Abstract

We propose optical path-length spectroscopy as a new approach to obtaining information from media that exhibit multiple light scattering. By using a backscattering technique based on low-coherence interferometry, we are able to determine the optical path-length distribution for light reflected from a random medium and to infer the value of the transport mean free path. We illustrate how a diffusion approximation model leads to a satisfactory description of depth-resolved profiles of the backscattered intensity and discuss potential applications of this technique.

© 1999 Optical Society of America

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References

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  1. R. C. Youngquist, S. Carr, and D. E. Davies, Opt. Lett. 12, 158 (1987).
    [CrossRef] [PubMed]
  2. J. M. Schmitt and S. H. Xiang, Opt. Lett. 23, 13 (1998).
    [CrossRef]
  3. D. A. Boas, K. K. Bizheva, and A. M. Siegel, Opt. Lett. 23, 5 (1998).
    [CrossRef]
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1971), Vol. 1, Chap. 9.
  5. A. Ishimaru, J. Opt. Soc. Am. 68, 8 (1978).
    [CrossRef]
  6. M. S. Patterson, B. Chance, and B. C. Wilson, Appl. Opt. 28, 12 (1989).
    [CrossRef]
  7. K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 22 (1990).
    [CrossRef]
  8. F. Liu, K. M. Yoo, and R. R. Alfano, Opt. Lett. 18, 6 (1993).
  9. A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
    [CrossRef]
  10. D. J. Durian, Phys. Rev. E 50, 5 (1994).
    [CrossRef]
  11. P. A. Lemieux, M. U. Vera, and D. J. Durian, Phys. Rev. E 57, 4 (1998).
    [CrossRef]
  12. H. Chou and W. V. Sorin, Hewlett-Packard J. 44(1), 52 (1993).
  13. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).
  14. M. U. Vera and D. J. Durian, Phys. Rev. E 53, 4 (1996).
    [CrossRef]
  15. D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, J. Phys. (France) 51, 2101 (1990).
    [CrossRef]

1998 (3)

J. M. Schmitt and S. H. Xiang, Opt. Lett. 23, 13 (1998).
[CrossRef]

D. A. Boas, K. K. Bizheva, and A. M. Siegel, Opt. Lett. 23, 5 (1998).
[CrossRef]

P. A. Lemieux, M. U. Vera, and D. J. Durian, Phys. Rev. E 57, 4 (1998).
[CrossRef]

1997 (1)

A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
[CrossRef]

1996 (1)

M. U. Vera and D. J. Durian, Phys. Rev. E 53, 4 (1996).
[CrossRef]

1994 (1)

D. J. Durian, Phys. Rev. E 50, 5 (1994).
[CrossRef]

1993 (2)

F. Liu, K. M. Yoo, and R. R. Alfano, Opt. Lett. 18, 6 (1993).

H. Chou and W. V. Sorin, Hewlett-Packard J. 44(1), 52 (1993).

1990 (2)

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, J. Phys. (France) 51, 2101 (1990).
[CrossRef]

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 22 (1990).
[CrossRef]

1989 (1)

1987 (1)

1978 (1)

A. Ishimaru, J. Opt. Soc. Am. 68, 8 (1978).
[CrossRef]

Alfano, R. R.

F. Liu, K. M. Yoo, and R. R. Alfano, Opt. Lett. 18, 6 (1993).

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 22 (1990).
[CrossRef]

Bizheva, K. K.

D. A. Boas, K. K. Bizheva, and A. M. Siegel, Opt. Lett. 23, 5 (1998).
[CrossRef]

Boas, D. A.

D. A. Boas, K. K. Bizheva, and A. M. Siegel, Opt. Lett. 23, 5 (1998).
[CrossRef]

Boreman, G.

A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
[CrossRef]

Carr, S.

Chance, B.

Chou, H.

H. Chou and W. V. Sorin, Hewlett-Packard J. 44(1), 52 (1993).

Davies, D. E.

Dogariu, A.

A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
[CrossRef]

Duderstadt, J. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Durian, D. J.

P. A. Lemieux, M. U. Vera, and D. J. Durian, Phys. Rev. E 57, 4 (1998).
[CrossRef]

M. U. Vera and D. J. Durian, Phys. Rev. E 53, 4 (1996).
[CrossRef]

D. J. Durian, Phys. Rev. E 50, 5 (1994).
[CrossRef]

Hamilton, L. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, J. Phys. (France) 51, 2101 (1990).
[CrossRef]

Ishimaru, A.

A. Ishimaru, J. Opt. Soc. Am. 68, 8 (1978).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1971), Vol. 1, Chap. 9.

Kutsche, C.

A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
[CrossRef]

Lemieux, P. A.

P. A. Lemieux, M. U. Vera, and D. J. Durian, Phys. Rev. E 57, 4 (1998).
[CrossRef]

Likamwa, P.

A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
[CrossRef]

Liu, F.

F. Liu, K. M. Yoo, and R. R. Alfano, Opt. Lett. 18, 6 (1993).

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 22 (1990).
[CrossRef]

Moudgil, B.

A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
[CrossRef]

Patterson, M. S.

Pine, D. J.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, J. Phys. (France) 51, 2101 (1990).
[CrossRef]

Schmitt, J. M.

Siegel, A. M.

D. A. Boas, K. K. Bizheva, and A. M. Siegel, Opt. Lett. 23, 5 (1998).
[CrossRef]

Sorin, W. V.

H. Chou and W. V. Sorin, Hewlett-Packard J. 44(1), 52 (1993).

Vera, M. U.

P. A. Lemieux, M. U. Vera, and D. J. Durian, Phys. Rev. E 57, 4 (1998).
[CrossRef]

M. U. Vera and D. J. Durian, Phys. Rev. E 53, 4 (1996).
[CrossRef]

Weitz, D. A.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, J. Phys. (France) 51, 2101 (1990).
[CrossRef]

Wilson, B. C.

Xiang, S. H.

Yoo, K. M.

F. Liu, K. M. Yoo, and R. R. Alfano, Opt. Lett. 18, 6 (1993).

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 22 (1990).
[CrossRef]

Youngquist, R. C.

Zhu, J. X.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, J. Phys. (France) 51, 2101 (1990).
[CrossRef]

Appl. Opt. (1)

Hewlett-Packard J. (1)

H. Chou and W. V. Sorin, Hewlett-Packard J. 44(1), 52 (1993).

J. Opt. Soc. Am. (1)

A. Ishimaru, J. Opt. Soc. Am. 68, 8 (1978).
[CrossRef]

J. Phys. (France) (1)

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, J. Phys. (France) 51, 2101 (1990).
[CrossRef]

Opt. Lett. (5)

R. C. Youngquist, S. Carr, and D. E. Davies, Opt. Lett. 12, 158 (1987).
[CrossRef] [PubMed]

J. M. Schmitt and S. H. Xiang, Opt. Lett. 23, 13 (1998).
[CrossRef]

D. A. Boas, K. K. Bizheva, and A. M. Siegel, Opt. Lett. 23, 5 (1998).
[CrossRef]

F. Liu, K. M. Yoo, and R. R. Alfano, Opt. Lett. 18, 6 (1993).

A. Dogariu, C. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 9 (1997).
[CrossRef]

Phys. Rev. E (3)

D. J. Durian, Phys. Rev. E 50, 5 (1994).
[CrossRef]

P. A. Lemieux, M. U. Vera, and D. J. Durian, Phys. Rev. E 57, 4 (1998).
[CrossRef]

M. U. Vera and D. J. Durian, Phys. Rev. E 53, 4 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 22 (1990).
[CrossRef]

Other (2)

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1971), Vol. 1, Chap. 9.

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Figures (1)

Fig. 1
Fig. 1

Values of normalized backscattered intensity corresponding to suspensions of polystyrene microspheres with diameters of 0.426 μm and with volume fractions of 10%, 5%, and 2.5%. Continuous curves, the fit with the functional form in Eq.  (1). For clarity, the normalized intensities have been scaled as indicated.

Equations (1)

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Js=4πlt/3-3/2z0vs-5/2exp-3z024slt,

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