Abstract

We investigate three-dimensional transfer functions in order to understand image formation in the recently proposed 4Pi confocal microscope [ J. Opt. Soc. Am. A9, 2159 ( 1992);Opt. Commun.93, 277 ( 1992)]. Both nonfluorescence and fluorescence imaging methods are considered, and the effects of apodization functions are taken into account. It is shown that for a 4Pi confocal system of finite-sized aperture the cutoff spatial frequency in the axial direction is larger than that in the transverse direction; this behavior is opposite that of conventional confocal systems, explaining the observation of high axial resolution in 4Pi confocal systems. In addition, the three-dimensional optical transfer function for a conventional confocal fluorescence microscope of high aperture is presented.

© 1994 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1994 (1)

1993 (1)

C. J. R. Sheppard, M. Gu, “Modelling of three-dimensional fluorescence images of muscle fibres—an application of the three-dimensional optical transfer function,” J. Microsc. 169, 339–345 (1993).
[CrossRef]

1992 (3)

1991 (3)

S. Kawata, R. Arimoto, O. Nakamura, “Three-dimensional optical-transfer-function analysis for a laser-scan fluorescence microscope with an extended detector,” J. Opt. Soc. Am. A 8, 171–176 (1991).
[CrossRef]

C. J. R. Sheppard, Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik 87, 129–132 (1991).

M. Gu, C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247–2263 (1991).
[CrossRef]

1990 (2)

1989 (2)

S. Kimura, C. Munakata, “Calculation of three-dimensional optical transfer function for a confocal scanning fluorescent microscope,” J. Opt. Soc. Am. A 6, 1015–1019 (1989).
[CrossRef]

C. J. Cogswell, C. J. R. Sheppard, “Imaging using confocal brightfield techniques,” Inst. Phys. Conf. Ser. 14, 633–638 (1989).

1987 (1)

1986 (1)

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik 74, 128–129 (1986).

1967 (1)

1964 (1)

Arimoto, R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Cogswell, C. J.

C. J. Cogswell, C. J. R. Sheppard, “Imaging using confocal brightfield techniques,” Inst. Phys. Conf. Ser. 14, 633–638 (1989).

C. J. R. Sheppard, C. J. Cogswell, “Reflection and transmission confocal microscopy,” in Optics in Medicine, Biology and Environmental Research, G. von Bally, S. Khanna, eds. (Elsevier, Amsterdam, 1993), pp. 310–315.

Frieden, B. R.

Gong, Y.

C. J. R. Sheppard, Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik 87, 129–132 (1991).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Gu, M.

C. J. R. Sheppard, M. Gu, Y. Kawata, S. Kawata, “Three-dimensional transfer functions for high-aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Modelling of three-dimensional fluorescence images of muscle fibres—an application of the three-dimensional optical transfer function,” J. Microsc. 169, 339–345 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Confocal fluorescent microscopy with a finite-sized circular detector,” J. Opt. Soc. Am. A 9, 151–153 (1992).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247–2263 (1991).
[CrossRef]

C. J. R. Sheppard, M. Gu, “3-D transfer functions in confocal scanning microscopy,” in Visualization in Biomedical Microscopies, A. Kriete, ed. (VCH, Weinheim, Germany, 1992), pp. 251–282.

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]

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

S. Hell, European Patent Application91121368.4 (1990/1992).

Kawata, S.

Kawata, Y.

Kimura, S.

Matthews, H. J.

McCutchen, C. W.

Munakata, C.

Nakamura, O.

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, Y. Kawata, S. Kawata, “Three-dimensional transfer functions for high-aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Modelling of three-dimensional fluorescence images of muscle fibres—an application of the three-dimensional optical transfer function,” J. Microsc. 169, 339–345 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Confocal fluorescent microscopy with a finite-sized circular detector,” J. Opt. Soc. Am. A 9, 151–153 (1992).
[CrossRef]

C. J. R. Sheppard, Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik 87, 129–132 (1991).

M. Gu, C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247–2263 (1991).
[CrossRef]

C. J. Cogswell, C. J. R. Sheppard, “Imaging using confocal brightfield techniques,” Inst. Phys. Conf. Ser. 14, 633–638 (1989).

C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. Am. A 4, 1354–1360 (1987).
[CrossRef]

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik 74, 128–129 (1986).

C. J. R. Sheppard, C. J. Cogswell, “Reflection and transmission confocal microscopy,” in Optics in Medicine, Biology and Environmental Research, G. von Bally, S. Khanna, eds. (Elsevier, Amsterdam, 1993), pp. 310–315.

C. J. R. Sheppard, “Scanning optical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.

C. J. R. Sheppard, M. Gu, “3-D transfer functions in confocal scanning microscopy,” in Visualization in Biomedical Microscopies, A. Kriete, ed. (VCH, Weinheim, Germany, 1992), pp. 251–282.

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]

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Appl. Opt. (1)

Inst. Phys. Conf. Ser. (1)

C. J. Cogswell, C. J. R. Sheppard, “Imaging using confocal brightfield techniques,” Inst. Phys. Conf. Ser. 14, 633–638 (1989).

J. Microsc. (1)

C. J. R. Sheppard, M. Gu, “Modelling of three-dimensional fluorescence images of muscle fibres—an application of the three-dimensional optical transfer function,” J. Microsc. 169, 339–345 (1993).
[CrossRef]

J. Mod. Opt. (1)

M. Gu, C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247–2263 (1991).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (7)

Opt. Commun. (1)

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]

Optik (2)

C. J. R. Sheppard, Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik 87, 129–132 (1991).

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik 74, 128–129 (1986).

Other (6)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

S. Hell, European Patent Application91121368.4 (1990/1992).

C. J. R. Sheppard, “Scanning optical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.

C. J. R. Sheppard, C. J. Cogswell, “Reflection and transmission confocal microscopy,” in Optics in Medicine, Biology and Environmental Research, G. von Bally, S. Khanna, eds. (Elsevier, Amsterdam, 1993), pp. 310–315.

C. J. R. Sheppard, M. Gu, “3-D transfer functions in confocal scanning microscopy,” in Visualization in Biomedical Microscopies, A. Kriete, ed. (VCH, Weinheim, Germany, 1992), pp. 251–282.

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