Abstract

To gain a better understanding of the spatiotemporal problems that are encountered in two-photon excitation fluorescence imaging through highly scattering media, we investigate how diffraction affects the three-dimensional intensity distribution of a focused, pulsed optical beam propagating inside a scattering medium. In practice, the full potential of the two-photon excitation fluorescence imaging is unrealized at long scattering depths, owing to the unwanted temporal and spatial broadening of the femtosecond excitation light pulse that reduces the energy density at the geometric focus while it increases the excitation energy density in the out-of-focus regions. To analyze the excitation intensity distribution, we modify the Monte Carlo–based photon-transport model to a semi-quantum-mechanical representation that combines the wave properties of light with the particle behavior of the propagating photons. In our model the propagating photon is represented by a plane wave with its propagation direction in the scattering medium determined by the Monte Carlo technique. The intensity distribution in the focal region is given by the square of the linear superposition of the various plane waves that arrive at different incident angles and optical path lengths. In the absence of scattering, the propagation model yields the intensity distribution that is predicted by the Huygens–Fresnel principle. We quantify the decrease of the energy density delivered at the geometric focus as a function of the optical depth to the mean-free-path ratio that yields the average number of scattering events that a photon encounters as it propagates toward the focus. Both isotropic and anisotropic scattering media are considered. Three values for the numerical aperture (NA) of the focusing lens are considered: NA = 0.25, 0.5, 0.75.

© 2000 Optical Society of America

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  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]
  2. C. Palmes-Saloma, C. Saloma, “Long-depth imaging of specific gene expressions in whole-mount mouse embryos with single-photon excitation confocal fluorescence microscopy and FISH,” J. Structural Biol. 131, 56–66 (2000).
    [CrossRef]
  3. C. Blanca, C. Saloma, “Monte Carlo analysis of two-photon fluorescence imaging through a scattering medium,” Appl. Opt. 37, 8092–8102 (1998).
    [CrossRef]
  4. V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.
  5. V. Daria, C. Blanca, O. Nakamura, S. Kawata, C. Saloma, “Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium,” Appl. Opt. 37, 7960–7967 (1998).
    [CrossRef]
  6. V. Daria, O. Nakamura, C. Palmes-Saloma, S. Kawata, “Enhanced depth penetration in imaging of turbid biological samples by two-photon fluorescence microscopy,” Jpn. J. Appl. Phys. 37, 959–961 (1998).
    [CrossRef]
  7. A. Egner, S. Hell, “Equivalence of the Huygens-Fresnel and Debye approach for the calculation of high aperture point-spread functions in the presence of refractive index mismatch,” J. Microsc. 193, 244–249 (1999).
    [CrossRef]
  8. O. Nakamura, “Fundamentals of two-photon microscopy,” Microsc. Res. Tech. 47, 165–171 (1999).
    [CrossRef] [PubMed]
  9. W. Denk, J. Strickler, W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  10. W. Denk, D. Piston, W. Webb, “Two-photon molecular excitation in laser-scanning microscopy,” in Handbook of Biological Confocal Microscopy2nd ed., J. Pawley, ed. (Plenum, New York, 1995).
    [CrossRef]
  11. C. Xu, W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
    [CrossRef]
  12. C. Blanca, C. Saloma, “Efficient analysis of temporal broadening of a pulsed focused Gaussian beam in scattering media,” Appl. Opt. 38, 5433–5437 (1999).
    [CrossRef]
  13. J. Schmitt, A. Knüttel, M. Yadlowski, “Confocal microscopy in turbid media,” J. Opt. Soc. A 11, 2226–2235 (1994).
    [CrossRef]
  14. X. Gan, M. Gu, “Spatial distribution of single-photon and two-photon fluorescence light in scattering media: Monte Carlo simulation,” Appl. Opt. 39, 1575–1579 (2000).
    [CrossRef]
  15. H. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  16. W. Cheong, S. Prahl, A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  17. M. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–369 (1999).
    [CrossRef]
  18. G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
    [CrossRef] [PubMed]
  19. A. Schonle, S. W. Hell, “Heating by absorption in the focus of an objective lens,” Opt. Lett. 23, 325–327 (1998).
    [CrossRef]
  20. P. Torok, P. Varga, Z. Laczik, G. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
    [CrossRef]
  21. P. Torok, P. Varga, Z. Laczik, G. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field,” J. Opt. Soc. Am. A 12, 2136–2144 (1995).
    [CrossRef]
  22. S. Hell, G. Reiner, C. Cremer, E. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–406 (1993).
    [CrossRef]
  23. T. Wilson, R. Juskaitis, “The axial response of confocal microscopes with high numerical aperture objective lenses,” Bioimaging 3, 35–38 (1995).
    [CrossRef]
  24. P. Hanninen, S. Hell, “Femtosecond pulse broadening in the focal region of a two-photon fluorescence microscope,” Bioimaging 2, 117–121 (1994).
    [CrossRef]
  25. M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Oxford, 1999).
    [CrossRef]
  26. S. Flock, M. Patterson, B. Wilson, D. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues: I. Model predictions and comparison with diffusion theory,” IEEE Trans. BioMed. Eng. 26, 1162–1168 (1989).
    [CrossRef]
  27. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).
  28. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
  29. E. Goldin, Waves and Photons: An Introduction to Quantum Optics (Wiley, New York, 1982).
  30. M. Havukainen, G. Drobny, S. Stenholm, V. Buzek, “Quantum simulations of optical systems,” J. Mod. Opt. 46, 1343–1367 (1999).
  31. W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, New York, 1993).
  32. J. Lock, E. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991).
    [CrossRef]
  33. C. Saloma, M. O. Cambaliza, “Single-Gaussian-beam interaction with a dielectric microsphere: radiation forces, multiple internal reflections, and caustic structures,” Appl. Opt. 34, 3522–3528 (1995).
    [CrossRef] [PubMed]

2000 (2)

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

X. Gan, M. Gu, “Spatial distribution of single-photon and two-photon fluorescence light in scattering media: Monte Carlo simulation,” Appl. Opt. 39, 1575–1579 (2000).
[CrossRef]

1999 (5)

C. Blanca, C. Saloma, “Efficient analysis of temporal broadening of a pulsed focused Gaussian beam in scattering media,” Appl. Opt. 38, 5433–5437 (1999).
[CrossRef]

M. Havukainen, G. Drobny, S. Stenholm, V. Buzek, “Quantum simulations of optical systems,” J. Mod. Opt. 46, 1343–1367 (1999).

M. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–369 (1999).
[CrossRef]

A. Egner, S. Hell, “Equivalence of the Huygens-Fresnel and Debye approach for the calculation of high aperture point-spread functions in the presence of refractive index mismatch,” J. Microsc. 193, 244–249 (1999).
[CrossRef]

O. Nakamura, “Fundamentals of two-photon microscopy,” Microsc. Res. Tech. 47, 165–171 (1999).
[CrossRef] [PubMed]

1998 (5)

V. Daria, O. Nakamura, C. Palmes-Saloma, S. Kawata, “Enhanced depth penetration in imaging of turbid biological samples by two-photon fluorescence microscopy,” Jpn. J. Appl. Phys. 37, 959–961 (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]

A. Schonle, S. W. Hell, “Heating by absorption in the focus of an objective lens,” Opt. Lett. 23, 325–327 (1998).
[CrossRef]

V. Daria, C. Blanca, O. Nakamura, S. Kawata, C. Saloma, “Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium,” Appl. Opt. 37, 7960–7967 (1998).
[CrossRef]

C. Blanca, C. Saloma, “Monte Carlo analysis of two-photon fluorescence imaging through a scattering medium,” Appl. Opt. 37, 8092–8102 (1998).
[CrossRef]

1996 (2)

1995 (4)

1994 (2)

J. Schmitt, A. Knüttel, M. Yadlowski, “Confocal microscopy in turbid media,” J. Opt. Soc. A 11, 2226–2235 (1994).
[CrossRef]

P. Hanninen, S. Hell, “Femtosecond pulse broadening in the focal region of a two-photon fluorescence microscope,” Bioimaging 2, 117–121 (1994).
[CrossRef]

1993 (1)

S. Hell, G. Reiner, C. Cremer, E. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–406 (1993).
[CrossRef]

1991 (1)

1990 (2)

W. Cheong, S. Prahl, A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

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

1989 (1)

S. Flock, M. Patterson, B. Wilson, D. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues: I. Model predictions and comparison with diffusion theory,” IEEE Trans. BioMed. Eng. 26, 1162–1168 (1989).
[CrossRef]

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Blanca, C.

Booker, G.

Boppart, S. A.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Oxford, 1999).
[CrossRef]

Bouma, B. E.

Buzek, V.

M. Havukainen, G. Drobny, S. Stenholm, V. Buzek, “Quantum simulations of optical systems,” J. Mod. Opt. 46, 1343–1367 (1999).

Cambaliza, M. O.

Cheong, W.

W. Cheong, S. Prahl, A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Cremer, C.

S. Hell, G. Reiner, C. Cremer, E. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–406 (1993).
[CrossRef]

Daria, V.

V. Daria, O. Nakamura, C. Palmes-Saloma, S. Kawata, “Enhanced depth penetration in imaging of turbid biological samples by two-photon fluorescence microscopy,” Jpn. J. Appl. Phys. 37, 959–961 (1998).
[CrossRef]

V. Daria, C. Blanca, O. Nakamura, S. Kawata, C. Saloma, “Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium,” Appl. Opt. 37, 7960–7967 (1998).
[CrossRef]

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

Denk, W.

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

W. Denk, D. Piston, W. Webb, “Two-photon molecular excitation in laser-scanning microscopy,” in Handbook of Biological Confocal Microscopy2nd ed., J. Pawley, ed. (Plenum, New York, 1995).
[CrossRef]

Drobny, G.

M. Havukainen, G. Drobny, S. Stenholm, V. Buzek, “Quantum simulations of optical systems,” J. Mod. Opt. 46, 1343–1367 (1999).

Egner, A.

A. Egner, S. Hell, “Equivalence of the Huygens-Fresnel and Debye approach for the calculation of high aperture point-spread functions in the presence of refractive index mismatch,” J. Microsc. 193, 244–249 (1999).
[CrossRef]

Flannery, B.

W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, New York, 1993).

Flock, S.

S. Flock, M. Patterson, B. Wilson, D. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues: I. Model predictions and comparison with diffusion theory,” IEEE Trans. BioMed. Eng. 26, 1162–1168 (1989).
[CrossRef]

Fujimoto, J. G.

Fujita, K.

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

Gan, X.

Goldin, E.

E. Goldin, Waves and Photons: An Introduction to Quantum Optics (Wiley, New York, 1982).

Golubovic, B.

Goodman, J.

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

Gu, M.

Hanninen, P.

P. Hanninen, S. Hell, “Femtosecond pulse broadening in the focal region of a two-photon fluorescence microscope,” Bioimaging 2, 117–121 (1994).
[CrossRef]

Havukainen, M.

M. Havukainen, G. Drobny, S. Stenholm, V. Buzek, “Quantum simulations of optical systems,” J. Mod. Opt. 46, 1343–1367 (1999).

Hell, S.

A. Egner, S. Hell, “Equivalence of the Huygens-Fresnel and Debye approach for the calculation of high aperture point-spread functions in the presence of refractive index mismatch,” J. Microsc. 193, 244–249 (1999).
[CrossRef]

P. Hanninen, S. Hell, “Femtosecond pulse broadening in the focal region of a two-photon fluorescence microscope,” Bioimaging 2, 117–121 (1994).
[CrossRef]

S. Hell, G. Reiner, C. Cremer, E. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–406 (1993).
[CrossRef]

Hell, S. W.

Hovenac, E.

Juskaitis, R.

T. Wilson, R. Juskaitis, “The axial response of confocal microscopes with high numerical aperture objective lenses,” Bioimaging 3, 35–38 (1995).
[CrossRef]

Kawata, S.

V. Daria, O. Nakamura, C. Palmes-Saloma, S. Kawata, “Enhanced depth penetration in imaging of turbid biological samples by two-photon fluorescence microscopy,” Jpn. J. Appl. Phys. 37, 959–961 (1998).
[CrossRef]

V. Daria, C. Blanca, O. Nakamura, S. Kawata, C. Saloma, “Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium,” Appl. Opt. 37, 7960–7967 (1998).
[CrossRef]

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

Knüttel, A.

J. Schmitt, A. Knüttel, M. Yadlowski, “Confocal microscopy in turbid media,” J. Opt. Soc. A 11, 2226–2235 (1994).
[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]

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

Laczik, Z.

Lock, J.

Nakamura, O.

O. Nakamura, “Fundamentals of two-photon microscopy,” Microsc. Res. Tech. 47, 165–171 (1999).
[CrossRef] [PubMed]

V. Daria, O. Nakamura, C. Palmes-Saloma, S. Kawata, “Enhanced depth penetration in imaging of turbid biological samples by two-photon fluorescence microscopy,” Jpn. J. Appl. Phys. 37, 959–961 (1998).
[CrossRef]

V. Daria, C. Blanca, O. Nakamura, S. Kawata, C. Saloma, “Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium,” Appl. Opt. 37, 7960–7967 (1998).
[CrossRef]

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

Palmes-Saloma, C.

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

V. Daria, O. Nakamura, C. Palmes-Saloma, S. Kawata, “Enhanced depth penetration in imaging of turbid biological samples by two-photon fluorescence microscopy,” Jpn. J. Appl. Phys. 37, 959–961 (1998).
[CrossRef]

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

Patterson, M.

S. Flock, M. Patterson, B. Wilson, D. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues: I. Model predictions and comparison with diffusion theory,” IEEE Trans. BioMed. Eng. 26, 1162–1168 (1989).
[CrossRef]

Piston, D.

W. Denk, D. Piston, W. Webb, “Two-photon molecular excitation in laser-scanning microscopy,” in Handbook of Biological Confocal Microscopy2nd ed., J. Pawley, ed. (Plenum, New York, 1995).
[CrossRef]

Prahl, S.

W. Cheong, S. Prahl, A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Press, W.

W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, New York, 1993).

Reiner, G.

S. Hell, G. Reiner, C. Cremer, E. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–406 (1993).
[CrossRef]

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Saloma, C.

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

C. Blanca, C. Saloma, “Efficient analysis of temporal broadening of a pulsed focused Gaussian beam in scattering media,” Appl. Opt. 38, 5433–5437 (1999).
[CrossRef]

C. Blanca, C. Saloma, “Monte Carlo analysis of two-photon fluorescence imaging through a scattering medium,” Appl. Opt. 37, 8092–8102 (1998).
[CrossRef]

V. Daria, C. Blanca, O. Nakamura, S. Kawata, C. Saloma, “Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium,” Appl. Opt. 37, 7960–7967 (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]

C. Saloma, M. O. Cambaliza, “Single-Gaussian-beam interaction with a dielectric microsphere: radiation forces, multiple internal reflections, and caustic structures,” Appl. Opt. 34, 3522–3528 (1995).
[CrossRef] [PubMed]

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

Schmitt, J.

J. Schmitt, A. Knüttel, M. Yadlowski, “Confocal microscopy in turbid media,” J. Opt. Soc. A 11, 2226–2235 (1994).
[CrossRef]

Schonle, A.

Stelzer, E.

S. Hell, G. Reiner, C. Cremer, E. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–406 (1993).
[CrossRef]

Stenholm, S.

M. Havukainen, G. Drobny, S. Stenholm, V. Buzek, “Quantum simulations of optical systems,” J. Mod. Opt. 46, 1343–1367 (1999).

Strickler, J.

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

Swanson, E. A.

Tearney, G. J.

Teukolsky, S.

W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, New York, 1993).

Torok, P.

van de Hulst, H.

H. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

van Rossum and Th. M. Nieuwenhuizen, M.

M. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–369 (1999).
[CrossRef]

Varga, P.

Vetterling, W.

W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, New York, 1993).

Webb, W.

C. Xu, W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
[CrossRef]

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

W. Denk, D. Piston, W. Webb, “Two-photon molecular excitation in laser-scanning microscopy,” in Handbook of Biological Confocal Microscopy2nd ed., J. Pawley, ed. (Plenum, New York, 1995).
[CrossRef]

Welch, A.

W. Cheong, S. Prahl, A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Wilson, B.

S. Flock, M. Patterson, B. Wilson, D. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues: I. Model predictions and comparison with diffusion theory,” IEEE Trans. BioMed. Eng. 26, 1162–1168 (1989).
[CrossRef]

Wilson, T.

T. Wilson, R. Juskaitis, “The axial response of confocal microscopes with high numerical aperture objective lenses,” Bioimaging 3, 35–38 (1995).
[CrossRef]

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Oxford, 1999).
[CrossRef]

Wyman, D.

S. Flock, M. Patterson, B. Wilson, D. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues: I. Model predictions and comparison with diffusion theory,” IEEE Trans. BioMed. Eng. 26, 1162–1168 (1989).
[CrossRef]

Xu, C.

Yadlowski, M.

J. Schmitt, A. Knüttel, M. Yadlowski, “Confocal microscopy in turbid media,” J. Opt. Soc. A 11, 2226–2235 (1994).
[CrossRef]

Appl. Opt. (5)

Bioimaging (2)

T. Wilson, R. Juskaitis, “The axial response of confocal microscopes with high numerical aperture objective lenses,” Bioimaging 3, 35–38 (1995).
[CrossRef]

P. Hanninen, S. Hell, “Femtosecond pulse broadening in the focal region of a two-photon fluorescence microscope,” Bioimaging 2, 117–121 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Cheong, S. Prahl, A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

IEEE Trans. BioMed. Eng. (1)

S. Flock, M. Patterson, B. Wilson, D. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues: I. Model predictions and comparison with diffusion theory,” IEEE Trans. BioMed. Eng. 26, 1162–1168 (1989).
[CrossRef]

J. Microsc. (2)

S. Hell, G. Reiner, C. Cremer, E. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–406 (1993).
[CrossRef]

A. Egner, S. Hell, “Equivalence of the Huygens-Fresnel and Debye approach for the calculation of high aperture point-spread functions in the presence of refractive index mismatch,” J. Microsc. 193, 244–249 (1999).
[CrossRef]

J. Mod. Opt. (1)

M. Havukainen, G. Drobny, S. Stenholm, V. Buzek, “Quantum simulations of optical systems,” J. Mod. Opt. 46, 1343–1367 (1999).

J. Opt. Soc. A (1)

J. Schmitt, A. Knüttel, M. Yadlowski, “Confocal microscopy in turbid media,” J. Opt. Soc. A 11, 2226–2235 (1994).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

J. Structural Biol. (1)

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

Jpn. J. Appl. Phys. (1)

V. Daria, O. Nakamura, C. Palmes-Saloma, S. Kawata, “Enhanced depth penetration in imaging of turbid biological samples by two-photon fluorescence microscopy,” Jpn. J. Appl. Phys. 37, 959–961 (1998).
[CrossRef]

Microsc. Res. Tech. (1)

O. Nakamura, “Fundamentals of two-photon microscopy,” Microsc. Res. Tech. 47, 165–171 (1999).
[CrossRef] [PubMed]

Opt. Lett. (2)

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]

Proc. R. Soc. London Ser. A (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Rev. Mod. Phys. (1)

M. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–369 (1999).
[CrossRef]

Science (1)

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

Other (7)

W. Denk, D. Piston, W. Webb, “Two-photon molecular excitation in laser-scanning microscopy,” in Handbook of Biological Confocal Microscopy2nd ed., J. Pawley, ed. (Plenum, New York, 1995).
[CrossRef]

H. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

V. Daria, C. Palmes-Saloma, K. Fujita, C. Saloma, O. Nakamura, H. Kondoh, S. Kawata, “Long depth imaging of turbid biological samples by two-photon microscopy,” in Proceedings of the Nineteenth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Nagoya, Japan) pp. 28–32.

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

M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Oxford, 1999).
[CrossRef]

E. Goldin, Waves and Photons: An Introduction to Quantum Optics (Wiley, New York, 1982).

W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, New York, 1993).

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Figures (10)

Fig. 1
Fig. 1

Axial intensity distributions I(0, 0, Δz) near the geometric focus at Δz = 0 of a uniformly illuminated (λ = 0.750 µm) focusing lens (NA = 0.4, n s = 1, d s = 160 µm, and f = 2.1 mm) derived with the modified MC technique with N o = 1 × 106 plane waves (circles) and N o = 16 × 106 plane waves (filled circles). The solution (solid curve) obtained with direct calculation of Eq. (1) is also shown for comparison.

Fig. 2
Fig. 2

Decrease of error ε in I(0, 0, Δz) with an increase in N o . The solid curve is obtained with ε = 0.150(N o )-0.646. For N o = 1 × 106, the normalized mean-square error is ε = 0.02.

Fig. 3
Fig. 3

Transverse intensity distribution I(r) in the focal plane (Δz = 0) for g ≈ 0. Three NA values are considered: (a) 0.25, (b) 0.5, (c) 0.75. Range of scattering depth is 0.063d s h ≤ 640 = 4d s . Parameters used are λ = 0.750 µm, n s = 1, d s = 160 µm, and N o = 16 × 106. Solid curve, 0.0625d s ; short-dashed curve, 2d s ; dotted curve, 1d s ; and long-dashed curve, 3d s .

Fig. 4
Fig. 4

Transverse intensity distribution I(r) in the focal plane (Δz = 0) for g = 0.9. Three NA values are considered: (a) 0.25, (b) 0.5, (c) 0.75. Range of scattering depth is 0.063d s h ≤ 640 = 4d s . Parameters used are λ = 0.750 µm, n s = 1, d s = 160 µm, and N o = 16 × 106. Solid curve, 0.06d s ; short-dashed curve, 2d s ; dotted curve, 1d s ; long-dashed curve, 3d s .

Fig. 5
Fig. 5

Plot of peak value I p of I(r, f) against scattering depth h for (a) g ≈ 0 and (b) g = 0.9. Three NA values are considered: NA = 0.25 (squares), 0.5 (circles), and 0.75 (triangles). Each point represents the average of five trials.

Fig. 6
Fig. 6

Axial intensity distribution I(0, Δz) at different h values for g ≈ 0. Three NA values are considered: (a) 0.25, (b) 0.5, (c) 0.75. Range of scattering depth is 0.063d s h ≤ 640 = 4d s . Parameters used are λ = 0.750 µm, n s = 1, d s = 160 µm, f = 2.1 mm, and N o = 16 × 106. Solid curve, 0.0625d s ; short-dashed curve, 2d s ; dotted curve, 1d s ; and long-dashed curve, 3d s .

Fig. 7
Fig. 7

Axial intensity distribution I(0, Δz) at different h values for g = 0.9. Three NA values are considered: (a) 0.25, (b) 0.5, (c) 0.75. Range of scattering depth is 0.063d s h ≤ 640 = 4d s . Parameters used are λ = 0.750 µm, n s = 1, d s = 160 µm, f = 2.1 mm, and N o = 16 × 106. Solid curve, 0.0625d s ; short-dashed curve, 2d s ; dotted curve, 1d s ; and long-dashed curve, 3d s .

Fig. 8
Fig. 8

Temporal pulse broadening at the geometric focus (at z = f = 2.1 mm) for g ≈ 0. Three NA values are considered: (a) 0.25, (b) 0.5, (c) 0.75. The Dirac-delta pulse is launched from the lens pupil (z = 0) at time t = 0. Range of scattering depth is 0.063d s h ≤ 640 = 4d s . Parameters used are λ = 0.750 µm, n s = 1, d s = 160 µm, f = 2.1 mm, and N o = 16 × 106. Solid curve, 0.0625d s ; short-dashed curve, 2d s ; dotted curve, 1d s ; and long-dashed curve, 3d s .

Fig. 9
Fig. 9

Temporal pulse broadening at the geometric focus (at z = f = 2.1 mm) for g = 0.9. Three NA values are considered: (a) 0.25, (b) 0.5, (c) 0.75. The Dirac-delta pulse is launched from the lens pupil (z = 0) at time t = 0. Range of scattering depth is 0.063d s h ≤ 640 = 4d s . Parameters used are λ = 0.750 µm, n s = 1, d s = 160 µm, f = 2.1 mm, and N o = 16 × 106. Solid curve, 0.0625d s ; short-dashed curve, 2d s ; dotted curve, 1d s ; and long-dashed curve, 3d s .

Fig. 10
Fig. 10

Plot of peak intensity T max of the light pulse T p (t) that arrives at the focus as a function of h for (a) g ≈ 0 and (b) g = 0.9. Three NA values are considered: 0.25 (squares), 0.5 (circles), and 0.75 (triangles).

Equations (13)

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UP=A Uξ, ψFξ, ψhξ, ψ; x, ydξdψ,
Fξ, ψ=Fρ=expikf2+ρ21/2-f,
d1=-ds ln Ξ,
cos θj=2g-11+g2-1-g222g-11-g+2gΞ2,
L=Q+nsd1+d2+ +dp,
ε=k |ImkΔz-ItkΔz|2/ |ItkΔz|2
F1PF1P0exp-1.045h/ds,
F1PF1P0exp-0.838h/ds
F2PF2P0exp-2.09h/ds,
F2PF2P0exp-1.676h/ds
ΔF2P=F2Po-F2P
F2P0=κ2Io+ΔIo2 exp-2.09h+Δh/ds,
F2Po=κ2Io+ΔIo2 exp-1.676h+Δh/ds,

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