Abstract

Red blood cells (RBCs) scatter light mainly in the forward direction, where the scattering phase function has a narrow peak. We performed an experimental investigation into the angular distribution of light scattered by blood in the small-angle domain. A highly diluted suspension of RBCs (hematocrits in the range 5×105102) was illuminated with a He–Ne laser with 633  nm wavelength. We focused our research on two main topics: the scattering efficiency of the RBCs given by the mean scattering cross section and the scattering anisotropy obtained from the angular distribution of the scattered photons. The collimated beam transmission and the angular distribution of scattered light were measured and compared with the predictions of the effective phase function model. The RBCs' mean scattering cross section and scattering anisotropy were obtained by fitting of the experimental data.

© 2006 Optical Society of America

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References

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  1. G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, and R. M. Heethaar, "Light-scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction," Appl. Opt. 32, 2266-2272 (1993).
    [CrossRef] [PubMed]
  2. L. O. Reynolds and N. J. McCormick, "Approximate two parameter phase function for light scattering," J. Opt. Soc. Am 70, 1206-1212 (1980).
    [CrossRef]
  3. M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, "Single scattering by red blood cells," Appl. Opt. 37, 7410-7418 (1998).
    [CrossRef]
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  5. A. A. Kokhanovsky, "Analytical solutions of multiple light scattering problems: a review," Meas. Sci. Technol. 13, 233-240 (2002).
  6. I. Turcu, "Effective phase function for light scattered by disperse systems--the small-angle approximation," J. Opt. A Pure Appl. Opt. 6, 537-543 (2004).
    [CrossRef]
  7. I. Turcu, "Effective phase function for light scattered by blood," Appl. Opt. 45, 639-647 (2006).
    [CrossRef]
  8. A. N. Shvalov, J. T. Soini, A. V. Chenyshev, P. A. Tarasov, E. Soini, and V. P. Maltsev, "Light-scattering properties of individual erythrocytes," Appl. Opt. 38, 230-235 (1999).
    [CrossRef]
  9. S. T. Tsinopoulos and D. Polyzos, "Scattering of He-Ne laser light by an average-sized red blood cell," Appl. Opt. 38, 5499-5510 (1999).
    [CrossRef]
  10. S. T. Tsinopoulos, E. J. Sellountos, and D. Polyzos, "Light scattering by aggregated red blood cells," Appl. Opt. 41, 1408-1417 (2002).
    [CrossRef] [PubMed]
  11. A. M. K. Nilsson, P. Asholm, A. Karlsson, and A. Anderson-Engels, "T-matrix computations of light scattered by red blood cells," Appl. Opt. 37, 2735-2748 (1998).
    [CrossRef]
  12. A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005).
    [CrossRef] [PubMed]
  13. L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
    [CrossRef] [PubMed]
  14. S. L. Jacques and L. Wang, "Monte Carlo modeling of light transport in tisue," in Optical Thermal Response of Laser-Irradiated Tissue, A.Welch and M.J. C.van Gemert, eds. (Plenum, 1995), pp. 73-100.
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. V. S. Lee and L. Tarassenko, "Absorption and multiple scattering by suspensions of aligned red blood cells," J. Opt. Soc. Am. A 8, 1135-1141 (1991).
  18. A. H. Gandjbakhche, P. Mills, and P. Snabre, "Light-scattering technique for study of orientation and deformation of red blood cells in a concentrated suspension," Appl. Opt. 33, 1070-1078 (1994).
    [PubMed]
  19. J. Kim and J. C. Lin, "Successive order scattering transport approximation for laser light propagation in whole blood medium," IEEE Trans. Biomed. Eng. 45, 505-510 (1998).
    [CrossRef] [PubMed]
  20. A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, "Influence of scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
    [CrossRef]
  21. A. Serov, W. Steenbergen, and F. de Mul, "Prediction of the photodetector signal generated by Doppler-induced speckle fluctuations: theory and some validations," J. Opt. Soc. Am. A 18, 622-630 (2001).
    [CrossRef]
  22. J. M. Steinke and A. P. Shepherd, "Comparison of Mie theory and the light scattering of red blood cells," Appl. Opt. 27, 4027-4033 (1988).
    [CrossRef] [PubMed]
  23. A. K. Dunn, A. Devor, H. Bolay, M. L. Andermann, M. A. Moskowitz, A. M. Dale, and D. A. Boas, "Simultaneous imaging of total cerebral hemoglobin concentration, oxygenation, and blood flow during functional activation," Opt. Lett. 28, 28-30 (2003).
    [CrossRef] [PubMed]
  24. L.-H. Wang and S. L. Jacques, "Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission," Phys. Med. Biol. 39, 2349-2354 (1994).
    [CrossRef] [PubMed]
  25. S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
    [CrossRef] [PubMed]
  26. J. D. Briers, "Laser Doppler speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
    [CrossRef]
  27. P. K. Dixon and D. J. Durian, "Speckle-visibility spectroscopy and variable granular fluidization," Phys. Rev. Lett. 90, 184302 (2003).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005).
[CrossRef] [PubMed]

2004 (1)

I. Turcu, "Effective phase function for light scattered by disperse systems--the small-angle approximation," J. Opt. A Pure Appl. Opt. 6, 537-543 (2004).
[CrossRef]

2003 (2)

2002 (2)

S. T. Tsinopoulos, E. J. Sellountos, and D. Polyzos, "Light scattering by aggregated red blood cells," Appl. Opt. 41, 1408-1417 (2002).
[CrossRef] [PubMed]

A. A. Kokhanovsky, "Analytical solutions of multiple light scattering problems: a review," Meas. Sci. Technol. 13, 233-240 (2002).

2001 (3)

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, "A scattering phase function for blood with physiological haematocrit," Phys. Med. Biol. 46, N65-N69 (2001).
[CrossRef] [PubMed]

J. D. Briers, "Laser Doppler speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

A. Serov, W. Steenbergen, and F. de Mul, "Prediction of the photodetector signal generated by Doppler-induced speckle fluctuations: theory and some validations," J. Opt. Soc. Am. A 18, 622-630 (2001).
[CrossRef]

2000 (1)

S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
[CrossRef] [PubMed]

1999 (4)

1998 (3)

1995 (1)

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

1994 (2)

A. H. Gandjbakhche, P. Mills, and P. Snabre, "Light-scattering technique for study of orientation and deformation of red blood cells in a concentrated suspension," Appl. Opt. 33, 1070-1078 (1994).
[PubMed]

L.-H. Wang and S. L. Jacques, "Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission," Phys. Med. Biol. 39, 2349-2354 (1994).
[CrossRef] [PubMed]

1993 (1)

1991 (1)

V. S. Lee and L. Tarassenko, "Absorption and multiple scattering by suspensions of aligned red blood cells," J. Opt. Soc. Am. A 8, 1135-1141 (1991).

1988 (1)

1980 (1)

L. O. Reynolds and N. J. McCormick, "Approximate two parameter phase function for light scattering," J. Opt. Soc. Am 70, 1206-1212 (1980).
[CrossRef]

Andermann, M. L.

Anderson-Engels, A.

Andersson-Engels, S.

A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005).
[CrossRef] [PubMed]

Asholm, P.

Boas, D. A.

Bolay, H.

Briers, J. D.

J. D. Briers, "Laser Doppler speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

Chance, B.

S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
[CrossRef] [PubMed]

Choe, R.

S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
[CrossRef] [PubMed]

Dale, A. M.

de Mul, F.

Devor, A.

Dixon, P. K.

P. K. Dixon and D. J. Durian, "Speckle-visibility spectroscopy and variable granular fluidization," Phys. Rev. Lett. 90, 184302 (2003).
[CrossRef] [PubMed]

Dunn, A. K.

Durian, D. J.

P. K. Dixon and D. J. Durian, "Speckle-visibility spectroscopy and variable granular fluidization," Phys. Rev. Lett. 90, 184302 (2003).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

Goldbach, T.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, "Influence of scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Hammer, M.

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, "A scattering phase function for blood with physiological haematocrit," Phys. Med. Biol. 46, N65-N69 (2001).
[CrossRef] [PubMed]

M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, "Single scattering by red blood cells," Appl. Opt. 37, 7410-7418 (1998).
[CrossRef]

He, J.

A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005).
[CrossRef] [PubMed]

Heethaar, R. M.

Hoekstra, A. G.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jacques, S. L.

S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

L.-H. Wang and S. L. Jacques, "Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission," Phys. Med. Biol. 39, 2349-2354 (1994).
[CrossRef] [PubMed]

S. L. Jacques and L. Wang, "Monte Carlo modeling of light transport in tisue," in Optical Thermal Response of Laser-Irradiated Tissue, A.Welch and M.J. C.van Gemert, eds. (Plenum, 1995), pp. 73-100.

Karlsson, A.

A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005).
[CrossRef] [PubMed]

A. M. K. Nilsson, P. Asholm, A. Karlsson, and A. Anderson-Engels, "T-matrix computations of light scattered by red blood cells," Appl. Opt. 37, 2735-2748 (1998).
[CrossRef]

Kim, J.

J. Kim and J. C. Lin, "Successive order scattering transport approximation for laser light propagation in whole blood medium," IEEE Trans. Biomed. Eng. 45, 505-510 (1998).
[CrossRef] [PubMed]

Kokhanovsky, A. A.

A. A. Kokhanovsky, "Analytical solutions of multiple light scattering problems: a review," Meas. Sci. Technol. 13, 233-240 (2002).

Kolb, A.

Kolkman, R.

Lee, V. S.

V. S. Lee and L. Tarassenko, "Absorption and multiple scattering by suspensions of aligned red blood cells," J. Opt. Soc. Am. A 8, 1135-1141 (1991).

Lin, J. C.

J. Kim and J. C. Lin, "Successive order scattering transport approximation for laser light propagation in whole blood medium," IEEE Trans. Biomed. Eng. 45, 505-510 (1998).
[CrossRef] [PubMed]

McCormick, N. J.

L. O. Reynolds and N. J. McCormick, "Approximate two parameter phase function for light scattering," J. Opt. Soc. Am 70, 1206-1212 (1980).
[CrossRef]

Michel, B.

Mills, P.

Moskowitz, M. A.

Nijhof, E. J.

Nilsson, A. M. K.

Polyzos, D.

Ramanujam, N.

S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
[CrossRef] [PubMed]

Reynolds, L. O.

L. O. Reynolds and N. J. McCormick, "Approximate two parameter phase function for light scattering," J. Opt. Soc. Am 70, 1206-1212 (1980).
[CrossRef]

Schwarzmaier, H.-J.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, "Influence of scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Schweitzer, D.

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, "A scattering phase function for blood with physiological haematocrit," Phys. Med. Biol. 46, N65-N69 (2001).
[CrossRef] [PubMed]

M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, "Single scattering by red blood cells," Appl. Opt. 37, 7410-7418 (1998).
[CrossRef]

Sellountos, E. J.

Serov, A.

Shepherd, A. P.

Shvalov, A. N.

Snabre, P.

Steenbergen, W.

Steinke, J. M.

Streekstra, G. J.

Swartling, J.

A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005).
[CrossRef] [PubMed]

Tarassenko, L.

V. S. Lee and L. Tarassenko, "Absorption and multiple scattering by suspensions of aligned red blood cells," J. Opt. Soc. Am. A 8, 1135-1141 (1991).

Thamm, E.

Tsinopoulos, S. T.

Turcu, I.

I. Turcu, "Effective phase function for light scattered by blood," Appl. Opt. 45, 639-647 (2006).
[CrossRef]

I. Turcu, "Effective phase function for light scattered by disperse systems--the small-angle approximation," J. Opt. A Pure Appl. Opt. 6, 537-543 (2004).
[CrossRef]

Vishnoi, G.

S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
[CrossRef] [PubMed]

Wang, L.

S. L. Jacques and L. Wang, "Monte Carlo modeling of light transport in tisue," in Optical Thermal Response of Laser-Irradiated Tissue, A.Welch and M.J. C.van Gemert, eds. (Plenum, 1995), pp. 73-100.

Wang, L.-H.

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

L.-H. Wang and S. L. Jacques, "Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission," Phys. Med. Biol. 39, 2349-2354 (1994).
[CrossRef] [PubMed]

Yaroslavsky, A. N.

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, "A scattering phase function for blood with physiological haematocrit," Phys. Med. Biol. 46, N65-N69 (2001).
[CrossRef] [PubMed]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, "Influence of scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Yaroslavsky, I. V.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, "Influence of scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

Zheng, L.-Q.

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Appl. Opt. (9)

J. M. Steinke and A. P. Shepherd, "Comparison of Mie theory and the light scattering of red blood cells," Appl. Opt. 27, 4027-4033 (1988).
[CrossRef] [PubMed]

G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, and R. M. Heethaar, "Light-scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction," Appl. Opt. 32, 2266-2272 (1993).
[CrossRef] [PubMed]

A. H. Gandjbakhche, P. Mills, and P. Snabre, "Light-scattering technique for study of orientation and deformation of red blood cells in a concentrated suspension," Appl. Opt. 33, 1070-1078 (1994).
[PubMed]

A. M. K. Nilsson, P. Asholm, A. Karlsson, and A. Anderson-Engels, "T-matrix computations of light scattered by red blood cells," Appl. Opt. 37, 2735-2748 (1998).
[CrossRef]

M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, "Single scattering by red blood cells," Appl. Opt. 37, 7410-7418 (1998).
[CrossRef]

A. N. Shvalov, J. T. Soini, A. V. Chenyshev, P. A. Tarasov, E. Soini, and V. P. Maltsev, "Light-scattering properties of individual erythrocytes," Appl. Opt. 38, 230-235 (1999).
[CrossRef]

S. T. Tsinopoulos and D. Polyzos, "Scattering of He-Ne laser light by an average-sized red blood cell," Appl. Opt. 38, 5499-5510 (1999).
[CrossRef]

S. T. Tsinopoulos, E. J. Sellountos, and D. Polyzos, "Light scattering by aggregated red blood cells," Appl. Opt. 41, 1408-1417 (2002).
[CrossRef] [PubMed]

I. Turcu, "Effective phase function for light scattered by blood," Appl. Opt. 45, 639-647 (2006).
[CrossRef]

Comput. Methods Programs Biomed. (1)

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng. (2)

A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005).
[CrossRef] [PubMed]

J. Kim and J. C. Lin, "Successive order scattering transport approximation for laser light propagation in whole blood medium," IEEE Trans. Biomed. Eng. 45, 505-510 (1998).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, "Influence of scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements," J. Biomed. Opt. 4, 47-53 (1999).
[CrossRef]

S. L. Jacques, N. Ramanujam, G. Vishnoi, R. Choe, and B. Chance, "Modeling photon transport in transabdominal fetal oximetry," J. Biomed. Opt. 5, 277-282 (2000).
[CrossRef] [PubMed]

J. Opt. A Pure Appl. Opt. (1)

I. Turcu, "Effective phase function for light scattered by disperse systems--the small-angle approximation," J. Opt. A Pure Appl. Opt. 6, 537-543 (2004).
[CrossRef]

J. Opt. Soc. Am (1)

L. O. Reynolds and N. J. McCormick, "Approximate two parameter phase function for light scattering," J. Opt. Soc. Am 70, 1206-1212 (1980).
[CrossRef]

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

Opt. Lett. (1)

Phys. Med. Biol. (2)

L.-H. Wang and S. L. Jacques, "Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission," Phys. Med. Biol. 39, 2349-2354 (1994).
[CrossRef] [PubMed]

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, "A scattering phase function for blood with physiological haematocrit," Phys. Med. Biol. 46, N65-N69 (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

P. K. Dixon and D. J. Durian, "Speckle-visibility spectroscopy and variable granular fluidization," Phys. Rev. Lett. 90, 184302 (2003).
[CrossRef] [PubMed]

Physiol. Meas. (1)

J. D. Briers, "Laser Doppler speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

Other (4)

V. S. Lee and L. Tarassenko, "Absorption and multiple scattering by suspensions of aligned red blood cells," J. Opt. Soc. Am. A 8, 1135-1141 (1991).

S. L. Jacques and L. Wang, "Monte Carlo modeling of light transport in tisue," in Optical Thermal Response of Laser-Irradiated Tissue, A.Welch and M.J. C.van Gemert, eds. (Plenum, 1995), pp. 73-100.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

A. A. Kokhanovsky, "Analytical solutions of multiple light scattering problems: a review," Meas. Sci. Technol. 13, 233-240 (2002).

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Figures (7)

Fig. 1
Fig. 1

Gaussian profiles of the transmitted collimated laser beam for several hematocrits. The sample was 1 mm thick. At hematocrits higher than 10−2 the Gaussian profiles are embedded in the scattered light and are no longer detectable.

Fig. 2
Fig. 2

Decrease of transmission with increasing hematocrit for three detecting devices: a CCD camera, a photodiode, and an UV∕VIS spectrophotometer. The best result for avoiding the scattering component is obtained by CCD camera measurements, which are quite well fitted by a one-parameter exponential decay. The other two data sets cannot be fitted by such a simple decay because of the relatively important contribution added by scattering.

Fig. 3
Fig. 3

(a) Speckled interference image of the light that has escaped from a 1   mm thick sample containing RBCs in suspension ( H = 10 3 ) captured by a CCD camera at 10   ms exposure time. (b) Image contrast reduction for the same light-scattering process obtained by increasing the exposure time at 100   ms and additionally by averaging the images captured successively during 3 min. Some parasitic interference fringes (with unknown cause and unobservable in the original images) appear because of use of the reducing contrast procedure.

Fig. 4
Fig. 4

Angle-resolved measurements for the averaged intensity of light scattered at small angles by RBCs in suspension, fitted with the corresponding theoretical dependency. For a 1 mm thick sample the scattering efficiency (a) increases with the increase of hematocrit up to 2 × 10 3 and (b) decreases with further increase of the sample hematocrit.

Fig. 5
Fig. 5

Dependence on hematocrit of the intensity of light scattered at small angles by RBCs in suspension. Solid curves, the best-fitting functions obtained by the effective phase function theory, expression (3). The peak-type curves become flatter with increase of θ, and the hematocrits corresponding to the maximum of each of the curves shift gradually to higher values.

Fig. 6
Fig. 6

Decrease of the effective scattering anisotropy with increase of the sample hematocrit. Solid curve, best-fit effective anisotropy function g ( τ ) . At very small hematocrits some discrepancies appear between the theoretical predictions and the experimental data.

Fig. 7
Fig. 7

Single-scattering anisotropy g obtained from the data sets measured at several deflecting angles. The values are the outcomes of the best fit of the hematocrit-dependent scattered light intensity (Fig. 5) with the corresponding theoretical expression [expression (3)]. The solid curve represents average single-scattering anisotropy g = 0.976.

Equations (7)

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

ϕ c ϕ 0 = e τ , τ = μ ext d ,
μ ext = μ a + μ s = σ a v H + σ s v H ( 1 H ) .
I s ϕ s ( H , θ ) Δ Ω , Δ Ω = sin θ Δθ Δφ = A / D 2 ,
ϕ s ( τ , θ ) ϕ 0 ( 1 e τ ) f eff ( τ , θ ) ,     τ = μ ext d σ s v H d ,
f eff ( τ , θ ) 1 2 1 g 2 ( τ ) [ 1 2 g ( τ ) cos θ + g 2 ( τ ) ] 3 / 2 ,
g ( τ ) = g [ ( τ 1 ) e τ + 1 e τ τ 1 ] ,
T ( H ) exp ( σ a + σ s v H d ) .

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