Abstract

Determination of the refractive index of hemoglobin solutions over a wide wavelength range remains challenging. A famous detour approach is the Kramers-Kronig (KK) analysis which can resolve the real part of complex refractive index from the imaginary part. However, KK analysis is limited by the contradiction between the requirement of semi-infinite frequency range and limited measured range. In this paper, based on the Multi-curve fitting method (MFM), continuous refractive index dispersion (CRID) of oxygenated and deoxygenated hemoglobin solutions are measured using a homemade symmetrical arm-linked apparatus in the continuous wavelength range with spectral resolution of about 0.259nm. A novel method to obtain the CRID is proposed.

© 2015 Optical Society of America

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References

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  1. J.-H. Fuhrhop, “Porphyrin assemblies and their scaffolds,” Langmuir 30(1), 1–12 (2014).
    [Crossref] [PubMed]
  2. G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt. 7(2), 244–247 (2002).
    [Crossref] [PubMed]
  3. Y. L. Jin, J. Y. Chen, L. Xu, and P. N. Wang, “Refractive index measurement for biomaterial samples by total internal reflection,” Phys. Med. Biol. 51(20), N371–N379 (2006).
    [Crossref] [PubMed]
  4. O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
    [Crossref] [PubMed]
  5. 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(6), 064019 (2005).
    [Crossref] [PubMed]
  6. M. Friebel and M. Meinke, “Model function to calculate the refractive index of native hemoglobin in the wavelength range of 250-1100 nm dependent on concentration,” Appl. Opt. 45(12), 2838–2842 (2006).
    [Crossref] [PubMed]
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  8. M. Meinke, I. Gersonde, M. Friebel, J. Helfmann, and G. Müller, “Chemometric determination of blood parameters using visible-near-infrared spectra,” Appl. Spectrosc. 59(6), 826–835 (2005).
    [Crossref] [PubMed]
  9. A. Nonoyama, A. Garcia-Lopez, L. H. Garcia-Rubio, G. F. Leparc, and R. L. Potter, “Hypochromicity in red blood cells: an experimental and theoretical investigation,” Biomed. Opt. Express 2(8), 2126–2143 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. O. Sydoruk, O. Zhernovaya, V. Tuchin, and A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis,” J. Biomed. Opt. 17(11), 115002 (2012).
    [Crossref] [PubMed]
  14. Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
    [Crossref] [PubMed]
  15. Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
    [Crossref] [PubMed]
  16. M. Born and E. Wolf, Principles of Optics, Pergamon, New York (1959).
  17. M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46(18), 3811–3820 (2007).
    [Crossref] [PubMed]

2015 (1)

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

2014 (2)

J.-H. Fuhrhop, “Porphyrin assemblies and their scaffolds,” Langmuir 30(1), 1–12 (2014).
[Crossref] [PubMed]

N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014).
[Crossref] [PubMed]

2012 (1)

O. Sydoruk, O. Zhernovaya, V. Tuchin, and A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis,” J. Biomed. Opt. 17(11), 115002 (2012).
[Crossref] [PubMed]

2011 (3)

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

A. Nonoyama, A. Garcia-Lopez, L. H. Garcia-Rubio, G. F. Leparc, and R. L. Potter, “Hypochromicity in red blood cells: an experimental and theoretical investigation,” Biomed. Opt. Express 2(8), 2126–2143 (2011).
[Crossref] [PubMed]

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[Crossref] [PubMed]

2007 (1)

2006 (2)

M. Friebel and M. Meinke, “Model function to calculate the refractive index of native hemoglobin in the wavelength range of 250-1100 nm dependent on concentration,” Appl. Opt. 45(12), 2838–2842 (2006).
[Crossref] [PubMed]

Y. L. Jin, J. Y. Chen, L. Xu, and P. N. Wang, “Refractive index measurement for biomaterial samples by total internal reflection,” Phys. Med. Biol. 51(20), N371–N379 (2006).
[Crossref] [PubMed]

2005 (2)

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(6), 064019 (2005).
[Crossref] [PubMed]

M. Meinke, I. Gersonde, M. Friebel, J. Helfmann, and G. Müller, “Chemometric determination of blood parameters using visible-near-infrared spectra,” Appl. Spectrosc. 59(6), 826–835 (2005).
[Crossref] [PubMed]

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(2), 028102 (2004).
[Crossref] [PubMed]

2002 (1)

G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt. 7(2), 244–247 (2002).
[Crossref] [PubMed]

1984 (1)

S. F. Shumilina, “Dispersion of real and imaginary part of the complex refractive index of hemoglobin in the range 450 to 820 nm,” Bullet. Beloruss. SSR Acad. Sci. 1, 79–84 (1984).

Aalders, M. C. G.

N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014).
[Crossref] [PubMed]

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(2), 028102 (2004).
[Crossref] [PubMed]

Bosschaart, N.

N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014).
[Crossref] [PubMed]

Chen, J. Y.

Y. L. Jin, J. Y. Chen, L. Xu, and P. N. Wang, “Refractive index measurement for biomaterial samples by total internal reflection,” Phys. Med. Biol. 51(20), N371–N379 (2006).
[Crossref] [PubMed]

Daimon, M.

Deng, Z.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Deng, Z. C.

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

Douplik, A.

O. Sydoruk, O. Zhernovaya, V. Tuchin, and A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis,” J. Biomed. Opt. 17(11), 115002 (2012).
[Crossref] [PubMed]

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[Crossref] [PubMed]

Edelman, G. J.

N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014).
[Crossref] [PubMed]

Faber, D. J.

N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014).
[Crossref] [PubMed]

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(2), 028102 (2004).
[Crossref] [PubMed]

Freivalds, T.

G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt. 7(2), 244–247 (2002).
[Crossref] [PubMed]

Friebel, M.

Fuhrhop, J.-H.

J.-H. Fuhrhop, “Porphyrin assemblies and their scaffolds,” Langmuir 30(1), 1–12 (2014).
[Crossref] [PubMed]

Garcia-Lopez, A.

Garcia-Rubio, L. H.

Gersonde, I.

Helfmann, J.

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(2), 028102 (2004).
[Crossref] [PubMed]

Jin, Y. L.

Y. L. Jin, J. Y. Chen, L. Xu, and P. N. Wang, “Refractive index measurement for biomaterial samples by total internal reflection,” Phys. Med. Biol. 51(20), N371–N379 (2006).
[Crossref] [PubMed]

Jurka, A.

G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt. 7(2), 244–247 (2002).
[Crossref] [PubMed]

Leparc, G. F.

Masumura, A.

Mazarevica, G.

G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt. 7(2), 244–247 (2002).
[Crossref] [PubMed]

Mei, J.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Meinke, M.

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(2), 028102 (2004).
[Crossref] [PubMed]

Müller, G.

Nonoyama, A.

Potter, R. L.

Shumilina, S. F.

S. F. Shumilina, “Dispersion of real and imaginary part of the complex refractive index of hemoglobin in the range 450 to 820 nm,” Bullet. Beloruss. SSR Acad. Sci. 1, 79–84 (1984).

Sun, T.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Sydoruk, O.

O. Sydoruk, O. Zhernovaya, V. Tuchin, and A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis,” J. Biomed. Opt. 17(11), 115002 (2012).
[Crossref] [PubMed]

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[Crossref] [PubMed]

Tian, J.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Tian, J. G.

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

Tuchin, V.

O. Sydoruk, O. Zhernovaya, V. Tuchin, and A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis,” J. Biomed. Opt. 17(11), 115002 (2012).
[Crossref] [PubMed]

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[Crossref] [PubMed]

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(2), 028102 (2004).
[Crossref] [PubMed]

van Leeuwen, T. G.

N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014).
[Crossref] [PubMed]

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(2), 028102 (2004).
[Crossref] [PubMed]

Wang, J.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

Wang, P. N.

Y. L. Jin, J. Y. Chen, L. Xu, and P. N. Wang, “Refractive index measurement for biomaterial samples by total internal reflection,” Phys. Med. Biol. 51(20), N371–N379 (2006).
[Crossref] [PubMed]

Xu, L.

Y. L. Jin, J. Y. Chen, L. Xu, and P. N. Wang, “Refractive index measurement for biomaterial samples by total internal reflection,” Phys. Med. Biol. 51(20), N371–N379 (2006).
[Crossref] [PubMed]

Ye, Q.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

Zhang, C.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Zhang, C. P.

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

Zhernovaya, O.

O. Sydoruk, O. Zhernovaya, V. Tuchin, and A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis,” J. Biomed. Opt. 17(11), 115002 (2012).
[Crossref] [PubMed]

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[Crossref] [PubMed]

Zhou, W.

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Zhou, W. Y.

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Spectrosc. (1)

Biomed. Opt. Express (1)

Bullet. Beloruss. SSR Acad. Sci. (1)

S. F. Shumilina, “Dispersion of real and imaginary part of the complex refractive index of hemoglobin in the range 450 to 820 nm,” Bullet. Beloruss. SSR Acad. Sci. 1, 79–84 (1984).

J. Biomed. Opt. (4)

O. Sydoruk, O. Zhernovaya, V. Tuchin, and A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis,” J. Biomed. Opt. 17(11), 115002 (2012).
[Crossref] [PubMed]

Q. Ye, J. Wang, Z. C. Deng, W. Y. Zhou, C. P. Zhang, and J. G. Tian, “Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method,” J. Biomed. Opt. 16(9), 097001 (2011).
[Crossref] [PubMed]

G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt. 7(2), 244–247 (2002).
[Crossref] [PubMed]

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(6), 064019 (2005).
[Crossref] [PubMed]

Langmuir (1)

J.-H. Fuhrhop, “Porphyrin assemblies and their scaffolds,” Langmuir 30(1), 1–12 (2014).
[Crossref] [PubMed]

Lasers Med. Sci. (1)

N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014).
[Crossref] [PubMed]

Phys. Med. Biol. (2)

Y. L. Jin, J. Y. Chen, L. Xu, and P. N. Wang, “Refractive index measurement for biomaterial samples by total internal reflection,” Phys. Med. Biol. 51(20), N371–N379 (2006).
[Crossref] [PubMed]

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[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(2), 028102 (2004).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

Z. Deng, J. Wang, Q. Ye, T. Sun, W. Zhou, J. Mei, C. Zhang, and J. Tian, “Continuous refractive index dispersion measurement based on derivative total reflection method,” Rev. Sci. Instrum. 86(4), 043101 (2015).
[Crossref] [PubMed]

Other (2)

M. Born and E. Wolf, Principles of Optics, Pergamon, New York (1959).

S. A. Prahl, “Optical absorption of hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/index.html (1999).

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Figures (4)

Fig. 1
Fig. 1 Experimental setup for reflectance measurement.
Fig. 2
Fig. 2 Plots of the CRID of (a) Hb and (b)HbO2 solutions with concentrations of 20, 40, 60, 80, 100, 120, 140, 280 and 320g/L (from lower to upper lines), respectively. Squares in (b) indicate RI values measured by DTRM at 632.8nm.
Fig. 3
Fig. 3 The measured CRID of 280g/L HbO2 and Hb solutions, compared with KK analysis.
Fig. 4
Fig. 4 CRID of HbO2 and Hb with concentration of (a) 140g/L, (b) 320g/L, compared with Ref.4

Equations (4)

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a 2 = b 2 + s 2 2 b s cos ( θ ) .
R i , j = ( R p , i , j + R s , i , j ) / 2
S ( N ) j = i = 1 i max [ R m , i , j R i , j ] 2
n ( ω ) = n P B S ( ω ) + 2 π P 0 ω ω 2 ω 2 k ( ω ) d ω

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