Abstract

As manifested in the similarity relation of diffuse light transport, it is difficult to assess single scattering characteristics from multiply scattered light. We take advantage of the limited validity of the diffusion approximation of light transport and demonstrate, experimentally and numerically, that even deep into the multiple scattering regime, time-resolved detection of transmitted light allows simultaneous assessment of both single scattering anisotropy and scattering mean free path, and therefore also macroscopic parameters like the diffusion constant and the transport mean free path. This is achieved via careful assessment of early light and matching against Monte Carlo simulations of radiative transfer.

© 2013 Optical Society of America

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  1. M. Mishchenko, L. Travis, and A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge Univ., 2006).
  2. A. J. Welch and M. J. C. Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Springer, 2010).
  3. A. Liemert and A. Kienle, Phys. Rev. A 83, 015804(2011).
    [CrossRef]
  4. E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
    [CrossRef]
  5. R. Graaff, J. Aarnoudse, F. Demul, and H. Jentink, Opt. Eng. 32, 244 (1993).
    [CrossRef]
  6. M. Patterson, B. Chance, and B. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef]
  7. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, Appl. Phys. Lett. 74, 874 (1999).
    [CrossRef]
  8. D. Grosenick, H. Wabnitz, H. Rinneberg, K. Moesta, and P. Schlag, Appl. Opt. 38, 2927 (1999).
    [CrossRef]
  9. F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
    [CrossRef]
  10. V. Ntziachristos and B. Chance, Med. Phys. 28, 1115 (2001).
    [CrossRef]
  11. T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
    [CrossRef]
  12. E. Alerstam and T. Svensson, Phys. Rev. E 85, 040301 (2012).
    [CrossRef]
  13. C. D’Andrea, E. A. Obraztsova, A. Farina, P. Taroni, G. Lanzani, and A. Pifferi, Appl. Opt. 51, 7858 (2012).
    [CrossRef]
  14. R. H. J. Kop, P. de Vries, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 79, 4369 (1997).
    [CrossRef]
  15. T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. R. Elaloufi, R. Carminati, and J.-J. Greffet, J. Opt. Soc. Am. A 21, 1430 (2004).
    [CrossRef]
  20. E. Alerstam, S. Andersson-Engels, and T. Svensson, J. Biomed. Opt. 13, 041304 (2008).
    [CrossRef]
  21. E. Alerstam, S. Andersson-Engels, and T. Svensson, Opt. Express 16, 10440 (2008).
    [CrossRef]
  22. A. Pifferi, P. Taroni, G. Valentini, and S. Andersson-Engels, Appl. Opt. 37, 2774 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. E. Alerstam, “Optical spectroscopy of turbid media: time-domain measurements and accelerated monte carlo modelling,” Ph.D. thesis, Lund University (2011).
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    [CrossRef]
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    [CrossRef]

2013

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, Nat. Photonics 7, 48 (2013).
[CrossRef]

2012

E. Alerstam and T. Svensson, Phys. Rev. E 85, 040301 (2012).
[CrossRef]

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
[CrossRef]

C. D’Andrea, E. A. Obraztsova, A. Farina, P. Taroni, G. Lanzani, and A. Pifferi, Appl. Opt. 51, 7858 (2012).
[CrossRef]

2011

A. Liemert and A. Kienle, Phys. Rev. A 83, 015804(2011).
[CrossRef]

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

2010

2008

E. Alerstam, S. Andersson-Engels, and T. Svensson, Opt. Express 16, 10440 (2008).
[CrossRef]

T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, J. Biomed. Opt. 13, 041304 (2008).
[CrossRef]

E. Alerstam, T. Svensson, and S. Andersson-Engels, J. Biomed. Opt. 13, 060054 (2008).
[CrossRef]

2006

2004

2001

V. Ntziachristos and B. Chance, Med. Phys. 28, 1115 (2001).
[CrossRef]

2000

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

1999

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, Appl. Phys. Lett. 74, 874 (1999).
[CrossRef]

D. Grosenick, H. Wabnitz, H. Rinneberg, K. Moesta, and P. Schlag, Appl. Opt. 38, 2927 (1999).
[CrossRef]

1998

1997

1996

A. Lagendijk and B. A. van Tiggelen, Phys. Rep. 270, 143 (1996).
[CrossRef]

A. Kienle and M. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef]

1993

R. Graaff, J. Aarnoudse, F. Demul, and H. Jentink, Opt. Eng. 32, 244 (1993).
[CrossRef]

1990

K. Yoo, F. Liu, and R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef]

K. M. Yoo and R. R. Alfano, Opt. Lett. 15, 320 (1990).
[CrossRef]

1989

Aarnoudse, J.

R. Graaff, J. Aarnoudse, F. Demul, and H. Jentink, Opt. Eng. 32, 244 (1993).
[CrossRef]

Aegerter, C. M.

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, Nat. Photonics 7, 48 (2013).
[CrossRef]

Alerstam, E.

E. Alerstam and T. Svensson, Phys. Rev. E 85, 040301 (2012).
[CrossRef]

E. Alerstam, T. Svensson, and S. Andersson-Engels, J. Biomed. Opt. 13, 060054 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, J. Biomed. Opt. 13, 041304 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, Opt. Express 16, 10440 (2008).
[CrossRef]

T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
[CrossRef]

E. Alerstam, “Optical spectroscopy of turbid media: time-domain measurements and accelerated monte carlo modelling,” Ph.D. thesis, Lund University (2011).

Alfano, R.

K. Yoo, F. Liu, and R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef]

Alfano, R. R.

Andersson-Engels, S.

E. Alerstam, T. Svensson, and S. Andersson-Engels, J. Biomed. Opt. 13, 060054 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, Opt. Express 16, 10440 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, J. Biomed. Opt. 13, 041304 (2008).
[CrossRef]

T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
[CrossRef]

A. Pifferi, P. Taroni, G. Valentini, and S. Andersson-Engels, Appl. Opt. 37, 2774 (1998).
[CrossRef]

Barthelemy, P.

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
[CrossRef]

Bouchard, J.-P.

Bührer, W.

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, Nat. Photonics 7, 48 (2013).
[CrossRef]

Carminati, R.

Chance, B.

V. Ntziachristos and B. Chance, Med. Phys. 28, 1115 (2001).
[CrossRef]

M. Patterson, B. Chance, and B. Wilson, Appl. Opt. 28, 2331 (1989).
[CrossRef]

Contini, D.

Cubeddu, R.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, Appl. Phys. Lett. 74, 874 (1999).
[CrossRef]

D’Andrea, C.

de Vries, P.

R. H. J. Kop, P. de Vries, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 79, 4369 (1997).
[CrossRef]

Delpy, D.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Demul, F.

R. Graaff, J. Aarnoudse, F. Demul, and H. Jentink, Opt. Eng. 32, 244 (1993).
[CrossRef]

Durian, D. J.

Einarsdóttír, M.

T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
[CrossRef]

Elaloufi, R.

Farina, A.

Fortin, M.

Fry, M.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Gemert, M. J. C.

A. J. Welch and M. J. C. Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Springer, 2010).

Graaff, R.

R. Graaff, J. Aarnoudse, F. Demul, and H. Jentink, Opt. Eng. 32, 244 (1993).
[CrossRef]

Greffet, J.-J.

Greffet, L. J.

Grosenick, D.

Guo, L.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Hanlon, E. B.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Hebden, J.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Hillman, E.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Itzkan, I.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Jedidi, R.

Jentink, H.

R. Graaff, J. Aarnoudse, F. Demul, and H. Jentink, Opt. Eng. 32, 244 (1993).
[CrossRef]

Johnson, P. M.

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
[CrossRef]

Kienle, A.

A. Liemert and A. Kienle, Phys. Rev. A 83, 015804(2011).
[CrossRef]

A. Kienle and M. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef]

Kop, R. H. J.

R. H. J. Kop, P. de Vries, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 79, 4369 (1997).
[CrossRef]

Lacis, A.

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

Lagendijk, A.

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
[CrossRef]

R. H. J. Kop, P. de Vries, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 79, 4369 (1997).
[CrossRef]

A. Lagendijk and B. A. van Tiggelen, Phys. Rep. 270, 143 (1996).
[CrossRef]

Lanzani, G.

Liemert, A.

A. Liemert and A. Kienle, Phys. Rev. A 83, 015804(2011).
[CrossRef]

Liu, F.

K. Yoo, F. Liu, and R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef]

Maret, G.

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, Nat. Photonics 7, 48 (2013).
[CrossRef]

Martelli, F.

Mermut, O.

Mishchenko, M.

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

Moesta, K.

Noiseux, I.

Ntziachristos, V.

V. Ntziachristos and B. Chance, Med. Phys. 28, 1115 (2001).
[CrossRef]

Obraztsova, E. A.

Patterson, M.

A. Kienle and M. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef]

M. Patterson, B. Chance, and B. Wilson, Appl. Opt. 28, 2331 (1989).
[CrossRef]

Perelman, L. T.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Pierrat, R.

Pifferi, A.

Qiu, L.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Rinneberg, H.

Rudnick, J.

Schlag, P.

Schmidt, F.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Sperling, T.

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, Nat. Photonics 7, 48 (2013).
[CrossRef]

Sprik, R.

R. H. J. Kop, P. de Vries, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 79, 4369 (1997).
[CrossRef]

Svanberg, K.

T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
[CrossRef]

Svensson, T.

E. Alerstam and T. Svensson, Phys. Rev. E 85, 040301 (2012).
[CrossRef]

E. Alerstam, T. Svensson, and S. Andersson-Engels, J. Biomed. Opt. 13, 060054 (2008).
[CrossRef]

T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, J. Biomed. Opt. 13, 041304 (2008).
[CrossRef]

E. Alerstam, S. Andersson-Engels, and T. Svensson, Opt. Express 16, 10440 (2008).
[CrossRef]

Taroni, P.

Torricelli, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, Appl. Phys. Lett. 74, 874 (1999).
[CrossRef]

Travis, L.

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

Turzhitsky, V.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Valentini, G.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, Appl. Phys. Lett. 74, 874 (1999).
[CrossRef]

A. Pifferi, P. Taroni, G. Valentini, and S. Andersson-Engels, Appl. Opt. 37, 2774 (1998).
[CrossRef]

van der Beek, T.

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
[CrossRef]

van Tiggelen, B. A.

A. Lagendijk and B. A. van Tiggelen, Phys. Rep. 270, 143 (1996).
[CrossRef]

Veilleux, I.

Vitkin, E.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Wabnitz, H.

Welch, A. J.

A. J. Welch and M. J. C. Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Springer, 2010).

Wiersma, D. S.

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
[CrossRef]

Wilson, B.

Yoo, K.

K. Yoo, F. Liu, and R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef]

Yoo, K. M.

Zaccanti, G.

Appl. Opt.

Appl. Phys. Lett.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, Appl. Phys. Lett. 74, 874 (1999).
[CrossRef]

J. Biomed. Opt.

E. Alerstam, S. Andersson-Engels, and T. Svensson, J. Biomed. Opt. 13, 041304 (2008).
[CrossRef]

E. Alerstam, T. Svensson, and S. Andersson-Engels, J. Biomed. Opt. 13, 060054 (2008).
[CrossRef]

J. Biophoton.

T. Svensson, E. Alerstam, M. Einarsdóttír, K. Svanberg, and S. Andersson-Engels, J. Biophoton. 1, 200 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Med. Phys.

V. Ntziachristos and B. Chance, Med. Phys. 28, 1115 (2001).
[CrossRef]

Nat. Commun.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. B. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587(2011).
[CrossRef]

Nat. Photonics

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, Nat. Photonics 7, 48 (2013).
[CrossRef]

Opt. Eng.

R. Graaff, J. Aarnoudse, F. Demul, and H. Jentink, Opt. Eng. 32, 244 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

A. Kienle and M. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef]

Phys. Rep.

A. Lagendijk and B. A. van Tiggelen, Phys. Rep. 270, 143 (1996).
[CrossRef]

Phys. Rev. A

A. Liemert and A. Kienle, Phys. Rev. A 83, 015804(2011).
[CrossRef]

Phys. Rev. B

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, Phys. Rev. B 85, 115401 (2012).
[CrossRef]

Phys. Rev. E

E. Alerstam and T. Svensson, Phys. Rev. E 85, 040301 (2012).
[CrossRef]

Phys. Rev. Lett.

R. H. J. Kop, P. de Vries, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 79, 4369 (1997).
[CrossRef]

K. Yoo, F. Liu, and R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef]

Rev. Sci. Instrum.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Other

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

A. J. Welch and M. J. C. Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Springer, 2010).

E. Alerstam, “Optical spectroscopy of turbid media: time-domain measurements and accelerated monte carlo modelling,” Ph.D. thesis, Lund University (2011).

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Figures (3)

Fig. 1.
Fig. 1.

Simulated time-resolved total transmission for a turbid slab with L/t=8 for g=0.0,0.1,,0.9 (ni=1.5, ne=1). Clearly, even deep into the multiple scattering regime, early dynamics can exhibit a significant dependence on g. This similarity breaking is clear evidence of diffusion breakdown. That a larger g (more forward scattering) reduce that amount of early light is related to the unscattered intensity decays with depth z as exp(z/s), and that having g approach one while keeping t fixed is accompanied by a reduction of s.

Fig. 2.
Fig. 2.

Ultrashort pulses at λ=810nm from a titanium-sapphire laser are injected in a small spot on the sample, and the central part (30 µm spot, monitored by CCD) of the transmission is collected and resolved in time using an ultrafast gating technique. Femtosecond time-resolution is achieved by overlapping the transmitted pulse with a femtosecond reference pulse (λ=1540nm) on a BBO crystal and monitoring sum-frequency generation at λ=532nm (a variable delay line gives access to the full TOF distribution).

Fig. 3.
Fig. 3.

Evaluation of experimental data based on MC. The left graph shows simulations for t=39μm and different g (0.1 to 0.9) and compares it with the experimental data. Experimental data is normalized to overlap with MC at late times where differences due to g are negligible. The right graph shows obtained fit merits (normalized to best fit) for the three best-matching g, revealing that the best least-squares fit is obtained for g=0.6 and t=39μm. Fitted t agree well with measurements on thicker slabs of the same material, and fitted g is in good agreement with Mie calculations.

Equations (1)

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D=13×s1g×vE,

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