Abstract

The real part of the complex refractive index of oxygenated native hemoglobin solutions dependent on concentration was determined in the wavelength range 250 to 1100  nm by Fresnel reflectance measurements. The hemoglobin solution was produced by physical hemolysis of human erythrocytes followed by ultracentrifugation and filtration. A model function is presented for calculating the refractive index of hemoglobin solutions depending on concentration in the wavelength range 250 to 1100  nm.

© 2006 Optical Society of America

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  1. A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
    [CrossRef]
  2. A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and 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, and B. J. Tromberg, eds., Proc. SPIE 2678, 314- 324 ( 1996).
    [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. D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
    [CrossRef]
  5. J. L. Stoddard and G. S. Adair, " The refractometric determination of hemoglobin," J. Chem. Biol. 57, 437- 454 ( 1923).
  6. M. Friebel and M. Meinke, " Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements," J. Biomed. Opt. 10, 064019 ( 2005).
    [CrossRef]
  7. Tabulated data from various sources compiled by S. Prahl at http://omlc.ogi.edu/spectra.
  8. O. W. Assendelft, Spectrophotometry of Hemoglobin Derivates (Royal Vangorcum, 1970).
  9. H. -H. Perkampus, UV-VIS Atlas of Organic Compounds, 2nd ed., part 2 (VCH Weinheim, 1992).
  10. R. Barer and S. Joseph, " Refractometry and interferometry of living cells," J. Opt. Soc. Am. 47, 545 ( 1956).
    [CrossRef]
  11. P. Latimer, " Anomalous dispersion of CS2 and CHCl2-theoretical predictions," J. Opt. Soc. Am. 51, 116- 118 ( 1961).
    [CrossRef]
  12. W. H. Orttung and J. Warner, " Refractive index dispersion in equine hemoglobin solution," J. Phys. Chem. 69, 3188- 3190 ( 1965).
    [CrossRef] [PubMed]
  13. J. D'Ans and E. Lax, Taschenbuch für Chemiker und Physiker, Makroskopische physikalisch-chemische Eigenschaften (Springer Verlag, 1967), pp. 627- 628.
  14. B. Herman, A. J. LaRocca, and R. E. Turner, " Atmospheric scattering," in The Infrared Handbook, W.W.Wolfe and G.J.Zissis, eds. (ERIM, 1978), Chap. 4, pp. 43- 45.
  15. G. Müller, " Spectroscopy with the evanescent wave in the visible region of the spectrum," Multichannel Image Detectors, Y. Talmi, ed., ACS Symp. Ser. 102, 239- 262 ( 1979).
    [CrossRef]
  16. R. B. Pennell, " Composition of normal human red cells," in The Red Blood Cell, C.Bishop and D.M.Surgenor, eds. (Academic, 1964), Chap. 2.
  17. G. Müller, K. Abraham, and M. Schaldach, " Quantitative ATR spectroscopy: some basic considerations," Appl. Opt. 20, 1182- 1190 ( 1981).
    [CrossRef] [PubMed]

2005 (1)

M. Friebel and M. Meinke, " Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements," J. Biomed. Opt. 10, 064019 ( 2005).
[CrossRef]

2004 (1)

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

1999 (1)

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
[CrossRef]

1998 (1)

1996 (1)

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and 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, and B. J. Tromberg, eds., Proc. SPIE 2678, 314- 324 ( 1996).
[CrossRef]

1981 (1)

1979 (1)

G. Müller, " Spectroscopy with the evanescent wave in the visible region of the spectrum," Multichannel Image Detectors, Y. Talmi, ed., ACS Symp. Ser. 102, 239- 262 ( 1979).
[CrossRef]

1965 (1)

W. H. Orttung and J. Warner, " Refractive index dispersion in equine hemoglobin solution," J. Phys. Chem. 69, 3188- 3190 ( 1965).
[CrossRef] [PubMed]

1961 (1)

1956 (1)

1923 (1)

J. L. Stoddard and G. S. Adair, " The refractometric determination of hemoglobin," J. Chem. Biol. 57, 437- 454 ( 1923).

Aalders, M. C. G.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

Abraham, K.

Adair, G. S.

J. L. Stoddard and G. S. Adair, " The refractometric determination of hemoglobin," J. Chem. Biol. 57, 437- 454 ( 1923).

Assendelft, O. W.

O. W. Assendelft, Spectrophotometry of Hemoglobin Derivates (Royal Vangorcum, 1970).

Barer, R.

D'Ans, J.

J. D'Ans and E. Lax, Taschenbuch für Chemiker und Physiker, Makroskopische physikalisch-chemische Eigenschaften (Springer Verlag, 1967), pp. 627- 628.

Dörschel, K.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
[CrossRef]

Faber, D. J.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

Friebel, M.

M. Friebel and M. Meinke, " Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements," J. Biomed. Opt. 10, 064019 ( 2005).
[CrossRef]

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
[CrossRef]

Goldbach, T.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and 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, and B. J. Tromberg, eds., Proc. SPIE 2678, 314- 324 ( 1996).
[CrossRef]

Hahn, A.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
[CrossRef]

Hammer, M.

Herman, B.

B. Herman, A. J. LaRocca, and R. E. Turner, " Atmospheric scattering," in The Infrared Handbook, W.W.Wolfe and G.J.Zissis, eds. (ERIM, 1978), Chap. 4, pp. 43- 45.

Hooper, B. A.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

Joseph, S.

Kolb, A.

LaRocca, A. J.

B. Herman, A. J. LaRocca, and R. E. Turner, " Atmospheric scattering," in The Infrared Handbook, W.W.Wolfe and G.J.Zissis, eds. (ERIM, 1978), Chap. 4, pp. 43- 45.

Latimer, P.

Lax, E.

J. D'Ans and E. Lax, Taschenbuch für Chemiker und Physiker, Makroskopische physikalisch-chemische Eigenschaften (Springer Verlag, 1967), pp. 627- 628.

Meinke, M.

M. Friebel and M. Meinke, " Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements," J. Biomed. Opt. 10, 064019 ( 2005).
[CrossRef]

Michel, B.

Mik, E. G.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

Müller, G.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
[CrossRef]

G. Müller, K. Abraham, and M. Schaldach, " Quantitative ATR spectroscopy: some basic considerations," Appl. Opt. 20, 1182- 1190 ( 1981).
[CrossRef] [PubMed]

G. Müller, " Spectroscopy with the evanescent wave in the visible region of the spectrum," Multichannel Image Detectors, Y. Talmi, ed., ACS Symp. Ser. 102, 239- 262 ( 1979).
[CrossRef]

Orttung, W. H.

W. H. Orttung and J. Warner, " Refractive index dispersion in equine hemoglobin solution," J. Phys. Chem. 69, 3188- 3190 ( 1965).
[CrossRef] [PubMed]

Pennell, R. B.

R. B. Pennell, " Composition of normal human red cells," in The Red Blood Cell, C.Bishop and D.M.Surgenor, eds. (Academic, 1964), Chap. 2.

Perkampus, H. -H.

H. -H. Perkampus, UV-VIS Atlas of Organic Compounds, 2nd ed., part 2 (VCH Weinheim, 1992).

Roggan, A.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
[CrossRef]

Schaldach, M.

Schwarzmaier, H. J.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and 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, and B. J. Tromberg, eds., Proc. SPIE 2678, 314- 324 ( 1996).
[CrossRef]

Schweitzer, D.

Stoddard, J. L.

J. L. Stoddard and G. S. Adair, " The refractometric determination of hemoglobin," J. Chem. Biol. 57, 437- 454 ( 1923).

Thamm, E.

Turner, R. E.

B. Herman, A. J. LaRocca, and R. E. Turner, " Atmospheric scattering," in The Infrared Handbook, W.W.Wolfe and G.J.Zissis, eds. (ERIM, 1978), Chap. 4, pp. 43- 45.

van Gemert, M. J. C.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

van Leeuwen, T. G.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

Warner, J.

W. H. Orttung and J. Warner, " Refractive index dispersion in equine hemoglobin solution," J. Phys. Chem. 69, 3188- 3190 ( 1965).
[CrossRef] [PubMed]

Yaroslavsky, A. N.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and 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, and B. J. Tromberg, eds., Proc. SPIE 2678, 314- 324 ( 1996).
[CrossRef]

Yaroslavsky, I. V.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and 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, and B. J. Tromberg, eds., Proc. SPIE 2678, 314- 324 ( 1996).
[CrossRef]

ACS Symp. Ser. (1)

G. Müller, " Spectroscopy with the evanescent wave in the visible region of the spectrum," Multichannel Image Detectors, Y. Talmi, ed., ACS Symp. Ser. 102, 239- 262 ( 1979).
[CrossRef]

Appl. Opt. (2)

J. Biomed. Opt. (2)

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, " Optical properties of circulating human blood in the wavelength range 400-2500 nm," J. Biomed. Opt. 4, 36- 46 ( 1999).
[CrossRef]

M. Friebel and M. Meinke, " Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements," J. Biomed. Opt. 10, 064019 ( 2005).
[CrossRef]

J. Chem. Biol. (1)

J. L. Stoddard and G. S. Adair, " The refractometric determination of hemoglobin," J. Chem. Biol. 57, 437- 454 ( 1923).

J. Opt. Soc. Am. (2)

J. Phys. Chem. (1)

W. H. Orttung and J. Warner, " Refractive index dispersion in equine hemoglobin solution," J. Phys. Chem. 69, 3188- 3190 ( 1965).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, " Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 28102 ( 2004).
[CrossRef]

Proc. SPIE (1)

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and 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, and B. J. Tromberg, eds., Proc. SPIE 2678, 314- 324 ( 1996).
[CrossRef]

Other (6)

Tabulated data from various sources compiled by S. Prahl at http://omlc.ogi.edu/spectra.

O. W. Assendelft, Spectrophotometry of Hemoglobin Derivates (Royal Vangorcum, 1970).

H. -H. Perkampus, UV-VIS Atlas of Organic Compounds, 2nd ed., part 2 (VCH Weinheim, 1992).

J. D'Ans and E. Lax, Taschenbuch für Chemiker und Physiker, Makroskopische physikalisch-chemische Eigenschaften (Springer Verlag, 1967), pp. 627- 628.

B. Herman, A. J. LaRocca, and R. E. Turner, " Atmospheric scattering," in The Infrared Handbook, W.W.Wolfe and G.J.Zissis, eds. (ERIM, 1978), Chap. 4, pp. 43- 45.

R. B. Pennell, " Composition of normal human red cells," in The Red Blood Cell, C.Bishop and D.M.Surgenor, eds. (Academic, 1964), Chap. 2.

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Figures (6)

Fig. 1
Fig. 1

Measured Fresnel reflections of Hb solutions of the concentration 0, 4.6, 10.4, 16.5, and 28 .7   g / dL dependent on wavelength.

Fig. 2
Fig. 2

Real part of the refractive index of Hb solutions of the concentration 0, 4.6, 10.4, 16.5, and 28 .7   g / dL in the wavelength range 250 1100   nm calculated from the Fresnel reflectance, and two n values for the Hb concentration 10.4 and 16.5 g / dL at 633   nm measured with an Abbe refractometer.

Fig. 3
Fig. 3

Relative refractive index n rel = n Hb / n H 2 O dependent on wavelength.

Fig. 4
Fig. 4

Mean relative refractive index for the wavelengths 430   nm and 800   nm dependent on Hb concentration.

Fig. 5
Fig. 5

Specific refractive increment β dependent on wavelength.

Fig. 6
Fig. 6

Real part of refractive index n for the four Hb concentrations from 4.6 to 28 .7   g / dL calculated from function (4) compared to the measured values in the wavelength range 250 1100   nm and a dispersion curve calculated for a Hb concentration of 32 g / dL .

Tables (1)

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Table 1 Specific Refractive Increment β Dependent on Wavelength with an Estimated Error of ±0.00003

Equations (4)

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

n Hb = n H 2 O + α c Hb ,
R = ( n 1 ) 2 + k 2 ( n + 1 ) 2 + k 2 ,
k = μ a λ / 4 π ,
n Hb ( λ , c Hb ) = n H 2 O ( λ ) [ β ( λ ) c Hb + 1 ] .

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