Abstract

We study the behavior of the point-spread function (PSF) of the confocal scanning optical microscope (CSOM) when the available optical energy density from the sample plane is low (<7.5 microJoule/micrometers2). The PSF profile is analyzed under three photon-limited imaging conditions: (1) reflection-type CSOM with a weak source and a perfectly reflecting sample, (2) reflection-type CSOM with a strong illumination source and a weak sample, and (3) fluorescence CSOM with a weak fluorescent sample. Linfoot’s image quality criteria of fidelity, structural content, and correlation quality are used to assess the reproducibility of the PSF profile as a function of the photon number. Low photon numbers yield a PSF profile that is difficult to maintain from one location in the sample plane to another. The optical sectioning capability of the CSOM was found to deteriorate more quickly against light power reduction than its transverse resolving power. The signal-to-noise ratio of the scanned CSOM image improves exponentially with the photon number from the sample plane. The noise that is generated by an unstable PSF has an average amplitude that decreases exponentially with the photon number and is significant only at low photon numbers. The CSOM image quality deteriorates because of spurious high-frequency components, degradation in the PSF dynamic range, and varying resolving power.

© 2002 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. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, 1999).
  4. A. J. den Dekker, A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
    [CrossRef]
  5. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  6. F. Huck, C. Fales, N. Haylo, R. Samms, K. Stacey, “Image gathering and processing: information and fidelity,” J. Opt. Soc. Am. A 2, 1644–1666 (1985).
    [CrossRef] [PubMed]
  7. M. Nazario, C. Saloma, “Signal recovery in sinusoid crossing sampling using the minimum negativity constraint,” Appl. Opt. 37, 2953–2963 (1998).
    [CrossRef]
  8. C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
    [CrossRef] [PubMed]
  9. C. Palmes-Saloma, C. Saloma, “Long-depth imaging of specific gene expressions in wholemount mouse embryos with single photon excitation confocal fluorescence microscope and FISH,” J. Struct. Biol. 131, 56–66 (2000).
    [CrossRef] [PubMed]
  10. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1988).
  11. A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
    [CrossRef]
  12. M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
    [CrossRef]

2000 (1)

C. Palmes-Saloma, C. Saloma, “Long-depth imaging of specific gene expressions in wholemount mouse embryos with single photon excitation confocal fluorescence microscope and FISH,” J. Struct. Biol. 131, 56–66 (2000).
[CrossRef] [PubMed]

1999 (2)

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[CrossRef]

M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

1998 (2)

M. Nazario, C. Saloma, “Signal recovery in sinusoid crossing sampling using the minimum negativity constraint,” Appl. Opt. 37, 2953–2963 (1998).
[CrossRef]

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

1997 (1)

1985 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, 1999).

den Dekker, A. J.

Fales, C.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1988).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Haylo, N.

Huck, F.

Kolobov, M.

M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

Kondoh, H.

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

Nazario, M.

Palmes-Saloma, C.

C. Palmes-Saloma, C. Saloma, “Long-depth imaging of specific gene expressions in wholemount mouse embryos with single photon excitation confocal fluorescence microscope and FISH,” J. Struct. Biol. 131, 56–66 (2000).
[CrossRef] [PubMed]

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1988).

Saloma, C.

C. Palmes-Saloma, C. Saloma, “Long-depth imaging of specific gene expressions in wholemount mouse embryos with single photon excitation confocal fluorescence microscope and FISH,” J. Struct. Biol. 131, 56–66 (2000).
[CrossRef] [PubMed]

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

M. Nazario, C. Saloma, “Signal recovery in sinusoid crossing sampling using the minimum negativity constraint,” Appl. Opt. 37, 2953–2963 (1998).
[CrossRef]

Samms, R.

Sheppard, C. J. R.

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

Stacey, K.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1988).

van den Bos, A.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1988).

Wilson, T.

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

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, 1999).

Zeilinger, A.

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

J. Struct. Biol. (1)

C. Palmes-Saloma, C. Saloma, “Long-depth imaging of specific gene expressions in wholemount mouse embryos with single photon excitation confocal fluorescence microscope and FISH,” J. Struct. Biol. 131, 56–66 (2000).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[CrossRef]

M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

Other (5)

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1988).

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

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

M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, 1999).

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Figures (5)

Fig. 1
Fig. 1

Optical setup used for the CSOM (unit magnification).

Fig. 2
Fig. 2

Normalized PSF profile (in logarithmic scale) for different N e values: (a) transverse and (b) axial. Values considered: N e = 103 (crosses), 104 (crossed squares), 105 (open squares), 106 (filled squares), 107 (open circles), and 108 (filled circles). Each data point represents the average of 400 trials. The theoretical curves are presented as solid curves.

Fig. 3
Fig. 3

Transverse PSF. Dependence of F (filled squares), Q (open squares) and C (open circles) with N e : (a) reflection CSOM with a weak source and a perfectly reflecting sample (λ e = 632.8 nm), (b) reflection CSOM with a strong source and a weak sample (λ e = 632.8 nm), and (c) fluorescence CSOM with a weak sample (λ e = 432 nm and λ f = 515 nm).

Fig. 4
Fig. 4

Axial PSF. Dependence of F (solid squares), Q (open squares) and C (open circles) with N e : (a) reflection CSOM with a weak source and a perfectly reflecting sample (λ e = 632.8 nm), (b) reflection CSOM with a strong source and a weak sample (λ e = 632.8 nm), and (c) fluorescence CSOM with a weak sample (λ e = 432 nm and λ f = 515 nm).

Fig. 5
Fig. 5

Image SNR as a function of N e : (a) transverse image of sample at u = 0, and (b) axial image for a reflection CSOM with a weak source (crosses) or a weak sample (squares), and a fluorescence CSOM with a weak sample (open circles). The solid curves in 5(a) and 5(b) are described by SNR = 8.775 exp(2.51N e ) and SNR = 18.628 exp(2.55N e ), respectively.

Equations (2)

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U0, v=Uo2J1vv,
Iu, 0=Io sinc2u/4,

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