Abstract

Light distribution in a strong turbid medium such as skin tissue depends on both the bulk optical properties and the profiles of the interfaces where mismatch in the refractive index occurs. We present recent results of a numerical investigation on the light distribution inside a human skin tissue phantom for a converging laser beam with a wavelength near 1 µm and its dependence on the roughness of the interfaces and index mismatch. The skin tissue is modeled by a two-layer structure, and within each layer the tissue is considered macroscopically homogeneous. The two interfaces that separate the epidermis from the ambient medium and the dermis are considered randomly rough. With a recently developed method of Monte Carlo simulation capable of treating inhomogeneous boundary conditions, light distributions in various cases of interface roughness and index mismatch are obtained, and their relevance to the measurements of optical parameters of the skin tissue and laser surgery under the skin surface are discussed.

© 2000 Optical Society of America

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  1. R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermotol. 77, 13–19 (1981).
    [CrossRef]
  2. M. J. C. van Gemert, S. L. Jacque, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
    [CrossRef] [PubMed]
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  4. B. C. Wilson, G. Adams, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
    [CrossRef] [PubMed]
  5. M. Keijzer, S. T. 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]
  6. R. Marchesini, C. Clemente, E. Pignoli, M. Brambilla, “Optical properties of in vitro epidermis and their possible relationship with optical properties of in vivo skin,” J. Photochem. Photobiol. B 16, 127–140 (1992).
    [CrossRef] [PubMed]
  7. R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis in vitro and in vivo,” Appl. Opt. 32, 435–447 (1993).
    [CrossRef] [PubMed]
  8. J. M. Schmitt, G. X. Zhou, E. C. Walker, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).
    [CrossRef] [PubMed]
  9. I. D. Miller, A. R. Veith, “Optical modelling of light distributions in skin tissue following laser irradiation,” Lasers Surg. Med. 13, 565–571 (1993).
    [CrossRef] [PubMed]
  10. W. Verkruysse, J. W. Pickering, J. F. Beek, M. Keijzer, M. J. C. van Germert, “Modeling the effect of wavelength on the pulsed dye laser treatment of port wine stains,” Appl. Opt. 32, 393–398 (1993).
    [CrossRef] [PubMed]
  11. M. Rajadhyaksha, R. R. Anderson, R. H. Webb, “Video-rate confocal scanning laser microscope for imaging human tissues in vivo,” Appl. Opt. 38, 2105–2115 (1999).
    [CrossRef]
  12. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
    [CrossRef]
  13. X. H. Hu, “Efficient use of Q-switched lasers in the treatment of cutaneous lesions,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems V, by R. R. Anderson, ed., Proc. SPIE2395, 586–591 (1995).
  14. Z. Song, K. Dong, X. H. Hu, J. Q. Lu, “Monte Carlo simulation of converging laser beams propagating in biological tissue,” Appl. Opt. 37, 2944–2949 (1999).
    [CrossRef]
  15. H. G. Burkitt, B. Young, J. W. Heath, Wheater’s Functional Histology, 3rd ed. (Longman Group, Edinburgh, 1993), Chap. 9.
  16. G. Plewig, T. Jansen, “Size and shape of corneocytes: variation with anatomic site and age,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Maibach, eds. (CRC, Boca Raton, Fla., 1996), Chap. III-3.
  17. C. el Gammal, A. M. Kligman, S. el Gammal, “Anatomy of the skin surface,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Mailbach, eds. (CRC, Boca Raton, Fla., 1996), Chap. I.
  18. N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
    [CrossRef]
  19. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
    [CrossRef]
  20. P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
    [CrossRef]
  21. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3.
  22. J. Q. Lu, A. A. Maradudin, T. Michel, “Enhanced backscattering from a rough dielectric film on a reflecting substrate,” J. Opt. Soc. Am. B 8, 311–317 (1991).
    [CrossRef]
  23. V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
    [CrossRef] [PubMed]
  24. Y. Du, M. Cariveau, G. W. Kalmus, J. Q. Lu, X. H. Hu, “Experimental study of optical properties of porcine skin dermis from 900 to 1500 nm,” in Optical Biopsy III, R. R. Alfano, ed., Proc. SPIE3917, 184–192 (2000).
    [CrossRef]

1999

1995

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

1993

1992

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

R. Marchesini, C. Clemente, E. Pignoli, M. Brambilla, “Optical properties of in vitro epidermis and their possible relationship with optical properties of in vivo skin,” J. Photochem. Photobiol. B 16, 127–140 (1992).
[CrossRef] [PubMed]

1991

1990

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

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

1989

M. J. C. van Gemert, S. L. Jacque, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

M. Keijzer, S. T. 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]

1984

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

1983

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

1981

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermotol. 77, 13–19 (1981).
[CrossRef]

Aarnoudse, J. G.

Adams, G.

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

Anderson, R. R.

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3.

Beek, J. F.

Bouma, B. E.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

Brambilla, M.

R. Marchesini, C. Clemente, E. Pignoli, M. Brambilla, “Optical properties of in vitro epidermis and their possible relationship with optical properties of in vivo skin,” J. Photochem. Photobiol. B 16, 127–140 (1992).
[CrossRef] [PubMed]

Brezinski, M. E.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

Burkitt, H. G.

H. G. Burkitt, B. Young, J. W. Heath, Wheater’s Functional Histology, 3rd ed. (Longman Group, Edinburgh, 1993), Chap. 9.

Cariveau, M.

Y. Du, M. Cariveau, G. W. Kalmus, J. Q. Lu, X. H. Hu, “Experimental study of optical properties of porcine skin dermis from 900 to 1500 nm,” in Optical Biopsy III, R. R. Alfano, ed., Proc. SPIE3917, 184–192 (2000).
[CrossRef]

Clemente, C.

R. Marchesini, C. Clemente, E. Pignoli, M. Brambilla, “Optical properties of in vitro epidermis and their possible relationship with optical properties of in vivo skin,” J. Photochem. Photobiol. B 16, 127–140 (1992).
[CrossRef] [PubMed]

Dassel, A. C. M.

de Mul, F. F. M.

Dong, K.

Du, Y.

Y. Du, M. Cariveau, G. W. Kalmus, J. Q. Lu, X. H. Hu, “Experimental study of optical properties of porcine skin dermis from 900 to 1500 nm,” in Optical Biopsy III, R. R. Alfano, ed., Proc. SPIE3917, 184–192 (2000).
[CrossRef]

el Gammal, C.

C. el Gammal, A. M. Kligman, S. el Gammal, “Anatomy of the skin surface,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Mailbach, eds. (CRC, Boca Raton, Fla., 1996), Chap. I.

el Gammal, S.

C. el Gammal, A. M. Kligman, S. el Gammal, “Anatomy of the skin surface,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Mailbach, eds. (CRC, Boca Raton, Fla., 1996), Chap. I.

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Fujimoto, J. G.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

Garcia, N.

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Graaff, R.

Heath, J. W.

H. G. Burkitt, B. Young, J. W. Heath, Wheater’s Functional Histology, 3rd ed. (Longman Group, Edinburgh, 1993), Chap. 9.

Hee, M. R.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

Hu, X. H.

Z. Song, K. Dong, X. H. Hu, J. Q. Lu, “Monte Carlo simulation of converging laser beams propagating in biological tissue,” Appl. Opt. 37, 2944–2949 (1999).
[CrossRef]

X. H. Hu, “Efficient use of Q-switched lasers in the treatment of cutaneous lesions,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems V, by R. R. Anderson, ed., Proc. SPIE2395, 586–591 (1995).

Y. Du, M. Cariveau, G. W. Kalmus, J. Q. Lu, X. H. Hu, “Experimental study of optical properties of porcine skin dermis from 900 to 1500 nm,” in Optical Biopsy III, R. R. Alfano, ed., Proc. SPIE3917, 184–192 (2000).
[CrossRef]

Ishimaru, A.

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

Jacque, S. L.

M. J. C. van Gemert, S. L. Jacque, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

Jacques, S. T.

M. Keijzer, S. T. 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]

Jansen, T.

G. Plewig, T. Jansen, “Size and shape of corneocytes: variation with anatomic site and age,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Maibach, eds. (CRC, Boca Raton, Fla., 1996), Chap. III-3.

Kalmus, G. W.

Y. Du, M. Cariveau, G. W. Kalmus, J. Q. Lu, X. H. Hu, “Experimental study of optical properties of porcine skin dermis from 900 to 1500 nm,” in Optical Biopsy III, R. R. Alfano, ed., Proc. SPIE3917, 184–192 (2000).
[CrossRef]

Keijzer, M.

W. Verkruysse, J. W. Pickering, J. F. Beek, M. Keijzer, M. J. C. van Germert, “Modeling the effect of wavelength on the pulsed dye laser treatment of port wine stains,” Appl. Opt. 32, 393–398 (1993).
[CrossRef] [PubMed]

M. Keijzer, S. T. 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]

Kligman, A. M.

C. el Gammal, A. M. Kligman, S. el Gammal, “Anatomy of the skin surface,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Mailbach, eds. (CRC, Boca Raton, Fla., 1996), Chap. I.

Koelink, M. H.

Lu, J. Q.

Maradudin, A. A.

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

J. Q. Lu, A. A. Maradudin, T. Michel, “Enhanced backscattering from a rough dielectric film on a reflecting substrate,” J. Opt. Soc. Am. B 8, 311–317 (1991).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Marchesini, R.

R. Marchesini, C. Clemente, E. Pignoli, M. Brambilla, “Optical properties of in vitro epidermis and their possible relationship with optical properties of in vivo skin,” J. Photochem. Photobiol. B 16, 127–140 (1992).
[CrossRef] [PubMed]

McGurn, A. R.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Mendez, E. R.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Michel, T.

J. Q. Lu, A. A. Maradudin, T. Michel, “Enhanced backscattering from a rough dielectric film on a reflecting substrate,” J. Opt. Soc. Am. B 8, 311–317 (1991).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Miller, I. D.

I. D. Miller, A. R. Veith, “Optical modelling of light distributions in skin tissue following laser irradiation,” Lasers Surg. Med. 13, 565–571 (1993).
[CrossRef] [PubMed]

Parrish, J. A.

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermotol. 77, 13–19 (1981).
[CrossRef]

Patterson, M. S.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Pickering, J. W.

Pignoli, E.

R. Marchesini, C. Clemente, E. Pignoli, M. Brambilla, “Optical properties of in vitro epidermis and their possible relationship with optical properties of in vivo skin,” J. Photochem. Photobiol. B 16, 127–140 (1992).
[CrossRef] [PubMed]

Plewig, G.

G. Plewig, T. Jansen, “Size and shape of corneocytes: variation with anatomic site and age,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Maibach, eds. (CRC, Boca Raton, Fla., 1996), Chap. III-3.

Prahl, S. A.

M. Keijzer, S. T. 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]

Rajadhyaksha, M.

Schmitt, J. M.

Song, Z.

Southern, J. F.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3.

Star, W. M.

M. J. C. van Gemert, S. L. Jacque, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

M. J. C. van Gemert, S. L. Jacque, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

Stoll, E.

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Tearney, G. J.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

Tran, P.

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

van Gemert, M. J. C.

M. J. C. van Gemert, S. L. Jacque, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

van Germert, M. J. C.

Veith, A. R.

I. D. Miller, A. R. Veith, “Optical modelling of light distributions in skin tissue following laser irradiation,” Lasers Surg. Med. 13, 565–571 (1993).
[CrossRef] [PubMed]

Verkruysse, W.

Walker, E. C.

Webb, R. H.

Welch, A. J.

M. Keijzer, S. T. 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, G. Adams, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Young, B.

H. G. Burkitt, B. Young, J. W. Heath, Wheater’s Functional Histology, 3rd ed. (Longman Group, Edinburgh, 1993), Chap. 9.

Zhou, G. X.

Zijlstra, W. G.

Ann. Phys.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Appl. Opt.

IEEE Trans. Biomed. Eng.

M. J. C. van Gemert, S. L. Jacque, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

J. Invest. Dermotol.

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermotol. 77, 13–19 (1981).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Photochem. Photobiol. B

R. Marchesini, C. Clemente, E. Pignoli, M. Brambilla, “Optical properties of in vitro epidermis and their possible relationship with optical properties of in vivo skin,” J. Photochem. Photobiol. B 16, 127–140 (1992).
[CrossRef] [PubMed]

Lasers Surg. Med.

I. D. Miller, A. R. Veith, “Optical modelling of light distributions in skin tissue following laser irradiation,” Lasers Surg. Med. 13, 565–571 (1993).
[CrossRef] [PubMed]

M. Keijzer, S. T. 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]

Med. Phys.

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

Opt. Lett.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 21, 2258–2260 (1995).
[CrossRef]

Phys. Med. Biol.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Phys. Rev. B

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

Phys. Rev. Lett.

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Other

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3.

Y. Du, M. Cariveau, G. W. Kalmus, J. Q. Lu, X. H. Hu, “Experimental study of optical properties of porcine skin dermis from 900 to 1500 nm,” in Optical Biopsy III, R. R. Alfano, ed., Proc. SPIE3917, 184–192 (2000).
[CrossRef]

X. H. Hu, “Efficient use of Q-switched lasers in the treatment of cutaneous lesions,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems V, by R. R. Anderson, ed., Proc. SPIE2395, 586–591 (1995).

H. G. Burkitt, B. Young, J. W. Heath, Wheater’s Functional Histology, 3rd ed. (Longman Group, Edinburgh, 1993), Chap. 9.

G. Plewig, T. Jansen, “Size and shape of corneocytes: variation with anatomic site and age,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Maibach, eds. (CRC, Boca Raton, Fla., 1996), Chap. III-3.

C. el Gammal, A. M. Kligman, S. el Gammal, “Anatomy of the skin surface,” in Bioengineering of the Skin: Skin Surface Imaging and Analysis, by K.-P. Wilhelm, P. Elsner, E. Berardesca, H. I. Mailbach, eds. (CRC, Boca Raton, Fla., 1996), Chap. I.

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

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Fig. 1
Fig. 1

Schematic drawing of the two-layer model for human skin tissue, with a converging laser beam of cone angle α incident upon the surface. All simulation results were obtained assuming a laser beam of Gaussian profile with α = 30° and the average thickness of the epidermis d = 60 µm.

Fig. 2
Fig. 2

Geometric relations among the various unit vectors at an interface between two media of different refractive index n i and n r .

Fig. 3
Fig. 3

Photon density in the yz plane with air as the ambient medium (n 0 = 1.00) and the rms height at the skin surface δ01 set at 0.2 µm. The parameters of the two-layer skin tissue model are given by n 1 = n 2 = 1.41, a 01 = 20 µm, μ a1 = 5.0 mm-1, μ s1 = 10.0 mm-1, g 1 = g 2 = 0.9, a 12 = 80 µm, δ12 = 20 µm, μ a2 = 0.5mm-1, and μ s2 = 5.0 mm-1.

Fig. 4
Fig. 4

Photon density z dependence on the z axis. Results from four simulation cases are displayed with different indices of the ambient medium n 0 and the rms height at the skin surface δ01. All other parameters remain the same as those in Fig. 3, and the dashed line indicates the position of the dermoepidermal junction.

Fig. 5
Fig. 5

Photon density in the yz plane with water as the ambient medium (n 0 = 1.33) and n 1 = 1.45, n 2 = 1.41, and δ12 = 10 µm. All other parameters are identical to those in Fig. 3.

Fig. 6
Fig. 6

Photon density z dependence on the z axis for three cases of different surface roughnesses at the dermoepidermal junction δ12. All other parameters remain the same for the three cases: n 0 = 1.33, n 1 = 1.45, a 01 = 20 µm, δ01 = 0.2 µm, μ a1 = 5.0 mm-1, μ s1 = 10.0 mm-1, g 1 = g 2 = 0.9, a 12 = 80 µm, n 2 = 1.41, μ a2 = 0.5 mm-1, and μ s2 = 5.0 mm-1. The dashed line indicates the position of the dermoepidermal junction.

Fig. 7
Fig. 7

Photon density z dependence on the z axis for four cases of different refractive indices of dermis n 2 with n 1 = 1.41 and δ12 = 10 µm. All other parameters are identical to those in Fig. 5, and the dashed line indicates the position of the dermoepidermal junction.

Equations (10)

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ζiR=0,
ζiRζiR=δi2 exp-R-R2/ai2,
ζR=2δaπ  XRexp-2R-R2a2dRXR * GR,
ζR=12π  xQgQexpiQ·RdQ,
4πRc cos φi  λ,
kRc1/3 cos φi  1,
r=2cos φin+i,
t=sinφr-φisin φin+ninri.
n=-ζxx-ζyy+zζx2+ζy2+11/2,
R=12tanφi-φrtanφi+φr2+sinφi-φrsinφi+φr2 for φi>0,

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