Abstract

We constructed an automated reflectometry system for accurate measurement of coherent reflectance curves of turbid samples and analyzed the presence of coherent and diffuse reflection near the specular reflection angle. An existing method has been validated to determine the complex refractive indices of turbid samples on the basis of nonlinear regression of the coherent reflectance curves by Fresnel’s equations. The complex refractive indices of fresh porcine skin epidermis and dermis tissues and Intralipid solutions were determined at eight wavelengths: 325, 442, 532, 633, 850, 1064, 1310, and 1557nm.

© 2005 Optical Society of America

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References

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  1. R. G. Barrera, A. Garcia-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
    [CrossRef]
  2. M. A. Bartlett, H. Jiang, “Effect of refractive index on the measurement of optical properties in turbid media,” Appl. Opt. 40, 1735–1741 (2001).
    [CrossRef]
  3. T. J. Farrell, M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).
    [CrossRef] [PubMed]
  4. X. Ma, J. Q. Lu, X. H. Hu, “Effect of surface roughness on determination of bulk tissue optical parameters,” Opt. Lett. 28, 2204–2206 (2003).
    [CrossRef] [PubMed]
  5. A. Godavarty, D. J. Hawrysz, R. Roy, E. M. Sevick-Muraca, “Influence of the refractive index-mismatch at the boundaries measured in fluorescence enhanced frequency-domain photon migration imaging,” Opt. Express 10, 653–662 (2002).
    [CrossRef] [PubMed]
  6. J. Fahrenfort, W. M. Visser, “On the determination of optical constants in the infrared by attenuated total reflection,” Spectrochim. Acta 18, 1103–1116 (1962).
    [CrossRef]
  7. W. Leupacher, A. Penzkofer, “Refractive-index measurement of absorbing condensed media,” Appl. Opt. 23, 1554–1558 (1984).
    [CrossRef] [PubMed]
  8. G. H. Pettit, M. N. Ediger, “Corneal-tissue absorption coefficients for 193- and 213-nm ultraviolet radiation,” Appl. Opt. 35, 3386–3391 (1996).
    [CrossRef] [PubMed]
  9. G. H. Meeten, A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6, 214–221 (1995).
    [CrossRef]
  10. H. Li, S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35, 1793–1795 (1996).
    [CrossRef] [PubMed]
  11. F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
    [CrossRef] [PubMed]
  12. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20, 2258–2260 (1995).
    [CrossRef] [PubMed]
  13. A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
    [CrossRef]
  14. X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
    [CrossRef] [PubMed]
  15. M. A. Everett, E. Yeargers, R. M. Sayre, R. L. Olson, “Penetration of epidermis by ultraviolet rays,” Photochem. Photobiol. 5, 533–542 (1966).
    [CrossRef] [PubMed]
  16. D. W. Marquardt, “An algorithm for least squares estimation of parameters,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 11, 431–441 (1963).
  17. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  18. G. Hale, M. Querry, “Optical constants of water in the 200 nm to 200  micrometer wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  19. J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
    [CrossRef]
  20. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

2003 (2)

R. G. Barrera, A. Garcia-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
[CrossRef]

X. Ma, J. Q. Lu, X. H. Hu, “Effect of surface roughness on determination of bulk tissue optical parameters,” Opt. Lett. 28, 2204–2206 (2003).
[CrossRef] [PubMed]

2002 (2)

A. Godavarty, D. J. Hawrysz, R. Roy, E. M. Sevick-Muraca, “Influence of the refractive index-mismatch at the boundaries measured in fluorescence enhanced frequency-domain photon migration imaging,” Opt. Express 10, 653–662 (2002).
[CrossRef] [PubMed]

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef] [PubMed]

2001 (2)

M. A. Bartlett, H. Jiang, “Effect of refractive index on the measurement of optical properties in turbid media,” Appl. Opt. 40, 1735–1741 (2001).
[CrossRef]

T. J. Farrell, M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).
[CrossRef] [PubMed]

2000 (1)

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef]

1996 (3)

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

G. H. Pettit, M. N. Ediger, “Corneal-tissue absorption coefficients for 193- and 213-nm ultraviolet radiation,” Appl. Opt. 35, 3386–3391 (1996).
[CrossRef] [PubMed]

H. Li, S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35, 1793–1795 (1996).
[CrossRef] [PubMed]

1995 (2)

1989 (1)

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

1984 (1)

1973 (1)

G. Hale, M. Querry, “Optical constants of water in the 200 nm to 200  micrometer wavelength region,” Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

1966 (1)

M. A. Everett, E. Yeargers, R. M. Sayre, R. L. Olson, “Penetration of epidermis by ultraviolet rays,” Photochem. Photobiol. 5, 533–542 (1966).
[CrossRef] [PubMed]

1963 (1)

D. W. Marquardt, “An algorithm for least squares estimation of parameters,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 11, 431–441 (1963).

1962 (1)

J. Fahrenfort, W. M. Visser, “On the determination of optical constants in the infrared by attenuated total reflection,” Spectrochim. Acta 18, 1103–1116 (1962).
[CrossRef]

Barrera, R. G.

Bartlett, M. A.

Boehlau-Godau, M.

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef]

Bolin, F. P.

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

Bouma, B. E.

Brezinski, M. E.

Ediger, M. N.

G. H. Pettit, M. N. Ediger, “Corneal-tissue absorption coefficients for 193- and 213-nm ultraviolet radiation,” Appl. Opt. 35, 3386–3391 (1996).
[CrossRef] [PubMed]

Everett, M. A.

M. A. Everett, E. Yeargers, R. M. Sayre, R. L. Olson, “Penetration of epidermis by ultraviolet rays,” Photochem. Photobiol. 5, 533–542 (1966).
[CrossRef] [PubMed]

Fahrenfort, J.

J. Fahrenfort, W. M. Visser, “On the determination of optical constants in the infrared by attenuated total reflection,” Spectrochim. Acta 18, 1103–1116 (1962).
[CrossRef]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).
[CrossRef] [PubMed]

Ference, R. J.

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

Fujimoto, J. G.

Garcia-Valenzuela, A.

Godavarty, A.

Hale, G.

G. Hale, M. Querry, “Optical constants of water in the 200 nm to 200  micrometer wavelength region,” Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

Hawrysz, D. J.

Hee, M. R.

Hu, X. H.

X. Ma, J. Q. Lu, X. H. Hu, “Effect of surface roughness on determination of bulk tissue optical parameters,” Opt. Lett. 28, 2204–2206 (2003).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

Jiang, H.

Jing, X. D.

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

Jones, I.

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

Knüttel, A.

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef]

Leupacher, W.

Li, H.

H. Li, S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35, 1793–1795 (1996).
[CrossRef] [PubMed]

Lu, J. Q.

X. Ma, J. Q. Lu, X. H. Hu, “Effect of surface roughness on determination of bulk tissue optical parameters,” Opt. Lett. 28, 2204–2206 (2003).
[CrossRef] [PubMed]

Ma, X.

X. Ma, J. Q. Lu, X. H. Hu, “Effect of surface roughness on determination of bulk tissue optical parameters,” Opt. Lett. 28, 2204–2206 (2003).
[CrossRef] [PubMed]

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least squares estimation of parameters,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 11, 431–441 (1963).

Meeten, G. H.

G. H. Meeten, A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6, 214–221 (1995).
[CrossRef]

North, A. N.

G. H. Meeten, A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6, 214–221 (1995).
[CrossRef]

Olson, R. L.

M. A. Everett, E. Yeargers, R. M. Sayre, R. L. Olson, “Penetration of epidermis by ultraviolet rays,” Photochem. Photobiol. 5, 533–542 (1966).
[CrossRef] [PubMed]

Page, J. H.

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

Patterson, M. S.

T. J. Farrell, M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).
[CrossRef] [PubMed]

Penzkofer, A.

Pettit, G. H.

G. H. Pettit, M. N. Ediger, “Corneal-tissue absorption coefficients for 193- and 213-nm ultraviolet radiation,” Appl. Opt. 35, 3386–3391 (1996).
[CrossRef] [PubMed]

Preuss, L. E.

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

Querry, M.

G. Hale, M. Querry, “Optical constants of water in the 200 nm to 200  micrometer wavelength region,” Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

Roy, R.

Sayre, R. M.

M. A. Everett, E. Yeargers, R. M. Sayre, R. L. Olson, “Penetration of epidermis by ultraviolet rays,” Photochem. Photobiol. 5, 533–542 (1966).
[CrossRef] [PubMed]

Schriemer, H. P.

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

Sevick-Muraca, E. M.

Sheng, P.

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

Southern, J. F.

Taylor, R. C.

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

Tearney, G. J.

Tian, J.

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef] [PubMed]

van de Hulst, H. C.

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

Visser, W. M.

J. Fahrenfort, W. M. Visser, “On the determination of optical constants in the infrared by attenuated total reflection,” Spectrochim. Acta 18, 1103–1116 (1962).
[CrossRef]

Wang, X.

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef] [PubMed]

Weitz, D. A.

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

Xie, S.

H. Li, S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35, 1793–1795 (1996).
[CrossRef] [PubMed]

Xue, L.

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef] [PubMed]

Yeargers, E.

M. A. Everett, E. Yeargers, R. M. Sayre, R. L. Olson, “Penetration of epidermis by ultraviolet rays,” Photochem. Photobiol. 5, 533–542 (1966).
[CrossRef] [PubMed]

Zhang, C.

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef] [PubMed]

Zhang, L.

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef] [PubMed]

Appl. Opt. (4)

G. H. Pettit, M. N. Ediger, “Corneal-tissue absorption coefficients for 193- and 213-nm ultraviolet radiation,” Appl. Opt. 35, 3386–3391 (1996).
[CrossRef] [PubMed]

H. Li, S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35, 1793–1795 (1996).
[CrossRef] [PubMed]

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

G. Hale, M. Querry, “Optical constants of water in the 200 nm to 200  micrometer wavelength region,” Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Biomed. Opt. (3)

T. J. Farrell, M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).
[CrossRef] [PubMed]

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef]

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

G. H. Meeten, A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6, 214–221 (1995).
[CrossRef]

Opt. Lett. (1)

X. Ma, J. Q. Lu, X. H. Hu, “Effect of surface roughness on determination of bulk tissue optical parameters,” Opt. Lett. 28, 2204–2206 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Photochem. Photobiol. (1)

M. A. Everett, E. Yeargers, R. M. Sayre, R. L. Olson, “Penetration of epidermis by ultraviolet rays,” Photochem. Photobiol. 5, 533–542 (1966).
[CrossRef] [PubMed]

Science (1)

J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. D. Jing, D. A. Weitz, “Group velocity in strongly scattering media,” Science 271, 634–637 (1996).
[CrossRef]

SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. (1)

D. W. Marquardt, “An algorithm for least squares estimation of parameters,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 11, 431–441 (1963).

Spectrochim. Acta (1)

J. Fahrenfort, W. M. Visser, “On the determination of optical constants in the infrared by attenuated total reflection,” Spectrochim. Acta 18, 1103–1116 (1962).
[CrossRef]

Other (2)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

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

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Figures (9)

Fig. 1
Fig. 1

Schematic of the reflectometry system: (a) the aligned position with θ = 45 ° ; PD1/PD2, photodiodes; C, chopper; (b) the varied position of the prism and sample by rotation from the aligned positions (dashed lines) through ϕ (dashed–dotted lines) and translation over distance a (solid lines).

Fig. 2
Fig. 2

Measured ( R s and R p ) and calculated ( R ̃ s and R ̃ p ) coherent reflectance versus incident angle for deionized water with s- and p-polarized incident beam at λ = 633 nm . Inset, full angular range.

Fig. 3
Fig. 3

Reflection signal versus rotation angle of the detector at incident angle of (a) θ = 45 ° , (b) θ = 70 ° with an s-polarized beam at λ = 633 nm for deionized water, 20% Intralipid solution, and porcine skin epidermis and dermis with an angular step of 0.125°. Error bars of approximately ± 5 % have been removed for clarity; the two vertical dashed lines indicate the angular acceptance range of the aperture in front of the photodiode.

Fig. 4
Fig. 4

Refractive indices of Intralipid samples versus concentration by weight: (a) real; (b) imaginary; inset, with the log scale.

Fig. 5
Fig. 5

(a) Real and (b) imaginary refractive indices of 20% Intralipid versus wavelength. The symbols and error bars are the mean values and standard deviations of five values of the refractive index, and the curves are provided as visual aids.

Fig. 6
Fig. 6

Real and imaginary indices of refraction of porcine skin dermis versus sample pressure. The symbols and error bars are the mean values and standard deviations of three values of the refractive index.

Fig. 7
Fig. 7

Measured ( R s and R p ) and calculated ( R ̃ s and R ̃ p ) coherent reflectance versus incident angle at λ = 1064 nm from one sample: (a) dermis with R 2 = 0.997 for s and 0.994 for p polarization, (b) epidermis with R 2 = 0.981 for both s and p polarization.

Fig. 8
Fig. 8

(a) Real and (b) imaginary refractive indices of porcine skin epidermis versus wavelength. The symbols and error bars are the mean values and standard deviations of nine values of the refractive index, and the curves are provided as visual aids.

Fig. 9
Fig. 9

(a) Real and (b) imaginary refractive index of porcine skin dermis versus wavelength. The symbols and error bars are defined as in Fig. 8, and the curves are provided as visual aids.

Equations (7)

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

sin ϕ = n 0 sin ( θ 45 ° ) ,
a = b [ sin ( 90 ° θ ) sin ( 45 ° + θ ) sin ( 45 ° ϕ ) sin ( 90 ° + ϕ ) ] ,
R s ( θ ) = C s ( θ ) I R ( s , θ ) I 0 ,
R p ( θ ) = C p ( θ ) I R ( p , θ ) I 0 ,
R ̃ s ( θ ) = n 0 cos θ [ ( n r + i n i ) 2 n 0 2 sin 2 θ ] 1 2 n 0 cos θ + [ ( n r + i n i ) 2 n 0 2 sin 2 θ ] 1 2 2 ,
R ̃ p ( θ ) = ( n r + i n i ) 2 cos θ n 0 [ ( n r + i n i ) 2 n 0 2 sin 2 θ ] 1 2 ( n r + i n i ) 2 cos θ + n 0 [ ( n r + i n i ) 2 n 0 2 sin 2 θ ] 1 2 2 .
R 2 = 1 j = 1 N ( R j R ̃ j ) 2 j = 1 N ( R j R ¯ ) 2 ,

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