Abstract

The angular and temporal distributions of light scattered around the backward direction from biological tissues are measured. An enhancement of scattered light intensity around the backward direction, which is associated with the weak photon localization, is observed. The transport mean free path lt and the absorption length la of the light in biological tissue can be obtained from the angular line shape of the coherent peak. The values lt and la can also be obtained from the temporal profile of the scattered pulse.

© 1990 Optical Society of America

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  1. Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 8, 831–845 (1984).
    [CrossRef]
  2. M. P. Van Albada, Ad Lagendijk, “Observation of weak localization of light in a random media,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  3. P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
    [CrossRef] [PubMed]
  4. E. Akkermans, P. E. Wolf, R. Maynard, “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
    [CrossRef] [PubMed]
  5. M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: Effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
    [CrossRef]
  6. P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental studies,” J. Phys. France 49, 63–67 (1988).
    [CrossRef]
  7. S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
    [CrossRef] [PubMed]
  8. S. Etemad, R. Thompson, M. J. Andrejco, “Weak Localization of Photons: Universal Fluctuations and Ensemble Averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
    [CrossRef] [PubMed]
  9. M. Rosenbluh, I. Edrei, M. Kaveh, I. Freud, “Precision determination of the line shape for coherently backscattered light from disordered solids: Comparison of vector and scalar theories,” Phys. Rev. A, 4458–4460 (1987).
    [CrossRef] [PubMed]
  10. M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of Weak Localization of Light in a Finite Slab: Anisotropy Effects and Light-Path Classification,” Phys. Rev. Lett. 58, 361–364 (1987).
    [CrossRef] [PubMed]
  11. K. M. Yoo, Y. Takiguchi, R. R. Alfano, “Weak Localization of Photons: Contributions from the Different Scattering Path-lengths,” IEEE Photon. Tech. Lett. 1, 94–96 (1989).
    [CrossRef]
  12. K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
    [CrossRef] [PubMed]
  13. G. A. Navarro, A. E. Profio, “Contrast in diaphanography of the breast,” Med. Phys. 15, 181–187 (1988).
    [CrossRef] [PubMed]

1989

K. M. Yoo, Y. Takiguchi, R. R. Alfano, “Weak Localization of Photons: Contributions from the Different Scattering Path-lengths,” IEEE Photon. Tech. Lett. 1, 94–96 (1989).
[CrossRef]

K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
[CrossRef] [PubMed]

1988

G. A. Navarro, A. E. Profio, “Contrast in diaphanography of the breast,” Med. Phys. 15, 181–187 (1988).
[CrossRef] [PubMed]

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental studies,” J. Phys. France 49, 63–67 (1988).
[CrossRef]

1987

S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[CrossRef] [PubMed]

M. Rosenbluh, I. Edrei, M. Kaveh, I. Freud, “Precision determination of the line shape for coherently backscattered light from disordered solids: Comparison of vector and scalar theories,” Phys. Rev. A, 4458–4460 (1987).
[CrossRef] [PubMed]

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of Weak Localization of Light in a Finite Slab: Anisotropy Effects and Light-Path Classification,” Phys. Rev. Lett. 58, 361–364 (1987).
[CrossRef] [PubMed]

1986

S. Etemad, R. Thompson, M. J. Andrejco, “Weak Localization of Photons: Universal Fluctuations and Ensemble Averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: Effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[CrossRef]

1985

M. P. Van Albada, Ad Lagendijk, “Observation of weak localization of light in a random media,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

1984

Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 8, 831–845 (1984).
[CrossRef]

Akkermans, E.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental studies,” J. Phys. France 49, 63–67 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

Alfano, R. R.

K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
[CrossRef] [PubMed]

K. M. Yoo, Y. Takiguchi, R. R. Alfano, “Weak Localization of Photons: Contributions from the Different Scattering Path-lengths,” IEEE Photon. Tech. Lett. 1, 94–96 (1989).
[CrossRef]

Andrejco, M. J.

S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, “Weak Localization of Photons: Universal Fluctuations and Ensemble Averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

Arya, K.

K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
[CrossRef] [PubMed]

Birman, J. L.

K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
[CrossRef] [PubMed]

Cwilich, G.

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: Effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[CrossRef]

Edrei, I.

M. Rosenbluh, I. Edrei, M. Kaveh, I. Freud, “Precision determination of the line shape for coherently backscattered light from disordered solids: Comparison of vector and scalar theories,” Phys. Rev. A, 4458–4460 (1987).
[CrossRef] [PubMed]

Etemad, S.

S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, “Weak Localization of Photons: Universal Fluctuations and Ensemble Averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

Freud, I.

M. Rosenbluh, I. Edrei, M. Kaveh, I. Freud, “Precision determination of the line shape for coherently backscattered light from disordered solids: Comparison of vector and scalar theories,” Phys. Rev. A, 4458–4460 (1987).
[CrossRef] [PubMed]

Ishimaru, A.

Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 8, 831–845 (1984).
[CrossRef]

Kaveh, M.

M. Rosenbluh, I. Edrei, M. Kaveh, I. Freud, “Precision determination of the line shape for coherently backscattered light from disordered solids: Comparison of vector and scalar theories,” Phys. Rev. A, 4458–4460 (1987).
[CrossRef] [PubMed]

Kuga, Y.

Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 8, 831–845 (1984).
[CrossRef]

Lagendijk, Ad

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of Weak Localization of Light in a Finite Slab: Anisotropy Effects and Light-Path Classification,” Phys. Rev. Lett. 58, 361–364 (1987).
[CrossRef] [PubMed]

M. P. Van Albada, Ad Lagendijk, “Observation of weak localization of light in a random media,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Mackintosh, F. C.

S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[CrossRef] [PubMed]

Maret, G.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental studies,” J. Phys. France 49, 63–67 (1988).
[CrossRef]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Maynard, R.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental studies,” J. Phys. France 49, 63–67 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

Navarro, G. A.

G. A. Navarro, A. E. Profio, “Contrast in diaphanography of the breast,” Med. Phys. 15, 181–187 (1988).
[CrossRef] [PubMed]

Profio, A. E.

G. A. Navarro, A. E. Profio, “Contrast in diaphanography of the breast,” Med. Phys. 15, 181–187 (1988).
[CrossRef] [PubMed]

Rosenbluh, M.

M. Rosenbluh, I. Edrei, M. Kaveh, I. Freud, “Precision determination of the line shape for coherently backscattered light from disordered solids: Comparison of vector and scalar theories,” Phys. Rev. A, 4458–4460 (1987).
[CrossRef] [PubMed]

Sajeev, J.

S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[CrossRef] [PubMed]

Stephen, M. J.

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: Effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[CrossRef]

Takiguchi, Y.

K. M. Yoo, Y. Takiguchi, R. R. Alfano, “Weak Localization of Photons: Contributions from the Different Scattering Path-lengths,” IEEE Photon. Tech. Lett. 1, 94–96 (1989).
[CrossRef]

Tang, G. C.

K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
[CrossRef] [PubMed]

Thompson, R.

S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, “Weak Localization of Photons: Universal Fluctuations and Ensemble Averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

van Albada, M. P.

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of Weak Localization of Light in a Finite Slab: Anisotropy Effects and Light-Path Classification,” Phys. Rev. Lett. 58, 361–364 (1987).
[CrossRef] [PubMed]

M. P. Van Albada, Ad Lagendijk, “Observation of weak localization of light in a random media,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

van der Mark, M. B.

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of Weak Localization of Light in a Finite Slab: Anisotropy Effects and Light-Path Classification,” Phys. Rev. Lett. 58, 361–364 (1987).
[CrossRef] [PubMed]

Wolf, P. E.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental studies,” J. Phys. France 49, 63–67 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Yoo, K. M.

K. M. Yoo, Y. Takiguchi, R. R. Alfano, “Weak Localization of Photons: Contributions from the Different Scattering Path-lengths,” IEEE Photon. Tech. Lett. 1, 94–96 (1989).
[CrossRef]

K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
[CrossRef] [PubMed]

IEEE Photon. Tech. Lett.

K. M. Yoo, Y. Takiguchi, R. R. Alfano, “Weak Localization of Photons: Contributions from the Different Scattering Path-lengths,” IEEE Photon. Tech. Lett. 1, 94–96 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 8, 831–845 (1984).
[CrossRef]

J. Phys. France

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental studies,” J. Phys. France 49, 63–67 (1988).
[CrossRef]

Med. Phys.

G. A. Navarro, A. E. Profio, “Contrast in diaphanography of the breast,” Med. Phys. 15, 181–187 (1988).
[CrossRef] [PubMed]

Phys. Rev. A

K. M. Yoo, K. Arya, G. C. Tang, J. L. Birman, R. R. Alfano, “Coherent Backscattering of a Picosecond Pulse from a Disordered Medium: Analysis of the Pulse Shape in the Time Domain,” Phys. Rev. A 39, 3728–3730 (1989).
[CrossRef] [PubMed]

M. Rosenbluh, I. Edrei, M. Kaveh, I. Freud, “Precision determination of the line shape for coherently backscattered light from disordered solids: Comparison of vector and scalar theories,” Phys. Rev. A, 4458–4460 (1987).
[CrossRef] [PubMed]

Phys. Rev. B

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: Effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[CrossRef]

Phys. Rev. Lett.

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of Weak Localization of Light in a Finite Slab: Anisotropy Effects and Light-Path Classification,” Phys. Rev. Lett. 58, 361–364 (1987).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, J. Sajeev, F. C. Mackintosh, “Weak localization of photons: Termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, “Weak Localization of Photons: Universal Fluctuations and Ensemble Averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

M. P. Van Albada, Ad Lagendijk, “Observation of weak localization of light in a random media,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic of experimental setup.

Fig. 2
Fig. 2

Angular distribution of intensity of light backscattered from human normal breast tissue. Solid curve is the theoretical fit from equation (1).

Fig. 3
Fig. 3

Angular distribution of intensity of light backscattered from human benign lung tissue. Solid curve is the theoretical fit from equation (1).

Fig. 4
Fig. 4

Intensity and the line shape of the coherent peak of the scattered light at various times after the 100 fs pulse incident on lung cancer tissue. The selected time segments for the curves from the top are: 4, 8, 13, 22, and 35 ps.

Fig. 5
Fig. 5

The temporal profiles of the scattered pulse from lung cancer tissue. The higher curve is for light scattered at 0 mrad and the lower one is at 3 mrad.

Fig. 6
Fig. 6

The temporal profiles of the scattered pulse from breast cancer tissue. The higher curve is for light scattered at 0 mrad and the lower one is at 3 mrad.

Equations (3)

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

α ( θ ) = 3 16 π { 1 + 2 z 0 l t + 1 ( 1 + q l t 2 [ 1 + 1 - exp ( - 2 q z 0 ) q l t ] } ,
q = [ q 2 + q a 2 ] 1 / 2 ,
q a 2 = 3 / ( l a l t ) .

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