Abstract

The light-scattering properties of dental enamel and dentin were measured at 543, 632, and 1053 nm. Angularly resolved scattering distributions for these materials were measured from 0° to 180° using a rotating goniometer. Surface scattering was minimized by immersing the samples in an index-matching bath. The scattering and absorption coefficients and the scattering phase function were deduced by comparing the measured scattering data with angularly resolved Monte Carlo light-scattering simulations. Enamel and dentin were best represented by a linear combination of a highly forward-peaked Henyey–Greenstein (HG) phase function and an isotropic phase function. Enamel weakly scatters light between 543 nm and 1.06 μm, with the scattering coefficient (μs) ranging from μs = 15 to 105 cm−1. The phase function is a combination of a HG function with g = 0.96 and a 30–60% isotropic phase function. For enamel, absorption is negligible. Dentin scatters strongly in the visible and near IR (μs ≅ 260 cm−1) and absorbs weakly (μa ≅ 4 cm−1). The scattering phase function for dentin is described by a HG function with g = 0.93 and a very weak isotropic scattering component (~2%).

© 1995 Optical Society of America

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  1. J. D. B. Featherstone, D. G. A. Nelson, “Laser effects on dental hard tissues.” Adv. Dent. Res. 1, 21–26 (1987).
    [PubMed]
  2. R. H. Stern, R. F. Sognnaes, “Laser beam effect on hard dental tissues,” J. Dent. Res. 43, 873 (1964).
  3. Y. Launay, S. Mordon, A. Cornil, J. M. Brunetaud, Y. Moschetto, “Thermal effects of lasers on dental tissues,” Lasers Surg. Med. 7, 473–477 (1987).
    [CrossRef] [PubMed]
  4. H. Yamamoto, K. Ooya, “Potential of YAG laser in caries prevention,” J. Oral Pathol. 38, 7–15 (1974).
    [CrossRef]
  5. J. J. ten Bosch, “General aspects of optical methods in dentistry,” Adv. Dent. Res. 1, 5–7 (1987).
    [PubMed]
  6. M. E. J. Curzon, J. D. B. Featherstone, “Chemical composition of enamel,” in Handbook of Experimental Aspects of Oral Biochemistry, E. P. Lazzan, ed. (CRC Press, Boca Raton, Fla., 1983), pp. 123–135.
  7. A. Linde, “Dentin: structure, chemistry, and formation,” in Dentine and Dentine Reactions in the Oral Cavity, A. Thylstrup, S. A. Leach, V. Qvist, eds. (IRL Press, Oxford, 1987), pp. 17–26.
  8. J. R. Zijp, J. J. ten Bosch, “Theoretical model for the scattering of light by dentin and comparison with measurements,” Appl. Opt. 32, 411–415 (1993).
    [CrossRef] [PubMed]
  9. D. Spitzer, J. J. ten Bosch, “The absorption and scattering of light in bovine and human dental enamel,” Calcif. Tissue Res. 17, 129–137 (1975).
    [CrossRef] [PubMed]
  10. J. J. ten Bosch, J. R. Zijp, “Optical properties of dentin,” in Dentine and Dentine Reactions in the Oral Cavity, A. Thylstrup, S. A. Leach, V. Qvist, eds. (IRL Press, Oxford, 1987), pp. 59–65.
  11. J. R. Zijp, J. J. ten Bosch, “Angular dependence of HeNe laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
    [CrossRef] [PubMed]
  12. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 15, pp. 297–322.
  13. D. Fried, J. D. B. Featherstone, D. Glena, B. Bordyn, W. Seka, “The light-scattering properties of dentin and enamel at 543, 632, and 1053 nm,” in Lasers in Orthopedic, Dental, and Veterinary Medicine II, D. Gal, S. J. O’Brien, C. Vangsness, J. M. White, H. A. Wigdor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1880, 240–245 (1993).
  14. D. G. A. Nelson, J. C. Barry, C. P. Shields, R. Glena, J. D. B. Featherstone, “Crystal morphology, composition and dissolution behavior of carbonated apatites prepared at controlled pH and temperature,” J. Colloid Interface Sci. 130, 467–479 (1989).
    [CrossRef]
  15. D. G. A. Nelson, J. D. B. Featherstone, “Preparation, analysis, and characterization of carbonated apatites,” Calcif. Tissue Int. 34, S69–S81 (1982).
    [PubMed]
  16. W. J. O’Brien, “Fraunhofer diffraction of light by human enamel,” J. Dent. Res. 67, 484–486 (1988).
    [CrossRef]
  17. B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
    [CrossRef]
  18. A. N. Witt, “Multiple scattering in reflection nebulae I. A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–36 (1977).
    [CrossRef]
  19. M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9, 148–154 (1989).
    [CrossRef] [PubMed]
  20. W.-F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  21. B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1989).
    [CrossRef]
  22. S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues-I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1990).
    [CrossRef]
  23. J. Haselgrove, J. Leigh, C. Yee, N.-G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 30–41 (1991).
  24. L. Wang, S. L. Jacques, “Monte Carlo modeling of light transport in multi-layered tissues in Standard C,” (M. D. Anderson Cancer Center, University of Texas, Houston, Tex., 1992).
  25. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980), Vol. 2.
  26. I. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]

1993 (1)

1991 (1)

J. R. Zijp, J. J. ten Bosch, “Angular dependence of HeNe laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
[CrossRef] [PubMed]

1990 (3)

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance 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 tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues-I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1990).
[CrossRef]

1989 (3)

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1989).
[CrossRef]

D. G. A. Nelson, J. C. Barry, C. P. Shields, R. Glena, J. D. B. Featherstone, “Crystal morphology, composition and dissolution behavior of carbonated apatites prepared at controlled pH and temperature,” J. Colloid Interface Sci. 130, 467–479 (1989).
[CrossRef]

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9, 148–154 (1989).
[CrossRef] [PubMed]

1988 (1)

W. J. O’Brien, “Fraunhofer diffraction of light by human enamel,” J. Dent. Res. 67, 484–486 (1988).
[CrossRef]

1987 (3)

J. J. ten Bosch, “General aspects of optical methods in dentistry,” Adv. Dent. Res. 1, 5–7 (1987).
[PubMed]

J. D. B. Featherstone, D. G. A. Nelson, “Laser effects on dental hard tissues.” Adv. Dent. Res. 1, 21–26 (1987).
[PubMed]

Y. Launay, S. Mordon, A. Cornil, J. M. Brunetaud, Y. Moschetto, “Thermal effects of lasers on dental tissues,” Lasers Surg. Med. 7, 473–477 (1987).
[CrossRef] [PubMed]

1982 (1)

D. G. A. Nelson, J. D. B. Featherstone, “Preparation, analysis, and characterization of carbonated apatites,” Calcif. Tissue Int. 34, S69–S81 (1982).
[PubMed]

1977 (1)

A. N. Witt, “Multiple scattering in reflection nebulae I. A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–36 (1977).
[CrossRef]

1975 (1)

D. Spitzer, J. J. ten Bosch, “The absorption and scattering of light in bovine and human dental enamel,” Calcif. Tissue Res. 17, 129–137 (1975).
[CrossRef] [PubMed]

1974 (1)

H. Yamamoto, K. Ooya, “Potential of YAG laser in caries prevention,” J. Oral Pathol. 38, 7–15 (1974).
[CrossRef]

1964 (1)

R. H. Stern, R. F. Sognnaes, “Laser beam effect on hard dental tissues,” J. Dent. Res. 43, 873 (1964).

1941 (1)

I. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

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 (1989).
[CrossRef]

Barry, J. C.

D. G. A. Nelson, J. C. Barry, C. P. Shields, R. Glena, J. D. B. Featherstone, “Crystal morphology, composition and dissolution behavior of carbonated apatites prepared at controlled pH and temperature,” J. Colloid Interface Sci. 130, 467–479 (1989).
[CrossRef]

Bordyn, B.

D. Fried, J. D. B. Featherstone, D. Glena, B. Bordyn, W. Seka, “The light-scattering properties of dentin and enamel at 543, 632, and 1053 nm,” in Lasers in Orthopedic, Dental, and Veterinary Medicine II, D. Gal, S. J. O’Brien, C. Vangsness, J. M. White, H. A. Wigdor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1880, 240–245 (1993).

Brunetaud, J. M.

Y. Launay, S. Mordon, A. Cornil, J. M. Brunetaud, Y. Moschetto, “Thermal effects of lasers on dental tissues,” Lasers Surg. Med. 7, 473–477 (1987).
[CrossRef] [PubMed]

Chance, B.

J. Haselgrove, J. Leigh, C. Yee, N.-G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 30–41 (1991).

Cheong, W.-F.

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

Cornil, A.

Y. Launay, S. Mordon, A. Cornil, J. M. Brunetaud, Y. Moschetto, “Thermal effects of lasers on dental tissues,” Lasers Surg. Med. 7, 473–477 (1987).
[CrossRef] [PubMed]

Curzon, M. E. J.

M. E. J. Curzon, J. D. B. Featherstone, “Chemical composition of enamel,” in Handbook of Experimental Aspects of Oral Biochemistry, E. P. Lazzan, ed. (CRC Press, Boca Raton, Fla., 1983), pp. 123–135.

Featherstone, J. D. B.

D. G. A. Nelson, J. C. Barry, C. P. Shields, R. Glena, J. D. B. Featherstone, “Crystal morphology, composition and dissolution behavior of carbonated apatites prepared at controlled pH and temperature,” J. Colloid Interface Sci. 130, 467–479 (1989).
[CrossRef]

J. D. B. Featherstone, D. G. A. Nelson, “Laser effects on dental hard tissues.” Adv. Dent. Res. 1, 21–26 (1987).
[PubMed]

D. G. A. Nelson, J. D. B. Featherstone, “Preparation, analysis, and characterization of carbonated apatites,” Calcif. Tissue Int. 34, S69–S81 (1982).
[PubMed]

M. E. J. Curzon, J. D. B. Featherstone, “Chemical composition of enamel,” in Handbook of Experimental Aspects of Oral Biochemistry, E. P. Lazzan, ed. (CRC Press, Boca Raton, Fla., 1983), pp. 123–135.

D. Fried, J. D. B. Featherstone, D. Glena, B. Bordyn, W. Seka, “The light-scattering properties of dentin and enamel at 543, 632, and 1053 nm,” in Lasers in Orthopedic, Dental, and Veterinary Medicine II, D. Gal, S. J. O’Brien, C. Vangsness, J. M. White, H. A. Wigdor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1880, 240–245 (1993).

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues-I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1990).
[CrossRef]

Fried, D.

D. Fried, J. D. B. Featherstone, D. Glena, B. Bordyn, W. Seka, “The light-scattering properties of dentin and enamel at 543, 632, and 1053 nm,” in Lasers in Orthopedic, Dental, and Veterinary Medicine II, D. Gal, S. J. O’Brien, C. Vangsness, J. M. White, H. A. Wigdor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1880, 240–245 (1993).

Glena, D.

D. Fried, J. D. B. Featherstone, D. Glena, B. Bordyn, W. Seka, “The light-scattering properties of dentin and enamel at 543, 632, and 1053 nm,” in Lasers in Orthopedic, Dental, and Veterinary Medicine II, D. Gal, S. J. O’Brien, C. Vangsness, J. M. White, H. A. Wigdor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1880, 240–245 (1993).

Glena, R.

D. G. A. Nelson, J. C. Barry, C. P. Shields, R. Glena, J. D. B. Featherstone, “Crystal morphology, composition and dissolution behavior of carbonated apatites prepared at controlled pH and temperature,” J. Colloid Interface Sci. 130, 467–479 (1989).
[CrossRef]

Greenstein, J. L.

I. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Haselgrove, J.

J. Haselgrove, J. Leigh, C. Yee, N.-G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 30–41 (1991).

Henyey, I. G.

I. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Jacques, S. L.

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

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9, 148–154 (1989).
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, “Monte Carlo modeling of light transport in multi-layered tissues in Standard C,” (M. D. Anderson Cancer Center, University of Texas, Houston, Tex., 1992).

Keijzer, M.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9, 148–154 (1989).
[CrossRef] [PubMed]

Launay, Y.

Y. Launay, S. Mordon, A. Cornil, J. M. Brunetaud, Y. Moschetto, “Thermal effects of lasers on dental tissues,” Lasers Surg. Med. 7, 473–477 (1987).
[CrossRef] [PubMed]

Leigh, J.

J. Haselgrove, J. Leigh, C. Yee, N.-G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 30–41 (1991).

Linde, A.

A. Linde, “Dentin: structure, chemistry, and formation,” in Dentine and Dentine Reactions in the Oral Cavity, A. Thylstrup, S. A. Leach, V. Qvist, eds. (IRL Press, Oxford, 1987), pp. 17–26.

Maris, M.

J. Haselgrove, J. Leigh, C. Yee, N.-G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 30–41 (1991).

Mordon, S.

Y. Launay, S. Mordon, A. Cornil, J. M. Brunetaud, Y. Moschetto, “Thermal effects of lasers on dental tissues,” Lasers Surg. Med. 7, 473–477 (1987).
[CrossRef] [PubMed]

Moschetto, Y.

Y. Launay, S. Mordon, A. Cornil, J. M. Brunetaud, Y. Moschetto, “Thermal effects of lasers on dental tissues,” Lasers Surg. Med. 7, 473–477 (1987).
[CrossRef] [PubMed]

Nelson, D. G. A.

D. G. A. Nelson, J. C. Barry, C. P. Shields, R. Glena, J. D. B. Featherstone, “Crystal morphology, composition and dissolution behavior of carbonated apatites prepared at controlled pH and temperature,” J. Colloid Interface Sci. 130, 467–479 (1989).
[CrossRef]

J. D. B. Featherstone, D. G. A. Nelson, “Laser effects on dental hard tissues.” Adv. Dent. Res. 1, 21–26 (1987).
[PubMed]

D. G. A. Nelson, J. D. B. Featherstone, “Preparation, analysis, and characterization of carbonated apatites,” Calcif. Tissue Int. 34, S69–S81 (1982).
[PubMed]

O’Brien, W. J.

W. J. O’Brien, “Fraunhofer diffraction of light by human enamel,” J. Dent. Res. 67, 484–486 (1988).
[CrossRef]

Ooya, K.

H. Yamamoto, K. Ooya, “Potential of YAG laser in caries prevention,” J. Oral Pathol. 38, 7–15 (1974).
[CrossRef]

Patterson, M. S.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues-I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1990).
[CrossRef]

Prahl, S. A.

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

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9, 148–154 (1989).
[CrossRef] [PubMed]

Seka, W.

D. Fried, J. D. B. Featherstone, D. Glena, B. Bordyn, W. Seka, “The light-scattering properties of dentin and enamel at 543, 632, and 1053 nm,” in Lasers in Orthopedic, Dental, and Veterinary Medicine II, D. Gal, S. J. O’Brien, C. Vangsness, J. M. White, H. A. Wigdor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1880, 240–245 (1993).

Shields, C. P.

D. G. A. Nelson, J. C. Barry, C. P. Shields, R. Glena, J. D. B. Featherstone, “Crystal morphology, composition and dissolution behavior of carbonated apatites prepared at controlled pH and temperature,” J. Colloid Interface Sci. 130, 467–479 (1989).
[CrossRef]

Sognnaes, R. F.

R. H. Stern, R. F. Sognnaes, “Laser beam effect on hard dental tissues,” J. Dent. Res. 43, 873 (1964).

Spitzer, D.

D. Spitzer, J. J. ten Bosch, “The absorption and scattering of light in bovine and human dental enamel,” Calcif. Tissue Res. 17, 129–137 (1975).
[CrossRef] [PubMed]

Stern, R. H.

R. H. Stern, R. F. Sognnaes, “Laser beam effect on hard dental tissues,” J. Dent. Res. 43, 873 (1964).

ten Bosch, J. J.

J. R. Zijp, J. J. ten Bosch, “Theoretical model for the scattering of light by dentin and comparison with measurements,” Appl. Opt. 32, 411–415 (1993).
[CrossRef] [PubMed]

J. R. Zijp, J. J. ten Bosch, “Angular dependence of HeNe laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
[CrossRef] [PubMed]

J. J. ten Bosch, “General aspects of optical methods in dentistry,” Adv. Dent. Res. 1, 5–7 (1987).
[PubMed]

D. Spitzer, J. J. ten Bosch, “The absorption and scattering of light in bovine and human dental enamel,” Calcif. Tissue Res. 17, 129–137 (1975).
[CrossRef] [PubMed]

J. J. ten Bosch, J. R. Zijp, “Optical properties of dentin,” in Dentine and Dentine Reactions in the Oral Cavity, A. Thylstrup, S. A. Leach, V. Qvist, eds. (IRL Press, Oxford, 1987), pp. 59–65.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 15, pp. 297–322.

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

Wang, L.

L. Wang, S. L. Jacques, “Monte Carlo modeling of light transport in multi-layered tissues in Standard C,” (M. D. Anderson Cancer Center, University of Texas, Houston, Tex., 1992).

Wang, N.-G.

J. Haselgrove, J. Leigh, C. Yee, N.-G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 30–41 (1991).

Welch, A. J.

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

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9, 148–154 (1989).
[CrossRef] [PubMed]

Wilson, B. C.

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

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues-I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1990).
[CrossRef]

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1989).
[CrossRef]

Witt, A. N.

A. N. Witt, “Multiple scattering in reflection nebulae I. A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–36 (1977).
[CrossRef]

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues-I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1990).
[CrossRef]

Yamamoto, H.

H. Yamamoto, K. Ooya, “Potential of YAG laser in caries prevention,” J. Oral Pathol. 38, 7–15 (1974).
[CrossRef]

Yee, C.

J. Haselgrove, J. Leigh, C. Yee, N.-G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 30–41 (1991).

Zijp, J. R.

J. R. Zijp, J. J. ten Bosch, “Theoretical model for the scattering of light by dentin and comparison with measurements,” Appl. Opt. 32, 411–415 (1993).
[CrossRef] [PubMed]

J. R. Zijp, J. J. ten Bosch, “Angular dependence of HeNe laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
[CrossRef] [PubMed]

J. J. ten Bosch, J. R. Zijp, “Optical properties of dentin,” in Dentine and Dentine Reactions in the Oral Cavity, A. Thylstrup, S. A. Leach, V. Qvist, eds. (IRL Press, Oxford, 1987), pp. 59–65.

Adv. Dent. Res. (2)

J. D. B. Featherstone, D. G. A. Nelson, “Laser effects on dental hard tissues.” Adv. Dent. Res. 1, 21–26 (1987).
[PubMed]

J. J. ten Bosch, “General aspects of optical methods in dentistry,” Adv. Dent. Res. 1, 5–7 (1987).
[PubMed]

Appl. Opt. (1)

Arch. Oral Biol. (1)

J. R. Zijp, J. J. ten Bosch, “Angular dependence of HeNe laser light scattering by bovine and human dentine,” Arch. Oral Biol. 36, 283–289 (1991).
[CrossRef] [PubMed]

Astrophys. J. (1)

I. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Astrophys. J. Suppl. Ser. (1)

A. N. Witt, “Multiple scattering in reflection nebulae I. A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–36 (1977).
[CrossRef]

Calcif. Tissue Int. (1)

D. G. A. Nelson, J. D. B. Featherstone, “Preparation, analysis, and characterization of carbonated apatites,” Calcif. Tissue Int. 34, S69–S81 (1982).
[PubMed]

Calcif. Tissue Res. (1)

D. Spitzer, J. J. ten Bosch, “The absorption and scattering of light in bovine and human dental enamel,” Calcif. Tissue Res. 17, 129–137 (1975).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

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

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Figures (9)

Fig. 1
Fig. 1

Schematic of the automated goniometer system showing the index-matching chamber (12-cm diameter), the sample, the photodiode detector, and the laser beam.

Fig. 2
Fig. 2

Scattering distributions for 50- (thick curve) and 1220- (thin curve) μm-thick sections of enamel at 1053 nm. Inset: transmission of unscattered (ballistic) light, slope μt = μa + μs ≈ 18 cm−1. Note that the intensity does not drop to zero (background signal) at 90° (Lambert’s cosine law) because of scattered light from the sides of the sample, particularly for thicker samples.

Fig. 3
Fig. 3

Scattering distribution for a 50-μm-thick enamel sample measured at 1053 nm (thick curve) and MC simulations (thin solid and dotted curves) using the input parameters of μa = 0, μs = 15 cm−1, g = 0.96, and fd = 0 and 0.35. The slow rise at θ > 120° is an experimental artifact (see Fig. 8).

Fig. 4
Fig. 4

Scattering distribution for a 1220-μm-thick enamel sample measured at 1053 nm (thick curve) and MC simulations (thin solid, dotted, and dashed curves) using the input parameters of μa = 0, μs = 15 cm−1, g = 0.96, and fd = 0.35 and 0.70. We conclude that the absorption coefficient for enamel at 1053 nm must be μa ≪ 1 cm−1 or (μa ≈ 0).

Fig. 5
Fig. 5

Scattering distribution for a 1220-μm-thick enamel sample measured at 1053 nm (thick curve) and MC simulations (thin solid, dotted, and dashed curves) using the input parameters of μs = 15 cm−1, g = 0.96, fd = 0, and μa = 0, 1, and 5 cm−1.

Fig. 6
Fig. 6

Scattering distribution measured at 632 nm for a sintered, 1220-μm-thick section of CAP (thick curve) and MC simulation (thin curve) with input parameters of μa = 0 cm−1, μs = 200 cm−1, and fd = 1.

Fig. 7
Fig. 7

Scattering distributions for 80- and 830-μm-thick sections of dentin measured at 1053 nm. The 80-μm section was measured with both ⊥ (thin solid curve) and ‖ (thin dotted curve) orientations of the dentinal tubules. The dotted curve at 0° on the 830-μm sample (thick solid curve) was masked by strong, stray light. The sharp rise at θ > 120° in the 80-μm-thick samples is an experimental artifact (see Fig. 8).

Fig. 8
Fig. 8

Scattering distribution measured for an 80-μm-thick dentin section from 0° to 170° measured at 632 nm, with (thick curve) and without (thin curve) a wedge-shaped absorbing mask placed behind the sample. The inset shows the position and shape of this mask. With the mask in place, only backscattered light that is due to bulk scattering in the sample is detected between 90° and 170°. The resulting, flat, backscatter distribution confirms that the source of the intensity rise in the scattering distribution of the unmasked sample (thick solid curve) at θ > 120° is caused by reflection of forward-scattered light at the wall of the index-matching chamber.

Fig. 9
Fig. 9

Scattering distribution for an 830-μm-thick dentin sample measured at 1053 nm (thick curve) and MC simulations (thin solid, dotted, and dashed curves) using the input parameters of μs = 210 cm−1, g = 0.93, fd = 0.02, and μa = 0, 3, 4, and 6 cm−1.

Tables (1)

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Table 1 Optical Properties of Dentin and Enamel Determined in this Study with Some Published Data for Comparisona

Equations (1)

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Φ ( cos θ ) = f d + ( 1 - f d ) [ ( 1 - g 2 ) ( 1 + g 2 - 2 g cos θ ) 3 / 2 ] .

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