Abstract

Fiber-optic-based oblique-incidence reflectometry is a simple and accurate method for measuring the absorption and reduced scattering coefficients μa and μs of semi-infinite turbid media. Obliquely incident light produces a spatial distribution of diffuse reflectance that is not centered about the point of light entry. The amount of shift in the center of diffuse reflectance is directly related to the medium’s diffusion length D. We developed a fiber-optic probe to deliver light obliquely and sample the relative profile of diffuse reflectance. Measurement in absolute units is not necessary. From the profile, it was possible to measure D, perform a curve fit for the effective attenuation coefficient μeff, and then calculate μa and μs. This method was verified with Monte Carlo simulations and tested on tissue phantoms. Our measurements of D and μeff had an accuracy of approximately 5%, thus giving us 10% and 5% accuracy for μa and μs, respectively.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L.-H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
    [CrossRef] [PubMed]
  2. J. W. Pickering, S. A. Prahl, N. Vanwieringen, J. F. Beek, H. J. C. M. Sterenborg, M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
    [CrossRef] [PubMed]
  3. S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to specify optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash.1993), pp. 211–226.
  4. 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]
  5. T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
    [CrossRef] [PubMed]
  6. L.-H. Wang, S. L. Jacques, L.-Q. Zheng, “MCML—Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
    [CrossRef] [PubMed]
  7. L.-H. 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, Texas, 1992). Note: available through e-mail to LWANG@tamu.edu.
  8. T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the non-invasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  9. R. A. J. Groenhius, J. J. T. Bosch, H. A. Ferwerdo, “Scattering and absorption of turbid materials determined from reflectance measurements. 1: theory,” Appl. Opt. 22, 2456–2462 (1983).
    [CrossRef]
  10. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterlin, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Section 15.5.
  11. L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser–Tissue Interaction V, S. L. Jacques, ed., Proc. SPIE2134A, 247–254 (1994).
  12. L.-H. Wang, S. L. Jacques, MIESPHR Program: Mie Theory for Scattering Spherical Particles (University of Texas M. D. Anderson Cancer Center, Houston, Texas, 1995). Note: available through anonymous ftp to laser.mda.uth.tmc.edu (129.106.60.92).
  13. L.-H. Wang, S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
    [CrossRef] [PubMed]
  14. L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
    [CrossRef]
  15. S.-P. Lin, “Oblique-incidence fiber-optic reflectometry for measuring absorption and scattering in turbid media,” M.S. thesis (Rice University, Houston, Texas, 1996).
  16. T. J. Farrell, M. S. Patterson, J. E. Hayward, B. C. Wilson, E. R. Beck, “Charge-coupled device and neural-network-based instrument for the noninvasive determination of tissue optical properties in vivo,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 117–128 (1994).
    [CrossRef]
  17. S.-P. Lin, L.-H. Wang, S. L. Jacques, F. K. Tittel, “Measurement of absorption and scattering spectra with oblique incidence reflectometry,” in Advances in Optical Imaging and Photon Migration, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996).

1996 (1)

1995 (2)

L.-H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, L.-Q. Zheng, “MCML—Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

1994 (1)

L.-H. Wang, S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
[CrossRef] [PubMed]

1993 (1)

1992 (2)

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (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 non-invasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

1983 (1)

Beck, E. R.

T. J. Farrell, M. S. Patterson, J. E. Hayward, B. C. Wilson, E. R. Beck, “Charge-coupled device and neural-network-based instrument for the noninvasive determination of tissue optical properties in vivo,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 117–128 (1994).
[CrossRef]

Beek, J. F.

Bosch, J. J. T.

Da Silva, L.

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

Farrell, T. J.

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (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 non-invasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, J. E. Hayward, B. C. Wilson, E. R. Beck, “Charge-coupled device and neural-network-based instrument for the noninvasive determination of tissue optical properties in vivo,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 117–128 (1994).
[CrossRef]

Ferwerdo, H. A.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterlin, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Section 15.5.

Groenhius, R. A. J.

Gutsche, A.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to specify optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash.1993), pp. 211–226.

Harder, J.

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

Hayward, J. E.

T. J. Farrell, M. S. Patterson, J. E. Hayward, B. C. Wilson, E. R. Beck, “Charge-coupled device and neural-network-based instrument for the noninvasive determination of tissue optical properties in vivo,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 117–128 (1994).
[CrossRef]

Hibst, R.

Jacques, S. L.

L.-H. Wang, S. L. Jacques, L.-Q. Zheng, “MCML—Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, MIESPHR Program: Mie Theory for Scattering Spherical Particles (University of Texas M. D. Anderson Cancer Center, Houston, Texas, 1995). Note: available through anonymous ftp to laser.mda.uth.tmc.edu (129.106.60.92).

S.-P. Lin, L.-H. Wang, S. L. Jacques, F. K. Tittel, “Measurement of absorption and scattering spectra with oblique incidence reflectometry,” in Advances in Optical Imaging and Photon Migration, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996).

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to specify optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash.1993), pp. 211–226.

L.-H. 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, Texas, 1992). Note: available through e-mail to LWANG@tamu.edu.

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser–Tissue Interaction V, S. L. Jacques, ed., Proc. SPIE2134A, 247–254 (1994).

Jancarik, J.

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

Kienle, A.

Lilge, L.

Lin, S.-P

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

Lin, S.-P.

S.-P. Lin, “Oblique-incidence fiber-optic reflectometry for measuring absorption and scattering in turbid media,” M.S. thesis (Rice University, Houston, Texas, 1996).

S.-P. Lin, L.-H. Wang, S. L. Jacques, F. K. Tittel, “Measurement of absorption and scattering spectra with oblique incidence reflectometry,” in Advances in Optical Imaging and Photon Migration, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996).

Mammini, B.

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

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]

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the non-invasive 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 a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, J. E. Hayward, B. C. Wilson, E. R. Beck, “Charge-coupled device and neural-network-based instrument for the noninvasive determination of tissue optical properties in vivo,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 117–128 (1994).
[CrossRef]

Pickering, J. W.

Prahl, S. A.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterlin, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Section 15.5.

Schwartz, J. A.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to specify optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash.1993), pp. 211–226.

Small, W.

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

Steiner, R.

Sterenborg, H. J. C. M.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterlin, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Section 15.5.

Tittel, F. K.

S.-P. Lin, L.-H. Wang, S. L. Jacques, F. K. Tittel, “Measurement of absorption and scattering spectra with oblique incidence reflectometry,” in Advances in Optical Imaging and Photon Migration, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996).

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to specify optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash.1993), pp. 211–226.

van Gemert, M. J. C.

Vanwieringen, N.

Vetterlin, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterlin, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Section 15.5.

Wang, L.-H.

L.-H. Wang, S. L. Jacques, L.-Q. Zheng, “MCML—Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, “Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium,” Appl. Opt. 34, 2362–2366 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, MIESPHR Program: Mie Theory for Scattering Spherical Particles (University of Texas M. D. Anderson Cancer Center, Houston, Texas, 1995). Note: available through anonymous ftp to laser.mda.uth.tmc.edu (129.106.60.92).

S.-P. Lin, L.-H. Wang, S. L. Jacques, F. K. Tittel, “Measurement of absorption and scattering spectra with oblique incidence reflectometry,” in Advances in Optical Imaging and Photon Migration, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996).

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to specify optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash.1993), pp. 211–226.

L.-H. 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, Texas, 1992). Note: available through e-mail to LWANG@tamu.edu.

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser–Tissue Interaction V, S. L. Jacques, ed., Proc. SPIE2134A, 247–254 (1994).

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]

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the non-invasive 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 a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, J. E. Hayward, B. C. Wilson, E. R. Beck, “Charge-coupled device and neural-network-based instrument for the noninvasive determination of tissue optical properties in vivo,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 117–128 (1994).
[CrossRef]

Zheng, L.-Q.

L.-H. Wang, S. L. Jacques, L.-Q. Zheng, “MCML—Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Appl. Opt. (4)

Comput. Methods Programs Biomed. (1)

L.-H. Wang, S. L. Jacques, L.-Q. Zheng, “MCML—Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Med. Phys. (1)

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

Phys. Med. Biol. (2)

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

L.-H. Wang, S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
[CrossRef] [PubMed]

Other (9)

L.-H. Wang, S.-P Lin, S. L. Jacques, F. K. Tittel, J. Harder, J. Jancarik, B. Mammini, W. Small, L. Da Silva, “Oblique-incidence reflectometry: one relative profile measurement of diffuse reflectance yields two optical parameters,” in Optical Biopsies, R. Cubeddu, S. R. Mordon, K. Svanberg, eds., Proc. SPIE2627, 165–175 (1995).
[CrossRef]

S.-P. Lin, “Oblique-incidence fiber-optic reflectometry for measuring absorption and scattering in turbid media,” M.S. thesis (Rice University, Houston, Texas, 1996).

T. J. Farrell, M. S. Patterson, J. E. Hayward, B. C. Wilson, E. R. Beck, “Charge-coupled device and neural-network-based instrument for the noninvasive determination of tissue optical properties in vivo,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 117–128 (1994).
[CrossRef]

S.-P. Lin, L.-H. Wang, S. L. Jacques, F. K. Tittel, “Measurement of absorption and scattering spectra with oblique incidence reflectometry,” in Advances in Optical Imaging and Photon Migration, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996).

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to specify optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash.1993), pp. 211–226.

L.-H. 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, Texas, 1992). Note: available through e-mail to LWANG@tamu.edu.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterlin, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), Section 15.5.

L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser–Tissue Interaction V, S. L. Jacques, ed., Proc. SPIE2134A, 247–254 (1994).

L.-H. Wang, S. L. Jacques, MIESPHR Program: Mie Theory for Scattering Spherical Particles (University of Texas M. D. Anderson Cancer Center, Houston, Texas, 1995). Note: available through anonymous ftp to laser.mda.uth.tmc.edu (129.106.60.92).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Diffuse reflectance from a semi-infinite tissue as modeled by Monte Carlo simulation versus the two-source diffusion theory model. μa = 0.4 cm-1, μs = 8 cm-1, and 1 mfp′ = 0.123 cm. (a) Normal incidence, (b) oblique incidence. For both (a) and (b), the two curves agree outside 1–2 mfp′ from the center of diffuse reflectance, which coincides with the light entry point in (a) but not in (b).

Fig. 2
Fig. 2

(a) Positions of point sources in the diffusion theory model for normal incidence, (b) positions of point sources in the diffusion theory model for oblique incidence. The y axis points off the page. ρ1 and ρ2 are the distances from the positive and the negative point sources, respectively, to the point of interest on the tissue surface at a radius r from the axis of the sources. θt is determined from Snell’s law (see Fig. 5 below).

Fig. 3
Fig. 3

(a) Sample of Monte Carlo simulated data after the removal of noise far from the point of entry as well as data within 1.5 mfp′ of the center of diffuse reflectance. The curve shown is the fitted result generated by our algorithm. To emphasize how well these curves agree with what we expected, in (b) we have plotted just the expected and the fitted curves without the simulation data. This particular simulation used (μs, μa) = (6 cm-1, 0.6 cm-1).

Fig. 4
Fig. 4

(a) Sample of data taken with oblique-incidence fiber-optic probe. As in Fig. 3, the curve shown is the fitted result generated by our algorithm. In (b) we have plotted just the expected and the fitted curves without the data to reiterate how well they agree. This particular phantom had (μs, μa) = (6 cm-1, 0.6 cm-1).

Fig. 5
Fig. 5

Three-dimensional perspective view of tissue surface, coordinate axes, and positions of light delivery and collection. The arrows represent the fibers in the probe. The arrows pointing up are the collection fibers and the curved arrow is the source fiber.

Tables (2)

Tables Icon

Table 1 Results from Monte Carlo Simulations

Tables Icon

Table 2 Results from Phantom Experiments

Equations (15)

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

mfp=1/μa+μs.
1/0.35μa+μsmfp.
3D1 mfp.
3D=1/0.35μa+μs.
Rr=3Dμeff+1ρ1exp-ρ1μeffρ12+3D+4AD×μeff+1ρ2exp-ρ2μeffρ22,
μeff=μa/D1/2.
A=1+ri/1-ri,
ri=-1.440nrel-2+0.710nrel-1+0.668+0.0636nrel,
nrel=ntissue/nambient.
D=Δx/3 sin θtissue.
μa=Dμeff2,
μs=1/3D-0.35μa.
μa=Dμeff2,
lnμa=lnD+2 lnμeff,
Δμa/μaΔD/D+2Δμeff/μeff.

Metrics