Abstract

We report first results of measurements by low-coherence Doppler interferometry of the path-length distribution of photons undergoing multiple scattering in a highly turbid medium. We use a Mach–Zehnder interferometer with multimode graded-index fibers and a superluminescent diode as the light source. The path-length distribution is obtained by recording of the heterodyne fluctuations that arise from the Brownian motion of particles in an Intralipid suspension as a function of the optical path length. The experimental path-length distribution is in good agreement with predictions of Monte Carlo simulations. In the heterodyne spectrum, an increase of the mean Doppler frequency with path length is observed.

© 2001 Optical Society of America

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References

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  1. A. P. Shepherd and P. Å. Öberg, Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, Mass., 1990).
    [CrossRef]
  2. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
    [CrossRef] [PubMed]
  3. D. A. Boas, K. K. Bizheva, and A. M. Siegel, Opt. Lett. 23, 319 (1998).
  4. Y. Imai and K. Tanaka, J. Opt. Soc. Am. 16, 2007 (1999).
    [CrossRef]
  5. F. F. M. de Mul, M. H. Koelink, M. L. Kok, P. J. Harmsma, J. Greve, R. Graaff, and J. G. Aarnoudse, Appl. Opt. 34, 6595 (1995).
    [CrossRef] [PubMed]
  6. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, and M. J. C. van Gemert, Appl. Opt. 30, 4507 (1991).
    [CrossRef] [PubMed]

1999 (1)

Y. Imai and K. Tanaka, J. Opt. Soc. Am. 16, 2007 (1999).
[CrossRef]

1998 (1)

1995 (1)

1991 (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, and M. J. C. van Gemert, Appl. Opt. 30, 4507 (1991).
[CrossRef] [PubMed]

Aarnoudse, J. G.

Bizheva, K. K.

Boas, D. A.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

de Mul, F. F. M.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Graaff, R.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Greve, J.

Harmsma, P. J.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Imai, Y.

Y. Imai and K. Tanaka, J. Opt. Soc. Am. 16, 2007 (1999).
[CrossRef]

Koelink, M. H.

Kok, M. L.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Moes, C. J. M.

Öberg, P. Å.

A. P. Shepherd and P. Å. Öberg, Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, Mass., 1990).
[CrossRef]

Prahl, S. A.

Puliafito, C.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Shepherd, A. P.

A. P. Shepherd and P. Å. Öberg, Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, Mass., 1990).
[CrossRef]

Siegel, A. M.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Tanaka, K.

Y. Imai and K. Tanaka, J. Opt. Soc. Am. 16, 2007 (1999).
[CrossRef]

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Y. Imai and K. Tanaka, J. Opt. Soc. Am. 16, 2007 (1999).
[CrossRef]

Opt. Lett. (1)

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Other (1)

A. P. Shepherd and P. Å. Öberg, Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, Mass., 1990).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the fiber-optic Mach–Zehnder interferometer used to measure the path-length distribution of Doppler-scattered photons in a cuvette filled with an aqueous suspension of Intralipid. SLD, superluminescent diode; D, detector. 95:5, 50:50, fiber couplers.

Fig. 2
Fig. 2

Spectra of the dark-current noise, Sdarkf, the reference-arm noise, Sreff, the ordinary Doppler signal, Ssamplef, and the total Doppler signals, Stotf for two positions of the reference-arm mirror. Position 1 corresponds to maximum interference, and position 2 is for widely different sample and reference path lengths.

Fig. 3
Fig. 3

Homodyne Doppler spectrum, Shomf, which is taken as Ssamplef-Sreff. The heterodyne signal, Shetf, is Stot,1f-Stot,2f. Inset, Stot,2f at position 2 and Sreff+Ssamplef-Sdarkf (the curves are indistinguishable).

Fig. 4
Fig. 4

ac power of the heterodyne Doppler signal normalized by the dc2 component as a function of optical path length in the reference channel (squares); positions 1 and 2 refer to Fig.  2. The experimental data for stock 10%-solids Intralipid are compared with the result of Monte Carlo (MC) simulations. The experimental and the simulated functions are normalized by the maximum value.

Fig. 5
Fig. 5

Weighted first moment as a function of the optical path length. Position 1 corresponds to the maximum of the interference effect as indicated in Fig.  4. The solid curve is a guide for the eye.

Equations (2)

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It=ER2+i,jEiSt*EjStΓLijt/c+2 ReER*iEiStΓLit=IR+Ihom+Ihet,
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