Abstract

It is known that signal level in single-, two- and three-photon confocal fluorescence microscopy increases with the size of the detector. Here we evaluate the signal-to-noise and the signal-to-background criteria for these microscopes. We investigate the effect of pinhole size on their ability to detect a weakly fluorescent point object in the presence of a uniformly fluorescence background. Numerical results based on a paraxial approximation theory show that optimization of these criteria gives an optimal value for pinhole size, which results in an improved imaging performance. The resulting improvement in noise performance, compared with the use of a large detector, is greater for three-photon than for two-photon confocal fluorescence microscopes.

© 1999 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, London, 1984).
  2. T. Wilson, Confocal Microscopy (Academic, London, 1990).
  3. M. Gu, Principles of Three-dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).
  4. J. B. Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, New York, 1994).
  5. P. C. Cheng, ed., Computer-Assisted Multidimensional Microscopies (Springer, New York, 1993).
  6. A. Kriete, ed., Visualization in Biomedical Microscopies, (Verlagsgesellschaft, Weinheim, Germany, 1992).
  7. C. J. R. Sheppard, R. Kompfner, “Resonant scanning optical microscope,” Appl. Opt. 17, 2879–2882 (1978).
    [CrossRef] [PubMed]
  8. W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  9. S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
    [CrossRef] [PubMed]
  10. 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]
  11. T. Wilson, A. R. Carlini, “Three-dimensional imaging in confocal imaging system with finite sized detectors,” J. Microsc. 149, 51–66 (1988).
    [CrossRef]
  12. C. J. R. Sheppard, C. J. Cogswell, M. Gu, “Signal strength and noise in confocal microscopy: factors influencing selection of an optimum detector aperture,” Scanning 13, 233–240 (1991).
    [CrossRef]
  13. W. W. Webb, K. S. Wells, D. R. Sandison, J. Strickler, Optical Microscopy for Biology (Wiley-Liss, New York, 1990).
  14. D. R. Sandison, W. W. Webb, “Background rejection and signal-to-noise optimization in confocal and alternative fluorescence microscopes,” Appl. Opt. 33, 603–615 (1994).
    [CrossRef] [PubMed]
  15. D. R. Sandison, D. W. Piston, W. W. Webb, “Background rejection and optimization of signal-to-noise in confocal microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological Specimens, J. K. Stevens, L. R. Mills, J. E. Trogadis, eds. (Academic, San Diego, Calif., 1994), Chap. 2, pp. 29–46.
    [CrossRef]
  16. D. R. Sandison, D. W. Piston, R. M. Williams, W. W. Webb, “Quantitative comparison of background rejection, signal-to-noise ratio, and resolution in confocal and full-field laser scanning microscopes,” Appl. Opt. 34, 3576–3587 (1995).
    [CrossRef] [PubMed]
  17. M. Gu, C. J. R. Sheppard, “Effects of finite-sized detector on the OTF of confocal fluorescent microscopy,” Optik 89, 65–69 (1991).
  18. M. Gu, C. J. R. Sheppard, “Effects of a finite-sized pinhole on 3-D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
    [CrossRef]
  19. C. J. R. Sheppard, “Image formation in three-photon fluorescence microscopy,” Bioimaging 4, 124–128 (1996).
    [CrossRef]
  20. M. Gu, X. S. Gan, “Effect of the detector size and the fluorescence wavelength on the resolution of three- and two-photon confocal microscopy,” Bioimaging 4, 129–137 (1996).
    [CrossRef]
  21. M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
    [CrossRef]
  22. X. S. Gan, C. J. R. Sheppard, “Detectability: a new criterion for evaluation of the confocal microscope,” Scanning 15, 187–192 (1993).
    [CrossRef]
  23. C.-M. Wang, S. E. Fraser, “The resolution improvement in two-photon laser scanning microscopy,” in Digest of OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997), p. 154.
  24. C. J. R. Sheppard, X. S. Gan, M. Gu, M. Roy, “Noise in confocal microscopes,” in The Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 363–371.
    [CrossRef]

1996 (3)

C. J. R. Sheppard, “Image formation in three-photon fluorescence microscopy,” Bioimaging 4, 124–128 (1996).
[CrossRef]

M. Gu, X. S. Gan, “Effect of the detector size and the fluorescence wavelength on the resolution of three- and two-photon confocal microscopy,” Bioimaging 4, 129–137 (1996).
[CrossRef]

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

1995 (2)

1994 (1)

1993 (2)

X. S. Gan, C. J. R. Sheppard, “Detectability: a new criterion for evaluation of the confocal microscope,” Scanning 15, 187–192 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of a finite-sized pinhole on 3-D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
[CrossRef]

1992 (1)

1991 (2)

C. J. R. Sheppard, C. J. Cogswell, M. Gu, “Signal strength and noise in confocal microscopy: factors influencing selection of an optimum detector aperture,” Scanning 13, 233–240 (1991).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of finite-sized detector on the OTF of confocal fluorescent microscopy,” Optik 89, 65–69 (1991).

1990 (1)

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

1988 (1)

T. Wilson, A. R. Carlini, “Three-dimensional imaging in confocal imaging system with finite sized detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

1978 (1)

Bahlmann, K.

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

Carlini, A. R.

T. Wilson, A. R. Carlini, “Three-dimensional imaging in confocal imaging system with finite sized detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

Cogswell, C. J.

C. J. R. Sheppard, C. J. Cogswell, M. Gu, “Signal strength and noise in confocal microscopy: factors influencing selection of an optimum detector aperture,” Scanning 13, 233–240 (1991).
[CrossRef]

Denk, W.

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

Fraser, S. E.

C.-M. Wang, S. E. Fraser, “The resolution improvement in two-photon laser scanning microscopy,” in Digest of OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997), p. 154.

Gan, X. S.

M. Gu, X. S. Gan, “Effect of the detector size and the fluorescence wavelength on the resolution of three- and two-photon confocal microscopy,” Bioimaging 4, 129–137 (1996).
[CrossRef]

X. S. Gan, C. J. R. Sheppard, “Detectability: a new criterion for evaluation of the confocal microscope,” Scanning 15, 187–192 (1993).
[CrossRef]

C. J. R. Sheppard, X. S. Gan, M. Gu, M. Roy, “Noise in confocal microscopes,” in The Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 363–371.
[CrossRef]

Gryczynski, I.

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

Gu, M.

M. Gu, X. S. Gan, “Effect of the detector size and the fluorescence wavelength on the resolution of three- and two-photon confocal microscopy,” Bioimaging 4, 129–137 (1996).
[CrossRef]

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of a finite-sized pinhole on 3-D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (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, C. J. Cogswell, M. Gu, “Signal strength and noise in confocal microscopy: factors influencing selection of an optimum detector aperture,” Scanning 13, 233–240 (1991).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of finite-sized detector on the OTF of confocal fluorescent microscopy,” Optik 89, 65–69 (1991).

C. J. R. Sheppard, X. S. Gan, M. Gu, M. Roy, “Noise in confocal microscopes,” in The Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 363–371.
[CrossRef]

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

Hell, S. W.

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

Kompfner, R.

Lakowicz, J. R.

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

Malak, H.

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

Piston, D. W.

D. R. Sandison, D. W. Piston, R. M. Williams, W. W. Webb, “Quantitative comparison of background rejection, signal-to-noise ratio, and resolution in confocal and full-field laser scanning microscopes,” Appl. Opt. 34, 3576–3587 (1995).
[CrossRef] [PubMed]

D. R. Sandison, D. W. Piston, W. W. Webb, “Background rejection and optimization of signal-to-noise in confocal microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological Specimens, J. K. Stevens, L. R. Mills, J. E. Trogadis, eds. (Academic, San Diego, Calif., 1994), Chap. 2, pp. 29–46.
[CrossRef]

Roy, M.

C. J. R. Sheppard, X. S. Gan, M. Gu, M. Roy, “Noise in confocal microscopes,” in The Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 363–371.
[CrossRef]

Sandison, D. R.

D. R. Sandison, D. W. Piston, R. M. Williams, W. W. Webb, “Quantitative comparison of background rejection, signal-to-noise ratio, and resolution in confocal and full-field laser scanning microscopes,” Appl. Opt. 34, 3576–3587 (1995).
[CrossRef] [PubMed]

D. R. Sandison, W. W. Webb, “Background rejection and signal-to-noise optimization in confocal and alternative fluorescence microscopes,” Appl. Opt. 33, 603–615 (1994).
[CrossRef] [PubMed]

D. R. Sandison, D. W. Piston, W. W. Webb, “Background rejection and optimization of signal-to-noise in confocal microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological Specimens, J. K. Stevens, L. R. Mills, J. E. Trogadis, eds. (Academic, San Diego, Calif., 1994), Chap. 2, pp. 29–46.
[CrossRef]

W. W. Webb, K. S. Wells, D. R. Sandison, J. Strickler, Optical Microscopy for Biology (Wiley-Liss, New York, 1990).

Schrader, M.

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard, “Image formation in three-photon fluorescence microscopy,” Bioimaging 4, 124–128 (1996).
[CrossRef]

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of a finite-sized pinhole on 3-D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
[CrossRef]

X. S. Gan, C. J. R. Sheppard, “Detectability: a new criterion for evaluation of the confocal microscope,” Scanning 15, 187–192 (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, C. J. Cogswell, M. Gu, “Signal strength and noise in confocal microscopy: factors influencing selection of an optimum detector aperture,” Scanning 13, 233–240 (1991).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of finite-sized detector on the OTF of confocal fluorescent microscopy,” Optik 89, 65–69 (1991).

C. J. R. Sheppard, R. Kompfner, “Resonant scanning optical microscope,” Appl. Opt. 17, 2879–2882 (1978).
[CrossRef] [PubMed]

C. J. R. Sheppard, X. S. Gan, M. Gu, M. Roy, “Noise in confocal microscopes,” in The Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 363–371.
[CrossRef]

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

Soini, M.

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

Strickler, J.

W. W. Webb, K. S. Wells, D. R. Sandison, J. Strickler, Optical Microscopy for Biology (Wiley-Liss, New York, 1990).

Strickler, J. H.

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

Tannous, T.

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

Wang, C.-M.

C.-M. Wang, S. E. Fraser, “The resolution improvement in two-photon laser scanning microscopy,” in Digest of OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997), p. 154.

Webb, W. W.

D. R. Sandison, D. W. Piston, R. M. Williams, W. W. Webb, “Quantitative comparison of background rejection, signal-to-noise ratio, and resolution in confocal and full-field laser scanning microscopes,” Appl. Opt. 34, 3576–3587 (1995).
[CrossRef] [PubMed]

D. R. Sandison, W. W. Webb, “Background rejection and signal-to-noise optimization in confocal and alternative fluorescence microscopes,” Appl. Opt. 33, 603–615 (1994).
[CrossRef] [PubMed]

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

W. W. Webb, K. S. Wells, D. R. Sandison, J. Strickler, Optical Microscopy for Biology (Wiley-Liss, New York, 1990).

D. R. Sandison, D. W. Piston, W. W. Webb, “Background rejection and optimization of signal-to-noise in confocal microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological Specimens, J. K. Stevens, L. R. Mills, J. E. Trogadis, eds. (Academic, San Diego, Calif., 1994), Chap. 2, pp. 29–46.
[CrossRef]

Wells, K. S.

W. W. Webb, K. S. Wells, D. R. Sandison, J. Strickler, Optical Microscopy for Biology (Wiley-Liss, New York, 1990).

Williams, R. M.

Wilson, T.

T. Wilson, A. R. Carlini, “Three-dimensional imaging in confocal imaging system with finite sized detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

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

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

Appl. Opt. (3)

Bioimaging (2)

C. J. R. Sheppard, “Image formation in three-photon fluorescence microscopy,” Bioimaging 4, 124–128 (1996).
[CrossRef]

M. Gu, X. S. Gan, “Effect of the detector size and the fluorescence wavelength on the resolution of three- and two-photon confocal microscopy,” Bioimaging 4, 129–137 (1996).
[CrossRef]

J. Biomed. Opt. (1)

S. W. Hell, K. Bahlmann, M. Schrader, M. Soini, H. Malak, I. Gryczynski, J. R. Lakowicz, “Three-photon excitation in fluorescence microscopy,” J. Biomed. Opt. 1, 71–74 (1996).
[CrossRef] [PubMed]

J. Microsc. (1)

T. Wilson, A. R. Carlini, “Three-dimensional imaging in confocal imaging system with finite sized detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

J. Mod. Opt. (1)

M. Gu, C. J. R. Sheppard, “Effects of a finite-sized pinhole on 3-D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
[CrossRef]

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

Opt. Commun. (1)

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

Optik (1)

M. Gu, C. J. R. Sheppard, “Effects of finite-sized detector on the OTF of confocal fluorescent microscopy,” Optik 89, 65–69 (1991).

Scanning (2)

X. S. Gan, C. J. R. Sheppard, “Detectability: a new criterion for evaluation of the confocal microscope,” Scanning 15, 187–192 (1993).
[CrossRef]

C. J. R. Sheppard, C. J. Cogswell, M. Gu, “Signal strength and noise in confocal microscopy: factors influencing selection of an optimum detector aperture,” Scanning 13, 233–240 (1991).
[CrossRef]

Science (1)

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

Other (10)

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

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

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

J. B. Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, New York, 1994).

P. C. Cheng, ed., Computer-Assisted Multidimensional Microscopies (Springer, New York, 1993).

A. Kriete, ed., Visualization in Biomedical Microscopies, (Verlagsgesellschaft, Weinheim, Germany, 1992).

W. W. Webb, K. S. Wells, D. R. Sandison, J. Strickler, Optical Microscopy for Biology (Wiley-Liss, New York, 1990).

D. R. Sandison, D. W. Piston, W. W. Webb, “Background rejection and optimization of signal-to-noise in confocal microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological Specimens, J. K. Stevens, L. R. Mills, J. E. Trogadis, eds. (Academic, San Diego, Calif., 1994), Chap. 2, pp. 29–46.
[CrossRef]

C.-M. Wang, S. E. Fraser, “The resolution improvement in two-photon laser scanning microscopy,” in Digest of OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997), p. 154.

C. J. R. Sheppard, X. S. Gan, M. Gu, M. Roy, “Noise in confocal microscopes,” in The Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), pp. 363–371.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

S/N ratio in confocal 1p-, 2p-, and 3p-fluoresence microscopes with pinhole normalized radius v d . In each case the S/N ratio is optimized for a particular pinhole size.

Fig. 2
Fig. 2

S/B ratio in confocal 1p-, 2p-, and 3p-fluoresence microscopes with pinhole normalized radius v d . The S/B ratio decreases with pinhole size.

Equations (11)

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

v=2πnλf r sin α
u=8πnλf z sin2α/2
Cl, s=F3|hv/β, u/β|2N3F3|hv, u|2F2Dv,
F3|hv, u|2=1lRe1-|s|l+l221/2.
Dv=1,v<vd0,otherwise,
vd=2πrd sin αMλf
F2Dv=vdJ1vdll.
ηpoint=1-J02vd-J12vd.
ηvolume  vdCl=0, s=0.
S/N=ηpointηvolume.
S/B=ηpointηvolume.

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