Abstract

A variance-reduction technique is described that greatly improves the efficiency of Monte Carlo simulations of reflection-mode confocal microscopy in anisotropically scattering media. The efficiency gain is large enough that the performance of confocal microscopes probing as deep as 5 scattering lengths can be simulated with a desktop computer. We use the technique to simulate the response of a true confocal microscope probing biological tissue, a problem that has been impractical to undertake by using conventional Monte Carlo methods. Our most important finding is that operation of a confocal microscope in the true confocal mode enables much more effective rejection of undesired scattered light than operation in the partially coherent mode, but the maximum probing depths of microscopes operated in either mode are similar (2–3 scattering lengths) in practice because of sensitivity limitations.

© 1996 Optical Society of America

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  1. S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
    [CrossRef] [PubMed]
  2. H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
    [CrossRef] [PubMed]
  3. G. Zaccanti, P. Donelli, “Attenuation of energy in time-gated transillumination imaging: numerical results,” Appl. Opt. 33, 7023–7030 (1994).
    [CrossRef] [PubMed]
  4. K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
    [CrossRef]
  5. H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
    [CrossRef]
  6. W. F. Cheong, S. A. Prahl, A. J. Walsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Elctron. 26, 2166–2185 (1990).
    [CrossRef]
  7. R. L. Fante, “Electromagnetic propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
    [CrossRef]
  8. J. M. Schmitt, A. Knüttel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235 (1994).
    [CrossRef]
  9. J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
    [CrossRef] [PubMed]
  10. T. Duracz, N. J. McCormick, “Multiple scattering corrections for lidar detection of obscured objects,” Appl. Opt. 29, 4170–4175 (1990).
    [CrossRef] [PubMed]
  11. P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
    [CrossRef]
  12. P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “Monte Carlo calculations of the modulation transfer function of an optical system operating in a turbid medium,” Appl. Opt. 32, 2813–2824 (1993).
    [CrossRef] [PubMed]
  13. One normalized optical unit is equal to λ/2π(NA), where λis the illumination wavelength and NA is the numerical aperture of the microscope. See M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).
  14. C. J. R. Sheppard, M. Gu, “Imaging performance of confocal fluorescence microscopes with finite-sized source,” J. Mod. Opt. 41, 1521–1530 (1994).
    [CrossRef]
  15. J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
    [CrossRef] [PubMed]
  16. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
    [CrossRef] [PubMed]
  17. T. Wilson, R. Juskaitis, “Scanning interference microscopy,” Bioimaging 2, 36–40 (1994).
    [CrossRef]
  18. G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
    [CrossRef]
  19. M. C. Jeruchim, P. M. Hahn, K. P. Smyntek, R. T. Ray, “An experimental investigation of conventional and efficient importance sampling,” IEEE Trans. Commun. 37, 578–587 (1989).
    [CrossRef]
  20. K. Ben-Letaief, J. S. Sadowsky, “New importance sampling methods for simulating sequential decoders,” IEEE Trans. Inf. Theory 39, 1716–1722 (1993).
    [CrossRef]
  21. K. Ben-Letaief, “Performance analysis of digital lightwave systems using efficient computer simulation techniques,” IEEE Trans. Commun. 43, 240–251 (1995).
    [CrossRef]
  22. I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1990), Chap. 7.
  23. S. Hell, G. Reiner, C. Cremer, E. H. K. Steltzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. (Oxford) 169, 391–405 (1993).
    [CrossRef]
  24. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1988), Chap. 7, pp. 216–217.
  25. S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
    [CrossRef] [PubMed]
  26. C. J. R. Sheppard, “Stray light and noise in confocal microscopy,” Micron Microsc. Acta 22, 239–243 (1991).
    [CrossRef]
  27. T. Sawatari, “Optical heterodyne scanning microscopy,” Appl. Opt. 12, 2766–2772 (1973).
    [CrossRef]
  28. Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
    [CrossRef]
  29. J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
    [CrossRef] [PubMed]

1995 (1)

K. Ben-Letaief, “Performance analysis of digital lightwave systems using efficient computer simulation techniques,” IEEE Trans. Commun. 43, 240–251 (1995).
[CrossRef]

1994 (7)

C. J. R. Sheppard, M. Gu, “Imaging performance of confocal fluorescence microscopes with finite-sized source,” J. Mod. Opt. 41, 1521–1530 (1994).
[CrossRef]

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

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

T. Wilson, R. Juskaitis, “Scanning interference microscopy,” Bioimaging 2, 36–40 (1994).
[CrossRef]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

G. Zaccanti, P. Donelli, “Attenuation of energy in time-gated transillumination imaging: numerical results,” Appl. Opt. 33, 7023–7030 (1994).
[CrossRef] [PubMed]

1993 (4)

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “Monte Carlo calculations of the modulation transfer function of an optical system operating in a turbid medium,” Appl. Opt. 32, 2813–2824 (1993).
[CrossRef] [PubMed]

K. Ben-Letaief, J. S. Sadowsky, “New importance sampling methods for simulating sequential decoders,” IEEE Trans. Inf. Theory 39, 1716–1722 (1993).
[CrossRef]

S. Hell, G. Reiner, C. Cremer, E. H. K. Steltzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. (Oxford) 169, 391–405 (1993).
[CrossRef]

1991 (4)

C. J. R. Sheppard, “Stray light and noise in confocal microscopy,” Micron Microsc. Acta 22, 239–243 (1991).
[CrossRef]

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

1990 (2)

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

T. Duracz, N. J. McCormick, “Multiple scattering corrections for lidar detection of obscured objects,” Appl. Opt. 29, 4170–4175 (1990).
[CrossRef] [PubMed]

1989 (2)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

M. C. Jeruchim, P. M. Hahn, K. P. Smyntek, R. T. Ray, “An experimental investigation of conventional and efficient importance sampling,” IEEE Trans. Commun. 37, 578–587 (1989).
[CrossRef]

1987 (1)

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

1981 (1)

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

1976 (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

1975 (1)

R. L. Fante, “Electromagnetic propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

1973 (1)

T. Sawatari, “Optical heterodyne scanning microscopy,” Appl. Opt. 12, 2766–2772 (1973).
[CrossRef]

Ben-Letaief, K.

K. Ben-Letaief, “Performance analysis of digital lightwave systems using efficient computer simulation techniques,” IEEE Trans. Commun. 43, 240–251 (1995).
[CrossRef]

K. Ben-Letaief, J. S. Sadowsky, “New importance sampling methods for simulating sequential decoders,” IEEE Trans. Inf. Theory 39, 1716–1722 (1993).
[CrossRef]

Bonner, R. F.

Bruscaglioni, P.

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “Monte Carlo calculations of the modulation transfer function of an optical system operating in a turbid medium,” Appl. Opt. 32, 2813–2824 (1993).
[CrossRef] [PubMed]

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

Cheong, W. F.

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

Cremer, C.

S. Hell, G. Reiner, C. Cremer, E. H. K. Steltzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. (Oxford) 169, 391–405 (1993).
[CrossRef]

Darbinjan, R. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

Davies, E. R.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Donelli, P.

Duracz, T.

Eckhaus, M. A.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

Elepov, B. S.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

Fante, R. L.

R. L. Fante, “Electromagnetic propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1988), Chap. 7, pp. 216–217.

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Fujii, Y.

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Fujimoto, J. G.

Gordon, H. R.

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

Gu, M.

C. J. R. Sheppard, M. Gu, “Imaging performance of confocal fluorescence microscopes with finite-sized source,” J. Mod. Opt. 41, 1521–1530 (1994).
[CrossRef]

Hahn, P. M.

M. C. Jeruchim, P. M. Hahn, K. P. Smyntek, R. T. Ray, “An experimental investigation of conventional and efficient importance sampling,” IEEE Trans. Commun. 37, 578–587 (1989).
[CrossRef]

Hee, M. R.

Hell, S.

S. Hell, G. Reiner, C. Cremer, E. H. K. Steltzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. (Oxford) 169, 391–405 (1993).
[CrossRef]

Igarashi, T.

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Ismaelli, A.

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “Monte Carlo calculations of the modulation transfer function of an optical system operating in a turbid medium,” Appl. Opt. 32, 2813–2824 (1993).
[CrossRef] [PubMed]

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

Izatt, J. A.

Jackson, P. C.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Jeruchim, M. C.

M. C. Jeruchim, P. M. Hahn, K. P. Smyntek, R. T. Ray, “An experimental investigation of conventional and efficient importance sampling,” IEEE Trans. Commun. 37, 578–587 (1989).
[CrossRef]

Juskaitis, R.

T. Wilson, R. Juskaitis, “Scanning interference microscopy,” Bioimaging 2, 36–40 (1994).
[CrossRef]

Kargin, B. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

Key, H.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Knüttel, A.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

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

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

Koblinger, L.

I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1990), Chap. 7.

Kunkel, K. E.

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Lux, I.

I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1990), Chap. 7.

Marchuk, G. I.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

McCormick, N. J.

Mikhailov, G. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

Nazaraliev, M. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

Owen, G. M.

Patterson, M. S.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Prahl, S. A.

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

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1988), Chap. 7, pp. 216–217.

Ray, R. T.

M. C. Jeruchim, P. M. Hahn, K. P. Smyntek, R. T. Ray, “An experimental investigation of conventional and efficient importance sampling,” IEEE Trans. Commun. 37, 578–587 (1989).
[CrossRef]

Reiner, G.

S. Hell, G. Reiner, C. Cremer, E. H. K. Steltzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. (Oxford) 169, 391–405 (1993).
[CrossRef]

Sadowsky, J. S.

K. Ben-Letaief, J. S. Sadowsky, “New importance sampling methods for simulating sequential decoders,” IEEE Trans. Inf. Theory 39, 1716–1722 (1993).
[CrossRef]

Sawatari, T.

T. Sawatari, “Optical heterodyne scanning microscopy,” Appl. Opt. 12, 2766–2772 (1973).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

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

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, “Imaging performance of confocal fluorescence microscopes with finite-sized source,” J. Mod. Opt. 41, 1521–1530 (1994).
[CrossRef]

C. J. R. Sheppard, “Stray light and noise in confocal microscopy,” Micron Microsc. Acta 22, 239–243 (1991).
[CrossRef]

Smyntek, K. P.

M. C. Jeruchim, P. M. Hahn, K. P. Smyntek, R. T. Ray, “An experimental investigation of conventional and efficient importance sampling,” IEEE Trans. Commun. 37, 578–587 (1989).
[CrossRef]

Steltzer, E. H. K.

S. Hell, G. Reiner, C. Cremer, E. H. K. Steltzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. (Oxford) 169, 391–405 (1993).
[CrossRef]

Swanson, E. A.

Takimoto, H.

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1988), Chap. 7, pp. 216–217.

Vettering, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1988), Chap. 7, pp. 216–217.

Walsh, A. J.

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

Weinman, J. A.

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Wells, P. N. T.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Wilson, B. C.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Wilson, T.

T. Wilson, R. Juskaitis, “Scanning interference microscopy,” Bioimaging 2, 36–40 (1994).
[CrossRef]

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Yadlowsky, M.

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

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

Zaccanti, G.

Appl. Opt. (5)

Bioimaging (1)

T. Wilson, R. Juskaitis, “Scanning interference microscopy,” Bioimaging 2, 36–40 (1994).
[CrossRef]

IEEE J. Quantum Elctron. (1)

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

IEEE Trans. Biomed. Eng. (1)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

IEEE Trans. Commun. (2)

M. C. Jeruchim, P. M. Hahn, K. P. Smyntek, R. T. Ray, “An experimental investigation of conventional and efficient importance sampling,” IEEE Trans. Commun. 37, 578–587 (1989).
[CrossRef]

K. Ben-Letaief, “Performance analysis of digital lightwave systems using efficient computer simulation techniques,” IEEE Trans. Commun. 43, 240–251 (1995).
[CrossRef]

IEEE Trans. Inf. Theory (1)

K. Ben-Letaief, J. S. Sadowsky, “New importance sampling methods for simulating sequential decoders,” IEEE Trans. Inf. Theory 39, 1716–1722 (1993).
[CrossRef]

J. Atmos. Sci. (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

J. Microsc. (Oxford) (1)

S. Hell, G. Reiner, C. Cremer, E. H. K. Steltzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. (Oxford) 169, 391–405 (1993).
[CrossRef]

J. Mod. Opt. (2)

P. Bruscaglioni, P. Donelli, A. Ismaelli, G. Zaccanti, “A numerical procedure for calculating the effect of a turbid medium on the MTF of an optical system,” J. Mod. Opt. 38, 129–142 (1991).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Imaging performance of confocal fluorescence microscopes with finite-sized source,” J. Mod. Opt. 41, 1521–1530 (1994).
[CrossRef]

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

Limnol. Oceanogr. (1)

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

Med. Phys. (1)

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Micron Microsc. Acta (1)

C. J. R. Sheppard, “Stray light and noise in confocal microscopy,” Micron Microsc. Acta 22, 239–243 (1991).
[CrossRef]

Opt. Commun. (1)

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Opt. Lett. (1)

Phys. Med. Biol. (3)

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

Proc. IEEE (1)

R. L. Fante, “Electromagnetic propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Other (4)

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1988), Chap. 7, pp. 216–217.

I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1990), Chap. 7.

One normalized optical unit is equal to λ/2π(NA), where λis the illumination wavelength and NA is the numerical aperture of the microscope. See M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

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Figures (6)

Fig. 1
Fig. 1

Example of the trajectory of a scattered photon in the simulated tissue medium. The polar angles θ1, θ2, …, θm, the azimuthal angles ϕ1, ϕ2, …, ϕm, and the scattering lengths l1, l2, …, lm referred to in the text are illustrated here for m = 3.

Fig. 2
Fig. 2

Model of a confocal microscope probing a thick biological tissue. The thick line with arrows shows an example of the trajectory of a photon traced from the source to the detector plane. Cylindrical symmetry is assumed with respect to the axes of lenses L1 and L2. This figure shows a cut through the optical axis in the xz plane. The lenses are in 4f arrangement with one of the focal planes located in the medium and the other located in the plane of the pinhole (f.l. stands for focal length). In all of the simulations discussed in this paper, I0 was normalized to 1. A detailed view of a photon trajectory within the area outlined by dotted lines is given in Fig. 1.

Fig. 3
Fig. 3

Comparison of the axial fluence values obtained as a function of probing depth, zf, from Monte Carlo simulations carried out with variance reduction (solid lines) and without variance reduction (symbols). The results of the simulations without variance reduction are not shown for the vp = 0.25 case, because too few photons were detected to generate meaningful values. For these simulations the following model parameters were assumed: λ = 1.3 μm, D = 4 mm, f = 8 mm, d = 7.9 mm, n2 = n1 = 1, g = 0.9, and lT = 100 μm.

Fig. 4
Fig. 4

Axial fluence versus probing depth, zf, obtained from simulations incorporating variance reduction: (a) large-radius pinhole (vp = 12), (b) small-radius pinhole (vp = 1). For these simulations the following model parameters were assumed: λ = 1.3 μm, D = 4 mm, f = 8 mm, n2 = n1 = 1, g = 0.9, and lT = 100 μm. The open circles are fluence values calculated with the conventional Monte Carlo method without variance reduction, with an axial bin size of 10 μm and 150 × 106 incident photons. The mean values given by the two simulations are roughly the same, but the variance of the values between adjacent bins obtained by the conventional method is significantly larger.

Fig. 5
Fig. 5

Quantitative comparison of the background-rejection ratio BR (see Section 4 of the text for a definition) computed from the Fig. 4 simulation results for the large-radius pinhole (vp = 12) and small-radius pinhole (vp = 1) cases. Marked on the curves are the values of the detected power fractions, PF, computed at various depths.

Fig. 6
Fig. 6

Surface plot of the logarithm of the detected fluence fraction Ψ(r, z) obtained by Monte Carlo simulation (with variance reduction) for a confocal microscope (vp = 1) focused 500 μm below the surface of a tissue (lT = 100 μm, g = 0.9). The other parameters used in the simulation are λ = 1.3 μm, D = 4 mm, f = 8 mm, and n2 = n1 = 1. Inset: Radial profile of Ψ in the focal plane (zf = 500 μm).

Equations (26)

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α = E [ I ( χ ) ] .
α ^ m c = 1 L l = 1 L I [ χ ( l ) ] .
w ( x ) = f χ ( x ) f χ * ( x ) .
α ^ i s = 1 L l = 1 L I [ χ ( l ) ] w [ χ ( l ) ] ,
f χ ( x ) = i = 0 m f θ ( θ i ) f ϕ ( ϕ i ) f l ( l i ) .
f χ * ( x ) = i = 0 m f θ * ( θ i ) f ϕ * ( ϕ i ) f l * ( l i ) ,
f θ * ( θ i ) = { p θ * ( θ i ) i I 0 p θ ( θ i ) i I 0 ,
f l * ( l i ) = { p l * ( l i ) i J 0 p l ( l i ) i J 0 ,
w ( x ) = i 0 , j 0 p θ ( θ i 0 ) p l ( l j 0 ) p θ * ( θ i 0 ) p l * ( l j 0 )             for all i 0 I 0 and j 0 J 0 .
W 0 = p l ( z 0 ) p l * ( z 0 ) = z f l T exp [ z 0 ( 1 z f - 1 l T ) ] .
r ( z 0 ) = r min [ 1 + ( z f - z 0 z r ) 2 ] 1 / 2 ,
r min 2 ( n 2 / n 1 ) f λ π D = ( n 2 / n 1 ) λ π ( NA ) .
x 0 = σ x r ( z 0 ) 2 - 2 ( log R ) / R ,
y 0 = σ y r ( z 0 ) 2 - 2 ( log R ) / R ,
p θ ( θ ) = 2 π 1 4 π 1 - g 2 ( 1 + g 2 - 2 g cos θ ) 3 / 2 ,
p θ * ( θ ) = p θ ( - θ ) = 2 π 1 4 π 1 - g 2 ( 1 + g 2 + 2 g cos θ ) 3 / 2 .
cos θ 1 = ( 1 - g ) 2 2 g ( 1 + g - 2 g υ ) 2 - 1 + g 2 2 g .
cos θ n = 1 + g 2 2 g - ( 1 - g ) 2 2 g ( 1 - g + 2 g υ ) 2             n 2.
W θ = p θ ( θ ) p θ * ( θ ) = ( 1 + g 2 + 2 g cos θ 1 + g 2 - 2 g cos θ ) 1 / 2 .
x d = α x [ f n 1 n 2 - ( z m + n 1 d n 2 ) ] - x m ,
y d = α y [ f n 1 n 2 - ( z m + n 1 d n 2 ) ] - y m .
Ψ ( r , z ) = 1 N V i = 1 N W i S m ( r , z ) ,
S m ( r , z ) = { 1 ( r - Δ R 2 , z - Δ Z 2 ) ( r m , z m ) ( r + Δ R 2 , z + Δ Z 2 ) and r m + 1 r d for z m + 1 = z d , 0 otherwise W i = W o , i W θ , i ,             r m = x m 2 + y m 2 , Δ R , Δ Z = radial and axial dimensions of a volume element , V = π r ( Δ R ) ( Δ Z ) .
Γ ( z ) = 1 N Δ Z i = 1 N W i S m ( r , z ) ,
S m ( r , z ) = { 1 z - Δ Z 2 z m z + Δ Z 2 for all r m and r m + 1 r d for z m + 1 = z d 0 otherwise ,
B R = z Γ ideal ( z ) z Γ ( z ) - z Γ ideal ( z ) ,

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