Abstract

We show that optical properties of dense biological tissues can be determined from backscattered power curves measured by a low-coherence reflectometer. Our measurement approach is based on a first-order scattering theory that relates the backscattered power to the total and backscattering cross sections of scatterers in a turbid medium. As a validation of the technique, measurements were made with a commercially available reflectometer on suspensions of polystyrene microspheres having known optical properties. With this reflectometer, which employs a 1300-nm LED source that emits less than 20 μW, we found that skin tissues could be probed to a depth of nearly 1 mm. Estimates of optical coefficients of human dermis and of a variety of excised animal tissues are given.

© 1993 Optical Society of America

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  1. W. F. Cheong, S. A. Prahl, A. J. Welsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  2. B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissue,” Photochem. Photobiol. 46, 601–608 (1987).
    [CrossRef] [PubMed]
  3. S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
    [CrossRef] [PubMed]
  4. V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
    [CrossRef] [PubMed]
  5. K. M. Yoo, Q. R. Xing, R. R. Alfano, “Imaging objects hidden in highly scattering media using femtosecond second-harmonic-generation cross-correlation time gating,” Opt. Lett. 16, 1019–1021 (1991).
    [CrossRef] [PubMed]
  6. K. M. Yoo, R. R. Alfano, “Determination of the scattering and absorption lengths from the temporal profile of a backscattered pulse,” Opt. Lett. 15, 276–278 (1990).
    [CrossRef] [PubMed]
  7. K. M. Yoo, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultra-fast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
    [CrossRef]
  8. M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
    [CrossRef]
  9. J. M. Schmitt, A. H. Gandjbakhche, R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31, 6535–6546 (1992).
    [CrossRef] [PubMed]
  10. K. Takada, I. Yokohama, K. Chida, J. Noda, “New measurement system for fault location in optical waveguide devices based on an interferometric technique,” Appl. Opt. 26, 1603–1606 (1987).
    [CrossRef] [PubMed]
  11. B. L. Danielson, C. D. Whittenburg, “Guided wave reflectometry with micrometer resolution,” Appl. Opt. 26, 2836–2842 (1987).
    [CrossRef] [PubMed]
  12. H. Booster, H. Chou, “Higher resolution for backscatter measurements,” Lasers Optron. 10, 27–29 (1991).
  13. D. Huang, J. Wang, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
    [CrossRef] [PubMed]
  14. 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]
  15. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5.
  16. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 120–123.
  17. F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
    [CrossRef]
  18. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 5, pp. 93–106.
  19. R. C. Anderson, E. V. Browell, “First- and second-order backscattering from clouds illuminated by finite beams,” Appl. Opt. 11, 1345–1351 (1972).
    [CrossRef] [PubMed]
  20. R. A. Sigelmann, J. M. Reid, “Analysis and measurement of ultrasound backscattering from an ensemble of scatterers excited by sine-wave bursts,” J. Acoust. Soc. Am. 53, 1351–1355 (1973).
    [CrossRef]
  21. F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
    [CrossRef] [PubMed]
  22. J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.
  23. J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Brit. J. Dermatol. 89, 467–476 (1973).
    [CrossRef]
  24. M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
    [CrossRef]
  25. M. K. Moaveni, “A multiple scattering field theory applied to whole blood,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1970).
  26. P. Parsa, S. L. Jacques, N. S. Nishioka, “Optical properties of rat liver between 350 and 2200 nm,” Appl. Opt. 28, 2325–2330 (1989).
    [CrossRef] [PubMed]
  27. J. L. Karagiannes, Z. Y. Zhang, B. Grossweiner, L. I. Grossweiner, “Applications of the 1-D diffusion approximation to the optics of tissue and tissue phantoms,” Appl. Opt. 28, 2311–2317 (1989).
    [CrossRef] [PubMed]
  28. R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981).
    [CrossRef] [PubMed]
  29. S. L. Jacques, C. A. Alter, S. H. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).
  30. R. Marchesini, A. Bertoni, S. Andreola, E. Melloni, A. E. Sichirollo, “Extinction and absorption coefficients and scattering phase functions of human tissues in vitro,” Appl. Opt. 28, 2318–2324 (1989).
    [CrossRef] [PubMed]
  31. H. A. Willis, J. H. van der Maas, R. G. J. Miller, eds., Laboratory Methods in Vibrational Spectroscopy (Wiley, New York, 1987).

1992 (2)

1991 (5)

K. M. Yoo, Q. R. Xing, R. R. Alfano, “Imaging objects hidden in highly scattering media using femtosecond second-harmonic-generation cross-correlation time gating,” Opt. Lett. 16, 1019–1021 (1991).
[CrossRef] [PubMed]

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

H. Booster, H. Chou, “Higher resolution for backscatter measurements,” Lasers Optron. 10, 27–29 (1991).

D. Huang, J. Wang, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[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]

1990 (4)

W. F. Cheong, S. A. Prahl, A. J. Welsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

K. M. Yoo, R. R. Alfano, “Determination of the scattering and absorption lengths from the temporal profile of a backscattered pulse,” Opt. Lett. 15, 276–278 (1990).
[CrossRef] [PubMed]

K. M. Yoo, R. R. Alfano, “Biological materials probed by the temporal and angular profiles of the backscattered ultra-fast laser pulses,” J. Opt. Soc. Am. B 7, 1685–1693 (1990).
[CrossRef]

1989 (5)

1987 (5)

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissue,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

S. L. Jacques, C. A. Alter, S. H. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

K. Takada, I. Yokohama, K. Chida, J. Noda, “New measurement system for fault location in optical waveguide devices based on an interferometric technique,” Appl. Opt. 26, 1603–1606 (1987).
[CrossRef] [PubMed]

B. L. Danielson, C. D. Whittenburg, “Guided wave reflectometry with micrometer resolution,” Appl. Opt. 26, 2836–2842 (1987).
[CrossRef] [PubMed]

1981 (1)

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

1973 (2)

R. A. Sigelmann, J. M. Reid, “Analysis and measurement of ultrasound backscattering from an ensemble of scatterers excited by sine-wave bursts,” J. Acoust. Soc. Am. 53, 1351–1355 (1973).
[CrossRef]

J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Brit. J. Dermatol. 89, 467–476 (1973).
[CrossRef]

1972 (1)

Alfano, R. R.

Alter, C. A.

S. L. Jacques, C. A. Alter, S. H. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Anderson, R.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Anderson, R. C.

Anderson, R. R.

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Andreola, S.

Bertoni, A.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 120–123.

Bolin, F. P.

Bonner, R. F.

Booster, H.

H. Booster, H. Chou, “Higher resolution for backscatter measurements,” Lasers Optron. 10, 27–29 (1991).

Browell, E. V.

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]

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Chida, K.

Chou, H.

H. Booster, H. Chou, “Higher resolution for backscatter measurements,” Lasers Optron. 10, 27–29 (1991).

Danielson, B. L.

Everall, J. D.

J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Brit. J. Dermatol. 89, 467–476 (1973).
[CrossRef]

Ference, R. J.

Flock, S. T.

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissue,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

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]

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Fujimoto, J. G.

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

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]

D. Huang, J. Wang, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5.

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]

Grossweiner, B.

Grossweiner, L. I.

Hee, M. R.

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

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]

Huang, D.

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

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]

D. Huang, J. Wang, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 120–123.

Ichimura, T.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Inaba, H.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 5, pp. 93–106.

Jacques, S. L.

P. Parsa, S. L. Jacques, N. S. Nishioka, “Optical properties of rat liver between 350 and 2200 nm,” Appl. Opt. 28, 2325–2330 (1989).
[CrossRef] [PubMed]

S. L. Jacques, C. A. Alter, S. H. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

John, S.

F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
[CrossRef]

Karagiannes, J. L.

Kondo, M.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Lin, C. P.

D. Huang, J. Wang, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[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]

MacKintosh, F. C.

F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
[CrossRef]

Marchesini, R.

Melloni, E.

Moaveni, M. K.

M. K. Moaveni, “A multiple scattering field theory applied to whole blood,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1970).

Nishioka, N. S.

Noda, J.

Parrish, J.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Parrish, J. A.

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Parsa, P.

Patterson, M. S.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissue,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Pitts, D.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Prahl, S. A.

W. F. Cheong, S. A. Prahl, A. J. Welsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Prahl, S. H.

S. L. Jacques, C. A. Alter, S. H. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Preuss, L. E.

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]

D. Huang, J. Wang, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Reid, J. M.

R. A. Sigelmann, J. M. Reid, “Analysis and measurement of ultrasound backscattering from an ensemble of scatterers excited by sine-wave bursts,” J. Acoust. Soc. Am. 53, 1351–1355 (1973).
[CrossRef]

Schmitt, J. M.

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]

Sichirollo, A. E.

Sigelmann, R. A.

R. A. Sigelmann, J. M. Reid, “Analysis and measurement of ultrasound backscattering from an ensemble of scatterers excited by sine-wave bursts,” J. Acoust. Soc. Am. 53, 1351–1355 (1973).
[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, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

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]

Takada, K.

Taylor, R. C.

Toida, M.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Urbach, F.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Wang, J.

D. Huang, J. Wang, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Welsh, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Whittenburg, C. D.

Whitton, J. T.

J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Brit. J. Dermatol. 89, 467–476 (1973).
[CrossRef]

Wilson, B. C.

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissue,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Xing, Q. R.

Yokohama, I.

Yoo, K. M.

Zhang, Z. Y.

Appl. Opt. (8)

R. C. Anderson, E. V. Browell, “First- and second-order backscattering from clouds illuminated by finite beams,” Appl. Opt. 11, 1345–1351 (1972).
[CrossRef] [PubMed]

K. Takada, I. Yokohama, K. Chida, J. Noda, “New measurement system for fault location in optical waveguide devices based on an interferometric technique,” Appl. Opt. 26, 1603–1606 (1987).
[CrossRef] [PubMed]

B. L. Danielson, C. D. Whittenburg, “Guided wave reflectometry with micrometer resolution,” Appl. Opt. 26, 2836–2842 (1987).
[CrossRef] [PubMed]

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

J. L. Karagiannes, Z. Y. Zhang, B. Grossweiner, L. I. Grossweiner, “Applications of the 1-D diffusion approximation to the optics of tissue and tissue phantoms,” Appl. Opt. 28, 2311–2317 (1989).
[CrossRef] [PubMed]

R. Marchesini, A. Bertoni, S. Andreola, E. Melloni, A. E. Sichirollo, “Extinction and absorption coefficients and scattering phase functions of human tissues in vitro,” Appl. Opt. 28, 2318–2324 (1989).
[CrossRef] [PubMed]

P. Parsa, S. L. Jacques, N. S. Nishioka, “Optical properties of rat liver between 350 and 2200 nm,” Appl. Opt. 28, 2325–2330 (1989).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Configuration of a low-coherence reflectometer based on a Michelson interferometer. The block in the center marked “50/50” represents a 50-50 beam splitter.

Fig. 2
Fig. 2

Geometry at the point of contact between the fiber probe and the sample medium.

Fig. 3
Fig. 3

Illustrations of idealized backscattered power curves measured on scattering media containing two layers having dissimilar attenuation coefficients (μ t 1 ≠ μ t 2) and backscattering coefficients (μ b 1 ≠ μ b 2). (a) Case 1. This curve corresponds to the case in which both coefficients are larger in the first layer (μ t 1 > μ t 2) and (μ b 1 > μ b 2). (b) Case 2. This curve corresponds to the case in which both coefficients are smaller in the first layer (μ t 1 < μ t 2 and μ b 1 < μ b 2). The power is plotted as a function of the total (round-trip) optical path length in the medium.

Fig. 4
Fig. 4

Divergence-corrected backscattered power curves measured on three suspensions, each containing microspheres of a particular size. All suspensions had the same optical density (μ t = 5 mm−1).

Fig. 5
Fig. 5

Slope of the logarithm of the backscattered power curves (divergence corrected) measured on all of the suspensions plotted against their attenuation coefficients measured by collimated transmission. Mixture 1 was made by mixing equal volumes of a suspension of 0.43-μm-diameter microspheres (μ t = 5 mm−1) and a suspension of 2.06-μm-diameter microspheres (μ t = 5 mm−1); mixture 2 was made by mixing equal volumes of a suspension of 0.43-μm-diameter microspheres (μ t = 5 mm−1) and a suspension of 2.06-μm-diameter microspheres (μ t = 1.25 mm−1).

Fig. 6
Fig. 6

Plot of the power ratio at zero depth measured on all suspensions versus the backscattering coefficients of the samples derived by Mie theory. See the caption of Fig. 5 for the composition of mixture 1 and mixture 2.

Fig. 7
Fig. 7

Power curves (divergence corrected) measured by the reflectometer with its fiber probe placed on three different sites of the body of a male subject. The probe was moved slightly during the scan to smooth irregularities caused by large-scale inhomogeneities in the tissue. The peak at a depth of zero was caused by specular reflection at the fiber–tissue interface.

Tables (3)

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Table 1 Optical Coefficients of Scattering Samples Containing Different Size Spheres

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Table 2 Optical Coefficients of Human Skin Tissues Measured by Optical Coherence Reflectometry at 1300 nm

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Table 3 Optical Coefficients of Bovine Tissues Measured by Optical Coherence Reflectometry at 1300 nm

Equations (9)

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L c = c 0 γ ( τ ) 2 d τ .
μ b = η σ b = η π k 2 f ( 180 ° ) 2 ,
P ( z ) = P i 0 d { ( 1 - R ) A ( h ) μ b exp ( - 2 μ t h ) γ [ ( z - h ) / c ] + R γ ( h / c ) } d h ,
A ( h ) = ( r s / 2 r s / 2 + h θ h ) 2 ,
P ( z ) P i K ( 1 - R ) μ b A ( z ) exp ( - 2 μ t z ) + R δ ( 0 ) .
P ( z ) P i K μ b A ( z ) exp ( - 2 μ t z )             for R = 0.
P ( 0 ) P i = K μ b = μ b 0 L c / 2 exp ( - 2 μ t h ) d h = μ b 2 μ t [ 1 - exp ( - μ t L c ) ]
μ b L c 2             for L c 1 / μ t ,
Δ P = P i [ 1 - L c μ b 1 2 μ t 1 0 z 1 exp ( - 2 μ t 1 z ) d z ] = P i { i - L c μ b 1 4 μ t 1 [ 1 - exp ( - 2 μ t 1 z 1 ) ] } .

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