Abstract

We introduce a novel method for determining analyte concentration as a function of depth in a highly scattering media by use of a dual-wavelength optical coherence tomography system. We account for the effect of scattering on the measured attenuation by using a second wavelength that is not absorbed by the sample. We assess the applicability of this technique by measuring the concentration of water in an Intralipid phantom, using a probe wavelength of 1.53 µm and a reference wavelength of 1.31 µm. The results of our study show a strong correlation between the measured absorption and the water content of the sample. The accuracy of the technique, however, was limited by the dominance of scattering over absorption in the turbid media. Thus, although the effects of scattering were minimized, significant errors remained in the calculated absorption values. More-accurate results could be obtained with the use of more powerful superluminescent diodes and a choice of wavelengths at which absorption effects are more significant relative to scattering.

© 1999 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  22. T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
    [CrossRef]
  25. W. V. Sorin, G. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–106 (1992).
    [CrossRef]
  26. Y. Pan, R. Birngruber, R. Engelhardt, “Contrast limits of coherence-gated imaging in scattering media,” Appl. Opt. 36, 2979–2983 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]

1998

1997

1995

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20, 2258–2260 (1995).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

1994

1993

1992

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

W. Cui, L. E. Ostrander, “The relationship of surface reflectance measurements to optical properties of layered biological media,” IEEE Trans. Biomed. Eng. 39, 194–201 (1992).
[CrossRef] [PubMed]

W. V. Sorin, G. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–106 (1992).
[CrossRef]

M. R. Hee, D. Huang, E. Swanson, J. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–98 (1992).
[CrossRef]

1991

J. C. Hebden, R. A. Kruger, K. S. Wong, “Time resolved imaging through a highly scattering medium,” Appl. Opt. 30, 788–794 (1991).
[CrossRef] [PubMed]

M. Gu, J. R. Sheppard, X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. A 8, 1755–1761 (1991).
[CrossRef]

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[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]

1990

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

1989

Barbieri, B.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Benaron, D. A.

D. A. Benaron, D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
[CrossRef] [PubMed]

Birngruber, R.

Bonner, R. F.

Bouma, B. E.

Brezinski, M. E.

Chance, B.

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]

Colston, B. W.

Cui, W.

W. Cui, L. E. Ostrander, “The relationship of surface reflectance measurements to optical properties of layered biological media,” IEEE Trans. Biomed. Eng. 39, 194–201 (1992).
[CrossRef] [PubMed]

da Silva, L. B.

de Boer, J. F.

Engelhardt, R.

Everett, M. J.

Fantini, S.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Fishkin, J. B.

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chancel, A. Katzir, eds., Proc. SPIE1431, 1–14 (1991).

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]

Franceschini-Fantini, M. A.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Fujimoto, J.

Fujimoto, J. G.

Gan, X.

Gratton, E.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chancel, A. Katzir, eds., Proc. SPIE1431, 1–14 (1991).

Gray, G. F.

W. V. Sorin, G. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–106 (1992).
[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]

Gu, M.

Hebden, J. C.

Hee, M. R.

Huang, D.

M. R. Hee, D. Huang, E. Swanson, J. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–98 (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]

Izatt, J. A.

Jackson, D. A.

A. G. Podoleanu, D. A. Jackson, “Combined optical coherence tomography and scanning laser ophthalmoscope,” Electron. Lett. 34, 1088–1089 (1998).
[CrossRef]

Jacques, S. L.

S. L. Jacques, J. S. Nelson, W. H. Wright, T. E. Milner, “Pulsed photothermal radiometry of port-wine-stain lesions,” Appl. Opt. 32, 2439–2446 (1993).
[CrossRef] [PubMed]

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
[CrossRef] [PubMed]

Knüttel, A.

Kruger, R. A.

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]

Maier, J. S.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Maitland, D. J.

Mantulin, W. W.

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chancel, A. Katzir, eds., Proc. SPIE1431, 1–14 (1991).

Milner, T. E.

Moes, C. J. M.

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[CrossRef]

Nelson, J. S.

Ostrander, L. E.

W. Cui, L. E. Ostrander, “The relationship of surface reflectance measurements to optical properties of layered biological media,” IEEE Trans. Biomed. Eng. 39, 194–201 (1992).
[CrossRef] [PubMed]

Owen, G. M.

Pan, Y.

Patterson, M. S.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, eds., Proc. SPIE1065, 115–122 (1989).

Podoleanu, A. G.

A. G. Podoleanu, D. A. Jackson, “Combined optical coherence tomography and scanning laser ophthalmoscope,” Electron. Lett. 34, 1088–1089 (1998).
[CrossRef]

Prahl, S. A.

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[CrossRef]

S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988).

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]

Schmitt, J. M.

Schönenberger, K.

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]

Schwartz, E.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, eds., Proc. SPIE1065, 115–122 (1989).

Sheppard, J. R.

Silva, L. B. D.

Sorin, W. V.

W. V. Sorin, G. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–106 (1992).
[CrossRef]

Southern, J. F.

Stevenson, D. K.

D. A. Benaron, D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
[CrossRef] [PubMed]

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]

Svaasand, L. O.

L. O. Svaasand, “Physics of laser-induced hyperthermia,” in Optical-Thermal Response of Laser Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1994), Chap. 22.

Swanson, E.

Swanson, E. A.

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[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]

Tearney, G. J.

van Gemert, M. J. C.

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[CrossRef]

van Marle, J.

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[CrossRef]

van Staveren, H. J.

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[CrossRef]

vandeVen, M. J.

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chancel, A. Katzir, eds., Proc. SPIE1431, 1–14 (1991).

Walker, S. A.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Wilson, B.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Wilson, B. C.

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, eds., Proc. SPIE1065, 115–122 (1989).

B. C. Wilson, “Measurement of tissue optical properties: methods and theories,” in Optical-Thermal Response of Laser Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1994), Chap. 8.

Wong, K. S.

Wright, W. H.

Appl. Opt.

Electron. Lett.

A. G. Podoleanu, D. A. Jackson, “Combined optical coherence tomography and scanning laser ophthalmoscope,” Electron. Lett. 34, 1088–1089 (1998).
[CrossRef]

IEEE J. Quantum Electron.

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

IEEE Photon. Technol. Lett.

W. V. Sorin, G. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–106 (1992).
[CrossRef]

IEEE Trans. Biomed. Eng.

S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
[CrossRef] [PubMed]

W. Cui, L. E. Ostrander, “The relationship of surface reflectance measurements to optical properties of layered biological media,” IEEE Trans. Biomed. Eng. 39, 194–201 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Med. Phys.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Opt. Eng.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Opt. Lett.

Science

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. A. Benaron, D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
[CrossRef] [PubMed]

Other

J. B. Fishkin, E. Gratton, M. J. vandeVen, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chancel, A. Katzir, eds., Proc. SPIE1431, 1–14 (1991).

S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988).

B. C. Wilson, “Measurement of tissue optical properties: methods and theories,” in Optical-Thermal Response of Laser Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1994), Chap. 8.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, eds., Proc. SPIE1065, 115–122 (1989).

L. O. Svaasand, “Physics of laser-induced hyperthermia,” in Optical-Thermal Response of Laser Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1994), Chap. 22.

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Figures (6)

Fig. 1
Fig. 1

OCQ setup: The system is based on a dual-wavelength low-coherence Michelson interferometer. One wavelength (1.53 µm) is both absorbed and scattered by the sample, whereas the second wavelength (1.31 µm) is predominantly scattered. The two wavelengths are coupled and collected from the interferometer by WDM’s. A scanning retroflector in the reference arm provides constructive interference signals from within the turbid sample. Discrimination between the wavelengths is achieved by the WDM’s and the lock-in amplifiers.

Fig. 2
Fig. 2

Scans and calculated ratio from a sample containing 99% water and 1% Intralipid. The reflected signal falls off exponentially with depth. The slopes of the 1.53- and the 1.31-µm signals represent the total attenuation at that wavelength.

Fig. 3
Fig. 3

Measured attenuation coefficients μ t at 1.31 µm. Because the 1.31-µm light is poorly absorbed by the sample, the measured μ t should be largely determined by μ s . That this is so is confirmed by the linear relationship between the measured attenuations and the Intralipid (scatter) concentration. The loss of linearity above an Intralipid concentration of 3% could be due to the collection of multiply scattered photons or to clumping of Intralipid particles.

Fig. 4
Fig. 4

Slopes of (a) the 1.31-µm and the (b) the 1.53-µm signals. The slopes represent the attenuations at each wavelength. At 1.31 µm, the attenuation is dominated by the scattering (μ t ≈ μ a ); at 1.53 µm, the attenuation includes the absorption (μ t = μ a + μ s ).

Fig. 5
Fig. 5

Calculated absorption at 1.53 µm at various scatter concentrations and water contents by (a) simple ratio of the signals at the two wavelengths given by Eq. (3.5) and (b) use of a scaling factor described in Eq. (3.6). In (a) there is a systematic decrease in calculated absorption with increasing scattering, indicating that the effect of scattering has not been completely eliminated. In (b) this trend has been eliminated by use of a scaling factor F = μ s (1.53 µm)/μ s (1.31 µm). The effect of scattering on the estimated absorption is now greatly reduced.

Fig. 6
Fig. 6

Calculated absorption at 1.53 µm as a function of water content. A best-fit slope of absorption versus water content gives 0.014-mm-1/% water content, a factor of 3 more than the expected value of 0.0047-mm-1/% water content. The reason for this discrepancy is the influence of the changes in water concentration on the ratio of the scattering coefficients at 1.53 and 1.31 µm. Note that there is significant variation (±1 mm-1) in the measured absorption coefficient at any given water concentration.

Equations (7)

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Iλz=Iλ0exp-μaλz,
μaλ=-1LlnIλLIλ0,
Iλz  exp(-3μa2+μaμs1-g1/2z).
Sλz=Rλzexp-2μtλz=Rλzexp-2μaλ+μsλz.
lnSλ1z-lnSλ2z=lnRλ1z-lnRλ2z-2μaλ1-μaλ2+μsλ1-μsλ2z.
lnSλ1z-F lnSλ2z=lnRλ1z-F lnRλ2z-2μaλ1+μsλ1-Fμsλ2z=lnRλ1z-F lnRλ2z-2μaλ1z.
μaλ1=-12ddzlnSλ1z-F lnSλ2z.

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