Abstract

We have determined the scattering delay time of Mie scatterers (r=255 nm quartz spheres in polyester resin) from a combination of steady-state (integrating-sphere) and time-resolved (frequency-domain) measurements performed in the multiple-scattering regime. The effective transport velocity of light was derived from intensity and phase measurements at four different wavelengths by using the time-integrated microscopic Beer–Lambert law. We could demonstrate a systematic underestimation of the effective transport velocity compared with the phase velocity in the medium. Assuming that this discrepancy was caused entirely by the transient nature of a single-scattering process, the data presented resulted in time delays of between 18 fs (λ=678 nm) and 177 fs (λ=1064 nm) per scattering event. For three out of four wavelengths investigated, the measured values are in excellent agreement with values predicted by a theoretical model for the scattering delay time based on Mie theory.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. B. Das, F. Liu, R. R. Alfano, “Time-resolved fluorescence and photon migration studies in biomedical and model random media,” Rep. Prog. Phys. 60, 227–292 (1997).
    [CrossRef]
  2. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I: Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
    [CrossRef] [PubMed]
  3. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  4. S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
    [CrossRef]
  5. S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
    [CrossRef] [PubMed]
  6. I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, H.-J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. 36, 6529–6538 (1997).
    [CrossRef]
  7. A. Kienle, T. Glanzmann, G. Wagnieres, H. van den Bergh, “Investigation of two-layered turbid media with time-resolved reflectance,” Appl. Opt. 37, 6852–6862 (1998).
    [CrossRef]
  8. A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
    [CrossRef]
  9. A. Bott, W. Zdunkowski, “Electromagnetic energy within dielectric spheres,” J. Opt. Soc. Am. A 4, 1361–1365 (1987).
    [CrossRef]
  10. M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
    [CrossRef] [PubMed]
  11. Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissue based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
    [CrossRef]
  12. H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
    [CrossRef]
  13. Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, 79–81 (1995).
    [CrossRef]
  14. H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
    [CrossRef] [PubMed]
  15. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  16. U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
    [CrossRef] [PubMed]
  17. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
    [CrossRef]
  18. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  19. S. Willmann, H.-J. Schwarzmaier, A. Terenji, I. V. Yaroslavsky, P. Hering, “Quantitative microspectrophotometry in turbid media,” Appl. Opt. 38, 4904–4913 (1999).
    [CrossRef]
  20. I. V. Yaroslavsky, A. N. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Inverse hybrid technique for the determination of the optical determination of the optical properties of turbid media,” Appl. Opt. 35, 6797–6809 (1996).
    [CrossRef] [PubMed]
  21. S. J. Madsen, E. R. Anderson, R. C. Haskell, B. J. Tromberg, “Portable, high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. 19, 1934–1936 (1994).
    [CrossRef] [PubMed]
  22. W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2184 (1990).
    [CrossRef]
  23. A. Roggan, K. Dörschel, O. Minet, D. Wolff, G. Müller, “The optical properties of biological tissue in the near infrared wavelength range—review and measurements,” in Laser-Induced Interstitial Thermotherapy, Press Monograph PM 25, G. Müller ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1995), pp. 10–44.

1999

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

S. Willmann, H.-J. Schwarzmaier, A. Terenji, I. V. Yaroslavsky, P. Hering, “Quantitative microspectrophotometry in turbid media,” Appl. Opt. 38, 4904–4913 (1999).
[CrossRef]

1998

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

A. Kienle, T. Glanzmann, G. Wagnieres, H. van den Bergh, “Investigation of two-layered turbid media with time-resolved reflectance,” Appl. Opt. 37, 6852–6862 (1998).
[CrossRef]

1997

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissue based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, H.-J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. 36, 6529–6538 (1997).
[CrossRef]

B. B. Das, F. Liu, R. R. Alfano, “Time-resolved fluorescence and photon migration studies in biomedical and model random media,” Rep. Prog. Phys. 60, 227–292 (1997).
[CrossRef]

C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I: Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

1996

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
[CrossRef]

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

I. V. Yaroslavsky, A. N. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Inverse hybrid technique for the determination of the optical determination of the optical properties of turbid media,” Appl. Opt. 35, 6797–6809 (1996).
[CrossRef] [PubMed]

1995

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, 79–81 (1995).
[CrossRef]

1994

1992

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

1991

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

1990

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2184 (1990).
[CrossRef]

1989

1987

1965

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
[CrossRef]

Alfano, R. R.

B. B. Das, F. Liu, R. R. Alfano, “Time-resolved fluorescence and photon migration studies in biomedical and model random media,” Rep. Prog. Phys. 60, 227–292 (1997).
[CrossRef]

Anderson, E. R.

Arridge, S. R.

C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I: Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bott, A.

Chance, B.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2184 (1990).
[CrossRef]

Cope, M.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Das, B. B.

B. B. Das, F. Liu, R. R. Alfano, “Time-resolved fluorescence and photon migration studies in biomedical and model random media,” Rep. Prog. Phys. 60, 227–292 (1997).
[CrossRef]

Delpy, D. T.

C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I: Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Dörschel, K.

A. Roggan, K. Dörschel, O. Minet, D. Wolff, G. Müller, “The optical properties of biological tissue in the near infrared wavelength range—review and measurements,” in Laser-Induced Interstitial Thermotherapy, Press Monograph PM 25, G. Müller ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1995), pp. 10–44.

Fantini, S.

Franceschini, M. A.

Glanzmann, T.

Goldbach, T.

Gratton, E.

Grosenick, D.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Haskell, R. C.

Hebden, C.

C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I: Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

Hering, P.

Hiruma, T.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

Kienle, A.

Lagendijk, A.

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

Liu, F.

B. B. Das, F. Liu, R. R. Alfano, “Time-resolved fluorescence and photon migration studies in biomedical and model random media,” Rep. Prog. Phys. 60, 227–292 (1997).
[CrossRef]

Lu, Z.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

Madsen, S. J.

Malitson, I. H.

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
[CrossRef]

Minet, O.

A. Roggan, K. Dörschel, O. Minet, D. Wolff, G. Müller, “The optical properties of biological tissue in the near infrared wavelength range—review and measurements,” in Laser-Induced Interstitial Thermotherapy, Press Monograph PM 25, G. Müller ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1995), pp. 10–44.

Miwa, M.

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

Müller, G.

A. Roggan, K. Dörschel, O. Minet, D. Wolff, G. Müller, “The optical properties of biological tissue in the near infrared wavelength range—review and measurements,” in Laser-Induced Interstitial Thermotherapy, Press Monograph PM 25, G. Müller ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1995), pp. 10–44.

Patterson, M. S.

Prahl, S. A.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2184 (1990).
[CrossRef]

Rinneberg, H.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Roggan, A.

A. Roggan, K. Dörschel, O. Minet, D. Wolff, G. Müller, “The optical properties of biological tissue in the near infrared wavelength range—review and measurements,” in Laser-Induced Interstitial Thermotherapy, Press Monograph PM 25, G. Müller ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1995), pp. 10–44.

Schubert, F.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Schwarzmaier, H.-J.

Sukowski, U.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Terenji, A.

Tip, A.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

Tromberg, B. J.

Tsuchiya, Y.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissue based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, 79–81 (1995).
[CrossRef]

Tuchin, V. V.

Urakami, T.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissue based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, 79–81 (1995).
[CrossRef]

van Albada, M. P.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

van den Bergh, H.

van Tiggelen, B. A.

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

Wagnieres, G.

Welch, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2184 (1990).
[CrossRef]

Willmann, S.

Wilson, B. C.

Wolff, D.

A. Roggan, K. Dörschel, O. Minet, D. Wolff, G. Müller, “The optical properties of biological tissue in the near infrared wavelength range—review and measurements,” in Laser-Induced Interstitial Thermotherapy, Press Monograph PM 25, G. Müller ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1995), pp. 10–44.

Yamashita, Y.

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

Yaroslavsky, A. N.

Yaroslavsky, I. V.

Zdunkowski, W.

Zhang, H.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2184 (1990).
[CrossRef]

J. Biomed. Opt.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
[CrossRef]

A. Bott, W. Zdunkowski, “Electromagnetic energy within dielectric spheres,” J. Opt. Soc. Am. A 4, 1361–1365 (1987).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, 79–81 (1995).
[CrossRef]

Opt. Commun.

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissue based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

Opt. Lett.

Phys. Med. Biol.

C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I: Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Phys. Rep.

A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996).
[CrossRef]

Phys. Rev. Lett.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

Rep. Prog. Phys.

B. B. Das, F. Liu, R. R. Alfano, “Time-resolved fluorescence and photon migration studies in biomedical and model random media,” Rep. Prog. Phys. 60, 227–292 (1997).
[CrossRef]

Other

A. Roggan, K. Dörschel, O. Minet, D. Wolff, G. Müller, “The optical properties of biological tissue in the near infrared wavelength range—review and measurements,” in Laser-Induced Interstitial Thermotherapy, Press Monograph PM 25, G. Müller ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1995), pp. 10–44.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic drawing of the laser-diode setup (LDD1–LDD3, laser-diode drivers; LD1–LD3, laser diodes; S1–3, shutters; FC1–FC3, fiber couplers; APD, avalanche photodiode; MPX, multiplexer).

Fig. 2
Fig. 2

Schematic drawing of the Nd:YAG laser setup (AMP, amplifier; P1, P2, crossed polarizers; EOM, electro-optical modulator (Pockels cell); FC, fiber coupler; APD, avalanche photodiode; LOCK-IN, lock-in detector).

Fig. 3
Fig. 3

Results of the cw measurement of μa and μs with the IS setup (squares, mean±standard error) and comparison with the scattering efficiency Qsca obtained from Mie calculations (curves).

Fig. 4
Fig. 4

Comparison of the effective transport velocity (squares, mean±standard error) with the phase velocity (dotted line) of the phantom.

Fig. 5
Fig. 5

Comparison of the experimentally determined scattering delay times (squares, mean±standard error) with the predictions of the Mie model (curve).

Equations (5)

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

τ(λ)=W(λ)σsca(λ)U0cphase,
τ=1μscphasecphaseveff-1,
Idc(t)exp(-μavefft).
t=ΔΦ/(2πΔf),
veff=-1μaΔ ln(Idc)Δt.

Metrics