Abstract

The time-honored Lambert law is widely applied for describing the angle resolved reflectance from illuminated turbid media. We show that this law is only exactly fulfilled for a very special set of geometrical and optical properties. In contrast to what is believed so far, we demonstrate theoretically and experimentally that huge deviations from the Lambert law are ubiquitous. This finding is important for many applications such as those in biomedical optics.

© 2011 Optical Society of America

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References

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  1. J. H. Lambert, Photometria sive de mensura et gradibus luminus, colorum et umbrae (Eberhard Klett, 1760).
  2. H. Gross, Handbook of Optical Systems; Volume 1: Fundamental of Technical Optics (Wiley-VCH, 2005).
  3. S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From few to many: illumination cone models for face recognition under variable lighting and pose,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 243–260 (2001).
  4. M. S. Patterson, B. Chance, and B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [PubMed]
  5. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, “Spatially-resolved absolute diffuse reflectance measurements for non-invasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
    [PubMed]
  6. F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light propagation through biological tissue and other diffusive media: theory, solutions, and software (SPIE Press Book, 2009).
    [PubMed]
  7. D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 2, 857–865 (1994).
  8. S. C. Gebhart, A. Mahadevan-Jansen, and W.-C. Lin, “Experimental and simulated angular profiles of fluorescence and diffuse reflectance emission from turbid media,” Appl. Opt. 44, 4884–4901 (2005).
    [PubMed]
  9. D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).
  10. V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
    [PubMed]
  11. J. Xia and G. Yao, “Angular distribution of diffuse reflectance in biological tissue,” Appl. Opt. 46, 6552–6560 (2007).
    [PubMed]
  12. R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16, 5907–5925 (2008).
    [PubMed]
  13. F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express 15, 486–500 (2007).
    [PubMed]
  14. R. Graaff, J. G. Arnoudse, F. F. M. de Mul, and H. W. Jentink, “Similarity relations for anisotropic scattering in absorbing media,” Opt. Eng. 32, 244–252 (1993).
  15. D. C. Van der Hulst, Multiple Light Scattering (Academic Press, 1980).
  16. A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet soft wood,” Opt. Express 16, 9895–9906 (2008).
    [PubMed]
  17. A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
    [PubMed]
  18. H. A. Yousif and E. Boutros, “A FORTRAN code for the scattering of EM plane waves by an infinitely long cylinder at oblique incidence,” Comput. Phys. Commun. 69, 406–414 (1992).
  19. Y. Sun, “Statistical ray method for deriving reflection models of rough surfaces,” J. Opt. Soc. Am. A 24, 724–744 (2007).
  20. P. Beckmann, A. Spizzichino, and A. Norwood, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, Inc., 1987).
  21. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).
  22. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).
  23. F. Voit, J. Schäfer, and A. Kienle, “Light scattering by multiple wpheres: comparison between Maxwell theory and radiative-transfer-theory calculations,” Opt. Lett. 34, 2593–2595 (2009).
    [PubMed]

2009 (1)

2008 (2)

2007 (4)

2006 (1)

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
[PubMed]

2005 (1)

2001 (1)

S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From few to many: illumination cone models for face recognition under variable lighting and pose,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 243–260 (2001).

2000 (1)

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

1996 (1)

1994 (1)

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 2, 857–865 (1994).

1993 (1)

R. Graaff, J. G. Arnoudse, F. F. M. de Mul, and H. W. Jentink, “Similarity relations for anisotropic scattering in absorbing media,” Opt. Eng. 32, 244–252 (1993).

1992 (1)

H. A. Yousif and E. Boutros, “A FORTRAN code for the scattering of EM plane waves by an infinitely long cylinder at oblique incidence,” Comput. Phys. Commun. 69, 406–414 (1992).

1989 (1)

Adler, D. C.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).

Arendt, J. T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Arnoudse, J. G.

R. Graaff, J. G. Arnoudse, F. F. M. de Mul, and H. W. Jentink, “Similarity relations for anisotropic scattering in absorbing media,” Opt. Eng. 32, 244–252 (1993).

Backman, V.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Badizadegan, K.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Belhumeur, P. N.

S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From few to many: illumination cone models for face recognition under variable lighting and pose,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 243–260 (2001).

Boutros, E.

H. A. Yousif and E. Boutros, “A FORTRAN code for the scattering of EM plane waves by an infinitely long cylinder at oblique incidence,” Comput. Phys. Commun. 69, 406–414 (1992).

Chance, B.

Chen, Y.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).

Connolly, J.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).

Crawford, J. M.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

D’Andrea, C.

Dasari, R. R.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

de Mul, F. F. M.

R. Graaff, J. G. Arnoudse, F. F. M. de Mul, and H. W. Jentink, “Similarity relations for anisotropic scattering in absorbing media,” Opt. Eng. 32, 244–252 (1993).

Durian, D. J.

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 2, 857–865 (1994).

Feld, M. S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Fitzmaurice, M.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Foschum, F.

Fujimoto, J. G.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).

Gebhart, S. C.

Georghiades, S.

S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From few to many: illumination cone models for face recognition under variable lighting and pose,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 243–260 (2001).

Graaff, R.

R. Graaff, J. G. Arnoudse, F. F. M. de Mul, and H. W. Jentink, “Similarity relations for anisotropic scattering in absorbing media,” Opt. Eng. 32, 244–252 (1993).

Gurjar, R. S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Hibst, R.

Huber, R.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).

Itzkan, I.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Jentink, H. W.

R. Graaff, J. G. Arnoudse, F. F. M. de Mul, and H. W. Jentink, “Similarity relations for anisotropic scattering in absorbing media,” Opt. Eng. 32, 244–252 (1993).

Kabani, S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Kienle, A.

Kline, E.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Kriegman, D. J.

S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From few to many: illumination cone models for face recognition under variable lighting and pose,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 243–260 (2001).

Levin, H. S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Lilge, L.

Lin, W.-C.

Mahadevan-Jansen, A.

Martelli, F.

McGilian, T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Michels, R.

Müller, M. G.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Patterson, M. S.

Perelman, L. T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Pifferi, A.

Schäfer, J.

Schmitt, J.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).

Seiler, M.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Shapshay, S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Steiner, R.

Sun, Y.

Taroni, P.

Valdez, T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Van Dam, J.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Voit, F.

Wallace, M. B.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Wilson, B. C.

Xia, J.

Yao, G.

Yousif, H. A.

H. A. Yousif and E. Boutros, “A FORTRAN code for the scattering of EM plane waves by an infinitely long cylinder at oblique incidence,” Comput. Phys. Commun. 69, 406–414 (1992).

Zaccanti, G.

Zhang, Q.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Zonios, G.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Appl. Opt. (4)

Comput. Phys. Commun. (1)

H. A. Yousif and E. Boutros, “A FORTRAN code for the scattering of EM plane waves by an infinitely long cylinder at oblique incidence,” Comput. Phys. Commun. 69, 406–414 (1992).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From few to many: illumination cone models for face recognition under variable lighting and pose,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 243–260 (2001).

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1, 709–716 (2007).

Nature (1)

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. S. Gurjar, M. G. Müller, Q. Zhang, G. Zonios, E. Kline, T. McGilian, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[PubMed]

Opt. Eng. (1)

R. Graaff, J. G. Arnoudse, F. F. M. de Mul, and H. W. Jentink, “Similarity relations for anisotropic scattering in absorbing media,” Opt. Eng. 32, 244–252 (1993).

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 2, 857–865 (1994).

Phys. Rev. Lett. (1)

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
[PubMed]

Other (7)

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light propagation through biological tissue and other diffusive media: theory, solutions, and software (SPIE Press Book, 2009).
[PubMed]

J. H. Lambert, Photometria sive de mensura et gradibus luminus, colorum et umbrae (Eberhard Klett, 1760).

H. Gross, Handbook of Optical Systems; Volume 1: Fundamental of Technical Optics (Wiley-VCH, 2005).

D. C. Van der Hulst, Multiple Light Scattering (Academic Press, 1980).

P. Beckmann, A. Spizzichino, and A. Norwood, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, Inc., 1987).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

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Figures (5)

Fig. 1
Fig. 1

Monte Carlo simulations for total reflectance versus polar angle (R(θ)/cos(θ)) are shown which were calculated for the special set of optical and geometrical parameters to obtain a Lambert surface (black and red curves) and calculated by varying one of these parameters as indicated in the legend.

Fig. 2
Fig. 2

Reflectance for different distances to the incident source and for different times after the incident pulse calculated with the Monte Carlo method using μs = 1 mm−1. a) R(θ)/cos(θ) is shown for a δ(r)-source and following distance ranges: 0 – 1 mm (red curve), 2 – 3 mm (green curve), and 4 – 5 mm (brown curve). b) R(θ)/cos(θ) is shown for a δ(t)-source and following time intervals: 5 – 6 ps (blue curve), 15 – 16 ps (green curve), 25 – 26 ps (red curve).

Fig. 3
Fig. 3

Reflectance versus polar and azimuthal angles for different positions relative to the incident source. R(θ,ϕ) is shown at a) x = −0.3 ± 0.1 mm, y = 0 mm; c) x = −1.9 ± 0.1 mm, y = 0 mm; d) x = −4.9 ±0.1 mm, y = 0 mm; b) Scheme of single scattering.

Fig. 4
Fig. 4

Measurements (blue solid curves) and Monte Carlo simulations (red dashed curves) of the total reflectance from Intralipid solutions. R(θ)/cos(θ) versus polar angle is shown for three solutions with different amounts of ink and for perpendicular incident light at a wavelength of 640 nm. The optical coefficients of the solutions are indicated in the figure.

Fig. 5
Fig. 5

Angular resolved total reflectance from soft wood. a) Model used for the Monte Carlo simulations (left); Cross section (y,z-plane) of the model (right); b) R(θ,ϕ) obtained from the Monte Carlo simulations; c) R(θ,ϕ) measured on a (optically semi-infinite) softwood sample at a wavelength of 640 nm.

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