Abstract

Continuous-wave measurement-based methods offer a rapid cost-effective way to determine optical properties in turbid media. This method requires a measure of the refractive index of the medium, which is often unknown a priori. Whereas previous studies have reported that the refractive index has little impact on the measurement of optical properties, here we show a significant effect of refractive indices on measurements, using both simulations and experiments. In addition we propose a noniterative method to determine the refractive index of the medium. This method can also provide an optimal initial guess of the optical properties for the standard iterative method for determining optical properties in turbid media. Our method is confirmed by simulations and experiments with latex spheres and Intralipid suspensions.

© 2001 Optical Society of America

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References

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  1. H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
    [CrossRef] [PubMed]
  2. R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis in vitro and in vivo,” Appl. Opt. 32, 435–447 (1993).
    [CrossRef] [PubMed]
  3. H. Jiang, “Enhanced photon-migration methods for particle sizing in concentrated suspensions,” AIChE. J. 44, 1740–1744 (1998).
    [CrossRef]
  4. M. Bartlett, H. Jiang, “Measurement of particle size distribution in concentrated, rapidly flowing potassium chloride (KCl) suspensions using continuous-wave photon migration techniques,” AIChE. J. 47, 60–65 (2001).
    [CrossRef]
  5. H. Jiang, J. Pierce, J. Kao, E. Sevick-Muraca, “Measurement of particle-size distribution and volume fraction in concentrated suspensions with photon migration techniques,” Appl. Opt. 36, 3310–3318 (1997).
    [CrossRef] [PubMed]
  6. M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  7. M. Gerken, G. W. Faris, “Frequency-domain immersion technique for accurate optical property measurements of turbid media,” Opt. Lett. 24, 1726–1728 (1992).
    [CrossRef]
  8. J. B. Fishkin, O. Coquoz, E. R. Anderson, M. Brenner, B. J. Tomberg, “Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject,” Appl. Opt. 36, 10–20 (1997).
    [CrossRef] [PubMed]
  9. T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  10. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
    [CrossRef] [PubMed]
  11. M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 93–104 (1997).
    [CrossRef] [PubMed]
  12. J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. 37, 3586–3593 (1998).
    [CrossRef]
  13. S. P. Lin, L. Wang, S. L. Jacques, F. K. Tittel, “Measurement of tissue optical properties by the use of oblique-incidence optical fiber reflectometry,” Appl. Opt. 36, 136–143 (1997).
    [CrossRef] [PubMed]
  14. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1. Theory,” Appl. Opt. 22, 2456–2462 (1983).
    [CrossRef] [PubMed]
  15. H. G. Van Staveren, C. Moes, J. van Marle, S. Prahl, M. J. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
    [CrossRef] [PubMed]
  16. U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
    [CrossRef] [PubMed]

2001 (1)

M. Bartlett, H. Jiang, “Measurement of particle size distribution in concentrated, rapidly flowing potassium chloride (KCl) suspensions using continuous-wave photon migration techniques,” AIChE. J. 47, 60–65 (2001).
[CrossRef]

1998 (2)

1997 (4)

1996 (2)

1995 (1)

H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

1993 (1)

1992 (2)

T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. Gerken, G. W. Faris, “Frequency-domain immersion technique for accurate optical property measurements of turbid media,” Opt. Lett. 24, 1726–1728 (1992).
[CrossRef]

1991 (1)

1989 (1)

1983 (1)

Aarnoudse, J. G.

Anderson, E. R.

Bartlett, M.

M. Bartlett, H. Jiang, “Measurement of particle size distribution in concentrated, rapidly flowing potassium chloride (KCl) suspensions using continuous-wave photon migration techniques,” AIChE. J. 47, 60–65 (2001).
[CrossRef]

Boas, D. A.

H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Brenner, M.

Chance, B.

H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

Coquoz, O.

Dassel, A. C. M.

de Mul, F. F. M.

Eick, A. A.

Faris, G. W.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Ferwerda, H. A.

Fishkin, J. B.

Foster, T. H.

Freyer, J. P.

Gerken, M.

Graaff, R.

Groenhuis, R. A. J.

Grosenick, D.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Hibst, R.

Hielscher, A. H.

Hull, E. L.

Jacques, S. L.

Jiang, H.

M. Bartlett, H. Jiang, “Measurement of particle size distribution in concentrated, rapidly flowing potassium chloride (KCl) suspensions using continuous-wave photon migration techniques,” AIChE. J. 47, 60–65 (2001).
[CrossRef]

H. Jiang, “Enhanced photon-migration methods for particle sizing in concentrated suspensions,” AIChE. J. 44, 1740–1744 (1998).
[CrossRef]

H. Jiang, J. Pierce, J. Kao, E. Sevick-Muraca, “Measurement of particle-size distribution and volume fraction in concentrated suspensions with photon migration techniques,” Appl. Opt. 36, 3310–3318 (1997).
[CrossRef] [PubMed]

Johnson, T. M.

Kao, J.

Kienle, A.

Koelink, M. H.

Lilge, L.

Lin, S. P.

Liu, H.

H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Moes, C.

Mourant, J. R.

Nichols, M. G.

Patterson, M. S.

Pierce, J.

Prahl, S.

Rinneberg, H.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Schubert, F.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Sevick-Muraca, E.

Shen, D.

Steiner, R.

Sukowski, U.

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

Ten Bosch, J. J.

Tittel, F. K.

Tomberg, B. J.

van Gemert, M. J.

van Marle, J.

Van Staveren, H. G.

Wang, L.

Wilson, B. C.

Yodh, A. G.

H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Zhong, Y.

H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Zijlstra, W. G.

AIChE. J. (2)

H. Jiang, “Enhanced photon-migration methods for particle sizing in concentrated suspensions,” AIChE. J. 44, 1740–1744 (1998).
[CrossRef]

M. Bartlett, H. Jiang, “Measurement of particle size distribution in concentrated, rapidly flowing potassium chloride (KCl) suspensions using continuous-wave photon migration techniques,” AIChE. J. 47, 60–65 (2001).
[CrossRef]

Appl. Opt. (10)

H. Jiang, J. Pierce, J. Kao, E. Sevick-Muraca, “Measurement of particle-size distribution and volume fraction in concentrated suspensions with photon migration techniques,” Appl. Opt. 36, 3310–3318 (1997).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis in vitro and in vivo,” Appl. Opt. 32, 435–447 (1993).
[CrossRef] [PubMed]

J. B. Fishkin, O. Coquoz, E. R. Anderson, M. Brenner, B. J. Tomberg, “Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject,” Appl. Opt. 36, 10–20 (1997).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 93–104 (1997).
[CrossRef] [PubMed]

J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. 37, 3586–3593 (1998).
[CrossRef]

S. P. Lin, L. Wang, S. L. Jacques, F. K. Tittel, “Measurement of tissue optical properties by the use of oblique-incidence optical fiber reflectometry,” Appl. Opt. 36, 136–143 (1997).
[CrossRef] [PubMed]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1. Theory,” Appl. Opt. 22, 2456–2462 (1983).
[CrossRef] [PubMed]

H. G. Van Staveren, C. Moes, J. van Marle, S. Prahl, M. J. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Med. Biol. (2)

H. Liu, D. A. Boas, Y. Zhong, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

U. Sukowski, F. Schubert, D. Grosenick, H. Rinneberg, “Preparation of solid phantoms with defined scattering and absorption properties for optical tomography,” Phys. Med. Biol. 41, 1823–1844 (1996).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Our experimental setup including light source, probe, sample CCD and spectrometer, and computer.

Fig. 2
Fig. 2

Reduced scattering coefficient is plotted versus wavelength for a sample of 0.998-µm-diameter latex spheres mixed in distilled water. Each curve was calculated from the same data set but with a different n rel value (0.8, 1.1, or 1.3).

Fig. 3
Fig. 3

Optimized μs is plotted versus given value of n rel for four sets of simulated data with given parameters μs = 0.25, 0.5, 1.0, and 1.5/mm; μ a = 0.005/mm; n rel = 1.1.

Fig. 4
Fig. 4

Optimized μ a is plotted versus given range of n rel for four sets of simulated data calculated from parameters μs = 0.25, 0.5, 1.0, and 1.5/mm (bottom to top, respectively); μ a = 0.005/mm; n rel = 1.1.

Fig. 5
Fig. 5

(a) Three-dimensional plot of error versus the incremented parameters μs and n rel with μ a held constant. (b) and (c) highlighted the global minimum of the error over the correct values of μs and n rel, respectively in two-dimensional plots. (d) illustrates the effect of 1% random noise on the global minimum.

Fig. 6
Fig. 6

Calculated error plotted versus n rel. The actual n rel was 1.1 and thus has the lowest error when there is 0% noise. Increasing noise shifts the minimum error away from the correct value.

Fig. 7
Fig. 7

Reduced scattering plotted versus wavelength for 0.998-µm-diameter latex spheres with concentration of 1.606 × 109 particles/ml. The plots show the agreement between μs calculated with the n rel from the new algorithm (solid curve) and Mie theory (dotted curve).

Fig. 8
Fig. 8

Reduced scattering plotted versus wavelength for 0.75-µm-diameter latex spheres with concentration of 1.581 × 1010 particles/ml. Each curve was calculated from the same data set but with a different n rel value (0.8, 1.05, or 1.3). The graph also consists of the predicted Mie theory result (solid curve) for this concentration. μs had 200 increments from 0.8 to 1.3/mm, μ a had 50 increments from 0.00001 to 0.0011/mm, and n rel had 200 increments from 0.8 to 1.3.

Fig. 9
Fig. 9

Reduced scattering plotted versus wavelength for 0.75-µm-diameter latex spheres with concentration of 2.01 × 1010 particles/ml. Each curve was calculated from the same data set but with a different n rel value (0.8, 0.95, or 1.3). The graph also consists of the predicted Mie theory result (solid curve) for this concentration. μs had 200 increments from 0.8 to 1.8 ./mm, μ a had 50 increments from 0.0001 to 0.0011/mm, and n rel had 200 increments from 0.8 to 1.3.

Fig. 10
Fig. 10

Reduced scattering coefficient versus wavelength for 1% Intralipid mixed with distilled water. Solid curve, shift caused by change of n rel with wavelength. Dotted curve, n rel held constant with wavelength.

Tables (1)

Tables Icon

Table 1 Accuracy of μs, μa, and nrel for Different Percentages of Noise a

Equations (7)

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

2Ψr-μaDΨr=-S0rD+3ΔS1r,
Ψr-2ADΩˆn·Ψr=0,
Rρ, μs, μa, A=14π1μs+μaμeff+1r1×exp-μeffr1r12 + 1μs + μa1 + 23 A×μeff + 1r2exp-μeffr2r22,
μeff=3μaμs+μa0.5,
r1=z-1μs+μa2+ρ20.5,
r2=z+1μs+μa1+43A2+ρ20.5,
rms %error=i=1MRρim-RρicRρim20.5,

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