Abstract

We describe a method for determining the reduced scattering and absorption coefficients of turbid biological media from the spatially resolved diffuse reflectance. A Sugeno Fuzzy Inference System in conjunction with data preprocessing techniques is employed to perform multivariate calibration and prediction on reflectance data generated by Monte Carlo simulations. The preprocessing consists of either a principal component analysis or a new, extended curve-fitting procedure originating from diffusion theory. Prediction tests on reflectance data with absorption coefficients between 0.04 and 0.06 mm-1 and reduced scattering coefficients between 0.45 and 0.99 mm-1 show the root-mean-square error of this method to be 0.25% for both coefficients. With reference to practical applications, we also describe how the prediction accuracy is affected by using relative instead of absolute reflectance data, by imposing measurement noise on the reflectance data, and by changing the number and the position of detectors.

© 1998 Optical Society of America

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References

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  1. A. J. Welch, M. J. C. van Gemert, W. M. Star, B. C. Wilson, “Overview of tissue optics,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 2.
  2. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 2: Measuring method and calibration,” Appl. Opt. 22, 2463–2467 (1983).
    [CrossRef] [PubMed]
  3. J. M. Schmitt, G. X. Zhou, E. C. Walker, R. T. Wall, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).
    [CrossRef] [PubMed]
  4. B. C. Wilson, S. L. Jacques, “Optical reflectance and transmission of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
    [CrossRef]
  5. T. J. Farrell, M. S. Patterson, B. C. Wilson, “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]
  6. T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
    [CrossRef] [PubMed]
  7. 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]
  8. J. R. Mourant, T. Fuselier, J. Boyer, T. M. Johnson, I. J. Bigio, “Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms,” Appl. Opt. 36, 949–957 (1997).
    [CrossRef] [PubMed]
  9. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980), Vols. 1 and 2.
  10. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time-resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
    [CrossRef] [PubMed]
  11. S. J. Madsen, B. C. Wilson, M. S. Patterson, T. D. Park, S. L. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
    [CrossRef] [PubMed]
  12. S. Fantini, M. A. Francheschini-Fantini, J. S. Maier, S. A. Walker, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
    [CrossRef]
  13. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. 1 and 2.
  14. S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissue,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 4.
  15. W. M. Star, “Diffusion theory of light transport,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 6.
  16. H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1994).
  17. T. Tagaki, M. Sugeno, “Fuzzy identifications of systems and its applications to modelling and control,” IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985).
    [CrossRef]
  18. S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues. II. Comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
    [CrossRef] [PubMed]
  19. W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  20. 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]
  21. L. Wang, S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-Layered Tissues in Standard C (University of Texas, M. D. Anderson Cancer Center, Houston, Tex., 1992).
  22. J. R. Mourant, J. Boyer, A. H. Hielscher, I. J. Bigio, “Influence of the scattering phase function on light transport measurements in turbid media performed with small source–detector separations,” Opt. Lett. 21, 546–548 (1996).
    [CrossRef] [PubMed]
  23. P. E. Andersen, J. S. Dam, P. M. Pedersen, P. Bjerring, “Local diffuse reflectance from a multilayered skin tissue model,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 515–526 (1997).
    [CrossRef]

1997

1996

1995

S. Fantini, M. A. Francheschini-Fantini, J. S. Maier, S. A. Walker, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

1992

T. J. Farrell, M. S. Patterson, B. C. Wilson, “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]

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

S. J. Madsen, B. C. Wilson, M. S. Patterson, T. D. Park, S. L. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

1990

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmission of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

J. M. Schmitt, G. X. Zhou, E. C. Walker, R. T. Wall, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).
[CrossRef] [PubMed]

1989

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues. II. Comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

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]

1985

T. Tagaki, M. Sugeno, “Fuzzy identifications of systems and its applications to modelling and control,” IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985).
[CrossRef]

1983

Andersen, P. E.

P. E. Andersen, J. S. Dam, P. M. Pedersen, P. Bjerring, “Local diffuse reflectance from a multilayered skin tissue model,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 515–526 (1997).
[CrossRef]

Bigio, I. J.

Bjerring, P.

P. E. Andersen, J. S. Dam, P. M. Pedersen, P. Bjerring, “Local diffuse reflectance from a multilayered skin tissue model,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 515–526 (1997).
[CrossRef]

Bolin, P.

Boyer, J.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Cubeddu, R.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time-resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Dam, J. S.

P. E. Andersen, J. S. Dam, P. M. Pedersen, P. Bjerring, “Local diffuse reflectance from a multilayered skin tissue model,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 515–526 (1997).
[CrossRef]

Fantini, S.

S. Fantini, M. A. Francheschini-Fantini, J. S. Maier, S. A. Walker, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, B. C. Wilson, “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]

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

Ference, R. J.

Ferwerda, H. A.

Flock, S. T.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues. II. Comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

Francheschini-Fantini, M. A.

S. Fantini, M. A. Francheschini-Fantini, J. S. Maier, S. A. Walker, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Fuselier, T.

Groenhuis, R. A. J.

Hefetz, Y.

Hibst, R.

Hielscher, A. H.

Hulst, H. C. van de

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980), Vols. 1 and 2.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. 1 and 2.

Jacques, S. L.

S. J. Madsen, B. C. Wilson, M. S. Patterson, T. D. Park, S. L. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmission of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissue,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 4.

L. Wang, S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-Layered Tissues in Standard C (University of Texas, M. D. Anderson Cancer Center, Houston, Tex., 1992).

Johnson, T. M.

Kienle, A.

Lilge, L.

Madsen, S. J.

Maier, J. S.

S. Fantini, M. A. Francheschini-Fantini, J. S. Maier, S. A. Walker, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Martens, H.

H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1994).

Mourant, J. R.

Næs, T.

H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1994).

Park, T. D.

Patterson, M. S.

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]

S. J. Madsen, B. C. Wilson, M. S. Patterson, T. D. Park, S. L. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, B. C. Wilson, “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]

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues. II. Comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

Pedersen, P. M.

P. E. Andersen, J. S. Dam, P. M. Pedersen, P. Bjerring, “Local diffuse reflectance from a multilayered skin tissue model,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 515–526 (1997).
[CrossRef]

Pifferi, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time-resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Preuss, L. E.

Schmitt, J. M.

Star, W. M.

A. J. Welch, M. J. C. van Gemert, W. M. Star, B. C. Wilson, “Overview of tissue optics,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 2.

W. M. Star, “Diffusion theory of light transport,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 6.

Steiner, R.

Sugeno, M.

T. Tagaki, M. Sugeno, “Fuzzy identifications of systems and its applications to modelling and control,” IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985).
[CrossRef]

Tagaki, T.

T. Tagaki, M. Sugeno, “Fuzzy identifications of systems and its applications to modelling and control,” IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985).
[CrossRef]

Taroni, P.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time-resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Taylor, R. C.

Ten Bosch, J. J.

Torricelli, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time-resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Valentini, G.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time-resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

van Gemert, M. J. C.

A. J. Welch, M. J. C. van Gemert, W. M. Star, B. C. Wilson, “Overview of tissue optics,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 2.

Walker, E. C.

Walker, S. A.

S. Fantini, M. A. Francheschini-Fantini, J. S. Maier, S. A. Walker, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Wall, R. T.

Wang, L.

S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissue,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 4.

L. Wang, S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-Layered Tissues in Standard C (University of Texas, M. D. Anderson Cancer Center, Houston, Tex., 1992).

Welch, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

A. J. Welch, M. J. C. van Gemert, W. M. Star, B. C. Wilson, “Overview of tissue optics,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 2.

Wilson, B. C.

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]

S. J. Madsen, B. C. Wilson, M. S. Patterson, T. D. Park, S. L. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, B. C. Wilson, “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]

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmission of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues. II. Comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

A. J. Welch, M. J. C. van Gemert, W. M. Star, B. C. Wilson, “Overview of tissue optics,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 2.

Zhou, G. X.

Appl. Opt.

IEEE J. Quantum Electron.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissue,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmission of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues. II. Comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

IEEE Trans. Syst. Man Cybern.

T. Tagaki, M. Sugeno, “Fuzzy identifications of systems and its applications to modelling and control,” IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985).
[CrossRef]

J. Opt. Soc. Am. A

Med. Phys.

T. J. Farrell, M. S. Patterson, B. C. Wilson, “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]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time-resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Opt. Eng.

S. Fantini, M. A. Francheschini-Fantini, J. S. Maier, S. A. Walker, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Opt. Lett.

Phys. Med. Biol.

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

Other

A. J. Welch, M. J. C. van Gemert, W. M. Star, B. C. Wilson, “Overview of tissue optics,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 2.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980), Vols. 1 and 2.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. 1 and 2.

S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissue,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 4.

W. M. Star, “Diffusion theory of light transport,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 6.

H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1994).

L. Wang, S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-Layered Tissues in Standard C (University of Texas, M. D. Anderson Cancer Center, Houston, Tex., 1992).

P. E. Andersen, J. S. Dam, P. M. Pedersen, P. Bjerring, “Local diffuse reflectance from a multilayered skin tissue model,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 515–526 (1997).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic setup for R d (r) measurements. The incident light I c is a continuous-wave collimated beam with diameter d. The radial source–detection distance is denoted r, and t is the thickness of the medium.

Fig. 2
Fig. 2

Monte Carlo-simulated reflectance profiles (symbols) and corresponding fits (solid curves), representing four corners of the main space.

Fig. 3
Fig. 3

μ a , μ s (mm-1), and g mapped to the fitting parameters z 0, z 1, and z 2 of the reflectance profiles. A, Plane section of subspace (small bold grid) embedded in plane section of main space (g = 0.95). B, Enlarged plane section of subspace (g = 0.91).

Fig. 4
Fig. 4

Prediction errors as a function of noise superimposed on the reflectance profiles from the subspace. The noise rms values are an average of the intensity-dependent noise at each detector of each profile. A, 46 detection spots; B, six detection spots.

Fig. 5
Fig. 5

Noise-dependent distributions of calibration mean weights assigned to each detection spot by the SFIS and the PCA (with three principal components) during calibration on the reflectance profiles from the subspace. The mean weights indicate the amount of information about, A, μ s ′ and, B, μ a collected from each detection spot.

Tables (4)

Tables Icon

Table 1 Prediction rms Errors of Absolute Reflectance Profiles from the Main Space and the Subspace

Tables Icon

Table 2 Prediction rms Errors of Relative Reflectance Profiles from the Main Space and the Subspace

Tables Icon

Table 3 Prediction rms Errors of Close- and Far-Distance Reflectance Profiles from the Subspacea

Tables Icon

Table 4 Prediction rms Errors of Reflectance Profiles from the Subspace with a Reduced Number of Detection Spots

Equations (4)

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

a = μ s / μ s + μ a 1 MFP = 1 / μ s + μ a     r ,   t .
0.01   mm - 1 < μ a < 0.10   mm - 1 ,   2.50   mm - 1 < μ s < 20.0   mm - 1 ,   0.80 < g < 0.99 ,   0.025   mm - 1 < μ s < 4.00   mm - 1 .
0.04   mm - 1 < μ a < 0.06   mm - 1 ,   9.00   mm - 1 < μ s < 11.0   mm - 1 ,   0.91 < g < 0.95 ,   0.45   mm - 1 < μ s < 0.99   mm - 1 .
R d r = z 0 r z 1 exp - z 2 r ,

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