Abstract

The spatially resolved reflectance of turbid media is studied at short source–detector separations (approximately one transport mean free path) with Monte Carlo simulations. For such distances we found that the first and second moments of the phase function play a significant role in the reflectance curve, whereas the effect of higher-order moments is weak. Second-order similarity relations are tested and are found efficient at reducing the number of relevant parameters necessary to predict the reflectance. Indeed, only the four following parameters are necessary: the refractive index, the absorption coefficient, the reduced scattering coefficient, and a phase function parameter γ that depends on the first and second moments of the phase function. For media of known γ, the absorption and reduced scattering coefficients can be determined from the intensity and the slope of the log of the reflectance, measured at a single distance. Other empirical properties of the reflectance are derived from the simulations, using short-distance measurements, which provide clues for determining the scattering and absorption properties. In particular, the slope of the square root of the reflectance does not depend on the absorption coefficient but depends on both the reduced scattering coefficient and the phase function parameter γ.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. 22, 2456–2462 (1983).
    [CrossRef] [PubMed]
  2. 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]
  3. B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in tissue in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed., Proc. SPIEIS06, 219–231 (1990).
  4. J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
    [CrossRef] [PubMed]
  5. T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  6. R. Bays, G. Wagnières, D. Robert, D. Braichotte, J.-F. Savary, P. Monnier, H. van den Bergh, “Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry,” Appl. Opt. 35, 1756–1766 (1996).
    [CrossRef] [PubMed]
  7. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
    [CrossRef] [PubMed]
  8. L. H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
    [CrossRef] [PubMed]
  9. R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
    [CrossRef] [PubMed]
  10. J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahlchristiansen, H. Orskov, “Correlation between blood-glucose concentration in diabetics and noninvasively measured tissue optical-scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
    [CrossRef] [PubMed]
  11. R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
    [CrossRef] [PubMed]
  12. F. Bevilacqua, “Local optical characterization of biological tissues in vitro and vivo,” Ph.D. dissertation No. 1781 (Swiss Federal Institute of Technology, Lausanne, Switzerland, 1998).
  13. F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
    [CrossRef]
  14. R. A. Bolt, J. J. Ten Bosch, “Method for measuring position-dependent volume reflection,” Appl. Opt. 32, 4641–4645 (1993).
    [CrossRef] [PubMed]
  15. A. Kienle, “Lichtausbreitung in biologischem Gewebe,” Ph.D. dissertation (Universität Ulm, Ulm, Germany, 1994).
  16. J. R. Mourant, J. Boyer, A. H. Hielscher, I. J. Bigio, “Influence of the scattering phase function on light transport measurements in turbid media performed with small source–detector separations,” Opt. Lett. 21, 546–548 (1996).
    [CrossRef] [PubMed]
  17. V. Venugopalan, J. S. You, B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
    [CrossRef]
  18. D. J. Durian, J. Rudnick, “Photon migration at short times and distances and in cases of strong absorption,” J. Opt. Soc. Am. A 14, 235–245 (1997).
    [CrossRef]
  19. A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
    [CrossRef]
  20. A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (1997).
    [CrossRef] [PubMed]
  21. H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas, and Applications (Academic, London, 1980), Vol. II.
  22. D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
    [CrossRef]
  23. D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for the interaction parameters in radiation transport,” Appl. Opt. 28, 5243–5249 (1989).
    [CrossRef] [PubMed]
  24. L. G. Henyey, J. L. Greenstein, “Diffuse radiation of the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
  25. S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficient and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
    [CrossRef] [PubMed]
  26. S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).
  27. 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]
  28. P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 454–465 (1993).
    [CrossRef]
  29. P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement. Part I: Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
    [CrossRef]
  30. A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
    [CrossRef] [PubMed]
  31. J. R. Zijp, J. J. ten Bosch, “Anisotropy of volume-backscattered light,” Appl. Opt. 36, 1671–1680 (1997).
    [CrossRef] [PubMed]
  32. S. T. Flock, M. S. Patterson, B. C. Wilson, D. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues—I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
    [CrossRef] [PubMed]
  33. M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light, steady-state diffuse-reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 93–104 (1997).
    [CrossRef] [PubMed]
  34. M. R. Jones, Y. Yamada, “Determination of the asymmetry parameter and scattering coefficient of turbid media from spatially resolved reflectance measurements,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 379–382.

1999 (1)

1998 (1)

V. Venugopalan, J. S. You, B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

1997 (7)

D. J. Durian, J. Rudnick, “Photon migration at short times and distances and in cases of strong absorption,” J. Opt. Soc. Am. A 14, 235–245 (1997).
[CrossRef]

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
[CrossRef]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[CrossRef] [PubMed]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahlchristiansen, H. Orskov, “Correlation between blood-glucose concentration in diabetics and noninvasively measured tissue optical-scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[CrossRef] [PubMed]

J. R. Zijp, J. J. ten Bosch, “Anisotropy of volume-backscattered light,” Appl. Opt. 36, 1671–1680 (1997).
[CrossRef] [PubMed]

M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light, steady-state diffuse-reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 93–104 (1997).
[CrossRef] [PubMed]

1996 (4)

1995 (2)

L. H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
[CrossRef] [PubMed]

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement. Part I: Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

1993 (1)

1992 (1)

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

1991 (1)

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

1989 (4)

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for the interaction parameters in radiation transport,” Appl. Opt. 28, 5243–5249 (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]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues—I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

1987 (3)

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficient 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. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
[CrossRef] [PubMed]

1983 (2)

1941 (1)

L. G. Henyey, J. L. Greenstein, “Diffuse radiation of the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Alter, C. A.

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

Andreola, S.

Bays, R.

Berger, M.

Bertoni, A.

Bevilacqua, F.

F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
[CrossRef]

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement. Part I: Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

F. Bevilacqua, “Local optical characterization of biological tissues in vitro and vivo,” Ph.D. dissertation No. 1781 (Swiss Federal Institute of Technology, Lausanne, Switzerland, 1998).

Bigio, I. J.

Bolt, R. A.

Bonner, R. F.

Boyer, J.

Braichotte, D.

Bruulsema, J. T.

de Haller, E. B.

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement. Part I: Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

Delpy, D. T.

P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

Depeursinge, C.

F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
[CrossRef]

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement. Part I: Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

Diamond, K. R.

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Durian, D. J.

Essenpreis, M.

P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

Farrell, T. J.

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahlchristiansen, H. Orskov, “Correlation between blood-glucose concentration in diabetics and noninvasively measured tissue optical-scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[CrossRef] [PubMed]

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

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in tissue in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed., Proc. SPIEIS06, 219–231 (1990).

Ferwerda, H. A.

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues—I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

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

Foster, T. H.

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation of the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Groenhuis, R. A. J.

Gross, J. D.

Havlin, S.

Hayward, J. E.

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahlchristiansen, H. Orskov, “Correlation between blood-glucose concentration in diabetics and noninvasively measured tissue optical-scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[CrossRef] [PubMed]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Heinemann, L.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation of the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hibst, R.

Hielscher, A. H.

Hull, E. L.

Jacques, S. L.

L. H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
[CrossRef] [PubMed]

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

Jones, M. R.

M. R. Jones, Y. Yamada, “Determination of the asymmetry parameter and scattering coefficient of turbid media from spatially resolved reflectance measurements,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 379–382.

Kienle, A.

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
[CrossRef]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[CrossRef] [PubMed]

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

A. Kienle, “Lichtausbreitung in biologischem Gewebe,” Ph.D. dissertation (Universität Ulm, Ulm, Germany, 1994).

Koschinsky, T.

Lilge, L.

Marchesini, R.

Marquet, P.

F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
[CrossRef]

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement. Part I: Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

Melloni, E.

Monnier, P.

Mourant, J. R.

Nichols, M. G.

Nossal, R.

Orskov, H.

Patterson, M. S.

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahlchristiansen, H. Orskov, “Correlation between blood-glucose concentration in diabetics and noninvasively measured tissue optical-scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[CrossRef] [PubMed]

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
[CrossRef]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[CrossRef] [PubMed]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

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

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues—I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for the interaction parameters in radiation transport,” Appl. Opt. 28, 5243–5249 (1989).
[CrossRef] [PubMed]

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

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in tissue in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed., Proc. SPIEIS06, 219–231 (1990).

Piguet, D.

Prahl, S. A.

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

Robert, D.

Rudnick, J.

Sandahlchristiansen, J.

Savary, J.-F.

Schmitt, J. M.

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

Sichirollo, A. E.

Steiner, R.

ten Bosch, J. J.

Tromberg, B. J.

F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
[CrossRef]

V. Venugopalan, J. S. You, B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas, and Applications (Academic, London, 1980), Vol. II.

van den Bergh, H.

van der Zee, P.

P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

Venugopalan, V.

V. Venugopalan, J. S. You, B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

Wagnières, G.

Wang, L. H.

Weersink, R. A.

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Weiss, G. H.

Wilson, B. C.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

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

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues—I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for the interaction parameters in radiation transport,” Appl. Opt. 28, 5243–5249 (1989).
[CrossRef] [PubMed]

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

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in tissue in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed., Proc. SPIEIS06, 219–231 (1990).

Wyman, D.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues—I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

Wyman, D. R.

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for the interaction parameters in radiation transport,” Appl. Opt. 28, 5243–5249 (1989).
[CrossRef] [PubMed]

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

Yamada, Y.

M. R. Jones, Y. Yamada, “Determination of the asymmetry parameter and scattering coefficient of turbid media from spatially resolved reflectance measurements,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 379–382.

You, J. S.

V. Venugopalan, J. S. You, B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

Zijp, J. R.

Appl. Opt. (11)

R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. 22, 2456–2462 (1983).
[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]

R. Bays, G. Wagnières, D. Robert, D. Braichotte, J.-F. Savary, P. Monnier, H. van den Bergh, “Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry,” Appl. Opt. 35, 1756–1766 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

L. H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
[CrossRef] [PubMed]

F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
[CrossRef]

R. A. Bolt, J. J. Ten Bosch, “Method for measuring position-dependent volume reflection,” Appl. Opt. 32, 4641–4645 (1993).
[CrossRef] [PubMed]

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for the interaction parameters in radiation transport,” Appl. Opt. 28, 5243–5249 (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]

J. R. Zijp, J. J. ten Bosch, “Anisotropy of volume-backscattered light,” Appl. Opt. 36, 1671–1680 (1997).
[CrossRef] [PubMed]

M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light, steady-state diffuse-reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 93–104 (1997).
[CrossRef] [PubMed]

Astrophys. J. (1)

L. G. Henyey, J. L. Greenstein, “Diffuse radiation of the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

IEEE Trans. Biomed. Eng. (2)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues—I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

J. Comput. Phys. (1)

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

J. Opt. Soc. Am. A (3)

Lasers Life Sci. (1)

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

Med. Phys. (2)

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

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

Opt. Eng. (1)

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled-device array measurement. Part I: Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

Opt. Lett. (2)

Photochem. Photobiol. (1)

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol. (2)

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[CrossRef] [PubMed]

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

Phys. Rev. E (1)

V. Venugopalan, J. S. You, B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

Other (6)

P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

M. R. Jones, Y. Yamada, “Determination of the asymmetry parameter and scattering coefficient of turbid media from spatially resolved reflectance measurements,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 379–382.

H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas, and Applications (Academic, London, 1980), Vol. II.

F. Bevilacqua, “Local optical characterization of biological tissues in vitro and vivo,” Ph.D. dissertation No. 1781 (Swiss Federal Institute of Technology, Lausanne, Switzerland, 1998).

A. Kienle, “Lichtausbreitung in biologischem Gewebe,” Ph.D. dissertation (Universität Ulm, Ulm, Germany, 1994).

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in tissue in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed., Proc. SPIEIS06, 219–231 (1990).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Geometry considered in the Monte Carlo simulations. The light source and the detectors are in contact with the turbid medium. Photons are emitted at ρ = 0, equally in all directions within a solid angle defined by the angle θmax. They are detected at variable distances ρ in the same solid angle defined by θmax.

Fig. 2
Fig. 2

Possible g2 values as a function of g1 values for Mie, pMHG, and pMPC phase functions. The region covered by the Henyey–Greenstein phase function (pHG) is represented by the line g2=g12. The line g2=g1 corresponds to the phase function ( piso+forward=(1/4π)[1-g1+2gδ(1-cos θ)]) (isotropic combined with forward peak) (Ref. 21). The diamonds represent a broad range of Mie phase functions (relative refractive index from 0.9 to 2 and size parameters from 1 to 25, from Table 20 in Ref. 21).

Fig. 3
Fig. 3

Comparison of gn values between pMPC and pMHG. The values of the moments g1 and g2 are identical for the two phase functions. Upper curves: g1=0.9,g2=0.81; lower curves: g1=0.5,g2=0.25.

Fig. 4
Fig. 4

Phase function parameter γ=(1-g2)/(1-g1) computed for Mie scattering. γ is plotted as a function of the ratio radius/wavelength for different refractive-index ratios n=nsphere/nmedium.

Fig. 5
Fig. 5

Effect of the first moment g1 on the reflectance for a constant second moment g2. This case is for mismatched refractive index n=1.4 and reduced albedo a=0.99.

Fig. 6
Fig. 6

(a) Role of the second moment on the reflectance for a fixed first moment g1=0.9. This case is for mismatched refractive index n=1.4 and reduced albedo a=0.99. (b) Close-up view of (a).

Fig. 7
Fig. 7

(a) Effect of the third and higher-order moments on the reflectance. The first two moments are fixed: g1=0.5,g2=0.25. The higher-moment values gn(n>2) of these phase functions are plotted in Fig. 3. This case is for mismatched refractive index n=1.4 and reduced albedo a=0.99. (b) Same as (a) but for fixed moments g1=0.9,g2=0.81.

Fig. 8
Fig. 8

Illustration of the second-order similarity relations. (a) All phase functions have the identical parameter γ=(1-g2)/(1-g1)=1.25. The reduced albedo is a=0.99. (b) The isotropic scattering can be approximated by a phase function with high g1 if g1=g2 (i.e., γ=1). The reduced albedo is a=0.99.

Fig. 9
Fig. 9

Relationship between the two parameters ρ2R and |ρ(/ρ)ln R|and the optical properties ρμs and a. Two different phase functions with the same first moment g1=0.916 were used (pHG with g1=0.916, γ=1.92 and pMie with g1=0.916,γ=2.23). This case is for mismatched boundary condition n=1.4.

Fig. 10
Fig. 10

(a) Plot of the parameter |ρ2(/ρ)R| for different phase functions and reduced albedos. The following phase functions were used: pMHG with g1=0.9, g2=0.9 (γ=1.0), pHG with g1=0.9, g2=0.81 (γ=1.9), and pMPC with g1=0.9, g2=0.75 (γ=2.5). This case is for mismatched refractive index n=1.4. (b) Plot of ρ(R(a=1) -R(a)) for different phase functions and reduced albedos. The phase functions and the refractive index are the same as those in (a).

Equations (26)

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

p(cos θ)=14π n(2n+1)gnPn(cos θ),
gn=2π0πPn(cos θ)p(cos θ)sin θ dθ.
pHG=14π 1-gHG2(1+gHG2-2gHG cos θ)3/2 .
pMHG=αpHG+(1-α)34π cos2 θ,α[0, 1].
g1=αgHG,g2=αgHG2+25(1-α),
g3=αgHG3,g4=αgHG4,  .
pMPC=αpPC+(1-α)34π cos2 θ,α[0, 1],
pPC=14π N+12N(1+cos θ)N.
g1=αgPC1,g2=αgPC2+25(1-α),
g3=αgPC3,g4=αgPC4, ,
gPC1=NN+2,
gPCn=gPCn-1N-n+1N+n+1=N(N-1)  (N-n+1)(N+2)  (N+n+1).
L(r, sˆ)=n=0N m=-nnamn(r)Ynm(sˆ),
μa*=μa,
μs*(1-gn*)=μs(1-gn),n=1,, N.
μa*=μa,
μs*(1-g1*)=μs(1-g1).
μs*(1-g2*)=μs(1-g2).
1-g21-g1=1-g2*1-g1*γ.
R(ρ, kμs, a, p)=1k2 R(kρ, μs, a, p).
R(ρ, μa, μs, γ)[A(ρ, μs, γ)+B(μs, μa)]2,
ρ R=Aρ (ρ, μs, γ).
ρ2ρ R=ρ22 Rρ ln R.
[R(ρ, μa=0, μs, γ)]1/2-[R(ρ, μa, μs, γ)]1/2
=B(μa=0, μs)-B(μa, μs).
[R(ρμs, a=1)]1/2-[R(ρμs, a)]1/2μsf(a),

Metrics