Abstract

We have investigated a method for solving the inverse problem of determining the optical properties of a two-layer turbid model. The method is based on deducing the optical properties (OPs) of the top layer from the absolute spatially resolved reflectance that results from photon migration within only the top layer by use of a multivariate calibration model. Then the OPs of the bottom layer are deduced from relative frequency-domain (FD) reflectance measurements by use of the two-layer FD diffusion model. The method was validated with Monte Carlo FD reflectance profiles and experimental measurements of two-layer phantoms. The results showed that the method is useful for two-layer models with interface depths of >5 mm; the OPs were estimated, within a relatively short time (<1 min), with a mean error of <10% for the Monte Carlo reflectance profiles and with errors of <25% for the phantom measurements.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain,” Appl. Opt. 39, 2235–2244 (2000).
    [CrossRef]
  22. G. Alexandrakis, D. R. Busch, G. W. Faris, M. S. Patterson, “Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid Monte Carlo diffusion model,” Appl. Opt. 40, 3810–3821 (2001).
    [CrossRef]
  23. G. H. Weiss, R. Nossal, R. F. Bonner, “Statistics of penetration depth of photons reemitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989).
    [CrossRef]
  24. M. S. Patterson, S. Anderson, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  28. S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller, D. Sliney, eds., Vol. IS5 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.
  29. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C—The Art of Scientific Computing, 2nd ed.(Cambridge U. Press, London, 1992).
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    [CrossRef]
  31. B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, “Phase measurements of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457–3481 (1998).
    [CrossRef]
  32. C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).
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    [CrossRef] [PubMed]
  34. G. Kumar, J. M. Schmitt, “Optimal probe geometry for near-infrared spectroscopy of biological tissue,” Appl. Opt. 36, 2286–2293 (1997).
    [CrossRef] [PubMed]
  35. R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
    [CrossRef] [PubMed]
  36. S. Yeh, O. S. Khalil, “Multivariate method for the determination of tissue optical properties from diffuse reflectance profiles,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 456–464 (1999).
    [CrossRef]
  37. F. Bevilacqua, D. Piguet, P. Marquet, B. J. Tromberg, “Invivo local determination of tissue optical properties,” in Photon Propagation in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 262–268 (1997).
  38. F. Bevilacqua, C. Depeursinge, “Monte Carlo study of diffuse reflectance at source–detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16, 2935–2945 (1999).
    [CrossRef]

2002 (1)

R. J. Hunter, M. S. Patterson, T. J. Farrell, J. E. Hayward, “Haemoglobin oxygenation of a two-layer tissue-simulating phantom for time-resolved reflectance: effect of top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (2)

1999 (1)

1998 (5)

1997 (5)

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, 1–12 (1997).
[CrossRef]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[CrossRef] [PubMed]

J. R. Mourant, I. J. Bigio, D. A. Jack, T. M. Johnson, “Measuring absorption coefficients in small volumes of highly scattering media: source–detector separations for which path lengths do not depend on scattering properties,” Appl. Opt. 36, 5655–5661 (1997).
[CrossRef] [PubMed]

G. Kumar, J. M. Schmitt, “Optimal probe geometry for near-infrared spectroscopy of biological tissue,” Appl. Opt. 36, 2286–2293 (1997).
[CrossRef] [PubMed]

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (2)

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[CrossRef] [PubMed]

M. S. Patterson, S. Anderson, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
[CrossRef] [PubMed]

1994 (2)

R. C. Haskel, L. O. Svaasand, T. T. Tasy, T. C. Feng, M. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
[CrossRef]

B. W. Pogue, M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

1993 (2)

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
[CrossRef] [PubMed]

1992 (1)

1989 (2)

S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
[CrossRef] [PubMed]

G. H. Weiss, R. Nossal, R. F. Bonner, “Statistics of penetration depth of photons reemitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989).
[CrossRef]

1983 (2)

Adam, G.

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Alexandrakis, G.

Anderson, S.

Arridge, S. R.

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

Aruna, P.

Bays, R.

A. Kienle, M. S. Patterson, N. Dognitz, R. Bays, G. Wagnieres, H. Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[CrossRef]

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Bergh, H.

Bevilacqua, F.

F. Bevilacqua, C. Depeursinge, “Monte Carlo study of diffuse reflectance at source–detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16, 2935–2945 (1999).
[CrossRef]

F. Bevilacqua, D. Piguet, P. Marquet, B. J. Tromberg, “Invivo local determination of tissue optical properties,” in Photon Propagation in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 262–268 (1997).

Bigio, I. J.

Bonner, R. F.

G. H. Weiss, R. Nossal, R. F. Bonner, “Statistics of penetration depth of photons reemitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989).
[CrossRef]

Bruulsema, J. T.

G. Alexandrakis, R. A. Weersink, J. T. Bruulsema, M. S. Patterson, “Estimation of the optical properties of two-layer tissue simulating phantoms from spatially resolved frequency-domain reflectance,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 155–163 (1999).
[CrossRef]

Burrus, C. S.

C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Busch, D. R.

Chance, B.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, “Phase measurements of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457–3481 (1998).
[CrossRef]

Cope, M.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, “Phase measurements of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457–3481 (1998).
[CrossRef]

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

Dalgaard, T.

Dam, J. S.

Delpy, D. T.

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[CrossRef] [PubMed]

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

Depeursinge, C.

Dognitz, N.

Engels, S. A.

Essenpries, M.

T. J. Farrell, M. S. Patterson, M. Essenpries, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998).
[CrossRef]

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

Fabricius, P. E.

Fantini, S.

Faris, G. W.

G. Alexandrakis, D. R. Busch, G. W. Faris, M. S. Patterson, “Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid Monte Carlo diffusion model,” Appl. Opt. 40, 3810–3821 (2001).
[CrossRef]

M. Gerken, G. W. Faris, “High-accuracy optical property measurements using a frequency domain technique,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 593–600 (1999).
[CrossRef]

Farrell, T. J.

R. J. Hunter, M. S. Patterson, T. J. Farrell, J. E. Hayward, “Haemoglobin oxygenation of a two-layer tissue-simulating phantom for time-resolved reflectance: effect of top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain,” Appl. Opt. 39, 2235–2244 (2000).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7410 (1998).
[CrossRef]

T. J. Farrell, M. S. Patterson, M. Essenpries, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998).
[CrossRef]

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (SPIE, Bellingham, Wash., 1990), pp. 219–231.

Feng, T. C.

Ferwerda, H. A.

Firbank, M.

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[CrossRef] [PubMed]

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C—The Art of Scientific Computing, 2nd ed.(Cambridge U. Press, London, 1992).

Foster, T. H.

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, 1–12 (1997).
[CrossRef]

Franceschini, M. A.

Gerken, M.

M. Gerken, G. W. Faris, “High-accuracy optical property measurements using a frequency domain technique,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 593–600 (1999).
[CrossRef]

Gratton, E.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, “Phase measurements of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457–3481 (1998).
[CrossRef]

M. A. Franceschini, S. Fantini, L. A. Paunescu, J. S. Maier, E. Gratton, “Influence of superficial layer in the quantitative spectroscopic study of strongly scattering media,” Appl. Opt. 37, 7447–7458 (1998).
[CrossRef]

Groenhuis, R. A. J.

Haselgrove, J. C.

Haskel, R. C.

Hayward, J. E.

R. J. Hunter, M. S. Patterson, T. J. Farrell, J. E. Hayward, “Haemoglobin oxygenation of a two-layer tissue-simulating phantom for time-resolved reflectance: effect of top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

Hefetz, Y.

Hibroka, M.

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

Hibst, R.

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]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Mueller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221 (1995).

Hull, E. L.

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, 1–12 (1997).
[CrossRef]

Hunter, R. J.

R. J. Hunter, M. S. Patterson, T. J. Farrell, J. E. Hayward, “Haemoglobin oxygenation of a two-layer tissue-simulating phantom for time-resolved reflectance: effect of top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

Jack, D. A.

Jacques, S. C.

Jacques, S. L.

S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
[CrossRef] [PubMed]

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller, D. Sliney, eds., Vol. IS5 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Johnson, T. M.

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller, D. Sliney, eds., Vol. IS5 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Khalil, O. S.

S. Yeh, O. S. Khalil, “Multivariate method for the determination of tissue optical properties from diffuse reflectance profiles,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 456–464 (1999).
[CrossRef]

Kienle, A.

A. Kienle, M. S. Patterson, N. Dognitz, R. Bays, G. Wagnieres, H. Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[CrossRef]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (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]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Mueller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221 (1995).

Kumar, G.

Leigh, J. S.

Lilge, L.

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]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Mueller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221 (1995).

Madsen, S. J.

Maier, J. S.

Marquet, P.

F. Bevilacqua, D. Piguet, P. Marquet, B. J. Tromberg, “Invivo local determination of tissue optical properties,” in Photon Propagation in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 262–268 (1997).

Martens, H.

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

McAdams, M.

McClellan, J. H.

C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Monnier, P.

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Mourant, J. R.

Naes, T.

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

Nichols, M. G.

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, 1–12 (1997).
[CrossRef]

Nossal, R.

G. H. Weiss, R. Nossal, R. F. Bonner, “Statistics of penetration depth of photons reemitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989).
[CrossRef]

Okada, E.

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[CrossRef] [PubMed]

Oppenheim, A. V.

C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Osei, E. K.

Park, Y. D.

Parks, T. W.

C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Patterson, M. S.

R. J. Hunter, M. S. Patterson, T. J. Farrell, J. E. Hayward, “Haemoglobin oxygenation of a two-layer tissue-simulating phantom for time-resolved reflectance: effect of top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

G. Alexandrakis, D. R. Busch, G. W. Faris, M. S. Patterson, “Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid Monte Carlo diffusion model,” Appl. Opt. 40, 3810–3821 (2001).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain,” Appl. Opt. 39, 2235–2244 (2000).
[CrossRef]

T. J. Farrell, M. S. Patterson, M. Essenpries, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7410 (1998).
[CrossRef]

A. Kienle, M. S. Patterson, N. Dognitz, R. Bays, G. Wagnieres, H. Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[CrossRef]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (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. S. Patterson, S. Anderson, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. C. 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, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (SPIE, Bellingham, Wash., 1990), pp. 219–231.

G. Alexandrakis, R. A. Weersink, J. T. Bruulsema, M. S. Patterson, “Estimation of the optical properties of two-layer tissue simulating phantoms from spatially resolved frequency-domain reflectance,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 155–163 (1999).
[CrossRef]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Mueller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221 (1995).

Paunescu, L. A.

Pedersen, C. B.

Pham, T. H.

Piguet, D.

F. Bevilacqua, D. Piguet, P. Marquet, B. J. Tromberg, “Invivo local determination of tissue optical properties,” in Photon Propagation in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 262–268 (1997).

Pogue, B. W.

B. W. Pogue, M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

Prahl, S. A.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller, D. Sliney, eds., Vol. IS5 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C—The Art of Scientific Computing, 2nd ed.(Cambridge U. Press, London, 1992).

Ramanujam, N.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, “Phase measurements of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457–3481 (1998).
[CrossRef]

Robert, D.

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Savary, J.

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Schafer, R. W.

C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Schmitt, J. M.

Schotland, J. C.

Schuessler, H. W.

C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Spott, T.

Steiner, R.

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]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Mueller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221 (1995).

Svaasand, L. O.

Tasy, T. T.

Ten Bosch, J. J.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C—The Art of Scientific Computing, 2nd ed.(Cambridge U. Press, London, 1992).

Theumann, J.

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Tomberg, B. J.

Tromberg, B.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, “Phase measurements of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457–3481 (1998).
[CrossRef]

Tromberg, B. J.

R. C. Haskel, L. O. Svaasand, T. T. Tasy, T. C. Feng, M. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
[CrossRef]

F. Bevilacqua, D. Piguet, P. Marquet, B. J. Tromberg, “Invivo local determination of tissue optical properties,” in Photon Propagation in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 262–268 (1997).

van den Bergh, H.

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C—The Art of Scientific Computing, 2nd ed.(Cambridge U. Press, London, 1992).

Vitkin, A.

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Wagnieres, G.

Weersink, R. A.

G. Alexandrakis, R. A. Weersink, J. T. Bruulsema, M. S. Patterson, “Estimation of the optical properties of two-layer tissue simulating phantoms from spatially resolved frequency-domain reflectance,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 155–163 (1999).
[CrossRef]

Weiss, G. H.

G. H. Weiss, R. Nossal, R. F. Bonner, “Statistics of penetration depth of photons reemitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989).
[CrossRef]

Welch, A. J.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller, D. Sliney, eds., Vol. IS5 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Weorgers, G.

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

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]

M. S. Patterson, S. Anderson, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
[CrossRef] [PubMed]

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. C. 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, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Mueller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221 (1995).

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (SPIE, Bellingham, Wash., 1990), pp. 219–231.

Yeh, S.

S. Yeh, O. S. Khalil, “Multivariate method for the determination of tissue optical properties from diffuse reflectance profiles,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 456–464 (1999).
[CrossRef]

Zee, P.

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

Appl. Opt. (16)

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, 1–12 (1997).
[CrossRef]

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]

J. S. Dam, C. B. Pedersen, T. Dalgaard, P. E. Fabricius, P. Aruna, S. A. Engels, “Fiber-optic probe for noninvasive real-time determination of tissue optical properties at multiple wavelengths,” Appl. Opt. 40, 1155–1164 (2001).
[CrossRef]

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. C. 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, M. Essenpries, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7410 (1998).
[CrossRef]

A. Kienle, M. S. Patterson, N. Dognitz, R. Bays, G. Wagnieres, H. Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[CrossRef]

M. A. Franceschini, S. Fantini, L. A. Paunescu, J. S. Maier, E. Gratton, “Influence of superficial layer in the quantitative spectroscopic study of strongly scattering media,” Appl. Opt. 37, 7447–7458 (1998).
[CrossRef]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements,” Appl. Opt. 22, 2456–2467 (1983).
[CrossRef] [PubMed]

T. H. Pham, T. Spott, L. O. Svaasand, B. J. Tomberg, “Quantifying the properties of two-layer turbid media with frequency-domain diffuse reflectance,” Appl. Opt. 39, 4733–4745 (2000).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain,” Appl. Opt. 39, 2235–2244 (2000).
[CrossRef]

G. Alexandrakis, D. R. Busch, G. W. Faris, M. S. Patterson, “Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid Monte Carlo diffusion model,” Appl. Opt. 40, 3810–3821 (2001).
[CrossRef]

M. S. Patterson, S. Anderson, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
[CrossRef] [PubMed]

J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
[CrossRef] [PubMed]

J. R. Mourant, I. J. Bigio, D. A. Jack, T. M. Johnson, “Measuring absorption coefficients in small volumes of highly scattering media: source–detector separations for which path lengths do not depend on scattering properties,” Appl. Opt. 36, 5655–5661 (1997).
[CrossRef] [PubMed]

G. Kumar, J. M. Schmitt, “Optimal probe geometry for near-infrared spectroscopy of biological tissue,” Appl. Opt. 36, 2286–2293 (1997).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng. (1)

S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

G. H. Weiss, R. Nossal, R. F. Bonner, “Statistics of penetration depth of photons reemitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989).
[CrossRef]

J. Opt. Soc. Am. A (2)

Lasers Surg. Med. (1)

R. Bays, G. Weorgers, D. Robert, J. Theumann, A. Vitkin, J. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Lasers Surg. Med. 21, 227–234 (1997).
[CrossRef] [PubMed]

Med. Phys. (1)

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Phys. Med. Biol. (5)

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[CrossRef] [PubMed]

M. Hibroka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef]

R. J. Hunter, M. S. Patterson, T. J. Farrell, J. E. Hayward, “Haemoglobin oxygenation of a two-layer tissue-simulating phantom for time-resolved reflectance: effect of top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, “Phase measurements of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457–3481 (1998).
[CrossRef]

Other (10)

C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, H. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab (Prentice-Hall, Englewood Cliffs, N.J., 1994).

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller, D. Sliney, eds., Vol. IS5 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C—The Art of Scientific Computing, 2nd ed.(Cambridge U. Press, London, 1992).

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

S. Yeh, O. S. Khalil, “Multivariate method for the determination of tissue optical properties from diffuse reflectance profiles,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 456–464 (1999).
[CrossRef]

F. Bevilacqua, D. Piguet, P. Marquet, B. J. Tromberg, “Invivo local determination of tissue optical properties,” in Photon Propagation in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 262–268 (1997).

M. Gerken, G. W. Faris, “High-accuracy optical property measurements using a frequency domain technique,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 593–600 (1999).
[CrossRef]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Mueller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221 (1995).

G. Alexandrakis, R. A. Weersink, J. T. Bruulsema, M. S. Patterson, “Estimation of the optical properties of two-layer tissue simulating phantoms from spatially resolved frequency-domain reflectance,” in Optical Tomography and Spectroscopy of Tissues III, B. Chance, R. R. Alfano, B. Tromberg, eds., Proc. SPIE3597, 155–163 (1999).
[CrossRef]

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (SPIE, Bellingham, Wash., 1990), pp. 219–231.

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Figures (15)

Fig. 1
Fig. 1

Depth-sensitivity profiles for several source-detector distances.

Fig. 2
Fig. 2

Maximum depth probed versus source-detector distances.

Fig. 3
Fig. 3

Depth-sensitivity profiles for several optical properties [mm-1] investigated with the same source-detector distance, d = 13 mm.

Fig. 4
Fig. 4

Inverse-problem algorithm.

Fig. 5
Fig. 5

Schematic of the apparatus.

Fig. 6
Fig. 6

Probe head: front view.

Fig. 7
Fig. 7

Monte Carlo reflectance profiles versus results of fitting with the proposed method for (a) l = 3.5 mm, μ a2 = 0.005 mm-1 (crosses) and (b) l = 6 mm, μ a2 = 0.02 mm-1 (open circles). Other optical properties: μ a1 = 0.01, μ s1 = 1.5, μ s2 = 1.0 [mm-1].

Fig. 8
Fig. 8

Effects of varying the interface depth on the accuracy of (a) top-layer optical properties and (b) bottom-layer optical properties. Optical properties used to generate the simulated reflectance profiles are μ a1 = 0.025, μ s1 = 1.5, μ a2 = 0.01, μ s2 = 1.0 [mm-1]; l = 2–10 mm.

Fig. 9
Fig. 9

(a) Absolute values for the mean and the maximum errors for interface depths 2 mm < 1 < 5 m and (b) absolute values for the mean and the maximum errors for interface depths 5 mm < l < 10 mm.

Fig. 10
Fig. 10

Experimental data obtained from phantoms PH1, PH2, and PH3 reflectance measurements: (a) cw reflectance measurement, (b) phase-delay measurements.

Fig. 11
Fig. 11

PH1 fitting results: (a) top-layer cw reflectance fitting, (b) bottom-layer cw reflectance fitting, (c) bottom-layer phase-delay fitting.

Fig. 12
Fig. 12

PH2 fitting results: (a) top-layer cw reflectance fitting, (b) bottom-layer cw reflectance fitting, (c) bottom-layer phase-delay fitting.

Fig. 13
Fig. 13

Absolute errors in measurement of the phantoms’ optical properties: (a) top-layer absorption, (b) top-layer scattering, (c) bottom-layer absorption, (d) bottom-layer scattering coefficients.

Fig. 14
Fig. 14

Reflectance measured at far distances (>8 mm) for the six phantoms.

Fig. 15
Fig. 15

Absolute errors of the bottom-layer optical properties (absorption, top; scattering, bottom) of PH1, PH2, and PH3 as obtained from three measurement techniques.

Tables (1)

Tables Icon

Table 1 Three Two-Layer Phantoms Used for Experimental Measurements

Equations (8)

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Eiz; d0, d1=Iid0, d1n,
Ez; d0, d1=i=0m Ez; d0, d1.
D12Φ1r, ω-μa1+j wc0Φ1r, ω=-δx, yz-z0expj wcm r 0zl,
D22Φ2r, ω-μa2+j wc0Φ2r, ω=0 lz,
Φ1r, z=0=12π0 φ1z=0sI0srds,
Rr, ω= 0.118Φ1r, z=0+0.306D×1z Φ1r, z, ω z=0.
Rr, ω= ¼ Φ1r, z=0+½ D1z Φ1r, z, ω z=0.
θr, ω=tan-1ImRr, ωReRr, ω.

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