Abstract

New expressions are presented for light propagation in media for the whole range of absorption and for isotropic as well as for anisotropic scattering with an average cosine of the scattering angle between 0 and 0.9995. The method is based on the rigorous solution of the transport equation for Rayleigh-Gans scattering. The calculated angular intensity distribution was used to determine the absorption parameter K. Expressions for K and the backscattering parameter S are given that can be used to improve existing photon diffusion and two- or four-flux models.

© 1989 Optical Society of America

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  1. W. G. Zijlstra, G. A. Mook, Medical Reflection Oximetry (Van Gorcum, Assen, The Netherlands, 1962).
  2. L. Reynolds, C. Johnson, A. Ishimaru, “Diffuse Reflectance from a Finite Blood Medium: Applications to the Modeling of Fiber Optic Catheters,” Appl. Opt. 15, 2059–2067 (1976).
    [CrossRef] [PubMed]
  3. J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for In Vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
    [CrossRef]
  4. Y. Shimada, I. Yoshiya, N. Oka, “Effects of Multiple Scattering and Peripheral Circulation on Arterial Oxygen Saturation Measured with a Pulse-Type Oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
    [CrossRef] [PubMed]
  5. L. Duteil, J. C. Bernengo, W. Schalla, “A Double Wavelength Laser Doppler System to Investigate Skin Microcirculation,” IEEE Trans. Biomed. Eng. BME-32, 439–447 (1985).
    [CrossRef]
  6. T. M. Smits, J. G. Aarnoudse, W. G. Zijlstra, “Red Blood Cell Flow in the Fetal Scalp During Hypoxemia in the Chronic Sheep Experiment: a Laser Dopper Flow Study,” Pediatr. Res. 20, 407–410 (1986).
    [CrossRef] [PubMed]
  7. V. C. Roberts, “Photoplethysmography—Fundamental Aspects of the Optical Properties of Blood in Motion,” Trans. Inst. MC 4, 101–106 (1982).
    [CrossRef]
  8. J. A. Nijboer, J. C. Dorlas, “The Origin of Inverted Waveforms in the Reflection Plethysmogram,” Br. J. Anaesth. 54, 1289–1293 (1982).
    [CrossRef] [PubMed]
  9. J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
    [CrossRef] [PubMed]
  10. R. R. Anderson, B. S. Parrish, J. A. Parrish, “The Optics of Human Skin,” J. Invest Dermatol. 77, 13–19 (1981).
    [CrossRef] [PubMed]
  11. S. Wan, R. R. Anderson, J. A. Parrish, “Analytical Modelling for the Optical Properties of the Skin with In Vitro and In Vivo Applications,” Photochem. Photobiol. 34, 493–499 (1981).
    [PubMed]
  12. R. J. Gush, T. A. King, M. I. V. Jayson, “Aspects of Laser Light Scattering from Skin Tissue with Application to Laser Doppler Blood Flow Measurement,” Phys. Med. Biol. 29, 1463–1476 (1984).
    [CrossRef] [PubMed]
  13. W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “New Trends in Photobiology, Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. B: Biol. 1, 149–167 (1987).
    [CrossRef]
  14. K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, MA, 1967).
  15. R. L. Longini, R. Zdrojkowski, “A Note on the Theory of Backscattering of Light by Living Tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
    [CrossRef]
  16. R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
    [CrossRef]
  17. C. C. Johnson, “Optical Diffusion in Blood,” IEEE Trans. Biomed. Eng. BME-17, 129–133 (1970).
    [CrossRef]
  18. A. Cohen, R. L. Longini, “Theoretical Determination of the Blood’s Relative Oxygen Saturation In Vivo,” Med. Biol. Eng. 9, 61–69 (1971).
    [CrossRef] [PubMed]
  19. P. S. Mudgett, L. W. Richards, “Multiple Scattering Calculations for Technology,” Appl. Opt. 10, 1485–1502 (1971).
    [CrossRef] [PubMed]
  20. K. Klier, “Absorption and Scattering in Plane Parallel Turbid Media,” J. Opt. Soc. Am. 62, 882–885 (1972).
    [CrossRef]
  21. S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from a Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
    [CrossRef]
  22. 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]
  23. V. Twersky, “Multiple Scattering of Waves and Optical Phenomena,” J. Opt. Soc. Am. 52, 145–171 (1962).
    [CrossRef] [PubMed]
  24. N. M. Anderson, P. Sekelj, “Light-Absorbing and Scattering Properties of Non-Haemolysed Blood,” Phys. Med. Biol. 12, 173–184 (1967).
    [CrossRef] [PubMed]
  25. V. Twersky, “Absorption and Multiple Scattering by Biological Suspensions,” J. Opt. Soc. Am. 60, 1084–1093 (1970).
    [CrossRef] [PubMed]
  26. J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Whole Blood Oximetry,” IEEE Trans. Biomed. Eng. BME-33, 294–301 (1986).
    [CrossRef]
  27. R. R. Meier, J.-S. Lee, D. E. Anderson, “Atmospheric Scattering of Middle UV Radiation from an Internal Source,” Appl. Opt. 17, 3216–3225 (1978).
    [CrossRef] [PubMed]
  28. J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
    [CrossRef] [PubMed]
  29. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  30. J. R. Mika, “Neutron Transport with Anisotropic Scattering,” Nucl. Sci. Eng. 11, 415–427 (1961).
  31. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965).
  32. H. C. van de Hulst, Multiple Light Scattering, Vols. 1–2 (Academic, New York, 1980).
  33. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  34. R. S. Chadwick, I-Dee Chang, “A Laser Study of the Motion of Particles Suspended in a Slow Viscous Shear Flow,” J. Colloid Interface Sci. 42, 516–534 (1973).
    [CrossRef]
  35. R. Bonner, R. Nossal, “Model for Laser Doppler Measurements of Blood Flow in Tissue,” Appl. Opt. 20, 2097–2107 (1981).
    [CrossRef] [PubMed]

1987 (1)

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “New Trends in Photobiology, Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. B: Biol. 1, 149–167 (1987).
[CrossRef]

1986 (3)

T. M. Smits, J. G. Aarnoudse, W. G. Zijlstra, “Red Blood Cell Flow in the Fetal Scalp During Hypoxemia in the Chronic Sheep Experiment: a Laser Dopper Flow Study,” Pediatr. Res. 20, 407–410 (1986).
[CrossRef] [PubMed]

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for In Vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Whole Blood Oximetry,” IEEE Trans. Biomed. Eng. BME-33, 294–301 (1986).
[CrossRef]

1985 (1)

L. Duteil, J. C. Bernengo, W. Schalla, “A Double Wavelength Laser Doppler System to Investigate Skin Microcirculation,” IEEE Trans. Biomed. Eng. BME-32, 439–447 (1985).
[CrossRef]

1984 (3)

R. J. Gush, T. A. King, M. I. V. Jayson, “Aspects of Laser Light Scattering from Skin Tissue with Application to Laser Doppler Blood Flow Measurement,” Phys. Med. Biol. 29, 1463–1476 (1984).
[CrossRef] [PubMed]

Y. Shimada, I. Yoshiya, N. Oka, “Effects of Multiple Scattering and Peripheral Circulation on Arterial Oxygen Saturation Measured with a Pulse-Type Oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
[CrossRef] [PubMed]

1983 (1)

1982 (2)

V. C. Roberts, “Photoplethysmography—Fundamental Aspects of the Optical Properties of Blood in Motion,” Trans. Inst. MC 4, 101–106 (1982).
[CrossRef]

J. A. Nijboer, J. C. Dorlas, “The Origin of Inverted Waveforms in the Reflection Plethysmogram,” Br. J. Anaesth. 54, 1289–1293 (1982).
[CrossRef] [PubMed]

1981 (3)

R. R. Anderson, B. S. Parrish, J. A. Parrish, “The Optics of Human Skin,” J. Invest Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical Modelling for the Optical Properties of the Skin with In Vitro and In Vivo Applications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

R. Bonner, R. Nossal, “Model for Laser Doppler Measurements of Blood Flow in Tissue,” Appl. Opt. 20, 2097–2107 (1981).
[CrossRef] [PubMed]

1980 (1)

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

1979 (1)

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from a Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

1978 (1)

1976 (1)

1973 (1)

R. S. Chadwick, I-Dee Chang, “A Laser Study of the Motion of Particles Suspended in a Slow Viscous Shear Flow,” J. Colloid Interface Sci. 42, 516–534 (1973).
[CrossRef]

1972 (1)

1971 (2)

P. S. Mudgett, L. W. Richards, “Multiple Scattering Calculations for Technology,” Appl. Opt. 10, 1485–1502 (1971).
[CrossRef] [PubMed]

A. Cohen, R. L. Longini, “Theoretical Determination of the Blood’s Relative Oxygen Saturation In Vivo,” Med. Biol. Eng. 9, 61–69 (1971).
[CrossRef] [PubMed]

1970 (3)

V. Twersky, “Absorption and Multiple Scattering by Biological Suspensions,” J. Opt. Soc. Am. 60, 1084–1093 (1970).
[CrossRef] [PubMed]

R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

C. C. Johnson, “Optical Diffusion in Blood,” IEEE Trans. Biomed. Eng. BME-17, 129–133 (1970).
[CrossRef]

1968 (1)

R. L. Longini, R. Zdrojkowski, “A Note on the Theory of Backscattering of Light by Living Tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

1967 (1)

N. M. Anderson, P. Sekelj, “Light-Absorbing and Scattering Properties of Non-Haemolysed Blood,” Phys. Med. Biol. 12, 173–184 (1967).
[CrossRef] [PubMed]

1962 (1)

1961 (1)

J. R. Mika, “Neutron Transport with Anisotropic Scattering,” Nucl. Sci. Eng. 11, 415–427 (1961).

1931 (1)

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Aarnoudse, J. G.

T. M. Smits, J. G. Aarnoudse, W. G. Zijlstra, “Red Blood Cell Flow in the Fetal Scalp During Hypoxemia in the Chronic Sheep Experiment: a Laser Dopper Flow Study,” Pediatr. Res. 20, 407–410 (1986).
[CrossRef] [PubMed]

Anderson, D. E.

Anderson, N. M.

N. M. Anderson, P. Sekelj, “Light-Absorbing and Scattering Properties of Non-Haemolysed Blood,” Phys. Med. Biol. 12, 173–184 (1967).
[CrossRef] [PubMed]

Anderson, R. R.

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical Modelling for the Optical Properties of the Skin with In Vitro and In Vivo Applications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

R. R. Anderson, B. S. Parrish, J. A. Parrish, “The Optics of Human Skin,” J. Invest Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Barker, D. J.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

Bernengo, J. C.

L. Duteil, J. C. Bernengo, W. Schalla, “A Double Wavelength Laser Doppler System to Investigate Skin Microcirculation,” IEEE Trans. Biomed. Eng. BME-32, 439–447 (1985).
[CrossRef]

Bonner, R.

Case, K. M.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, MA, 1967).

Chadwick, R. S.

R. S. Chadwick, I-Dee Chang, “A Laser Study of the Motion of Particles Suspended in a Slow Viscous Shear Flow,” J. Colloid Interface Sci. 42, 516–534 (1973).
[CrossRef]

Chang, I-Dee

R. S. Chadwick, I-Dee Chang, “A Laser Study of the Motion of Particles Suspended in a Slow Viscous Shear Flow,” J. Colloid Interface Sci. 42, 516–534 (1973).
[CrossRef]

Cohen, A.

A. Cohen, R. L. Longini, “Theoretical Determination of the Blood’s Relative Oxygen Saturation In Vivo,” Med. Biol. Eng. 9, 61–69 (1971).
[CrossRef] [PubMed]

Cotterill, J. A.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

Dawson, J. B.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

de Cosnac, B.

J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
[CrossRef] [PubMed]

Dorlas, J. C.

J. A. Nijboer, J. C. Dorlas, “The Origin of Inverted Waveforms in the Reflection Plethysmogram,” Br. J. Anaesth. 54, 1289–1293 (1982).
[CrossRef] [PubMed]

Duteil, L.

L. Duteil, J. C. Bernengo, W. Schalla, “A Double Wavelength Laser Doppler System to Investigate Skin Microcirculation,” IEEE Trans. Biomed. Eng. BME-32, 439–447 (1985).
[CrossRef]

Ellis, D. J.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

Feather, J. W.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

Ferwerda, H. A.

Fisher, G. W.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

Graham, M. D.

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from a Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

Grassam, E.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

Groenhuis, R. A. J.

Gush, R. J.

R. J. Gush, T. A. King, M. I. V. Jayson, “Aspects of Laser Light Scattering from Skin Tissue with Application to Laser Doppler Blood Flow Measurement,” Phys. Med. Biol. 29, 1463–1476 (1984).
[CrossRef] [PubMed]

Hung, B. M.

J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
[CrossRef] [PubMed]

Ishimaru, A.

Jarry, G.

J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
[CrossRef] [PubMed]

Jayson, M. I. V.

R. J. Gush, T. A. King, M. I. V. Jayson, “Aspects of Laser Light Scattering from Skin Tissue with Application to Laser Doppler Blood Flow Measurement,” Phys. Med. Biol. 29, 1463–1476 (1984).
[CrossRef] [PubMed]

Johnson, C.

Johnson, C. C.

C. C. Johnson, “Optical Diffusion in Blood,” IEEE Trans. Biomed. Eng. BME-17, 129–133 (1970).
[CrossRef]

King, T. A.

R. J. Gush, T. A. King, M. I. V. Jayson, “Aspects of Laser Light Scattering from Skin Tissue with Application to Laser Doppler Blood Flow Measurement,” Phys. Med. Biol. 29, 1463–1476 (1984).
[CrossRef] [PubMed]

Klier, K.

Kubelka, P.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Lansiart, A.

J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
[CrossRef] [PubMed]

Lee, J.-S.

Longini, R. L.

A. Cohen, R. L. Longini, “Theoretical Determination of the Blood’s Relative Oxygen Saturation In Vivo,” Med. Biol. Eng. 9, 61–69 (1971).
[CrossRef] [PubMed]

R. L. Longini, R. Zdrojkowski, “A Note on the Theory of Backscattering of Light by Living Tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

Maarek, J. M.

J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
[CrossRef] [PubMed]

Marijnissen, J. P. A.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “New Trends in Photobiology, Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. B: Biol. 1, 149–167 (1987).
[CrossRef]

Meier, R. R.

Meindl, J. D.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for In Vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

Mihm, F. G.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for In Vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

Mika, J. R.

J. R. Mika, “Neutron Transport with Anisotropic Scattering,” Nucl. Sci. Eng. 11, 415–427 (1961).

Mook, G. A.

W. G. Zijlstra, G. A. Mook, Medical Reflection Oximetry (Van Gorcum, Assen, The Netherlands, 1962).

Mudgett, P. S.

Munk, F.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Nijboer, J. A.

J. A. Nijboer, J. C. Dorlas, “The Origin of Inverted Waveforms in the Reflection Plethysmogram,” Br. J. Anaesth. 54, 1289–1293 (1982).
[CrossRef] [PubMed]

Nossal, R.

Oka, N.

Y. Shimada, I. Yoshiya, N. Oka, “Effects of Multiple Scattering and Peripheral Circulation on Arterial Oxygen Saturation Measured with a Pulse-Type Oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

Parrish, B. S.

R. R. Anderson, B. S. Parrish, J. A. Parrish, “The Optics of Human Skin,” J. Invest Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Parrish, J. A.

R. R. Anderson, B. S. Parrish, J. A. Parrish, “The Optics of Human Skin,” J. Invest Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical Modelling for the Optical Properties of the Skin with In Vitro and In Vivo Applications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

Pisharoty, N. R.

R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

Reynolds, L.

Richards, L. W.

Roberts, V. C.

V. C. Roberts, “Photoplethysmography—Fundamental Aspects of the Optical Properties of Blood in Motion,” Trans. Inst. MC 4, 101–106 (1982).
[CrossRef]

Schalla, W.

L. Duteil, J. C. Bernengo, W. Schalla, “A Double Wavelength Laser Doppler System to Investigate Skin Microcirculation,” IEEE Trans. Biomed. Eng. BME-32, 439–447 (1985).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for In Vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

Sekelj, P.

N. M. Anderson, P. Sekelj, “Light-Absorbing and Scattering Properties of Non-Haemolysed Blood,” Phys. Med. Biol. 12, 173–184 (1967).
[CrossRef] [PubMed]

Shepherd, A. P.

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Whole Blood Oximetry,” IEEE Trans. Biomed. Eng. BME-33, 294–301 (1986).
[CrossRef]

Shimada, Y.

Y. Shimada, I. Yoshiya, N. Oka, “Effects of Multiple Scattering and Peripheral Circulation on Arterial Oxygen Saturation Measured with a Pulse-Type Oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

Smits, T. M.

T. M. Smits, J. G. Aarnoudse, W. G. Zijlstra, “Red Blood Cell Flow in the Fetal Scalp During Hypoxemia in the Chronic Sheep Experiment: a Laser Dopper Flow Study,” Pediatr. Res. 20, 407–410 (1986).
[CrossRef] [PubMed]

Star, W. M.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “New Trends in Photobiology, Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. B: Biol. 1, 149–167 (1987).
[CrossRef]

Steinke, J. M.

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Whole Blood Oximetry,” IEEE Trans. Biomed. Eng. BME-33, 294–301 (1986).
[CrossRef]

Takatani, S.

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from a Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

Ten Bosch, J. J.

Twersky, V.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

H. C. van de Hulst, Multiple Light Scattering, Vols. 1–2 (Academic, New York, 1980).

van Gemert, M. J. C.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “New Trends in Photobiology, Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. B: Biol. 1, 149–167 (1987).
[CrossRef]

Wan, S.

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical Modelling for the Optical Properties of the Skin with In Vitro and In Vivo Applications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

Yoshiya, I.

Y. Shimada, I. Yoshiya, N. Oka, “Effects of Multiple Scattering and Peripheral Circulation on Arterial Oxygen Saturation Measured with a Pulse-Type Oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

Zdrojkowski, R.

R. L. Longini, R. Zdrojkowski, “A Note on the Theory of Backscattering of Light by Living Tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

Zdrojkowski, R. J.

R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

Zijlstra, W. G.

T. M. Smits, J. G. Aarnoudse, W. G. Zijlstra, “Red Blood Cell Flow in the Fetal Scalp During Hypoxemia in the Chronic Sheep Experiment: a Laser Dopper Flow Study,” Pediatr. Res. 20, 407–410 (1986).
[CrossRef] [PubMed]

W. G. Zijlstra, G. A. Mook, Medical Reflection Oximetry (Van Gorcum, Assen, The Netherlands, 1962).

Zweifel, P. F.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, MA, 1967).

Ann. Biomed. Eng. (1)

J. M. Maarek, G. Jarry, B. de Cosnac, A. Lansiart, B. M. Hung, “A Simulation Method for the Study of Laser Transillumination of Biological Tissues,” Ann. Biomed. Eng. 12, 281–304 (1984).
[CrossRef] [PubMed]

Appl. Opt. (5)

Br. J. Anaesth. (1)

J. A. Nijboer, J. C. Dorlas, “The Origin of Inverted Waveforms in the Reflection Plethysmogram,” Br. J. Anaesth. 54, 1289–1293 (1982).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng. (7)

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for In Vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

L. Duteil, J. C. Bernengo, W. Schalla, “A Double Wavelength Laser Doppler System to Investigate Skin Microcirculation,” IEEE Trans. Biomed. Eng. BME-32, 439–447 (1985).
[CrossRef]

R. L. Longini, R. Zdrojkowski, “A Note on the Theory of Backscattering of Light by Living Tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

C. C. Johnson, “Optical Diffusion in Blood,” IEEE Trans. Biomed. Eng. BME-17, 129–133 (1970).
[CrossRef]

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from a Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Whole Blood Oximetry,” IEEE Trans. Biomed. Eng. BME-33, 294–301 (1986).
[CrossRef]

J. Colloid Interface Sci. (1)

R. S. Chadwick, I-Dee Chang, “A Laser Study of the Motion of Particles Suspended in a Slow Viscous Shear Flow,” J. Colloid Interface Sci. 42, 516–534 (1973).
[CrossRef]

J. Invest Dermatol. (1)

R. R. Anderson, B. S. Parrish, J. A. Parrish, “The Optics of Human Skin,” J. Invest Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (3)

J. Photochem. Photobiol. B: Biol. (1)

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “New Trends in Photobiology, Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. B: Biol. 1, 149–167 (1987).
[CrossRef]

Med. Biol. Eng. (1)

A. Cohen, R. L. Longini, “Theoretical Determination of the Blood’s Relative Oxygen Saturation In Vivo,” Med. Biol. Eng. 9, 61–69 (1971).
[CrossRef] [PubMed]

Med. Biol. Eng. Comput. (1)

Y. Shimada, I. Yoshiya, N. Oka, “Effects of Multiple Scattering and Peripheral Circulation on Arterial Oxygen Saturation Measured with a Pulse-Type Oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

Nucl. Sci. Eng. (1)

J. R. Mika, “Neutron Transport with Anisotropic Scattering,” Nucl. Sci. Eng. 11, 415–427 (1961).

Pediatr. Res. (1)

T. M. Smits, J. G. Aarnoudse, W. G. Zijlstra, “Red Blood Cell Flow in the Fetal Scalp During Hypoxemia in the Chronic Sheep Experiment: a Laser Dopper Flow Study,” Pediatr. Res. 20, 407–410 (1986).
[CrossRef] [PubMed]

Photochem. Photobiol. (1)

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical Modelling for the Optical Properties of the Skin with In Vitro and In Vivo Applications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

Phys. Med. Biol. (3)

R. J. Gush, T. A. King, M. I. V. Jayson, “Aspects of Laser Light Scattering from Skin Tissue with Application to Laser Doppler Blood Flow Measurement,” Phys. Med. Biol. 29, 1463–1476 (1984).
[CrossRef] [PubMed]

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, J. W. Feather, “A Theoretical and Experimental Study of Light Absorption and Scattering by In Vivo Skin,” Phys. Med. Biol. 25, 695–709 (1980).
[CrossRef] [PubMed]

N. M. Anderson, P. Sekelj, “Light-Absorbing and Scattering Properties of Non-Haemolysed Blood,” Phys. Med. Biol. 12, 173–184 (1967).
[CrossRef] [PubMed]

Trans. Inst. MC (1)

V. C. Roberts, “Photoplethysmography—Fundamental Aspects of the Optical Properties of Blood in Motion,” Trans. Inst. MC 4, 101–106 (1982).
[CrossRef]

Z. Tech. Phys. (1)

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Other (5)

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965).

H. C. van de Hulst, Multiple Light Scattering, Vols. 1–2 (Academic, New York, 1980).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, MA, 1967).

W. G. Zijlstra, G. A. Mook, Medical Reflection Oximetry (Van Gorcum, Assen, The Netherlands, 1962).

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Figures (8)

Fig. 1
Fig. 1

Light propagation in a thin layer of absorbing and scattering material.

Fig. 2
Fig. 2

Path length in a thin layer for photons with an incident angle of incidence θ.

Fig. 3
Fig. 3

Rayleigh-Gans and Henyey-Greenstein angular scattering distributions for single scattering and g = 0.995.

Fig. 4
Fig. 4

Average photon path length multiplier dl/dz(=Ka) for isotropic scattering. (+ = rigorous calculation; Δ = Klier20).

Fig. 5
Fig. 5

Diffusion constant multiplier F = ν/νd for isotropic scattering (□ = rigorous calculation; ⋄ = Klier20).

Fig. 6
Fig. 6

Coefficients fi for the description of the Rayleigh-Gans scatter distributions for i = 1–100 and 2πa/λ = 0,1,2,5,10,20,50,100.

Fig. 7
Fig. 7

Diffusion constant multiplier F = ν/νd for 2πa/λ = 0,1,2,5,10,20,50,100. [Δ, rigorous calculation; —, prediction with Eqs. (33)(35) and A,Bk and Bs from Table I.]

Fig. 8
Fig. 8

Average photon path length multiplier δ/dz(=Ka) for 2πa/λ = 0,1,2,5,10,20,50,100. [□, rigorous calculation; —, prediction with Eqs. (33)(34) and A and Bk from Table I.]

Tables (1)

Tables Icon

Table I Average Values of the Cosine of, the Scattering Angle g for Rayleigh-Gans Scattering and Constants A, Bk, and Bs for the Calculation of K and S for Rayleigh-Gans Scattering

Equations (36)

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

( 2 Σ a / D ) Ψ ( φ , θ , z ) = ( 1 / D ) S ( φ , θ , z ) ,
D = 1 3 [ Σ s ( 1 g ) + Σ a ] .
d I ( z ) = K I ( z ) d z S I ( z ) d z + S J ( z ) d z ,
d J ( z ) = K J ( z ) d z S J ( z ) d z + S I ( z ) d z ,
I ( z ) = A exp ( α z ) + A exp ( + α z ) ,
J ( z ) = B exp ( α z ) + B exp ( + α z ) ,
α 2 = K 2 + 2 K S .
K = d l d z Σ a ,
K / Σ a = d l / d z = 1 1 | 1 μ | Φ ( μ ) | μ | d μ 1 1 Φ ( μ ) | μ | d μ ,
K = 2 Σ a .
S = 3 4 Σ s ( 1 g ) 1 4 Σ a .
α 2 = Σ a / D = Σ a [ 3 Σ s ( 1 g ) + 3 Σ a ] .
α = K = 2 Σ a
α = K = Σ a .
μ d Ψ ( z , μ ) ( Σ a + Σ s ) d z + Ψ ( z , μ ) = c 2 4 π f ( Ω · Ω ) Ψ ( z , Ω ) d Ω
Ψ ( z , μ ) = Φ ( μ ) exp [ ( Σ a + Σ s ) z / ν ] ,
Λ ( ν ) 1 c ν i = 0 N ( 2 i + 1 ) f i Φ i Q i ( ν ) = 0 ,
Φ i = ν ( 1 c f i 1 ) Φ i 1 2 i 1 i i 1 i Φ i 2 ,
Φ 0 = 1 ,
Φ 1 = ν ( 1 c ) .
Φ ( μ ) = c ν 2 ( ν μ ) i = 0 N ( 2 i + 1 ) f i Φ i P i ( μ ) ,
α 2 = Σ a D = ( Σ a + Σ s ν ) 2
α 2 = K 2 + 2 K S .
Λ ( ν ) = 1 c ν 2 ln ( 1 + 1 / ν 1 1 / ν ) .
f ( μ ) = i = 0 N 2 i + 1 4 π f i P i ( μ ) .
f i = 2 π 1 1 f ( μ ) P i ( μ ) d μ .
I ( θ ) = ( 1 + μ 2 2 ) { 3 ( u a ) 3 [ sin ( u a ) u a cos ( u a ) ] } 2 ,
u = 4 π n λ sin ( θ / 2 ) .
f ( μ ) = 1 2 π I ( μ ) / 1 1 I ( μ ) d μ .
f ( μ ) = 1 4 π 1 g 2 ( 1 + g 2 2 μ g ) 3 / 2
F ν ν d = α d α ,
ν d = 1 / [ 3 ( 1 c ) ( 1 c g ) ] 1 / 2 ,
Σ s Σ s ( 1 g ) A ( g ) ,
c Σ s Σ a + Σ s = 1 ( 1 c ) / [ c ( 1 g ) A ( g ) ] + 1 .
K / Σ a = 1 + [ c ] B k ( g ) ,
S / Σ s = ( 1 g ) [ 0 . 25 + 0 . 50 c + B s ( g ) ( 1 c ) 2 . 3 ] ,

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