Abstract

Using a novel experimental geometry, we measured the ballistic attenuation of low-coherence optical fields propagating in multiple-scattering media. The high dynamic range and the angular filtering capability permit detecting the ballistic component through random media thicker than 20 mean free paths. Owing to the accuracy of the technique, we observe deviations from the standard Lambert–Beer law that are induced by the broad incident optical spectrum. We discuss the significance of these observations, their dependence on the type of scattering, and several potential applications.

© 2000 Optical Society of America

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  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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. U. Morgner, W. Drexler, F. X. Kartner, X. D. Li, C. Pitris, E. P. Ippen, J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25, 111–113 (2000).
    [CrossRef]
  3. G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
    [CrossRef]
  4. G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
    [CrossRef]
  5. J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  7. A. A. Chabanov, A. Z. Genack, “Field distributions in the crossover from ballistic to diffusive wave propagation,” Phys. Rev. E 56, 1338–1341 (1997).
    [CrossRef]
  8. Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
    [CrossRef]
  9. G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert–Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
    [CrossRef]
  10. W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 1. Open detector,” Appl. Opt. 21, 2405–2420 (1982).
    [CrossRef] [PubMed]
  11. M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging,” J. Opt. Soc. Am. 14, 216–223 (1997).
    [CrossRef]
  12. G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
    [CrossRef]
  13. M. R. Hee, J. A. Izatt, J. M. Jacobson, J. G. Fujimoto, “Femtosecond transillumination optical coherence tomography,” Opt. Lett. 18, 950–952 (1993).
    [CrossRef] [PubMed]
  14. M. R. Hee, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Femtosecond transillumination tomography in thick tissues,” Opt. Lett. 18, 1107–1109 (1993).
    [CrossRef] [PubMed]
  15. B. B. Das, K. M. Yoo, R. R. Alfano, “Ultrafast time-gated imaging in thick tissues: a step toward optical mammography,” Opt. Lett. 18, 1092–1094 (1993).
    [CrossRef] [PubMed]
  16. S. G. Demos, R. R. Alfano, “Temporal gating in highly scattering media by degree of optical polarization,” Opt. Lett. 21, 161–163 (1996).
    [CrossRef] [PubMed]
  17. A. Dogariu, I. Uozumi, T. Asakura, “Ballistic propagation of light through fractal gels,” Waves Random Media 4, 1–6 (1994).
    [CrossRef]
  18. H. P. Chiang, W. S. Chang, J. Wang, “Imaging through random media by using cw broadband interferometry,” Opt. Lett. 18, 546–548 (1993).
    [CrossRef] [PubMed]
  19. R. J. Zdrojkowski, R. L. Longini, “Optical transmission through whole blood illuminated with highly collimated light,” J. Opt. Soc. Am. 59, 898–904 (1969).
  20. J. M. Schmitt, A. Knuttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
    [CrossRef] [PubMed]

2000 (2)

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

U. Morgner, W. Drexler, F. X. Kartner, X. D. Li, C. Pitris, E. P. Ippen, J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25, 111–113 (2000).
[CrossRef]

1999 (2)

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
[CrossRef]

1997 (3)

M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging,” J. Opt. Soc. Am. 14, 216–223 (1997).
[CrossRef]

G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
[CrossRef]

A. A. Chabanov, A. Z. Genack, “Field distributions in the crossover from ballistic to diffusive wave propagation,” Phys. Rev. E 56, 1338–1341 (1997).
[CrossRef]

1996 (1)

1994 (1)

A. Dogariu, I. Uozumi, T. Asakura, “Ballistic propagation of light through fractal gels,” Waves Random Media 4, 1–6 (1994).
[CrossRef]

1993 (5)

1991 (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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1988 (1)

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert–Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

1982 (1)

1969 (1)

Alfano, R. R.

Asakura, T.

A. Dogariu, I. Uozumi, T. Asakura, “Ballistic propagation of light through fractal gels,” Waves Random Media 4, 1–6 (1994).
[CrossRef]

Bonner, R. F.

Bruscaglioni, P.

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert–Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov, A. Z. Genack, “Field distributions in the crossover from ballistic to diffusive wave propagation,” Phys. Rev. E 56, 1338–1341 (1997).
[CrossRef]

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chang, W. S.

Chiang, H. P.

Damaschini, V.

G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
[CrossRef]

Das, B. B.

Demos, S. G.

Dogariu, A.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
[CrossRef]

A. Dogariu, I. Uozumi, T. Asakura, “Ballistic propagation of light through fractal gels,” Waves Random Media 4, 1–6 (1994).
[CrossRef]

Dorn, P.

M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging,” J. Opt. Soc. Am. 14, 216–223 (1997).
[CrossRef]

Drexler, W.

Duderstadt, J. J.

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

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

Genack, A. Z.

M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging,” J. Opt. Soc. Am. 14, 216–223 (1997).
[CrossRef]

A. A. Chabanov, A. Z. Genack, “Field distributions in the crossover from ballistic to diffusive wave propagation,” Phys. Rev. E 56, 1338–1341 (1997).
[CrossRef]

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hamilton, L. J.

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

Hee, M. R.

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Ippen, E. P.

Ishimaru, A.

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

Izatt, J. A.

Jacobson, J. M.

Jarry, G.

G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
[CrossRef]

Jones, I. P.

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

Jurczak, M.

G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
[CrossRef]

Kartner, F. X.

Keiser, R.

G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
[CrossRef]

Kempe, M.

M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging,” J. Opt. Soc. Am. 14, 216–223 (1997).
[CrossRef]

Knuttel, A.

Li, X. D.

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Longini, R. L.

Morgner, U.

Mujat, C.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

Page, J. H.

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

Pitris, C.

Popescu, G.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
[CrossRef]

Puliafito, C. 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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Rudolph, W.

M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging,” J. Opt. Soc. Am. 14, 216–223 (1997).
[CrossRef]

Schmitt, J. M.

Schriemer, H. P.

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sheng, P.

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

Steimer, E.

G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
[CrossRef]

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

M. R. Hee, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Femtosecond transillumination tomography in thick tissues,” Opt. Lett. 18, 1107–1109 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tam, W. G.

Uozumi, I.

A. Dogariu, I. Uozumi, T. Asakura, “Ballistic propagation of light through fractal gels,” Waves Random Media 4, 1–6 (1994).
[CrossRef]

Wang, J.

Weitz, D. A.

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

Yoo, K. M.

Zaccanti, G.

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert–Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

Zardecki, A.

Zdrojkowski, R. J.

Zhang, Z. Q.

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (1)

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert–Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

J. Opt. (1)

G. Jarry, E. Steimer, V. Damaschini, M. Jurczak, R. Keiser, “Coherent components of forward light propagation through scattering media,” J. Opt. 28, 83–89 (1997).
[CrossRef]

J. Opt. Soc. Am. (2)

M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging,” J. Opt. Soc. Am. 14, 216–223 (1997).
[CrossRef]

R. J. Zdrojkowski, R. L. Longini, “Optical transmission through whole blood illuminated with highly collimated light,” J. Opt. Soc. Am. 59, 898–904 (1969).

Opt. Lett. (7)

Phys. Rev. E (3)

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

A. A. Chabanov, A. Z. Genack, “Field distributions in the crossover from ballistic to diffusive wave propagation,” Phys. Rev. E 56, 1338–1341 (1997).
[CrossRef]

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, P. Sheng, “Wave propagation and scattering in random media,” Phys. Rev. E 60, 4843–4850 (1999).
[CrossRef]

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. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Waves Random Media (1)

A. Dogariu, I. Uozumi, T. Asakura, “Ballistic propagation of light through fractal gels,” Waves Random Media 4, 1–6 (1994).
[CrossRef]

Other (2)

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

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

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Figures (2)

Fig. 1
Fig. 1

Experimental setup: S, source; D, detector. The interference peaks correspond to different interfaces, as indicated.

Fig. 2
Fig. 2

Ballistic attenuation for suspensions of different particle sizes. The data are scaled as indicated; the dashed lines represent negative exponentials, whereas the solid lines are given by Eq. (3). The inset shows the relative difference between the transmission given by Eq. (3) and that of the Lambert–Beer law as a function of optical thickness L/l s .

Equations (3)

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

EDt=E0texpiks+E11texpikL11+E12texpikL12+E21texpikL21+E22texpikL22.
IDs=I0+i,j1,2 Ii,j|gks-Lij|cosks-Lij.
TΔλλ0=-+ SΔλλ-λ0exp-NσsλLdλ.

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