Abstract

In this work, we report experiments and a theoretical scheme of photon transport in the frequency domain of rigid turbid media. We have employed spectral multi-speckle intensity correlations to estimate optical properties as the transport mean free path and the absorption length of turbid systems. We propose a scheme based on the photon diffusion model using an effective path-length distribution in the backscattering configuration and take explicitly into account the particles scattering anisotropy parameter ${g}$. By studying rigid Teflon slabs and polymer matrices doped with polystyrene particles of different degrees of scattering anisotropy, we find that the proposed model adequately describes our experimental results. Our hypothesis for the diffuse transport of backscattered photons in the weak multiple scattering regime is further validated using a numerical simulation scheme of speckle dynamics, based on the Copula method.

© 2020 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Time-resolved study of optical properties and microscopic dynamics during the drying of TiO2 films by spectral diffusing wave spectroscopy

Angel A. Duran-Ledezma, Damián Jacinto-Méndez, and Luis F. Rojas-Ochoa
Appl. Opt. 57(2) 208-216 (2018)

Depolarization of backscattered linearly polarized light

Luis Fernando Rojas-Ochoa, David Lacoste, Ralf Lenke, Peter Schurtenberger, and Frank Scheffold
J. Opt. Soc. Am. A 21(9) 1799-1804 (2004)

References

  • View by:
  • |
  • |
  • |

  1. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
    [Crossref]
  2. R. Lenke and G. Maret, Multiple Scattering of Light: Coherent Backscattering and Transmission, W. Brown, ed. (Gordon & Breach, 2000), pp. 1–72.
  3. L. Yanga, J. Sunb, and A. Wu, “Measurements of optical parameters of the fat emulsion,” Adv. Mater. Res. 510, 822–826 (2012).
    [Crossref]
  4. B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
    [Crossref]
  5. S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
    [Crossref]
  6. S. Panigrahi, J. Fade, H. Ramachandran, and M. Alouini, “Theoretical optimal modulation frequencies for scattering parameter estimation and ballistic photon filtering in diffusing media,” Opt. Express 24, 16066–16083 (2016).
    [Crossref]
  7. A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, 1990), p. 207.
  8. A. Mikhailovskaya, J. Fade, and J. Crassous, “Speckle decorrelation with wavelength shift as a simple way to image transport mean free path,” Eur. Phys. J. Appl. Phys. 85, 30701 (2019).
    [Crossref]
  9. L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
    [Crossref]
  10. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev Lett. 60, 1134–1137 (1988).
    [Crossref]
  11. J. W. Goodman, Statistical Optics (Wiley, 1985).
  12. A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331 (1990).
    [Crossref]
  13. D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A. 25, 231–237 (2008).
    [Crossref]
  14. A. A. Duran-Ledezma, D. Jacinto-Méndez, and L. F. Rojas-Ochoa, “Time-resolved study of optical properties and microscopic dynamics during the drying of TiO2 films by spectral diffusing wave spectroscopy,” Appl. Opt. 57, 208–216 (2018).
    [Crossref]
  15. F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B. 40, 2383–2406 (1989).
    [Crossref]
  16. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [Crossref]
  17. E. Kogan and M. Kaveh, “Effect of absorption on long-range correlations in random media,” Phys. Rev B. 45, 1049–1051 (1992).
    [Crossref]
  18. J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev B. 45, 658–666 (1992).
    [Crossref]
  19. L. F. Rojas, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
    [Crossref]
  20. S. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev A. 44, 3948–3959 (1991).
    [Crossref]
  21. R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
    [Crossref]
  22. D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. France 51, 2101–2127 (1990).
    [Crossref]
  23. M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
    [Crossref]
  24. M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response from a random medium from speckle intensity frequency correlations,” J. Opt. Soc. Am. A 20, 2057–2070 (2003).
    [Crossref]
  25. C. Haro, G. J. Ojeda, and L. F. Rojas, “Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media,” J. Chem. Phys. 134, 244902 (2011).
    [Crossref]
  26. C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
    [Crossref]
  27. A. C. Völker, P. Zakharov, B. Weber, F. Buck, and F. Scheffold, “Quantitative modeling of laser speckle imaging,” Opt. Express 13, 9782–9787 (2005).
    [Crossref]
  28. L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
    [Crossref]
  29. A. Kienle, M. S. Patterson, L. Ott, and R. Steiner, “Determination of the scattering coefficient and the anisotropy factor from laser Doppler spectra of liquids including blood,” Appl. Opt. 35, 3404–3412 (1996).
    [Crossref]

2019 (1)

A. Mikhailovskaya, J. Fade, and J. Crassous, “Speckle decorrelation with wavelength shift as a simple way to image transport mean free path,” Eur. Phys. J. Appl. Phys. 85, 30701 (2019).
[Crossref]

2018 (1)

2016 (2)

S. Panigrahi, J. Fade, H. Ramachandran, and M. Alouini, “Theoretical optimal modulation frequencies for scattering parameter estimation and ballistic photon filtering in diffusing media,” Opt. Express 24, 16066–16083 (2016).
[Crossref]

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

2012 (1)

L. Yanga, J. Sunb, and A. Wu, “Measurements of optical parameters of the fat emulsion,” Adv. Mater. Res. 510, 822–826 (2012).
[Crossref]

2011 (2)

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

C. Haro, G. J. Ojeda, and L. F. Rojas, “Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media,” J. Chem. Phys. 134, 244902 (2011).
[Crossref]

2008 (2)

D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A. 25, 231–237 (2008).
[Crossref]

R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
[Crossref]

2005 (2)

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[Crossref]

A. C. Völker, P. Zakharov, B. Weber, F. Buck, and F. Scheffold, “Quantitative modeling of laser speckle imaging,” Opt. Express 13, 9782–9787 (2005).
[Crossref]

2004 (1)

L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
[Crossref]

2003 (1)

2002 (2)

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
[Crossref]

L. F. Rojas, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[Crossref]

2000 (1)

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

1996 (1)

1994 (1)

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref]

1992 (2)

E. Kogan and M. Kaveh, “Effect of absorption on long-range correlations in random media,” Phys. Rev B. 45, 1049–1051 (1992).
[Crossref]

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev B. 45, 658–666 (1992).
[Crossref]

1991 (1)

S. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev A. 44, 3948–3959 (1991).
[Crossref]

1990 (2)

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. France 51, 2101–2127 (1990).
[Crossref]

A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331 (1990).
[Crossref]

1989 (1)

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B. 40, 2383–2406 (1989).
[Crossref]

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev Lett. 60, 1134–1137 (1988).
[Crossref]

1941 (1)

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

Alouini, M.

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[Crossref]

Ben Braham, N.

R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
[Crossref]

Bina, M.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

Buck, F.

Carminati, R.

R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
[Crossref]

Cerchiari, G.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev Lett. 60, 1134–1137 (1988).
[Crossref]

Crassous, J.

A. Mikhailovskaya, J. Fade, and J. Crassous, “Speckle decorrelation with wavelength shift as a simple way to image transport mean free path,” Eur. Phys. J. Appl. Phys. 85, 30701 (2019).
[Crossref]

de Boer, J. F.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev B. 45, 658–666 (1992).
[Crossref]

Drake, J. M.

A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331 (1990).
[Crossref]

Duncan, D. D.

D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A. 25, 231–237 (2008).
[Crossref]

Duran-Ledezma, A. A.

Escobedo, M. A.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

Essenpreis, M.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

Fade, J.

A. Mikhailovskaya, J. Fade, and J. Crassous, “Speckle decorrelation with wavelength shift as a simple way to image transport mean free path,” Eur. Phys. J. Appl. Phys. 85, 30701 (2019).
[Crossref]

S. Panigrahi, J. Fade, H. Ramachandran, and M. Alouini, “Theoretical optimal modulation frequencies for scattering parameter estimation and ballistic photon filtering in diffusing media,” Opt. Express 24, 16066–16083 (2016).
[Crossref]

Farrell, T. J.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

Ferri, F.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

Genack, A. Z.

A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331 (1990).
[Crossref]

A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, 1990), p. 207.

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[Crossref]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

Greenstein, J. L.

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

Haro, C.

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

C. Haro, G. J. Ojeda, and L. F. Rojas, “Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media,” J. Chem. Phys. 134, 244902 (2011).
[Crossref]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[Crossref]

Henyey, L. G.

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

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. France 51, 2101–2127 (1990).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev Lett. 60, 1134–1137 (1988).
[Crossref]

Hermann, M.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

Jacinto-Méndez, D.

John, S.

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B. 40, 2383–2406 (1989).
[Crossref]

Kaveh, M.

E. Kogan and M. Kaveh, “Effect of absorption on long-range correlations in random media,” Phys. Rev B. 45, 1049–1051 (1992).
[Crossref]

Kienle, A.

Kirkpatrick, S. J.

D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A. 25, 231–237 (2008).
[Crossref]

Kogan, E.

E. Kogan and M. Kaveh, “Effect of absorption on long-range correlations in random media,” Phys. Rev B. 45, 1049–1051 (1992).
[Crossref]

Kramer, U.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

Lacoste, D.

L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
[Crossref]

Lagendijk, A.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev B. 45, 658–666 (1992).
[Crossref]

Lenke, R.

L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
[Crossref]

R. Lenke and G. Maret, Multiple Scattering of Light: Coherent Backscattering and Transmission, W. Brown, ed. (Gordon & Breach, 2000), pp. 1–72.

Lovallo, M.

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

MacKintosh, F. C.

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B. 40, 2383–2406 (1989).
[Crossref]

Maret, G.

R. Lenke and G. Maret, Multiple Scattering of Light: Coherent Backscattering and Transmission, W. Brown, ed. (Gordon & Breach, 2000), pp. 1–72.

Mikhailovskaya, A.

A. Mikhailovskaya, J. Fade, and J. Crassous, “Speckle decorrelation with wavelength shift as a simple way to image transport mean free path,” Eur. Phys. J. Appl. Phys. 85, 30701 (2019).
[Crossref]

Moreno, L. R.

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

Nickell, S.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

Ojeda, G. J.

C. Haro, G. J. Ojeda, and L. F. Rojas, “Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media,” J. Chem. Phys. 134, 244902 (2011).
[Crossref]

Ott, L.

Panigrahi, S.

Patterson, M. S.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

A. Kienle, M. S. Patterson, L. Ott, and R. Steiner, “Determination of the scattering coefficient and the anisotropy factor from laser Doppler spectra of liquids including blood,” Appl. Opt. 35, 3404–3412 (1996).
[Crossref]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref]

Pierrat, R.

R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
[Crossref]

Pine, D. J.

S. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev A. 44, 3948–3959 (1991).
[Crossref]

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. France 51, 2101–2127 (1990).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev Lett. 60, 1134–1137 (1988).
[Crossref]

Pogue, B. W.

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref]

Ramachandran, H.

Ramirez, A.

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

Rojas, L. F.

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

C. Haro, G. J. Ojeda, and L. F. Rojas, “Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media,” J. Chem. Phys. 134, 244902 (2011).
[Crossref]

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
[Crossref]

L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
[Crossref]

L. F. Rojas, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[Crossref]

Rojas-Ochoa, L. F.

Romer, S.

L. F. Rojas, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[Crossref]

Scheffold, F.

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
[Crossref]

A. C. Völker, P. Zakharov, B. Weber, F. Buck, and F. Scheffold, “Quantitative modeling of laser speckle imaging,” Opt. Express 13, 9782–9787 (2005).
[Crossref]

L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
[Crossref]

L. F. Rojas, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[Crossref]

Schurtenberger, P.

L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
[Crossref]

L. F. Rojas, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[Crossref]

Steiner, R.

Sunb, J.

L. Yanga, J. Sunb, and A. Wu, “Measurements of optical parameters of the fat emulsion,” Adv. Mater. Res. 510, 822–826 (2012).
[Crossref]

Telesca, L.

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

van Albada, M. P.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev B. 45, 658–666 (1992).
[Crossref]

Völker, A. C.

Webb, K. J.

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response from a random medium from speckle intensity frequency correlations,” J. Opt. Soc. Am. A 20, 2057–2070 (2003).
[Crossref]

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
[Crossref]

Weber, B.

Webster, M. A.

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response from a random medium from speckle intensity frequency correlations,” J. Opt. Soc. Am. A 20, 2057–2070 (2003).
[Crossref]

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
[Crossref]

Weiner, A. M.

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response from a random medium from speckle intensity frequency correlations,” J. Opt. Soc. Am. A 20, 2057–2070 (2003).
[Crossref]

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
[Crossref]

Weitz, D. A.

S. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev A. 44, 3948–3959 (1991).
[Crossref]

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. France 51, 2101–2127 (1990).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev Lett. 60, 1134–1137 (1988).
[Crossref]

Wu, A.

L. Yanga, J. Sunb, and A. Wu, “Measurements of optical parameters of the fat emulsion,” Adv. Mater. Res. 510, 822–826 (2012).
[Crossref]

Yanga, L.

L. Yanga, J. Sunb, and A. Wu, “Measurements of optical parameters of the fat emulsion,” Adv. Mater. Res. 510, 822–826 (2012).
[Crossref]

Zakharov, P.

Zhu, J. X.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. France 51, 2101–2127 (1990).
[Crossref]

Zhu, S. X.

S. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev A. 44, 3948–3959 (1991).
[Crossref]

Zuccolotto, A. B.

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

Adv. Mater. Res. (1)

L. Yanga, J. Sunb, and A. Wu, “Measurements of optical parameters of the fat emulsion,” Adv. Mater. Res. 510, 822–826 (2012).
[Crossref]

Appl. Opt. (2)

Astrophys. J. (1)

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

Eur. Phys. J. Appl. Phys. (1)

A. Mikhailovskaya, J. Fade, and J. Crassous, “Speckle decorrelation with wavelength shift as a simple way to image transport mean free path,” Eur. Phys. J. Appl. Phys. 85, 30701 (2019).
[Crossref]

Eur. Phys. J. Spec. Top. (1)

L. F. Rojas, M. Bina, G. Cerchiari, M. A. Escobedo, F. Ferri, and F. Scheffold, “Photon path length distribution in random media from spectral speckle intensity correlations,” Eur. Phys. J. Spec. Top. 199, 167–180 (2011).
[Crossref]

Europhys. Lett. (2)

C. Haro, M. Lovallo, L. R. Moreno, A. Ramirez, L. F. Rojas, A. B. Zuccolotto, and L. Telesca, “Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel,” Europhys. Lett. 115, 47004 (2016).
[Crossref]

A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331 (1990).
[Crossref]

J. Chem. Phys. (1)

C. Haro, G. J. Ojeda, and L. F. Rojas, “Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media,” J. Chem. Phys. 134, 244902 (2011).
[Crossref]

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

J. Opt. Soc. Am. A. (2)

D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A. 25, 231–237 (2008).
[Crossref]

L. F. Rojas, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A. 21, 1799–1804 (2004).
[Crossref]

J. Phys. France (1)

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. France 51, 2101–2127 (1990).
[Crossref]

Opt. Commun. (1)

R. Pierrat, N. Ben Braham, L. F. Rojas, R. Carminati, and F. Scheffold, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18–22 (2008).
[Crossref]

Opt. Express (2)

Phys. Med. Biol. (3)

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref]

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. 45, 2873–2886 (2000).
[Crossref]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[Crossref]

Phys. Rev A. (1)

S. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev A. 44, 3948–3959 (1991).
[Crossref]

Phys. Rev B. (2)

E. Kogan and M. Kaveh, “Effect of absorption on long-range correlations in random media,” Phys. Rev B. 45, 1049–1051 (1992).
[Crossref]

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev B. 45, 658–666 (1992).
[Crossref]

Phys. Rev Lett. (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev Lett. 60, 1134–1137 (1988).
[Crossref]

Phys. Rev. B. (1)

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B. 40, 2383–2406 (1989).
[Crossref]

Phys. Rev. E (1)

L. F. Rojas, S. Romer, F. Scheffold, and P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[Crossref]

Phys. Rev. Lett. (1)

M. A. Webster, K. J. Webb, and A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
[Crossref]

Other (3)

A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, 1990), p. 207.

J. W. Goodman, Statistical Optics (Wiley, 1985).

R. Lenke and G. Maret, Multiple Scattering of Light: Coherent Backscattering and Transmission, W. Brown, ed. (Gordon & Breach, 2000), pp. 1–72.

Cited By

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

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1. Experimental setup for the SSIC measurements in backscattering geometry. The laser light ($\lambda \sim785\;{\rm nm}$) is coupled into an optical fiber (OF) and passed through a collimator (CL) before being directed onto one sample face (S). A neutral density attenuator (ND) controls the output intensity from the laser. A line of the laser is separated and directed to the Fabry–Perot interferometer (FP). A polarizer (P) is in front of the CCD camera. The speckle pattern is collected by a CCD camera, and the resulting frames are stored in a computer. An arbitrary function generator (AFG) allows to tune the full frequency range in the laser, $\sim1200\;{\rm GHz} $ via the laser control box (CB).
Fig. 2.
Fig. 2. Spectral intensity correlation function ${g_{{I_{{\rm Ref}N}}}}({\Delta \nu})$ measured in the backscattering geometry for a Teflon slab of thickness $L = 5\;{\rm cm} $. Circles are experiments, and the continuous line indicates the best fit using Eqs. (11)–(13), where $\gamma = 1.76$ and $n = 24$. The blue crosses correspond to the results of numerical simulations of SICF.
Fig. 3.
Fig. 3. Intensity correlation functions of polymer matrices doped with polystyrene particles. Symbols correspond to experiments and continuous lines to the theoretical calculations. The cross symbols are the results from the numerical simulations described in the text. (a) System doped with particles of 88 nm diameter, whose anisotropy factor is $g = 0.02$, where we estimate a value of $\gamma = 4.67$. (b) System doped with particles of 200 nm diameter and an anisotropy factor $g = 0.55$, where we estimate a value of $\gamma = 4.80$. (c) System doped with particles of 752 nm diameter and an anisotropy factor $g = 0.82$, where a value of $\gamma = 4.21$ is obtained.

Tables (2)

Tables Icon

Table 1. Preparation Parameters of the Polymer Matrices Used

Tables Icon

Table 2. Optical Properties of the Polymer Matrices Used, as Obtained with the SSIC Technique

Equations (22)

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

P R ( s ) = c π D l ( 4 s 3 / 2 ) [ ( γ 1 ) exp ( 3 4 s ( γ 1 ) 2 ) + ( γ + 1 ) exp ( 3 4 s ( γ + 1 ) 2 ) ] ,
P R C ( s ) = P R ( s ) ( 1 exp ( s n ) ) ,
f ( g ) = g ( 2 g ) 2 , 1 g 1 ,
P R N ( s , g ) = 1 N ( g ) P R ( s ) [ 1 f ( g ) exp ( s n ) ] exp ( s l a ) ,
N ( g ) = exp ( γ 3 l a ) cosh ( 3 l a ) f ( g ) exp ( γ 3 l a ( 1 + l a n ) ) × cosh ( 3 l a ( 1 + l a n ) ) .
G E ( Δ ν , g ) = E ( ν ) E ( ν + Δ ν ) = I ( ν ) R e ( 0 P R N ( s , g ) exp ( i 2 π Δ ν s / c ) d s ) ,
g I ( Δ ν , g ) = | 0 P R N ( s , g ) exp ( i 2 π Δ ν s / c ) d s | 2 .
g E ( Δ ν , g = 0 ) = 1 N R e { exp ( γ q ) cosh ( q ) } ,
q = c l a D l + i 2 π Δ ν D l .
g I R e f N ( Δ ν ) = 1 2 N 2 exp ( 2 γ α ) [ cosh ( 2 α ) + cos ( 2 β ) ] ,
α = c 2 l a D l 1 + ( 2 π Δ ν l a c ) 2 + 1 ,
β = c 2 l a D l 1 + ( 2 π Δ ν l a c ) 2 1 .
g E ( Δ ν , g ) = R e { [ 1 N exp ( ( α + i β ) γ ) cosh ( ( α + i β ) ) 1 N f ( g ) exp ( ( α + i β ) γ ) cosh ( ( α + i β ) ) ] } ,
α = c 2 l a D l ( 1 + l a n ) 2 + ( 2 π Δ ν l a c ) 2 + ( 1 + l a n ) ,
β = c 2 l a D l ( 1 + l a n ) + ( 2 π Δ ν l a c ) 2 ( 1 + l a n ) .
g I R e f N ( Δ ν , g ) = I ~ ( ν ) I ~ ( ν + Δ ν ) = | g E R e f N ( Δ ν , g ) | 2 ,
ρ = exp { σ Δ Φ 2 } ,
g I exp ( Δ ν ) = I ~ ( ν ) I ~ ( ν + Δ ν ) exp = 1 N i j = 0 N i 1 I ~ j I ~ j + 1 ,
P ( g , θ ) = 1 4 π 1 g 2 ( 1 + g 2 2 g cos θ ) 3 / 2 .
P ( g , θ π ) ( 1 4 π ) 1 g 2 ( 1 + g 2 + 2 g ) 3 / 2 = ( 1 4 π ) 1 g 2 [ ( 1 + g ) 2 ] 3 / 2 = ( 1 4 π ) ( 1 g ) ( 1 + g ) ( 1 + g ) 3 = ( 1 4 π ) ( 1 g ) ( 1 + g ) 2 .
P ( 1 g , π ) = ( 1 4 π ) g ( 2 g ) 2 .
f ( g ) = 4 π P ( 1 g , θ π ) = g ( 2 g ) 2 .