Abstract

The three-dimensional coherent transfer function of confocal coherent anti-Stokes Raman scattering microscopy was derived theoretically. The three-dimensional optical transfer function was also derived under the weak-contrast assumption. The effect of a pinhole in front of the detector on the optical transfer function was estimated, and it was found that the cutoff frequency of the optical transfer function is independent of the pinhole. Micrometer-order spatial resolution along the optical axis was also experimentally demonstrated.

© 2001 Optical Society of America

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References

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  1. T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).
  2. W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  3. W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
    [CrossRef] [PubMed]
  4. G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
    [CrossRef] [PubMed]
  5. N. M. Sijtsema, S. D. Wouters, C. J. de Grauw, C. Otto, J. Greve, “Confocal direct imaging Raman microscope: design and applications in biology,” Appl. Spectrosc. 52, 348–355 (1998).
    [CrossRef]
  6. M. D. Duncan, J. Reintjes, T. J. Manuccia, “Scanning coherent anti-Stokes Raman microscope,” Opt. Lett. 7, 350–352 (1982).
    [CrossRef] [PubMed]
  7. M. D. Duncan, J. Reintjes, T. J. Manuccia, “Imaging biological compounds using the coherent anti-Stokes Raman scattering microscope,” Opt. Eng. 24, 352–355 (1985).
    [CrossRef]
  8. M. D. Duncan, “Molecular discrimination and contrast enhancement using a scanning coherent anti-Stokes Raman microscope,” Opt. Commun. 50, 307–312 (1984).
    [CrossRef]
  9. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  10. M. D. Levenson, S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, Orlando, Fla., 1988).
  11. M. Hashimoto, T. Araki, “Coherent anti-Stokes Raman scattering microscope,” in 18th Congress of the International Commission for Optics: Optics for the Next Millennium, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 496–497 (1999).
    [CrossRef]
  12. A. Zumbusch, G. R. Holtom, X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
    [CrossRef]
  13. N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
    [CrossRef]
  14. O. Nakamura, S. Kawata, “Three-dimensional transfer-function analysis of the tomographic capability of a confocal fluorescence microscope,” J. Opt. Soc. Am. A 7, 522–526 (1990).
    [CrossRef] [PubMed]
  15. J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent anti-Stokes Raman spectroscopy,” in Vibrational Spectra and Structure, J. R. During, ed. (Elsevier, New York, 1977), Vol. 6, Chap. 3, pp. 173–225.

1999 (1)

A. Zumbusch, G. R. Holtom, X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

1998 (1)

1994 (1)

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

1990 (3)

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

O. Nakamura, S. Kawata, “Three-dimensional transfer-function analysis of the tomographic capability of a confocal fluorescence microscope,” J. Opt. Soc. Am. A 7, 522–526 (1990).
[CrossRef] [PubMed]

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

1985 (2)

N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
[CrossRef]

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Imaging biological compounds using the coherent anti-Stokes Raman scattering microscope,” Opt. Eng. 24, 352–355 (1985).
[CrossRef]

1984 (1)

M. D. Duncan, “Molecular discrimination and contrast enhancement using a scanning coherent anti-Stokes Raman microscope,” Opt. Commun. 50, 307–312 (1984).
[CrossRef]

1982 (1)

Araki, T.

M. Hashimoto, T. Araki, “Coherent anti-Stokes Raman scattering microscope,” in 18th Congress of the International Commission for Optics: Optics for the Next Millennium, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 496–497 (1999).
[CrossRef]

Arndt-Jovin, D. J.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

de Grauw, C. J.

de Mul, F. F. M.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

Delaney, K. R.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Denk, W.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

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

Duncan, M. D.

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Imaging biological compounds using the coherent anti-Stokes Raman scattering microscope,” Opt. Eng. 24, 352–355 (1985).
[CrossRef]

M. D. Duncan, “Molecular discrimination and contrast enhancement using a scanning coherent anti-Stokes Raman microscope,” Opt. Commun. 50, 307–312 (1984).
[CrossRef]

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Scanning coherent anti-Stokes Raman microscope,” Opt. Lett. 7, 350–352 (1982).
[CrossRef] [PubMed]

Gelperin, A.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Greve, J.

N. M. Sijtsema, S. D. Wouters, C. J. de Grauw, C. Otto, J. Greve, “Confocal direct imaging Raman microscope: design and applications in biology,” Appl. Spectrosc. 52, 348–355 (1998).
[CrossRef]

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

Harvey, A. B.

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent anti-Stokes Raman spectroscopy,” in Vibrational Spectra and Structure, J. R. During, ed. (Elsevier, New York, 1977), Vol. 6, Chap. 3, pp. 173–225.

Hashimoto, M.

M. Hashimoto, T. Araki, “Coherent anti-Stokes Raman scattering microscope,” in 18th Congress of the International Commission for Optics: Optics for the Next Millennium, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 496–497 (1999).
[CrossRef]

Holtom, G. R.

A. Zumbusch, G. R. Holtom, X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

Jovin, T. M.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

Kano, S.

M. D. Levenson, S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, Orlando, Fla., 1988).

Kawata, S.

Kleinfeld, D.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Levenson, M. D.

M. D. Levenson, S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, Orlando, Fla., 1988).

Manuccia, T. J.

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Imaging biological compounds using the coherent anti-Stokes Raman scattering microscope,” Opt. Eng. 24, 352–355 (1985).
[CrossRef]

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Scanning coherent anti-Stokes Raman microscope,” Opt. Lett. 7, 350–352 (1982).
[CrossRef] [PubMed]

McDonald, J. R.

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent anti-Stokes Raman spectroscopy,” in Vibrational Spectra and Structure, J. R. During, ed. (Elsevier, New York, 1977), Vol. 6, Chap. 3, pp. 173–225.

Nakamura, O.

Nibler, J. W.

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent anti-Stokes Raman spectroscopy,” in Vibrational Spectra and Structure, J. R. During, ed. (Elsevier, New York, 1977), Vol. 6, Chap. 3, pp. 173–225.

Otto, C.

N. M. Sijtsema, S. D. Wouters, C. J. de Grauw, C. Otto, J. Greve, “Confocal direct imaging Raman microscope: design and applications in biology,” Appl. Spectrosc. 52, 348–355 (1998).
[CrossRef]

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

Puppels, G. J.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

Reintjes, J.

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Imaging biological compounds using the coherent anti-Stokes Raman scattering microscope,” Opt. Eng. 24, 352–355 (1985).
[CrossRef]

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Scanning coherent anti-Stokes Raman microscope,” Opt. Lett. 7, 350–352 (1982).
[CrossRef] [PubMed]

Robert-Nicoud, M.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

Shaub, W. M.

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent anti-Stokes Raman spectroscopy,” in Vibrational Spectra and Structure, J. R. During, ed. (Elsevier, New York, 1977), Vol. 6, Chap. 3, pp. 173–225.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Sijtsema, N. M.

Streibl, N.

Strickler, J. H.

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

Strowbridge, B. W.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Tank, D. W.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Webb, W. W.

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

Wouters, S. D.

Xie, X. S.

A. Zumbusch, G. R. Holtom, X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

Yuste, R.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Zumbusch, A.

A. Zumbusch, G. R. Holtom, X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

Appl. Spectrosc. (1)

J. Neurosci. Methods (1)

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, “Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

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

Nature (1)

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman micro-spectroscopy,” Nature 347, 301–303 (1990).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. D. Duncan, “Molecular discrimination and contrast enhancement using a scanning coherent anti-Stokes Raman microscope,” Opt. Commun. 50, 307–312 (1984).
[CrossRef]

Opt. Eng. (1)

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Imaging biological compounds using the coherent anti-Stokes Raman scattering microscope,” Opt. Eng. 24, 352–355 (1985).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Zumbusch, G. R. Holtom, X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[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 (5)

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

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

M. D. Levenson, S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, Orlando, Fla., 1988).

M. Hashimoto, T. Araki, “Coherent anti-Stokes Raman scattering microscope,” in 18th Congress of the International Commission for Optics: Optics for the Next Millennium, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 496–497 (1999).
[CrossRef]

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent anti-Stokes Raman spectroscopy,” in Vibrational Spectra and Structure, J. R. During, ed. (Elsevier, New York, 1977), Vol. 6, Chap. 3, pp. 173–225.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the CARS process. If the difference frequency between ω1 and ω2 beams is coincident with the frequency of the molecular vibration, the CARS emission has a peak. ω1 and ω2 are angular frequencies of the input beams; Ω is the angular frequency of molecular vibration; ω3(=2ω1-ω2) is the angular frequency of the CARS emission.

Fig. 2
Fig. 2

Configuration of the CARS microscope.

Fig. 3
Fig. 3

(a) Frequency cutoff of the field of three photons E(μ,η) in Eq. (3). (b) Frequency cutoff of the coherent transfer function of confocal CARS microscopy, CTF(μ,η) in Eq. (9). The frequency cutoff of CTF(μ,η) is the same as those of G(0, μ,η) in Eq. (15) and G(x2, μ,η)dx2 in Eqs. (18).

Fig. 4
Fig. 4

OTF of confocal and nonconfocal CARS microscopy and confocal fluorescence microscopy: (a) along the μ axis (η=0), (b) along the η axis (μ=0). Solid curves, real-part OTF’s of confocal CARS microscopy; dashed curves, those of nonconfocal CARS microscopy; dotted curves, OTF’s of confocal fluorescence microscopy. Each OTF is normalized at (η, μ)=(0,0). The top axes of both figures indicate the normalized frequency divided by NA(=0.9)/λ(=532 nm).

Fig. 5
Fig. 5

Z-axis resolution of the CARS microscope. (a) Intensity change of CARS emission when the beam spot is moved from the benzene layer to the glass layer. (b) Circles, the differential of (a); solid curve, results of Gaussian fitting to the circles. The observed Raman shift is 992 cm-1(=ω1-ω2).

Equations (22)

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

PCARS=χ(3)E1E1E2*,
PCARS(x1, z1, x0, z0)=χ(3)(x1+x0, z1+z0)h1(x1, z1)h1(x1, z1)h2*(x1, z1)=χ(3)(x1+x0, z1+z0)e(x1, z1),
E(μ, η)=F[e(x1, z1)]=H2*(μ, η)[H1(μ, η)H1(μ, η)],
Hi(μ, η)=pi(μ)δ{η-[(1/λi)2-μ2]1/2},
pi(μ)=10<|μ|<NA/niλi,
pi(μ)=0otherwise,
u(x2, x0, z0) PCARS(x1, z1, x0, z0)×h3(x2-x1,-z1)d2x1dz1,
U(x2, μ, η)C(x2, μ, η)Χ(3)(μ, η),
C(x2, μ, η)= H3(μ, η)E(μ-μ, η-η)×exp[-2πi(x2μ)]d2μdη,
CTF(μ, η)=C(0, μ, η)=E(μ, η)H3(μ, η).
χ(3)(x, z)=χ(3)¯[1+breal(x, z)+ibimag(x, z)],
i(x2, x0, z0)=|u(x2, x0, z0)|2.
I(x2, μ, η)|χ(3)¯|2{|D(x2)|2δ(μ, η)+[G(x2, μ, η)+G*(x2,-μ,-η)]×Breal(μ, η)+i[G(x2, μ, η)-G*(x2,-μ,-η)]Bimag(μ, η)},
D(x2)= E(μ, η)H3(μ, η)×exp(-2πix2μ)d2μdη,
G(x2, μ, η)= E*(μ, η)H3*(μ, η)×exp{2πix2μ}C(x2, μ, η)d2μdη,
OTFrealcf(μ, η)=G(0, μ, η)+G*(0,-μ,-η),
OTFimagcf(μ, η)=G(0, μ, η)-G*(0,-μ,-η),
G(0, μ, η)= E*(μ, η)H3*(μ, η)d2μdη×[E(μ, η)H3(μ, η)].
OTFrealncf(μ, η)= G(x2, μ, η)dx2+ G*(x2,-μ,-η)dx2,
OTFimagncf(μ, η)= G(x2, μ, η)dx2- G*(x2,-μ,-η)dx2,
 G(x2, μ, η)dx2=E(μ, η) E*(μ, η)×H3*(μ, η)dηH3(μ, η).
n3λ32 n1λ1-n2λ2+NA224λ22 2 λ2n2-λ1n1,

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