Abstract

The temporal profiles of ultrashort laser pulses scattered in random media with different experimental geometries were measured and analyzed by using the photon flux and the photon density predicted by the diffusion theory. The scattered laser pulse profiles detected by an optical fiber inside an infinite random medium are found to be described by the photon density. For a semi-infinite medium, the scattered pulse profile emitted from the surface of the medium can be described by either the photon density or the photon flux. These results can be consistently explained by the diffuse intensity (radiance) of transport theory.

© 1993 Optical Society of America

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References

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  1. C. C. Johnson, IEEE Trans. Biomed. Eng. 17, 129 (1970).
    [CrossRef] [PubMed]
  2. R. J. Zdrojkowski, N. R. Pisharoty, IEEE Trans. Biomed. Eng. 17, 122 (1970).
    [CrossRef] [PubMed]
  3. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, Appl. Opt. 22, 2456 (1983).R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, Appl. Opt. 22, 2463 (1983).
    [CrossRef] [PubMed]
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 9.
  5. G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
    [CrossRef] [PubMed]
  6. J. M. Drake, A. Z. Genack, Phys. Rev. Lett. 63, 259 (1989).
    [CrossRef] [PubMed]
  7. M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2231 (1989).
  8. S. L. Jacques, IEEE Trans. Biomed. Eng. 36, 1155 (1989).
    [CrossRef] [PubMed]
  9. K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990); K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett., erratum 65, 2210 (1990).
    [CrossRef] [PubMed]
  10. M. Lax, V. Nayaranamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), pp. 229–235.

1990 (1)

K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990); K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett., erratum 65, 2210 (1990).
[CrossRef] [PubMed]

1989 (3)

J. M. Drake, A. Z. Genack, Phys. Rev. Lett. 63, 259 (1989).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2231 (1989).

S. L. Jacques, IEEE Trans. Biomed. Eng. 36, 1155 (1989).
[CrossRef] [PubMed]

1987 (1)

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

1983 (1)

1970 (2)

C. C. Johnson, IEEE Trans. Biomed. Eng. 17, 129 (1970).
[CrossRef] [PubMed]

R. J. Zdrojkowski, N. R. Pisharoty, IEEE Trans. Biomed. Eng. 17, 122 (1970).
[CrossRef] [PubMed]

Alfano, R. R.

K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990); K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett., erratum 65, 2210 (1990).
[CrossRef] [PubMed]

Chance, B.

M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2231 (1989).

Drake, J. M.

J. M. Drake, A. Z. Genack, Phys. Rev. Lett. 63, 259 (1989).
[CrossRef] [PubMed]

Ferwerda, H. A.

Fleury, P. A.

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

Fulton, R. C.

M. Lax, V. Nayaranamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), pp. 229–235.

Genack, A. Z.

J. M. Drake, A. Z. Genack, Phys. Rev. Lett. 63, 259 (1989).
[CrossRef] [PubMed]

Groenhuis, R. A. J.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 9.

Jacques, S. L.

S. L. Jacques, IEEE Trans. Biomed. Eng. 36, 1155 (1989).
[CrossRef] [PubMed]

Johnson, C. C.

C. C. Johnson, IEEE Trans. Biomed. Eng. 17, 129 (1970).
[CrossRef] [PubMed]

Lax, M.

M. Lax, V. Nayaranamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), pp. 229–235.

Liu, F.

K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990); K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett., erratum 65, 2210 (1990).
[CrossRef] [PubMed]

McCall, S. L.

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

Nayaranamurti, V.

M. Lax, V. Nayaranamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), pp. 229–235.

Patterson, M. S.

M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2231 (1989).

Pisharoty, N. R.

R. J. Zdrojkowski, N. R. Pisharoty, IEEE Trans. Biomed. Eng. 17, 122 (1970).
[CrossRef] [PubMed]

Ten Bosch, J. J.

Watson, G. H.

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

Wilson, B. C.

M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2231 (1989).

Yoo, K. M.

K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990); K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett., erratum 65, 2210 (1990).
[CrossRef] [PubMed]

Zdrojkowski, R. J.

R. J. Zdrojkowski, N. R. Pisharoty, IEEE Trans. Biomed. Eng. 17, 122 (1970).
[CrossRef] [PubMed]

Appl. Opt. (2)

IEEE Trans. Biomed. Eng. (3)

S. L. Jacques, IEEE Trans. Biomed. Eng. 36, 1155 (1989).
[CrossRef] [PubMed]

C. C. Johnson, IEEE Trans. Biomed. Eng. 17, 129 (1970).
[CrossRef] [PubMed]

R. J. Zdrojkowski, N. R. Pisharoty, IEEE Trans. Biomed. Eng. 17, 122 (1970).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990); K. M. Yoo, F. Liu, R. R. Alfano, Phys. Rev. Lett., erratum 65, 2210 (1990).
[CrossRef] [PubMed]

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

J. M. Drake, A. Z. Genack, Phys. Rev. Lett. 63, 259 (1989).
[CrossRef] [PubMed]

Other (2)

M. Lax, V. Nayaranamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), pp. 229–235.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 9.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagrams of the different experimental geometries: (i) backscattering in an infinite medium, (ii) backscattering from a semi-infinite medium.

Fig. 2
Fig. 2

Normalized temporal profiles of a backscattered pulse in an infinite Intralipid solution for different r and scatterer concentrations: (a) 20 mm and 0.48%, (b) 10 mm and 0.48%, (c) 30 mm and 0.24%. The solid, dotted, and dashed curves are the experimental results, the fitting by Eq. (2), and the fitting by Eq. (3), respectively.

Fig. 3
Fig. 3

Normalized temporal profiles of a backscattered pulse from a semi-infinite Intralipid solution for different r and scatterer concentrations: (a) 30 mm and 0.48%, (b) 20 mm and 0.48%, (c) same as (a) but with a black plate inserted between the source and detection fibers. The solid and dashed curves are the experimental results and the fitting by Eqs. (4) and (5), respectively.

Equations (5)

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n ( r , t ) t = D 2 n ( r , t ) ν l a n ( r , t ) + δ ( r ) δ ( t ) ,
n ( r , t ) = 1 ( 4 π D t ) 3 / 2 exp ( r 2 4 D t ν t l a ) ,
j ( r , t ) = s ˆ r 2 t n ( r , t ) .
n ( r , t ) = 1 ( 4 π D t ) 3 / 2 exp ( r 2 4 D t ν t l a ) × [ 1 exp ( z 0 2 D t ) ] ,
j ( r , t ) = 1 ( 4 π D t ) 3 / 2 exp ( r 2 4 D t ν t l a ) exp ( z 0 2 D t ) z 0 t ,

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