Abstract

We describe the three-dimensional (3-D) image formation and data acquisition in a stage scanning 4Pi confocal fluorescence microscope with the use of two-photon excitation. The 3-D point-spread functions of the 4Pi confocal and regular confocal microscope are measured and compared. Particular emphasis is given to the data acquisition procedure. 4Pi confocal microscopy results in a point-spread function that is 4 times sharper than that of a regular confocal microscope, ultimately leading to superior 3-D imaging of translucent fluorescent specimens. For a two-photon excitation wavelength of approximately 800 nm, we obtain an axial resolution of 140 nm.

© 1997 Optical Society of America

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References

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  1. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  2. T. Wilson, Confocal Microscopy (Academic, London, 1990).
  3. J. Pawley, Handbook of Biological Confocal Microscopy (Plenum, New York, 1995).
  4. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).
  5. 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. 157, 3–20 (1990).
    [CrossRef]
  6. S. 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]
  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. W. Hell, “Improvement of lateral resolution in far-field light microscopy using two-photon excitation with offset beams,” Opt. Commun. 106, 19–22 (1994).
    [CrossRef]
  9. W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
    [CrossRef] [PubMed]
  10. H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
    [CrossRef]
  11. M. Müller, G. J. Brakenhoff, “Using offset interfering beams for improved resolution in confocal imaging: the potential of the PSAF-technique,” Bioimaging 4, 179–186 (1996).
    [CrossRef]
  12. M. Vaez-Iravani, D. I. Kavaldjiev, “Resolution beyond the diffraction limit using frequency-domain field confinement in scanning microscopy,” Ultramicrosc. 61, 105–110 (1995).
    [CrossRef]
  13. M. Gu, C. J. R. Sheppard, “Three-dimensional transfer functions in 4Pi confocal microscopes,” J. Opt. Soc. Am. A 11, 1619–1627 (1994).
    [CrossRef]
  14. M. Schrader, S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc. 183, 189–193 (1996).
    [CrossRef]
  15. P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
    [CrossRef]
  16. M. Schrader, M. Kozubek, S. W. Hell, T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
    [CrossRef] [PubMed]
  17. Y. Kawata, K. Fujita, O. Nakamura, S. Kawata, “4Pi confocal optical system with phase conjugation,” Opt. Lett. 21, 1415–1417 (1996).
    [CrossRef] [PubMed]
  18. C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. Am. A 4, 1354–1360 (1987).
    [CrossRef]
  19. P. J. Shaw, “Comparison of wide-field/deconvolution and confocal microscopy for 3D imaging,” in Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 373–385.
    [CrossRef]
  20. M. Schrader, S. W. Hell, H. T. M. van der Voort, “Potential of confocal microscopes to resolve in the 50–100 nm range,” Appl. Phys. Lett. 69, 3644–3646 (1996).
    [CrossRef]
  21. S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with resolution in the 100-nm range,” J. Microsc. 187, 1–5 (1997).
    [CrossRef] [PubMed]

1997

M. Schrader, M. Kozubek, S. W. Hell, T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
[CrossRef] [PubMed]

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with resolution in the 100-nm range,” J. Microsc. 187, 1–5 (1997).
[CrossRef] [PubMed]

1996

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Potential of confocal microscopes to resolve in the 50–100 nm range,” Appl. Phys. Lett. 69, 3644–3646 (1996).
[CrossRef]

Y. Kawata, K. Fujita, O. Nakamura, S. Kawata, “4Pi confocal optical system with phase conjugation,” Opt. Lett. 21, 1415–1417 (1996).
[CrossRef] [PubMed]

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

H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
[CrossRef]

M. Müller, G. J. Brakenhoff, “Using offset interfering beams for improved resolution in confocal imaging: the potential of the PSAF-technique,” Bioimaging 4, 179–186 (1996).
[CrossRef]

1995

M. Vaez-Iravani, D. I. Kavaldjiev, “Resolution beyond the diffraction limit using frequency-domain field confinement in scanning microscopy,” Ultramicrosc. 61, 105–110 (1995).
[CrossRef]

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

1994

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

S. W. Hell, “Improvement of lateral resolution in far-field light microscopy using two-photon excitation with offset beams,” Opt. Commun. 106, 19–22 (1994).
[CrossRef]

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. 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]

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. 157, 3–20 (1990).
[CrossRef]

1987

Bailey, B.

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]

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. 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. 157, 3–20 (1990).
[CrossRef]

Brakenhoff, G. J.

M. Müller, G. J. Brakenhoff, “Using offset interfering beams for improved resolution in confocal imaging: the potential of the PSAF-technique,” Bioimaging 4, 179–186 (1996).
[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. 157, 3–20 (1990).
[CrossRef]

Carrington, W. A.

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Cremer, C.

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

Farkas, D. L.

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]

Fay, F. S.

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Fogarty, K. E.

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Fujita, K.

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).

Hänninen, P. E.

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

Hell, S.

S. 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]

Hell, S. W.

M. Schrader, M. Kozubek, S. W. Hell, T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
[CrossRef] [PubMed]

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with resolution in the 100-nm range,” J. Microsc. 187, 1–5 (1997).
[CrossRef] [PubMed]

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Potential of confocal microscopes to resolve in the 50–100 nm range,” Appl. Phys. Lett. 69, 3644–3646 (1996).
[CrossRef]

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

H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
[CrossRef]

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

S. W. Hell, “Improvement of lateral resolution in far-field light microscopy using two-photon excitation with offset beams,” Opt. Commun. 106, 19–22 (1994).
[CrossRef]

Isenberg, G.

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Kano, H.

H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
[CrossRef]

Kavaldjiev, D. I.

M. Vaez-Iravani, D. I. Kavaldjiev, “Resolution beyond the diffraction limit using frequency-domain field confinement in scanning microscopy,” Ultramicrosc. 61, 105–110 (1995).
[CrossRef]

Kawata, S.

Kawata, Y.

Kozubek, M.

Lanni, F.

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]

Lynch, R. M.

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

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. 157, 3–20 (1990).
[CrossRef]

Matthews, H. J.

Moore, E. D. W.

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Müller, M.

M. Müller, G. J. Brakenhoff, “Using offset interfering beams for improved resolution in confocal imaging: the potential of the PSAF-technique,” Bioimaging 4, 179–186 (1996).
[CrossRef]

Nakamura, O.

Pawley, J.

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

Salo, J.

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

Schrader, M.

M. Schrader, M. Kozubek, S. W. Hell, T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
[CrossRef] [PubMed]

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with resolution in the 100-nm range,” J. Microsc. 187, 1–5 (1997).
[CrossRef] [PubMed]

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Potential of confocal microscopes to resolve in the 50–100 nm range,” Appl. Phys. Lett. 69, 3644–3646 (1996).
[CrossRef]

H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
[CrossRef]

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

Shaw, P. J.

P. J. Shaw, “Comparison of wide-field/deconvolution and confocal microscopy for 3D imaging,” in Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 373–385.
[CrossRef]

Sheppard, C. J. R.

Soini, E.

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

Stelzer, E. H. K.

S. 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]

Taylor, D. L.

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]

Vaez-Iravani, M.

M. Vaez-Iravani, D. I. Kavaldjiev, “Resolution beyond the diffraction limit using frequency-domain field confinement in scanning microscopy,” Ultramicrosc. 61, 105–110 (1995).
[CrossRef]

van der Voort, H. T. M.

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with resolution in the 100-nm range,” J. Microsc. 187, 1–5 (1997).
[CrossRef] [PubMed]

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Potential of confocal microscopes to resolve in the 50–100 nm range,” Appl. Phys. Lett. 69, 3644–3646 (1996).
[CrossRef]

H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
[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. 157, 3–20 (1990).
[CrossRef]

van Kempen, G.

H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
[CrossRef]

Wilson, T.

M. Schrader, M. Kozubek, S. W. Hell, T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
[CrossRef] [PubMed]

T. Wilson, Confocal Microscopy (Academic, London, 1990).

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

Appl. Phys. Lett.

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, C. Cremer, “2-photon excitation 4pi confocal microscope—enhanced axial resolution microscope for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Potential of confocal microscopes to resolve in the 50–100 nm range,” Appl. Phys. Lett. 69, 3644–3646 (1996).
[CrossRef]

Bioimaging

H. Kano, H. T. M. van der Voort, M. Schrader, G. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996).
[CrossRef]

M. Müller, G. J. Brakenhoff, “Using offset interfering beams for improved resolution in confocal imaging: the potential of the PSAF-technique,” Bioimaging 4, 179–186 (1996).
[CrossRef]

J. Microsc.

M. Schrader, S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc. 183, 189–193 (1996).
[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. 157, 3–20 (1990).
[CrossRef]

S. W. Hell, M. Schrader, H. T. M. van der Voort, “Far-field fluorescence microscopy with resolution in the 100-nm range,” J. Microsc. 187, 1–5 (1997).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Nature (London)

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]

Opt. Commun.

S. W. Hell, “Improvement of lateral resolution in far-field light microscopy using two-photon excitation with offset beams,” Opt. Commun. 106, 19–22 (1994).
[CrossRef]

S. 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]

Opt. Lett.

Science

W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution in three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Ultramicrosc.

M. Vaez-Iravani, D. I. Kavaldjiev, “Resolution beyond the diffraction limit using frequency-domain field confinement in scanning microscopy,” Ultramicrosc. 61, 105–110 (1995).
[CrossRef]

Other

P. J. Shaw, “Comparison of wide-field/deconvolution and confocal microscopy for 3D imaging,” in Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 373–385.
[CrossRef]

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

T. Wilson, Confocal Microscopy (Academic, London, 1990).

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

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

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Figures (6)

Fig. 1
Fig. 1

4Pi-confocal microscope. Laser light coming from a pinhole is split into two parts by a beam splitter (BSD), thus illuminating simultaneously two opposing high-aperture lenses. The light originating from the sample is collected by the lens L2 and directed toward a detector pinhole. The relative phase of the illumination wave fronts is adjusted by means of a piezoelectrically driven mirror. The lens L2 is fixed and the lens L1 is adjusted with a precision of 10–20 nm with respect to L2. The sample is scanned with a piezoelectric stage of high precision to render a 3-D image.

Fig. 2
Fig. 2

Calculated PSF of a single lens (above) compared with calculated PSF of a 4Pi arrangement (below). 4Pi microscopy makes use of two opposing objective lenses of high numerical aperture (here N.A. = 1.4 oil and λ = 500 nm) with a common focus. The coherent addition of the electric fields yields a steep main maximum and two lobes in the axial direction. The center panels outline the focal intensities in a plane that contains the optical axis, whereas the right-hand panels show the corresponding surface plots. As with the single lens PSF’s, the 4Pi PSF gives the relative probability that a photon from a pinhole arrives at a certain point in the focal region when propagated simultaneously through both lenses. The 4Pi PSF is shown for constructive interference of the illuminating waves at the focal point.

Fig. 3
Fig. 3

Axial responses through the bead images (PSF’s) of Fig. 5: a, confocal; b, 4Pi confocal; c, lobe function l(r, z); and d, peak function hpeak. The peak function quantifies the axial resolution of a TPE 4Pi confocal microscope with deconvolution by the inverse of l(r, z). A comparison of view d with view a shows a fourfold increase of the axial resolution in 4Pi confocal microscopy.

Fig. 4
Fig. 4

Block diagram of control and data acquisition system for 4Pi microscope.

Fig. 5
Fig. 5

Axial image of 115-nm bead, which, as a good approximation, corresponds to (top) PSF of the confocal microscope, (middle) 4Pi confocal microscope, and (bottom) 4Pi confocal microscope after inverse point filtering.

Fig. 6
Fig. 6

Axial slice through 3-D data stack of clustered beads as performed with confocal microscope (left-hand panel) and 4Pi confocal microscope (right-hand panel). The intensity profiles are performed along the marked line in the image. The 4Pi confocal image of the same object is fundamentally superior in signal and in resolution.

Equations (7)

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

hu, v=c01Pρexp-12iuρ2J0vρρdρ,
v=2π/λnr sin α,  u=4π/λnz sin2α/2
hconf=hillu, v×hdetu/β, v/β,
hill,4Pi=h1,illu, v+h2,ill-u, v.
h4Pir, z2=lr, zzhpeakr, z2.
hpeakr, z2h4Pir, z2zl-1z.
Ir, z=hpeakr, z2zOr, z=h4Pir, z2zOr, zzl-1r, z.

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