Abstract

Stochastic interference of partially coherent light multiple scattered by a random medium is considered. The relationship between the second- and third-order moments of intensity fluctuations in random interference patterns, the coherence function of probe radiation, and the probability density of path differences for the interfering partial waves in the medium are established. The obtained relationships were verified using the statistical analysis of spectrally selected fluorescence radiation emitted by the laser-pumped dye-doped random medium. Rhodamine 6G water solution was applied as the doping agent for the ensembles of densely packed silica grains which were pumped by the CW radiation (532 nm) from the diode-pumped solid state laser. Experimentally observed abrupt decay of the second- and third-order moments of fluorescence intensity fluctuations for the wavelengths ranging from 620 nm to 680 nm is interpreted in terms of amplification of spontaneous emission at large dye concentrations. This paper discusses the new optical probe of random media defined as “the reference-free path length interferometry with the intensity moments analysis”.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  29. D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Speckle spectroscopy of fluorescent randomly inhomogeneous media,” Quantum Electron. 46(11), 1047–1054 (2016).
    [Crossref]
  30. D. A. Zimnyakov, V. V. Tuchin, and A. G. Yodh, “Characteristic scales of optical field depolarization and decorrelation for multiple scattering media and tissues,” J. Biomed. Opt. 4(1), 157–163 (1999).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  33. D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
    [Crossref]

2017 (1)

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Stochastic interference of fluorescence radiation in random media with large inhomogeneities,” Opt. Commun. 387, 121–127 (2017).
[Crossref]

2016 (2)

2014 (1)

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

2013 (1)

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2007 (2)

2006 (3)

2004 (2)

D. A. Zimnyakov, J.-T. Oh, Y. P. Sinichkin, V. A. Trifonov, and E. V. Gurianov, “Polarization-sensitive speckle spectroscopy of random media beyond the diffusion limit,” J. Opt. Soc. Am. A 21(1), 59–70 (2004).
[Crossref]

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

2003 (1)

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[Crossref] [PubMed]

2002 (1)

V. Viasnoff, F. Lequeux, and D. J. Pine, “Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics,” Rev. Sci. Instrum. 73(6), 2336–2344 (2002).
[Crossref]

1999 (2)

D. A. Zimnyakov, V. V. Tuchin, and A. G. Yodh, “Characteristic scales of optical field depolarization and decorrelation for multiple scattering media and tissues,” J. Biomed. Opt. 4(1), 157–163 (1999).
[Crossref] [PubMed]

M. C. W. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[Crossref]

1997 (2)

N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275(5308), 1920–1922 (1997).
[Crossref] [PubMed]

C. A. Thompson, K. J. Webb, and A. M. Weiner, “Imaging in scattering media by use of laser speckle,” J. Opt. Soc. Am. A 14(9), 2269–2277 (1997).
[Crossref]

1995 (3)

D. S. Wiersma, M. P. V. Albada, A. Lagendijk, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74(21), 4193–4196 (1995).
[Crossref] [PubMed]

T. M. Nieuwenhuizen and M. C. W. van Rossum, “Intensity distributions of waves transmitted through a multiple scattering medium,” Phys. Rev. Lett. 74(14), 2674–2677 (1995).
[Crossref] [PubMed]

E. Kogan and M. Kaveh, “Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium,” Phys. Rev. B Condens. Matter 52(6), R3813–R3815 (1995).
[Crossref] [PubMed]

1991 (1)

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B Condens. Matter 43(7), 5934–5938 (1991).
[Crossref] [PubMed]

1989 (1)

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B Condens. Matter 40(4), 2383–2406 (1989).
[Crossref] [PubMed]

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[Crossref] [PubMed]

1987 (1)

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of brownian motion of scatterers,” Zeitschrift für Physik B 65(4), 409–413 (1987).
[Crossref]

1986 (1)

O. V. Angelsky and P. P. Maksimyak, “The investigation of the transformation phenomenon of the longitudinal correlation function of the field propagating in the light scattering medium,” Opt. Spectrosc. 60(2), 331–336 (1986).

1985 (1)

M. P. V. Albada, A. Lagendijk, and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref] [PubMed]

1982 (1)

Albada, M. P. V.

D. S. Wiersma, M. P. V. Albada, A. Lagendijk, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74(21), 4193–4196 (1995).
[Crossref] [PubMed]

M. P. V. Albada, A. Lagendijk, and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref] [PubMed]

Angelsky, O. V.

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Optical correlation diagnostics of rough surfaces with large surface inhomogeneities,” Opt. Express 14(16), 7299–7311 (2006).
[Crossref] [PubMed]

O. V. Angelsky and P. P. Maksimyak, “The investigation of the transformation phenomenon of the longitudinal correlation function of the field propagating in the light scattering medium,” Opt. Spectrosc. 60(2), 331–336 (1986).

Asharchuk, I. A.

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Stochastic interference of fluorescence radiation in random media with large inhomogeneities,” Opt. Commun. 387, 121–127 (2017).
[Crossref]

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Speckle spectroscopy of fluorescent randomly inhomogeneous media,” Quantum Electron. 46(11), 1047–1054 (2016).
[Crossref]

Baker, W. B.

Bissig, H.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Bret, B. P. J.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[Crossref] [PubMed]

Brun, A.

Brunel, L.

Cardinaux, F.

P. Zakharov, F. Cardinaux, and F. Scheffold, “Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(1), 011413 (2006).
[Crossref] [PubMed]

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[Crossref] [PubMed]

Chekmasov, S. P.

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

Cheng, R.

Cipelletti, L.

L. Brunel, A. Brun, P. Snabre, and L. Cipelletti, “Adaptive Speckle Imaging Interferometry: a new technique for the analysis of microstructure dynamics, drying processes and coating formation,” Opt. Express 15(23), 15250–15259 (2007).
[Crossref] [PubMed]

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Detre, J. A.

Dietsche, G.

Dong, L.

Durduran, T.

Durian, D. J.

N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275(5308), 1920–1922 (1997).
[Crossref] [PubMed]

Fisher, D. S.

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B Condens. Matter 43(7), 5934–5938 (1991).
[Crossref] [PubMed]

Gannon, K.

Gisler, T.

Gurianov, E. V.

Hanson, S. G.

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[Crossref] [PubMed]

Hwang, J. W.

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

Imhof, A.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[Crossref] [PubMed]

Irwin, D.

Isaeva, E. A.

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

Ishimaru, A.

Jaillon, F.

John, S.

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B Condens. Matter 40(4), 2383–2406 (1989).
[Crossref] [PubMed]

Johnson, P. M.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[Crossref] [PubMed]

Jung, H. W.

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

Kaveh, M.

E. Kogan and M. Kaveh, “Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium,” Phys. Rev. B Condens. Matter 52(6), R3813–R3815 (1995).
[Crossref] [PubMed]

Kavuri, V.

Kim, S. H.

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

Ko, T.

Kogan, E.

E. Kogan and M. Kaveh, “Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium,” Phys. Rev. B Condens. Matter 52(6), R3813–R3815 (1995).
[Crossref] [PubMed]

Kuga, Y.

Lagendijk, A.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[Crossref] [PubMed]

D. S. Wiersma, M. P. V. Albada, A. Lagendijk, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74(21), 4193–4196 (1995).
[Crossref] [PubMed]

D. S. Wiersma, M. P. V. Albada, A. Lagendijk, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74(21), 4193–4196 (1995).
[Crossref] [PubMed]

M. P. V. Albada, A. Lagendijk, and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref] [PubMed]

M. P. V. Albada, A. Lagendijk, and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref] [PubMed]

Lee, J. Y.

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

Lee, S. J.

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

Lequeux, F.

V. Viasnoff, F. Lequeux, and D. J. Pine, “Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics,” Rev. Sci. Instrum. 73(6), 2336–2344 (2002).
[Crossref]

Li, J.

Li, Z.

MacKintosh, F. C.

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B Condens. Matter 40(4), 2383–2406 (1989).
[Crossref] [PubMed]

Maksimyak, A. P.

Maksimyak, P. P.

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Optical correlation diagnostics of rough surfaces with large surface inhomogeneities,” Opt. Express 14(16), 7299–7311 (2006).
[Crossref] [PubMed]

O. V. Angelsky and P. P. Maksimyak, “The investigation of the transformation phenomenon of the longitudinal correlation function of the field propagating in the light scattering medium,” Opt. Spectrosc. 60(2), 331–336 (1986).

Maret, G.

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of brownian motion of scatterers,” Zeitschrift für Physik B 65(4), 409–413 (1987).
[Crossref]

Menon, N.

N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275(5308), 1920–1922 (1997).
[Crossref] [PubMed]

Middleton, A. A.

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B Condens. Matter 43(7), 5934–5938 (1991).
[Crossref] [PubMed]

Mullen, M. T.

Nieuwenhuizen, T. M.

T. M. Nieuwenhuizen and M. C. W. van Rossum, “Intensity distributions of waves transmitted through a multiple scattering medium,” Phys. Rev. Lett. 74(14), 2674–2677 (1995).
[Crossref] [PubMed]

Nieuwenhuizen, Th. M.

M. C. W. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[Crossref]

Ninck, M.

Oh, J.-T.

Ortolf, C.

Parthasarathy, A. B.

Pine, D. J.

V. Viasnoff, F. Lequeux, and D. J. Pine, “Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics,” Rev. Sci. Instrum. 73(6), 2336–2344 (2002).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[Crossref] [PubMed]

Rivas, J. G.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[Crossref] [PubMed]

Rojas-Ochoa, L. F.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Romer, S.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Scheffold, F.

P. Zakharov, F. Cardinaux, and F. Scheffold, “Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(1), 011413 (2006).
[Crossref] [PubMed]

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Schenkel, S.

Schurtenberger, P.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Shang, Y.

Sina, J. S.

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

Sinichkin, Y. P.

Skipetrov, S. E.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Snabre, P.

Stradner, A.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Sviridov, A. P.

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Stochastic interference of fluorescence radiation in random media with large inhomogeneities,” Opt. Commun. 387, 121–127 (2017).
[Crossref]

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Speckle spectroscopy of fluorescent randomly inhomogeneous media,” Quantum Electron. 46(11), 1047–1054 (2016).
[Crossref]

Symons, T. B.

Thompson, C. A.

Trappe, V.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Trifonov, V. A.

Tuchin, V. V.

D. A. Zimnyakov, V. V. Tuchin, and A. G. Yodh, “Characteristic scales of optical field depolarization and decorrelation for multiple scattering media and tissues,” J. Biomed. Opt. 4(1), 157–163 (1999).
[Crossref] [PubMed]

Urban, C.

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Ushakova, O. V.

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

van Rossum, M. C. W.

M. C. W. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[Crossref]

T. M. Nieuwenhuizen and M. C. W. van Rossum, “Intensity distributions of waves transmitted through a multiple scattering medium,” Phys. Rev. Lett. 74(14), 2674–2677 (1995).
[Crossref] [PubMed]

van Tiggelen, B. A.

D. S. Wiersma, M. P. V. Albada, A. Lagendijk, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74(21), 4193–4196 (1995).
[Crossref] [PubMed]

Viasnoff, V.

V. Viasnoff, F. Lequeux, and D. J. Pine, “Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics,” Rev. Sci. Instrum. 73(6), 2336–2344 (2002).
[Crossref]

Vilensky, M. A.

Wang, D.

Webb, K. J.

Weiner, A. M.

Weitz, D. A.

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[Crossref] [PubMed]

Wiersma, D. S.

D. S. Wiersma, M. P. V. Albada, A. Lagendijk, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74(21), 4193–4196 (1995).
[Crossref] [PubMed]

Wolf, P. E.

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of brownian motion of scatterers,” Zeitschrift für Physik B 65(4), 409–413 (1987).
[Crossref]

Yodh, A. G.

Yoon, K.

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

Yu, G.

Yuvchenko, S. A.

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Stochastic interference of fluorescence radiation in random media with large inhomogeneities,” Opt. Commun. 387, 121–127 (2017).
[Crossref]

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Speckle spectroscopy of fluorescent randomly inhomogeneous media,” Quantum Electron. 46(11), 1047–1054 (2016).
[Crossref]

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

Zakharov, P.

P. Zakharov, F. Cardinaux, and F. Scheffold, “Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(1), 011413 (2006).
[Crossref] [PubMed]

Zhao, Y.

Zimnyakov, D. A.

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Stochastic interference of fluorescence radiation in random media with large inhomogeneities,” Opt. Commun. 387, 121–127 (2017).
[Crossref]

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Speckle spectroscopy of fluorescent randomly inhomogeneous media,” Quantum Electron. 46(11), 1047–1054 (2016).
[Crossref]

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

D. A. Zimnyakov and M. A. Vilensky, “Blink speckle spectroscopy of scattering media,” Opt. Lett. 31(4), 429–431 (2006).
[Crossref] [PubMed]

D. A. Zimnyakov, J.-T. Oh, Y. P. Sinichkin, V. A. Trifonov, and E. V. Gurianov, “Polarization-sensitive speckle spectroscopy of random media beyond the diffusion limit,” J. Opt. Soc. Am. A 21(1), 59–70 (2004).
[Crossref]

D. A. Zimnyakov, V. V. Tuchin, and A. G. Yodh, “Characteristic scales of optical field depolarization and decorrelation for multiple scattering media and tissues,” J. Biomed. Opt. 4(1), 157–163 (1999).
[Crossref] [PubMed]

Appl. Opt. (1)

Biomed. Opt. Express (2)

J. Biomed. Opt. (1)

D. A. Zimnyakov, V. V. Tuchin, and A. G. Yodh, “Characteristic scales of optical field depolarization and decorrelation for multiple scattering media and tissues,” J. Biomed. Opt. 4(1), 157–163 (1999).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

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

Langmuir (1)

J. Y. Lee, J. W. Hwang, H. W. Jung, S. H. Kim, S. J. Lee, K. Yoon, and D. A. Weitz, “Fast dynamics and relaxation of colloidal drops during the drying process using multispeckle diffusing wave spectroscopy,” Langmuir 29(3), 861–866 (2013).
[Crossref] [PubMed]

Opt. Commun. (1)

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Stochastic interference of fluorescence radiation in random media with large inhomogeneities,” Opt. Commun. 387, 121–127 (2017).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Opt. Spectrosc. (1)

O. V. Angelsky and P. P. Maksimyak, “The investigation of the transformation phenomenon of the longitudinal correlation function of the field propagating in the light scattering medium,” Opt. Spectrosc. 60(2), 331–336 (1986).

Phys. Rev. B Condens. Matter (3)

F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B Condens. Matter 40(4), 2383–2406 (1989).
[Crossref] [PubMed]

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B Condens. Matter 43(7), 5934–5938 (1991).
[Crossref] [PubMed]

E. Kogan and M. Kaveh, “Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium,” Phys. Rev. B Condens. Matter 52(6), R3813–R3815 (1995).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[Crossref] [PubMed]

P. Zakharov, F. Cardinaux, and F. Scheffold, “Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(1), 011413 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

T. M. Nieuwenhuizen and M. C. W. van Rossum, “Intensity distributions of waves transmitted through a multiple scattering medium,” Phys. Rev. Lett. 74(14), 2674–2677 (1995).
[Crossref] [PubMed]

D. S. Wiersma, M. P. V. Albada, A. Lagendijk, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74(21), 4193–4196 (1995).
[Crossref] [PubMed]

M. P. V. Albada, A. Lagendijk, and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[Crossref] [PubMed]

Prog. Colloid Polym. Sci. (1)

F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti, and P. Schurtenberger, “New trends in optical microrheology of complex fluids and gels,” Prog. Colloid Polym. Sci. 123, 141–146 (2004).

Quantum Electron. (2)

D. A. Zimnyakov, I. A. Asharchuk, S. A. Yuvchenko, and A. P. Sviridov, “Speckle spectroscopy of fluorescent randomly inhomogeneous media,” Quantum Electron. 46(11), 1047–1054 (2016).
[Crossref]

D. A. Zimnyakov, J. S. Sina, S. A. Yuvchenko, E. A. Isaeva, S. P. Chekmasov, and O. V. Ushakova, “Low-coherence interferometry as a method for assessing the transport parameters in randomly inhomogeneous media,” Quantum Electron. 44(1), 59–64 (2014).
[Crossref]

Rev. Mod. Phys. (1)

M. C. W. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[Crossref]

Rev. Sci. Instrum. (1)

V. Viasnoff, F. Lequeux, and D. J. Pine, “Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics,” Rev. Sci. Instrum. 73(6), 2336–2344 (2002).
[Crossref]

Science (1)

N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275(5308), 1920–1922 (1997).
[Crossref] [PubMed]

Zeitschrift für Physik B (1)

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of brownian motion of scatterers,” Zeitschrift für Physik B 65(4), 409–413 (1987).
[Crossref]

Other (3)

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

J. W. Goodman, Statistical Optics (Wiley Classics Library Edition, 2000).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

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Figures (7)

Fig. 1
Fig. 1

The simulated distributions ρ( I/ I ) in the cases of the deterministic value | E 0i |=1 (1, 3) and random uniform distribution of the phasor amplitudes (2, 4). The number of statistically independent phasors used in the simulation procedure is equal to 500; the sample size applied for the reconstruction of ρ( I/ I ) is equal to 10000. The cases (1, 2) correspond to coherent summation of the random phasors ( s i s m / l c = 1.0⋅10−3) and the cases (3, 4) correspond to the partially coherent summation ( s i s m / l c = 1.0).

Fig. 2
Fig. 2

The plot of values J 1 ( l c , Δs ) and J 2 ( l c , Δs ) for the various shapes of ρ( Δs, Δs ) ; a – open triangles; b – closed circles; c – open circles. The Δs / l c ratios are equal to: i – 0; ii – 0.318; iii – 0.637; iv – 0.955; v – 1.273; vi – 1.592; vii – 2.228; viii – 3.183. Dashed line – the power-law approximation of the relationship between J 1 ( l c , Δs ) and J 2 ( l c , Δs ) .

Fig. 3
Fig. 3

Arrangement of the experiment. 1 – the CW pumping laser ( λ 1 = 532 nm, the output power is 50 mW); 2 – the concave lens with the focal length of −200 mm; 3 – the sample under study; 4 – the confocal system; 5 – the pinhole diaphragm; 6 – the monochromator; 7 – the processing unit (PC). The fluorescence radiation with the wavelength λ 2 is detected while scanning along the xdirection; Δz is the scan depth. Units 4 −7 are parts of the Horiba Jobin Yvon LabRam HR800 assembly.

Fig. 4
Fig. 4

The values of second- ( M 2 ) and third-order ( M 3 ) moments of fluorescence intensity versus the wavelength; 1 - M 2 ; 2 - M 3 . Inset: the distribution of fluorescence intensity at λ= 575 nm along the arbitrarily chosen scan trace; the scan depth is 150 μm.

Fig. 5
Fig. 5

Distributions of the probability density of path length difference ρ( Δs ) ; 1 - L μ s = 12; 2 - L μ s = 1.6; 3 - L μ s = 0.4; 4 - L μ s = 0.16. Inset: distributions of the path length probability density ρ( s ) ; 1 - L μ s = 12; 2 - L μ s = 0.16.

Fig. 6
Fig. 6

The values of third-order moments of fluorescence intensity versus the values of second-order moment; 1 – empirical data presented in Fig. 3; 2 – theoretical dependence for the exponential form of ρ( Δs ) . The ratios Δs / l c are equal to: i – 0; ii – 0.318; iii – 0.637; iv – 1.273; v – 2.546.

Fig. 7
Fig. 7

The recovered values of the average path length propagation of fluorescence radiation in the examined layers versus the wavelength. 1 – the recovery using the considered intensity moments analysis; 2 – the recovery using the numerical inversion of the functional J 1 ( l c , Δs ) (in accordance with [28, 29]).

Equations (22)

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I( t ) ¯ = E( t ) E * ( t ) ¯ = | E( t ) | 2 ¯ = | i N E i ( t )exp{ j φ i ( t ) } | 2 ¯ ,
I( t ) ¯ = i N i N E i ( t ) E i ( t )exp[ j{ φ i ( t ) φ i ( t ) } ] ¯ = = i N i N I i ( t ) I i ( t ) exp[ j{ φ i ( t ) φ i ( t ) } ] ¯ .
I( t ) ¯ = i N I i ( t ) ¯ + i N i i N I i ( t ) I i ( t ) cos[ k( s i s i )+Δϕ( t, s i s i ) ] ¯ ,
I i ( t ) I i ( t ) cos[ k( s i s i )+Δϕ( t, s i s i ) ] ¯ = = I i ( t ) ¯ I i ( t ) ¯ cos[ k( s i s i )+Δϕ( t, s i s i ) ] ¯ = I i ( t ) ¯ I i ( t ) ¯ cos[ Δϕ( t, s i s i ) ] ¯ cos[ k( s i s i ) ] I i ( t ) ¯ I i ( t ) ¯ sin[ Δϕ( t, s i s i ) ] ¯ sin[ k( s i s i ) ]= = I i ( t ) ¯ I i ( t ) ¯ Q 2 ( s i s i )+ S 2 ( s i s i ) cos[ k( s i s i )Ψ( s i s i ) ],
Q( s i s i )= 1 T 0 T cos[ Δϕ( t, s i s i ) ]dt; S( s i s i )= 1 T 0 T sin[ Δϕ( t, s i s i ) ]dt ; tg{ Ψ( s i s i ) }= S( s i s i ) / Q( s i s i ) ,
g( s i s i )= sin{ π( s i s i ) / l c } / { π( s i s i ) / l c } exp{ jk( s i s i ) },
I= i N E 0i 2 + i N i i N E 0i E 0 i cos{ k( s i s i ) }| g( s i s i ) | .
I 2 = ( i N E 0i 2 + i N i i N E 0i E 0 i cos{ k( s i s i ) }| g( s i s i ) | ) 2 ,
I 3 = ( i N E 0i 2 + i N i i N E 0i E 0 i cos{ k( s i s i ) }| g( s i s i ) | ) 3
I 2 = ( N+2 m N( N1 ) /2 cos( kΔ s m )| g( Δ s m ) | ) 2 ,
I 3 = ( N+2 m N( N1 ) /2 cos( kΔ s m )| g( Δ s m ) | ) 3 ,
I 2 = N 2 +4N m N( N1 ) /2 cos( kΔ s m )| g( Δ s m ) | + +4 ( m N( N1 ) /2 cos( kΔ s m )| g( Δ s m ) | ) 2 , I 3 = N 3 +6 N 2 m N( N1 ) /2 cos( kΔ s m )| g( Δ s m ) | + +12N ( m N( N1 ) /2 cos( kΔ s m )| g( Δ s m ) | ) 2 + +8 ( m N( N1 ) /2 cos( kΔ s m )| g( Δ s m ) | ) 3 .
M 2 = I 2 I 2 =1+ N1 N 0 | g( Δs ) | 2 ρ( Δs, Δs )d( Δs ) 1+ 0 | g( Δs ) | 2 ρ( Δs, Δs )d( Δs ) .
M 3 = I 3 I 3 =1+3 N1 N 0 | g( Δs ) | 2 ρ( Δs, Δs )d( Δs ) + +2 ( N1 ) 2 N 2 ( 0 | g( Δs ) |ρ( Δs, Δs )d( Δs ) ) 3 1+3 0 | g( Δs ) | 2 ρ( Δs, Δs )d( Δs ) +2 ( 0 | g( Δs ) |ρ( Δs, Δs )d( Δs ) ) 3 .
ρ( Δs, Δs )={ 2 0 ρ( s+Δs )ρ( s )ds ,Δs0; 0,Δs<0,
I =2 I ,II ; I 2 = ( I + I II ) 2 = I 2 +2 I I II + I II 2 ; I 3 = ( I + I II ) 3 = I 3 +3 I 2 I II +3 I I II 2 + I II 3 ; M 2 = I 2 I 2 = 2 I ,II 2 +2 I ,II 2 4 I ,II 2 = 1 2 I ,II 2 I ,II 2 + 1 2 ; M 3 = I 3 I 3 = 2 I ,II 3 +6 I ,II 2 I ,II 8 I ,II 3 = 1 4 I ,II 3 I ,II 3 + 3 4 I ,II 2 I ,II 2 .
{ M 2 = I 2 I 2 1+ 1 2 0 | g( Δs ) | 2 ρ( Δs, Δs )d( Δs ) ; M 3 = I 3 I 3 1+ 3 2 0 | g( Δs ) | 2 ρ( Δs, Δs )d( Δs ) + + 1 2 ( 0 | g( Δs ) |ρ( Δs, Δs )d( Δs ) ) 3 .
J 1 ( l c , Δs )= 0 | sin( πΔs / l c ) πΔs / l c | 2 ρ( Δs, Δs )d( Δs ) ; J 2 ( l c , Δs )= ( 0 | sin( πΔs / l c ) πΔs / l c |ρ( Δs, Δs )d( Δs ) ) 3
Δs l c =0 J 1 ( l c , Δs )= J 2 ( l c , Δs )=1; Δs l c = J 1 ( l c , Δs )= J 2 ( l c , Δs )=0
ρ( Δs, Δs )={ ( 2 3 Δs )( 1 Δs 3 Δs ),0Δs3 Δs ; 0,Δs<0;Δs>3 Δs ;
J 2 ( l c , Δs ) { J 1 ( l c , Δs ) } γ
I λ = 1 4 10 3 h=1 4 j=1 10 i=1 100 I i,j,h,λ ; I λ 2 = 1 4 10 3 h=1 4 j=1 10 i=1 100 I i,j,h,λ 2 ; I λ 3 = 1 4 10 3 h=1 4 j=1 10 i=1 100 I i,j,h,λ 3 .

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