Abstract

A highly diluted suspension of red blood cells (hematocrit 0.01) was illuminated with an Ar or a dye laser in the wavelength range of 458–660 nm. The extinction and the angle-resolved intensity of scattered light were measured and compared with the predictions of Mie theory, the Rayleigh–Gans approximation, and the anomalous diffraction approximation. Furthermore, empirical phase functions were fitted to the measurements. The measurements were in satisfactory agreement with the predictions of Mie theory. However, better agreement was found with the anomalous diffraction model. In the Rayleigh–Gans approximation, only small-angle scattering is described appropriately. The scattering phase function of erythrocytes may be represented by the Gegenbauer kernel phase function.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1998

A. G. Borovoi, E. I. Naats, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3, 364–372 (1998).
[CrossRef] [PubMed]

1995

B. Michel, “Statistical method to calculate extinction by small irregularly shaped particles,” J. Opt. Soc. Am. A 12, 2471–2481 (1995).
[CrossRef]

K. Rinzema, B. J. Hoenders, H. A. Ferwerda, J. J. Ten Bosch, “Analytic calculation of the radiance in an anisotropically scattering medium close to the source,” Pure Appl. Opt. 4, 629–642 (1995).
[CrossRef]

1991

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Laser Med. Sci. 6, 155–168 (1991).
[CrossRef]

1988

1986

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. 33, 98–107 (1986).
[CrossRef] [PubMed]

1985

1980

1976

1970

1961

1954

R. Barer, S. Joseph, “Refractometry of living cells,” Q. J. Microsc. Sci. 95, 399–406 (1954).

1941

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

Barer, R.

R. Barer, S. Joseph, “Refractometry of living cells,” Q. J. Microsc. Sci. 95, 399–406 (1954).

Bohren, F. G.

F. G. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Borovoi, A. G.

A. G. Borovoi, E. I. Naats, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3, 364–372 (1998).
[CrossRef] [PubMed]

Dörschel, K.

A. Roggan, M. Friebe, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood,” in Laser–Tissue Interaction, Tissue Optics, and Laser Welding, G. P. Delacretaz, L. O. Svaasand, R. W. Steiner, R. Pini, G. Godlewski, eds., Proc. SPIE3195, 51–63 (1998).
[CrossRef]

Epstein, E. A.

Ferwerda, H. A.

K. Rinzema, B. J. Hoenders, H. A. Ferwerda, J. J. Ten Bosch, “Analytic calculation of the radiance in an anisotropically scattering medium close to the source,” Pure Appl. Opt. 4, 629–642 (1995).
[CrossRef]

Friebe, M.

A. Roggan, M. Friebe, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood,” in Laser–Tissue Interaction, Tissue Optics, and Laser Welding, G. P. Delacretaz, L. O. Svaasand, R. W. Steiner, R. Pini, G. Godlewski, eds., Proc. SPIE3195, 51–63 (1998).
[CrossRef]

Goldbach, T.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Different phase function approximation to determine optical properties of blood: a comparison,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 324–330 (1997).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “The optical properties of blood in the near infrared spectral range,” in Optical Diagnostics of Living Cells and Biofluids, D. L. Farkas, R. C. Leif, A. V. Priezzhev, T. Asakura, B. J. Tromberg, eds., Proc. SPIE2678, 314–324 (1996).
[CrossRef]

Greenstein, J. L.

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

Grinbaum, A.

Hahn, A.

A. Roggan, M. Friebe, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood,” in Laser–Tissue Interaction, Tissue Optics, and Laser Welding, G. P. Delacretaz, L. O. Svaasand, R. W. Steiner, R. Pini, G. Godlewski, eds., Proc. SPIE3195, 51–63 (1998).
[CrossRef]

Henyey, L. G.

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

Hoenders, B. J.

K. Rinzema, B. J. Hoenders, H. A. Ferwerda, J. J. Ten Bosch, “Analytic calculation of the radiance in an anisotropically scattering medium close to the source,” Pure Appl. Opt. 4, 629–642 (1995).
[CrossRef]

Huffman, D. R.

F. G. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimaru, A.

Johnson, C.

Joseph, S.

R. Barer, S. Joseph, “Refractometry of living cells,” Q. J. Microsc. Sci. 95, 399–406 (1954).

Kortüm, G.

G. Kortüm, Reflexionsspektroskopie (Springer-Verlag, Berlin, 1969).
[CrossRef]

Latimer, P.

McCormick, N. J.

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. 33, 98–107 (1986).
[CrossRef] [PubMed]

Metz, M. H.

Michel, B.

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. 33, 98–107 (1986).
[CrossRef] [PubMed]

Müller, G.

A. Roggan, M. Friebe, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood,” in Laser–Tissue Interaction, Tissue Optics, and Laser Welding, G. P. Delacretaz, L. O. Svaasand, R. W. Steiner, R. Pini, G. Godlewski, eds., Proc. SPIE3195, 51–63 (1998).
[CrossRef]

Naats, E. I.

A. G. Borovoi, E. I. Naats, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3, 364–372 (1998).
[CrossRef] [PubMed]

Patterson, M. S.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Laser Med. Sci. 6, 155–168 (1991).
[CrossRef]

Pennell, R. B.

R. B. Pennell, “Composition of normal human red cells,” in The Red Blood Cell, C. Bishop, D. M. Surgenor, eds. (Academic, New York, 1964).

Reynolds, L. O.

Rinzema, K.

K. Rinzema, B. J. Hoenders, H. A. Ferwerda, J. J. Ten Bosch, “Analytic calculation of the radiance in an anisotropically scattering medium close to the source,” Pure Appl. Opt. 4, 629–642 (1995).
[CrossRef]

Roggan, A.

A. Roggan, M. Friebe, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood,” in Laser–Tissue Interaction, Tissue Optics, and Laser Welding, G. P. Delacretaz, L. O. Svaasand, R. W. Steiner, R. Pini, G. Godlewski, eds., Proc. SPIE3195, 51–63 (1998).
[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. 33, 98–107 (1986).
[CrossRef] [PubMed]

Schwarzmaier, H.-J.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “The optical properties of blood in the near infrared spectral range,” in Optical Diagnostics of Living Cells and Biofluids, D. L. Farkas, R. C. Leif, A. V. Priezzhev, T. Asakura, B. J. Tromberg, eds., Proc. SPIE2678, 314–324 (1996).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Different phase function approximation to determine optical properties of blood: a comparison,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 324–330 (1997).
[CrossRef]

Shepherd, A. P.

Steinke, J. M.

Ten Bosch, J. J.

K. Rinzema, B. J. Hoenders, H. A. Ferwerda, J. J. Ten Bosch, “Analytic calculation of the radiance in an anisotropically scattering medium close to the source,” Pure Appl. Opt. 4, 629–642 (1995).
[CrossRef]

Twersky, V.

Tycko, D. H.

van Assendelft, O. W.

O. W. van Assendelft, Spectrophotometry of Hemoglobin Derivatives (Roal Vangorcum, Assen, 1970).

Wilson, B. C.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Laser Med. Sci. 6, 155–168 (1991).
[CrossRef]

Wintrobe, M. M.

M. M. Wintrobe, Clinical Hematology (Lea and Febiger, Philadelphia, 1981).

Wyman, D. R.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Laser Med. Sci. 6, 155–168 (1991).
[CrossRef]

Yaroslavsky, A. N.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “The optical properties of blood in the near infrared spectral range,” in Optical Diagnostics of Living Cells and Biofluids, D. L. Farkas, R. C. Leif, A. V. Priezzhev, T. Asakura, B. J. Tromberg, eds., Proc. SPIE2678, 314–324 (1996).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Different phase function approximation to determine optical properties of blood: a comparison,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 324–330 (1997).
[CrossRef]

Yaroslavsky, I. V.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Different phase function approximation to determine optical properties of blood: a comparison,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 324–330 (1997).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “The optical properties of blood in the near infrared spectral range,” in Optical Diagnostics of Living Cells and Biofluids, D. L. Farkas, R. C. Leif, A. V. Priezzhev, T. Asakura, B. J. Tromberg, eds., Proc. SPIE2678, 314–324 (1996).
[CrossRef]

Appl. Opt.

Astrophys. J.

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

IEEE Trans. Biomed. Eng.

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. 33, 98–107 (1986).
[CrossRef] [PubMed]

J. Biomed. Opt.

A. G. Borovoi, E. I. Naats, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3, 364–372 (1998).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Laser Med. Sci.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Laser Med. Sci. 6, 155–168 (1991).
[CrossRef]

Pure Appl. Opt.

K. Rinzema, B. J. Hoenders, H. A. Ferwerda, J. J. Ten Bosch, “Analytic calculation of the radiance in an anisotropically scattering medium close to the source,” Pure Appl. Opt. 4, 629–642 (1995).
[CrossRef]

Q. J. Microsc. Sci.

R. Barer, S. Joseph, “Refractometry of living cells,” Q. J. Microsc. Sci. 95, 399–406 (1954).

Other

R. B. Pennell, “Composition of normal human red cells,” in The Red Blood Cell, C. Bishop, D. M. Surgenor, eds. (Academic, New York, 1964).

G. Kortüm, Reflexionsspektroskopie (Springer-Verlag, Berlin, 1969).
[CrossRef]

O. W. van Assendelft, Spectrophotometry of Hemoglobin Derivatives (Roal Vangorcum, Assen, 1970).

M. M. Wintrobe, Clinical Hematology (Lea and Febiger, Philadelphia, 1981).

A. Roggan, M. Friebe, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood,” in Laser–Tissue Interaction, Tissue Optics, and Laser Welding, G. P. Delacretaz, L. O. Svaasand, R. W. Steiner, R. Pini, G. Godlewski, eds., Proc. SPIE3195, 51–63 (1998).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “The optical properties of blood in the near infrared spectral range,” in Optical Diagnostics of Living Cells and Biofluids, D. L. Farkas, R. C. Leif, A. V. Priezzhev, T. Asakura, B. J. Tromberg, eds., Proc. SPIE2678, 314–324 (1996).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Different phase function approximation to determine optical properties of blood: a comparison,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 324–330 (1997).
[CrossRef]

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

F. G. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (8)

Fig. 1
Fig. 1

Refractive index of erythrocytes: solid curve, real part n′; dashed–dotted curve, imaginary part n″.

Fig. 2
Fig. 2

Scattering phase function of latex speres in water: solid curve, Mie calculation; squares, measurement.

Fig. 3
Fig. 3

Scattering phase function of red blood cells at 577 nm: symbols, measurement; solid curve, Mie theory; dashed curve, anomalous diffraction; dotted curve, Rayleigh–Gans approximation.

Fig. 4
Fig. 4

Scattering phase function of red blood cells at 577 nm: symbols. measurement; solid curve, Henyey–Greenstein phase function; dotted curve, Gegenbauer kernel phase function (α = 1.5).

Fig. 5
Fig. 5

Mean-square deviation of the fitted Gegenbauer kernel phase function from the measurements versus parameter α.

Fig. 6
Fig. 6

Extinction cross section of erythrocytes.

Fig. 7
Fig. 7

Volume distribution of the erythrocytes in the examined specimen.

Fig. 8
Fig. 8

Theoretical calculations of scattering and absorption cross sections of erythrocytes.

Tables (2)

Tables Icon

Table 1 Mean Values and Standard Deviations of the Difference Between Angle-Resolved Measurements and Theoretical Predictions

Tables Icon

Table 2 Scattering and Absorption Cross Sections Calculated from Mie, Rayleigh–Gans, and Anomalous Diffraction Theories

Equations (28)

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

μ s = H 1 - H V   σ s
E r = f r ˆ exp ikR R
f r ˆ = k 2 4 π V E r ε r r - 1 exp - ik r ˆ · r d 3 r .
σ s = 4 π | f r ˆ | 2 d ω ,
σ ext = 4 π k Im e ˆ p · f e ˆ z ,
p r ˆ = 4 π σ ext   | f r ˆ | 2 ,
W 0 = σ s σ ext = 1 4 π 4 π   p r ˆ d ω .
σ a = V   k · ε r | E r | 2 d 3 r .
σ s = 2 π k 2 n = 1 2 n + 1 | a n | 2 + | b n | 2 , σ ext = 2 π k 2 n = 1 2 n + 1 Re a n + b n ,
p ϑ = 1 k 2 r 2 | S 1 | 2 + | S 2 | 2 ,
S 1 ϑ = n = 1 2 n + 1 n n + 1 × a n P n 1 cos   ϑ sin   ϑ + b n d d ϑ   P n 1 cos   ϑ , S 2 ϑ = n = 1 2 n + 1 n n + 1 × b n P n 1 cos   ϑ sin   ϑ + a n d d ϑ   P n 1 cos   ϑ .
f k s = k 2 4 π V ε r - 1 exp i k s · r d 3 r ,
η r ,   τ = 1   inside   the   particle 0   elsewhere ,
η r ,   a ˆ = H ξ cos   υ - r ,     cos   υ = r ˆ · a ˆ ,
χ r = 1 2 - 1 1   H ξ x - r d x .
f k s = k ε r - 1 0   r χ r sin k s r d r .
ξ cos   υ = 3 sin   υ 4 + 0.75 ,
χ r = 1 for   0 r 0.75 , 4 - 2 4 3   r - 1 1 / 2 1 / 2 for   0.75 < r 3.75 . 0 for   r > 3.75
σ a = k · ε r · V .
Φ x ,   y = k   n r η x ,   y ,   z - 1 d z ,
f ϑ ,   φ = k 2 π i     exp - ik   sin   ϑ x   cos   φ + y   sin   φ exp i Φ x ,   y - 1 d x d y ,
- 1 1   p μ d μ = W 0   with   μ = cos   ϑ .
p μ = 1 4 π W 0 1 - g 2 1 + g 2 - 2 g μ 3 / 2 ,
p μ = α g π W 0 ×   1 - g 2 2 α 1 + g 2 α - 1 - g 2 α 1 + g 2 - 2 g μ 1 + α with   | g | 1 ,   α > - 1 2 .
μ ¯ = 1 1 μ p ( μ ) d μ W 0
n = ln 10 λ 4 π   ε μ λ c ,
T = exp - μ a + μ s d = exp - H V   σ a + H 1 - H V   σ s d
σ ext = σ a + σ s = V Hd ln   T ,

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