Abstract

A system is described and evaluated for the simultaneous measurement of the intrinsic optical properties of tissue: the scattering coefficient, the absorption coefficient, and the anisotropy factor. This system synthesizes the theory of two integrating spheres and an intervening scattering sample with the inverse adding–doubling algorithm, which employs the adding–doubling solution of the radiative transfer equation to determine the optical properties from the measurement of the light flux within each sphere and of the unscattered transmission. The optical properties may be determined simultaneously, which allows for measurements to be made while the sample undergoes heating, chemical change, or some other external stimulus. An experimental validation of the system with tissue phantoms resulted in the determination of the optical properties with a <5% deviation when the optical density was between 1 and 10 and the albedo was between 0.4 and 0.95.

© 1993 Optical Society of America

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References

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  1. S. A. Prahl, M. J. C. van Gemert, A. J. Welch, “Determining the optical properties of turbid media using the adding–doubling method,” Appl. Opt. 32, 559–568 (1993).
    [CrossRef] [PubMed]
  2. W.-F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  3. F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiberoptic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
    [CrossRef] [PubMed]
  4. S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 4, 309–333 (1987).
  5. 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]
  6. R. Marchesini, A. Bertoni, S. Andreola, E. Melloni, A. E. Sichirollo, “Extinction and absorption coefficients and scattering phase functions of human tissues inυitro,” Appl. Opt. 28, 2318–2324 (1989).
    [CrossRef] [PubMed]
  7. J. R. Zijp, J. J. Ten Bosch, “Angular dependence of HeNe-laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
    [CrossRef] [PubMed]
  8. L. O. Svassand, R. Ellingsen, “Optical properties of human brain,” Photochem. Photobiol. 38, 293–299 (1983).
    [CrossRef]
  9. B. C. Wilson, W. P. Jeeves, D. M. Lowe, “In vivo and postmortem measurements of the attenuation spectra of light in mammalian tissues,” Photochem. Photobiol. 42, 153–162 (1985).
    [CrossRef] [PubMed]
  10. J. P. A. Marijnissen, W. M. Star, “Quantitative light dosimetry inυitro and inυivo,” Lasers Med. Sci. 2, 235–242 (1987).
    [CrossRef]
  11. R. A. J. Groenhuis, J. J. Ten Bosch, H. A. Ferwerda, “Scattering and absorption of turbid materials determined from reflection measurements. 2: measuring method and calibration,” Appl. Opt. 22, 2463–2467 (1983).
    [CrossRef] [PubMed]
  12. J. M. Schmitt, G. X. Zhou, E. C. Walker, R. T. Wall, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).
    [CrossRef] [PubMed]
  13. J. S. Macleod, D. Blanc, M. J. Cottes, “Measurement of the optical absorption coefficients at 1.06 μm of various tissues using the photoacoustic effect,” Lasers Surg. Med. 8, 143 (A) (1988).
  14. U. Bernini, M. Marotta, G. Martino, P. Russo, “Spectropho-toacoustic method for quantitative estimation of haem protein content in wet tissue,” Phys. Med. Biol. 36, 391–396 (1991).
    [CrossRef] [PubMed]
  15. 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]
  16. K. M. Yoo, F. Liu, R. R. Alfano, “Angle and time resolved studies of backscattering of light from biological tissues,” in Laser–Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 260–271 (1990).
  17. F. H. Long, N. S. Nishioha, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461–466 (1987).
    [CrossRef] [PubMed]
  18. S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1218 (1991).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. G. E. Miller, A. J. Sant, “Incomplete integrating sphere,” J. Opt. Soc. Am. 48, 828–831 (1958).
    [CrossRef]
  22. D. G. Goebel. “Generalized integrating-sphere theory,” Appl. Opt. 6, 125–128 (1967).
    [CrossRef] [PubMed]
  23. F. J. J. Clarke, J. A. Compton, “Correction methods for integrating sphere measurements of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
    [CrossRef]
  24. A. Roos, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474 (1991).
    [CrossRef] [PubMed]
  25. J. W. Pickering, C. J. M. Moes, H. J. C. M. Sterenborg, S. A. Prahl, M. J. C. van Gemert, “Two integrating spheres with an intervening scattering sample,” J. Opt. Soc. Am. A 9, 621–631 (1992).
    [CrossRef]
  26. C. J. M. Moes, M. J. C. van Gemert, W. M. Star, J. P. A. Marijnissen, S. A. Prahl, “Measurement and calculations of the energy and fluence rate in scattering and absorbing phantom at 633 nm,” Appl. Opt. 28, 2292–2296 (1988).
    [CrossRef]
  27. H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991)
    [CrossRef] [PubMed]

1993 (1)

1992 (1)

1991 (5)

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1218 (1991).
[CrossRef]

J. R. Zijp, J. J. Ten Bosch, “Angular dependence of HeNe-laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
[CrossRef] [PubMed]

U. Bernini, M. Marotta, G. Martino, P. Russo, “Spectropho-toacoustic method for quantitative estimation of haem protein content in wet tissue,” Phys. Med. Biol. 36, 391–396 (1991).
[CrossRef] [PubMed]

A. Roos, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474 (1991).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991)
[CrossRef] [PubMed]

1990 (2)

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

J. M. Schmitt, G. X. Zhou, E. C. Walker, R. T. Wall, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).
[CrossRef] [PubMed]

1989 (3)

1988 (2)

J. S. Macleod, D. Blanc, M. J. Cottes, “Measurement of the optical absorption coefficients at 1.06 μm of various tissues using the photoacoustic effect,” Lasers Surg. Med. 8, 143 (A) (1988).

C. J. M. Moes, M. J. C. van Gemert, W. M. Star, J. P. A. Marijnissen, S. A. Prahl, “Measurement and calculations of the energy and fluence rate in scattering and absorbing phantom at 633 nm,” Appl. Opt. 28, 2292–2296 (1988).
[CrossRef]

1987 (4)

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 4, 309–333 (1987).

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]

F. H. Long, N. S. Nishioha, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461–466 (1987).
[CrossRef] [PubMed]

J. P. A. Marijnissen, W. M. Star, “Quantitative light dosimetry inυitro and inυivo,” Lasers Med. Sci. 2, 235–242 (1987).
[CrossRef]

1986 (1)

F. J. J. Clarke, J. A. Compton, “Correction methods for integrating sphere measurements of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

1985 (1)

B. C. Wilson, W. P. Jeeves, D. M. Lowe, “In vivo and postmortem measurements of the attenuation spectra of light in mammalian tissues,” Photochem. Photobiol. 42, 153–162 (1985).
[CrossRef] [PubMed]

1983 (2)

1967 (1)

1958 (1)

1954 (1)

1920 (1)

Alfano, R. R.

K. M. Yoo, F. Liu, R. R. Alfano, “Angle and time resolved studies of backscattering of light from biological tissues,” in Laser–Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 260–271 (1990).

Alter, C. A.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 4, 309–333 (1987).

Anderson, R. R.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1218 (1991).
[CrossRef]

Andreola, S.

Bernini, U.

U. Bernini, M. Marotta, G. Martino, P. Russo, “Spectropho-toacoustic method for quantitative estimation of haem protein content in wet tissue,” Phys. Med. Biol. 36, 391–396 (1991).
[CrossRef] [PubMed]

Bertoni, A.

Blanc, D.

J. S. Macleod, D. Blanc, M. J. Cottes, “Measurement of the optical absorption coefficients at 1.06 μm of various tissues using the photoacoustic effect,” Lasers Surg. Med. 8, 143 (A) (1988).

Bolin, F. P.

Bruggemann, U.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1218 (1991).
[CrossRef]

Chance, B.

Cheong, W.-F.

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

Clarke, F. J. J.

F. J. J. Clarke, J. A. Compton, “Correction methods for integrating sphere measurements of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

Compton, J. A.

F. J. J. Clarke, J. A. Compton, “Correction methods for integrating sphere measurements of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

Cottes, M. J.

J. S. Macleod, D. Blanc, M. J. Cottes, “Measurement of the optical absorption coefficients at 1.06 μm of various tissues using the photoacoustic effect,” Lasers Surg. Med. 8, 143 (A) (1988).

Deutsch, T. F.

F. H. Long, N. S. Nishioha, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461–466 (1987).
[CrossRef] [PubMed]

Ellingsen, R.

L. O. Svassand, R. Ellingsen, “Optical properties of human brain,” Photochem. Photobiol. 38, 293–299 (1983).
[CrossRef]

Ference, R. J.

Ferwerda, H. A.

Flock, S. T.

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]

Goebel, D. G.

Groenhuis, R. A. J.

Jacques, S. L.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 4, 309–333 (1987).

Jacquez, J. A.

Jeeves, W. P.

B. C. Wilson, W. P. Jeeves, D. M. Lowe, “In vivo and postmortem measurements of the attenuation spectra of light in mammalian tissues,” Photochem. Photobiol. 42, 153–162 (1985).
[CrossRef] [PubMed]

Kuppenheim, H. F.

Liu, F.

K. M. Yoo, F. Liu, R. R. Alfano, “Angle and time resolved studies of backscattering of light from biological tissues,” in Laser–Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 260–271 (1990).

Long, F. H.

F. H. Long, N. S. Nishioha, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461–466 (1987).
[CrossRef] [PubMed]

Lowe, D. M.

B. C. Wilson, W. P. Jeeves, D. M. Lowe, “In vivo and postmortem measurements of the attenuation spectra of light in mammalian tissues,” Photochem. Photobiol. 42, 153–162 (1985).
[CrossRef] [PubMed]

Macleod, J. S.

J. S. Macleod, D. Blanc, M. J. Cottes, “Measurement of the optical absorption coefficients at 1.06 μm of various tissues using the photoacoustic effect,” Lasers Surg. Med. 8, 143 (A) (1988).

Marchesini, R.

Marijnissen, J. P. A.

Marotta, M.

U. Bernini, M. Marotta, G. Martino, P. Russo, “Spectropho-toacoustic method for quantitative estimation of haem protein content in wet tissue,” Phys. Med. Biol. 36, 391–396 (1991).
[CrossRef] [PubMed]

Martino, G.

U. Bernini, M. Marotta, G. Martino, P. Russo, “Spectropho-toacoustic method for quantitative estimation of haem protein content in wet tissue,” Phys. Med. Biol. 36, 391–396 (1991).
[CrossRef] [PubMed]

Melloni, E.

Miller, G. E.

Moes, C. J. M.

Nishioha, N. S.

F. H. Long, N. S. Nishioha, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461–466 (1987).
[CrossRef] [PubMed]

Patterson, M. S.

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]

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]

Pickering, J. W.

Prahl, S. A.

Preuss, L. E.

Roos, A.

Russo, P.

U. Bernini, M. Marotta, G. Martino, P. Russo, “Spectropho-toacoustic method for quantitative estimation of haem protein content in wet tissue,” Phys. Med. Biol. 36, 391–396 (1991).
[CrossRef] [PubMed]

Sant, A. J.

Schmitt, J. M.

Sichirollo, A. E.

Star, W. M.

Sterenborg, H. J. C. M.

Svassand, L. O.

L. O. Svassand, R. Ellingsen, “Optical properties of human brain,” Photochem. Photobiol. 38, 293–299 (1983).
[CrossRef]

Taylor, A. H.

Taylor, R. C.

Ten Bosch, J. J.

van Gemert, M. J. C.

van Marie, J.

van Staveren, H. J.

Vitkin, I. A.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1218 (1991).
[CrossRef]

Walker, E. C.

Wall, R. T.

Welch, A. J.

S. A. Prahl, M. J. C. van Gemert, A. J. Welch, “Determining the optical properties of turbid media using the adding–doubling method,” Appl. Opt. 32, 559–568 (1993).
[CrossRef] [PubMed]

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

Wilson, B. C.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1218 (1991).
[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]

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]

B. C. Wilson, W. P. Jeeves, D. M. Lowe, “In vivo and postmortem measurements of the attenuation spectra of light in mammalian tissues,” Photochem. Photobiol. 42, 153–162 (1985).
[CrossRef] [PubMed]

Yoo, K. M.

K. M. Yoo, F. Liu, R. R. Alfano, “Angle and time resolved studies of backscattering of light from biological tissues,” in Laser–Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 260–271 (1990).

Zhou, G. X.

Zijp, J. R.

J. R. Zijp, J. J. Ten Bosch, “Angular dependence of HeNe-laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
[CrossRef] [PubMed]

Appl. Opt. (9)

D. G. Goebel. “Generalized integrating-sphere theory,” Appl. Opt. 6, 125–128 (1967).
[CrossRef] [PubMed]

R. A. J. Groenhuis, J. J. Ten Bosch, H. A. Ferwerda, “Scattering and absorption of turbid materials determined from reflection measurements. 2: measuring method and calibration,” Appl. Opt. 22, 2463–2467 (1983).
[CrossRef] [PubMed]

C. J. M. Moes, M. J. C. van Gemert, W. M. Star, J. P. A. Marijnissen, S. A. Prahl, “Measurement and calculations of the energy and fluence rate in scattering and absorbing phantom at 633 nm,” Appl. Opt. 28, 2292–2296 (1988).
[CrossRef]

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiberoptic cladding method,” Appl. Opt. 28, 2297–2303 (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 inυitro,” Appl. Opt. 28, 2318–2324 (1989).
[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]

A. Roos, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474 (1991).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991)
[CrossRef] [PubMed]

S. A. Prahl, M. J. C. van Gemert, A. J. Welch, “Determining the optical properties of turbid media using the adding–doubling method,” Appl. Opt. 32, 559–568 (1993).
[CrossRef] [PubMed]

Arch. Oral Biol. (1)

J. R. Zijp, J. J. Ten Bosch, “Angular dependence of HeNe-laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
[CrossRef] [PubMed]

Color Res. Appl. (1)

F. J. J. Clarke, J. A. Compton, “Correction methods for integrating sphere measurements of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

Lasers Life Sci. (1)

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 4, 309–333 (1987).

Lasers Med. Sci. (1)

J. P. A. Marijnissen, W. M. Star, “Quantitative light dosimetry inυitro and inυivo,” Lasers Med. Sci. 2, 235–242 (1987).
[CrossRef]

Lasers Surg. Med. (2)

J. S. Macleod, D. Blanc, M. J. Cottes, “Measurement of the optical absorption coefficients at 1.06 μm of various tissues using the photoacoustic effect,” Lasers Surg. Med. 8, 143 (A) (1988).

F. H. Long, N. S. Nishioha, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461–466 (1987).
[CrossRef] [PubMed]

Med. Phys. (1)

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]

Photochem. Photobiol. (2)

L. O. Svassand, R. Ellingsen, “Optical properties of human brain,” Photochem. Photobiol. 38, 293–299 (1983).
[CrossRef]

B. C. Wilson, W. P. Jeeves, D. M. Lowe, “In vivo and postmortem measurements of the attenuation spectra of light in mammalian tissues,” Photochem. Photobiol. 42, 153–162 (1985).
[CrossRef] [PubMed]

Phys. Med. Biol. (2)

U. Bernini, M. Marotta, G. Martino, P. Russo, “Spectropho-toacoustic method for quantitative estimation of haem protein content in wet tissue,” Phys. Med. Biol. 36, 391–396 (1991).
[CrossRef] [PubMed]

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1218 (1991).
[CrossRef]

Other (1)

K. M. Yoo, F. Liu, R. R. Alfano, “Angle and time resolved studies of backscattering of light from biological tissues,” in Laser–Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 260–271 (1990).

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Figures (4)

Fig. 1
Fig. 1

(a) Diffuse light may irradiate the sample through the beam first irradiating the sidewall of the sphere. (b) Alternatively collimated light may directly irradiate the sample. In all cases a baffle is placed between the sample and the detector to prevent detection of specularly reflected light. In the double-sphere system the sample is placed between the spheres, and the unscattered collimated transmitted light is permitted to leave the system (c).

Fig. 2
Fig. 2

Uncertainty in the calculated reflectance is always greatest when the reflectance (and hence the signal) is low. For a single sphere diffuse irradiation leads to a much greater uncertainty in the reflectance than collimated irradiation because there is a signal generated prior to the reflection by the sample. With the double-sphere system the uncertainty in reflectance is increased because of the exchange of light between the spheres, but it is still smallest for collimated irradiation, and this uncertainty is smaller than for diffuse irradiation in the single sphere.

Fig. 3
Fig. 3

Experimental apparatus consisting of two integrating spheres with an intervening sample. A He–Ne laser (632.8 nm) directs light directly onto the sample through a chopper. The signal is detected by photodiodes placed on the walls of the two spheres and a distance from the exit port of the transmittance sphere. The signals from the photodiodes and the frequency of the chopper are fed into a lock-in amplifier.

Fig. 4
Fig. 4

(a) Measured albedo, (b) anisotropy g, (c) scattering coefficient μs, and (d) absorption coefficient μa for each subgroup of constant albedo (which is highest at the left and declines to the right). Within each subgroup the optical depth varies from a maximum of 16.3 to a minimum of 0.1. The highest optical depth is always at the left of the subgroup and declines to the right.

Tables (4)

Tables Icon

Table 1 Voltage Measurements Required to Determine V%

Tables Icon

Table 2 Effect of the Change in Each Variable on the Reflectance for a Given Uncertainty in that Variable at Rd = 0.41, As/A = 0.03, b1 = 0.8, b2 = 0.25 and for Diffuse Incident Lighta

Tables Icon

Table 3 Accuracy to Which Optical Properties Can Be Determined

Tables Icon

Table 4 Optical Properties of Tissue Phantoms

Equations (34)

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

P d = b 1 ( 1 R d A s A ) 1 b 2 R d P ,
b 1 = A δ A m 1 m α , b 2 = A s A 1 1 m α ,
α = [ A ( A s + A δ + A a ) ] / A .
P d = b 1 ( α R c d + R c ) 1 b 2 R d P ,
P d = b 1 α T d 1 b 2 R d P ,
P d = b 1 ( T c + α T c d ) 1 b 2 R d P ,
P d = b 1 r ( 1 b 2 t R d ) ( 1 b 2 r R d ) ( 1 b 2 t R d ) b 2 r b 2 t T d 2 P ,
P d = b 1 t b 2 r m r α t T d ( 1 b 2 r R d ) ( 1 b 2 t R d ) b 2 r b 2 t T d 2 P .
P d = b 1 r [ ( R c + α r R c d ) ( 1 b 2 t R d ) + α r b 2 t T d ( T c d + m t T c ) ] ( 1 b 2 r R d ) ( 1 b 2 t R d ) b 2 r b 2 t T d 2 P ,
P d = b 1 t [ ( T c + α t T c d ) ( 1 b 2 r R d ) + α t b 2 r T d ( R c d + m r R c ) ] ( 1 b 2 r R d ) ( 1 b 2 t R d ) b 2 r b 2 t T d 2 P .
V = K P d ,
P d = 1 K ( V V 0 ) .
T c = V c V c , 0 V c , ref V c , ref 0 = V c % ,
P d , ref = P ϕ ( R ref , A s , A , A a , m ) ,
P = P d , ref ϕ = 1 K ( V ref V ref , 0 ) ϕ ,
P d P = ϕ ( V V 0 ) ( V ref V ref , 0 ) = ϕ V % ,
P d P b 1 .
b 1 b 1 1 ϕ .
V % = b 1 .
b 2 = b 1 V % V % R d s ,
m = A s A + b 2 α b 2 .
b 1 = V % α R c d s ( 1 b 2 R d s ) ,
μ a = τ ( 1 a ) d , μ s = a τ d .
R d = b 1 V % b 1 A s A b 2 V % .
( Δ R d ) 2 = i ( R d X i Δ X i ) 2 .
V % = V V dark V ref V dark ,
V r % corrected = V r % F 1 V r , ref 0 % F 2 V t , ref 0 % ,
V t % corrected = V t % F 3 V r , ref 0 % F 4 V t , ref 0 % ,
F 1 = ( 1 b 2 r R d ) ( 1 b 2 t R d ) ( 1 b 2 r R d ) ( 1 b 2 t R d ) b 2 r b 2 t T d 2 ,
F 3 = ( 1 b 2 r R d ) b 1 r b 1 t b 2 r m r α t T d ( 1 b 2 r R d ) ( 1 b 2 t R d ) b 2 r b 2 t T d 2 .
F 2 = T c ( 1 b 2 t R d ) b 1 t × b 1 r b 2 t m t α r T d ( 1 b 2 t R d ) ( 1 b 2 r R d ) b 2 t b 2 r T d 2 ,
F 4 = T c ( 1 b 2 t R d ) ( 1 b 2 r R d ) ( 1 b 2 t R d ) ( 1 b 2 r R d ) b 2 t b 2 r T d 2 .
g = 0 . 70 ± 0 . 05 , μ s o = ( 0 . 6 ± 0 . 1 ) mL 1 L cm 1 , μ a o = ( 0 . 12 ± 0 . 03 ) mL 1 L cm 1 .
μ s o = ( 0 . 56 ± 0 . 03 ) mL 1 L cm 1 , μ a o = ( 0 . 115 ± 0 . 002 ) mL 1 L cm 1

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