 (1997).
[CrossRef] [PubMed]

Giese, G.

M. Schrader, K. Bahlmann, G. Giese, S. W. Hell, “4Pi-confocal imaging in fixed biological specimens,” Biophys. J. 75, 1659–1668 (1998).
[CrossRef] [PubMed]

Gu, M.

M. Gu, C. J. R. Sheppard, “Three-dimensional transfer functions in 4Pi confocal microscopes,” J. Opt. Soc. Am. A 11, 1619–1627 (1994).
[CrossRef]

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996), p. 142.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. (Oxford) 198, 82–87 (2000).
[CrossRef]

M. G. L. Gustafsson, “Extended resolution fluorescence microscopy,” Curr. Opin. Struct. Biol. 9, 627–634 (1999).
[CrossRef] [PubMed]

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. (Oxford) 195, 10–16 (1999).
[CrossRef]

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “Sevenfold improvement of axial resolution in 3D widefield microscopy using two objective lenses,” in Three-Dimensional Microscopy: Image Acquisition and Processing II, T. Wilson, C. J. Cogswell, eds., Proc. SPIE2412, 147–156 (1995).
[CrossRef]

Hänninen, P. E.

S. W. Hell, M. Schrader, P. E. Hänninen, E. Soini, “Resolving fluorescence beads at 100–200 distance with a two-photon 4Pi-microscope working in the near infrared,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

Heintzmann, R.

R. Heintzmann, C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” in Optical Biopsies and Microscopic Techniques III, I. J. Bigio, H. Schneckenburger, J. Slavik, K. Svanberg, P. M. Viallet, eds., Proc. SPIE3568, 185–195 (1998).
[CrossRef]

Hell, S.

M. Nagorni, S. Hell, “4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150-nm resolution,” J. Struct. Bio. 123, 236–247 (1998).
[CrossRef]

S. Hell, E. H. K. Stelzer, “Properties of a 4Pi-confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
[CrossRef]

Hell, S. W.

K. Bahlmann, S. W. Hell, “Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses,” Appl. Opt. 39, 1653–1658 (2000).
[CrossRef]

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, S. W. Hell, “Fluorescence microscopy with diffraction resolution limit broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000).
[CrossRef]

M. Schrader, K. Bahlmann, G. Giese, S. W. Hell, “4Pi-confocal imaging in fixed biological specimens,” Biophys. J. 75, 1659–1668 (1998).
[CrossRef] [PubMed]

S. W. Hell, M. Nagorni, “4Pi confocal microscopy with alternate interference,” Opt. Lett. 23, 1567–1569 (1998).
[CrossRef]

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with three-dimensional resolution in the 100 nm range,” J. Microsc. (Oxford) 185, 1–5 (1997).
[CrossRef]

M. Schrader, S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc. (Oxford) 183, 189–193 (1996).

S. W. Hell, M. Schrader, P. E. Hänninen, E. Soini, “Resolving fluorescence beads at 100–200 distance with a two-photon 4Pi-microscope working in the near infrared,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

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

S. W. Hell, E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

K. Bahlmann, S. Jakobs, S. W. Hell, “4Pi-confocal microscopy of live cells,” Ultramicroscopy (to be published).

S. W. Hell, “Increasing the resolution of far-field fluorescence light microscopy by point-spread-function engineering,” in Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York, 1997), Vol. 5, pp. 361–422.

Hörler, H.

R. Freimann, S. Pentz, H. Hörler, “Development of a standing-wave fluorescence microscope with high nodal plane flatness,” J. Microsc. 187, 193–200 (1997).
[CrossRef] [PubMed]

Jakobs, S.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, S. W. Hell, “Fluorescence microscopy with diffraction resolution limit broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000).
[CrossRef]

K. Bahlmann, S. Jakobs, S. W. Hell, “4Pi-confocal microscopy of live cells,” Ultramicroscopy (to be published).

Klar, T. A.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, S. W. Hell, “Fluorescence microscopy with diffraction resolution limit broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000).
[CrossRef]

Krishnamurthi, V.

V. Krishnamurthi, B. Bailey, F. Lanni, “Image processing in 3-D standing wave fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 18–25 (1996).
[CrossRef]

Lanni, F.

F. Lanni, B. Bailey, D. L. Farkas, D. L. Taylor, “Excitation field synthesis as a means for obtaining enhanced axial resolution in fluorescence microscopy,” Bioimaging 1, 187–192 (1994).
[CrossRef]

B. Bailey, D. L. Farkas, D. L. Taylor, F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature (London) 366, 44–48 (1993).
[CrossRef]

V. Krishnamurthi, B. Bailey, F. Lanni, “Image processing in 3-D standing wave fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 18–25 (1996).
[CrossRef]

F. Lanni, Applications of Fluorescence in the Biomedical Sciences, 1st ed. (Liss, New York, 1986).

Malfanti, F.

M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, H. T. M. Van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. (Oxford) 157, 3–20 (1990).
[CrossRef]

Nagorni, M.

S. W. Hell, M. Nagorni, “4Pi confocal microscopy with alternate interference,” Opt. Lett. 23, 1567–1569 (1998).
[CrossRef]

M. Nagorni, S. Hell, “4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150-nm resolution,” J. Struct. Bio. 123, 236–247 (1998).
[CrossRef]

Pawley, J.

J. Pawley, Handbook of Biological Confocal Microscopy (Plenum, New York, 1995).

Pentz, S.

R. Freimann, S. Pentz, H. Hörler, “Development of a standing-wave fluorescence microscope with high nodal plane flatness,” J. Microsc. 187, 193–200 (1997).
[CrossRef] [PubMed]

Richards, B.

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

Schrader, M.

M. Schrader, K. Bahlmann, G. Giese, S. W. Hell, “4Pi-confocal imaging in fixed biological specimens,” Biophys. J. 75, 1659–1668 (1998).
[CrossRef] [PubMed]

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with three-dimensional resolution in the 100 nm range,” J. Microsc. (Oxford) 185, 1–5 (1997).
[CrossRef]

M. Schrader, S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc. (Oxford) 183, 189–193 (1996).

S. W. Hell, M. Schrader, P. E. Hänninen, E. Soini, “Resolving fluorescence beads at 100–200 distance with a two-photon 4Pi-microscope working in the near infrared,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

Sedat, J. W.

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. (Oxford) 195, 10–16 (1999).
[CrossRef]

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “Sevenfold improvement of axial resolution in 3D widefield microscopy using two objective lenses,” in Three-Dimensional Microscopy: Image Acquisition and Processing II, T. Wilson, C. J. Cogswell, eds., Proc. SPIE2412, 147–156 (1995).
[CrossRef]

Sheppard, C. J. R.

M. Gu, C. J. R. Sheppard, “Three-dimensional transfer functions in 4Pi confocal microscopes,” J. Opt. Soc. Am. A 11, 1619–1627 (1994).
[CrossRef]

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Soini, E.

S. W. Hell, M. Schrader, P. E. Hänninen, E. Soini, “Resolving fluorescence beads at 100–200 distance with a two-photon 4Pi-microscope working in the near infrared,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

Stelzer, E. H. K.

S. Hell, E. H. K. Stelzer, “Properties of a 4Pi-confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
[CrossRef]

S. W. Hell, E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

Strickler, J. H.

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

Taylor, D. L.

F. Lanni, B. Bailey, D. L. Farkas, D. L. Taylor, “Excitation field synthesis as a means for obtaining enhanced axial resolution in fluorescence microscopy,” Bioimaging 1, 187–192 (1994).
[CrossRef]

B. Bailey, D. L. Farkas, D. L. Taylor, F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature (London) 366, 44–48 (1993).
[CrossRef]

van der Voort, H. T. M.

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with three-dimensional resolution in the 100 nm range,” J. Microsc. (Oxford) 185, 1–5 (1997).
[CrossRef]

M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, H. T. M. Van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. (Oxford) 157, 3–20 (1990).
[CrossRef]

Webb, W. W.

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

Wichmann, J.

Wilson, T.

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Wolf, E.

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

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1993).

Appl. Opt.

K. Bahlmann, S. W. Hell, “Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses,” Appl. Opt. 39, 1653–1658 (2000).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Comparison of the intensity PSF’s of the SWM, the I5M, and the conventional wide-field, confocal, 4Pi confocal type C, two-photon 4Pi confocal type A, and two-photon 4Pi confocal type C microscopes. (a) Excitation, detection, and effective PSF’s, shown in the upper, center, and bottom panels, respectively. The LUT emphasizes weak regions of the PSF. The aliasing effect in the excitation PSF of the SWM is due to the LUT. (b) Axial profiles along the optic axis (upper row) are compared with axial profiles through a laterally offset point characterized by an intensity of 10% of that found at the geometric focal point (lower row). Whereas in the conventional microscope, the SWM, and the I5M the lateral defocus is associated with pronounced changes in the axial profiles, in the confocalized systems the shape of the profiles is largely unaltered, so that their effective PSF’s can be factorized into a radial and an axial function.

Fig. 2
Fig. 2

Comparison of the modulus of the OTF’s of the SWM, the I5M, and the conventional wide-field, confocal, 4Pi confocal type C, two-photon 4Pi confocal type A, and two-photon 4Pi confocal type C microscopes, calculated numerically by Fourier-transforming the PSF in Fig. 1. (a) Excitation OTF (upper panels), detection OTF (center panels), and effective OTF (bottom panels). The zero-frequency point is in the center of each panel. The maxial frequency displayed in the kr and kz directions is kmax=(2π/80) nm-1. The LUT is the same as that in Fig. 1. (b) Axial profiles through the center of the OTF. In spite of the fact that the OTF’s of the interference-based microscopes all feature a larger maximum bandwidth in the Z direction, they fundamentally differ in contiguity and strength within the region bordered by the highest frequency. Note the pronounced frequency gaps in the SWM and the depressions in the I5M.

Fig. 3
Fig. 3

Comparison of the modulus of the OTF’s of the SWM, the I5M, and the 4Pi confocal type C, two-photon 4Pi confocal type A, and two-photon 4Pi confocal type C microscopes for a numerical aperture of (a) 1.25 (oil) and (b) 1.4 (oil), corresponding to half-aperture angles of 56° and 68°, respectively. The axial profiles through the center of the respective OTF are shown in (b). The profiles reveal that high aperture angles are mandatory for obtaining a contiguous OTF. The OTF of the two-photon 4Pi confocal microscope of type A and type C at NA=1.4 should be contrasted with the other imaging modes.

Fig. 4
Fig. 4

OTF’s of the 4Pi confocal microscopes of (left) single-photon type C, (center) two-photon type A, and (right) two-photon type C for the same conditions as those in Fig. 2, except for the fact that a finite-sized detection pinhole diameter was chosen corresponding to 87% of the Airy disk, as is the case also in a practical system. (b) Comparison of the axial profiles through the center of the OTF calculated for the finite pinhole (solid curves) and the infinitesimally small pinhole (dotted curves). The increase of the pinhole diameter reduces the content of the OTF in the depressions; however, the overall performance of the microscopes remains largely unchanged, except for the 4Pi confocal type C microscope, where the depressions may reach low values.  

Fig. 5
Fig. 5

Measured OTF’s of a two-photon 4Pi confocal microscope of type A and its 1D linear deconvolution along the optic axis. (a) OTF (left), inverse filter (center), and resulting effective OTF (right). (b) Corresponding axial profiles through the OTF center show how the inverse filter removes the local minima and the fringes in the OTF. The insets (upper right) display the corresponding axial profiles in the spatial domain. The dotted line in the left-hand panel shows the theoretical OTF calculated for the finite pinhole size used in the experiment. Note the excellent agreement between theoretical (dotted curve) and experimental performance (solid curves).

Fig. 6
Fig. 6

4Pi confocal microscopy allows deconvolution by direct linear inversion. Raw XZ image data of microtubules of a mouse fibroblast cell obtained by a two-photon 4Pi confocal microscope of type A. Linear deconvolution in the spatial domain (upper row) and in the frequency domain (lower row) yield almost identical results, shown in the boxed panel on the left-hand side. The comparison with its confocal counterpart (boxed image, right) reveals a fourfold improved axial resolution in the 4Pi confocal microscope.

Equations (18)

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hlens(u, v)=12π02πdϕ|E1(u, v, ϕ)|2,
E1(u, v, ϕ)=-iA(I0+I2cos 2ϕ)-iAI2sin 2ϕ-2AI1cos ϕ,
I0(u, v)=0αmaxdθ(cos1/2 θ sin θ)(1+cos θ)×J0v sin θsin αexpiu cos θsin2 α,
I1(u, v)=0αmaxdθ(cos1/2 θ sin2 θ)×J1v sin θsin αexpiu cos θsin2 α,
I2(u, v)=0αmaxdθ(cos1/2 θ sin θ)(1-cos θ)×J2v sin θsin αexpiu cos θsin2 α.
hexc/det 4Pi(u, v)=12π02πdϕ|E1(u, v, ϕ)+E2(u, v, ϕ)|2
=4A2[(Re I0)2+2(Im I1)2+(Re I2)2],
E2(u, v, ϕ)=1000-1000-1E1(-u, v, -ϕ).
hexcSWM(z)=Iconstcos2(k0z+φ),
hexcI5M(z)=Iconst0αmaxdθ sin θ cos2(k0z cos θ).
hexcI5M(z)=Iconst0R02πdvdϕ v|E1(u, v, ϕ)+E2(u, v, ϕ)|2.
h4Pi(r, z)c(r)hl(z).
hl(z)hpeak(z)l(z).
ce=Ll-1,
00c00=l0l-1l-200l1l0l-1l-20l2l1l0l-1l-20l2l1l0l-100l2l1l0 l-2-1l-1-1l0-1l1-1l2-1.
dr=soslr-s.
F(k)=H*(k)|H(k)|2+μ G(k),
Fp(k)=G(k)/L(k).

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