Aubry, Alexandre (2008) Approche matricielle de l'opérateur de propagation des ondes ultrasonores en milieu diffusant aléatoire. PhD thesis Physique, Laboratoire Ondes et Acoustique - ESPCI , Paris VI p.250.

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Abstract

Cette thèse étudie les propriétés de l'opérateur de propagation des ondes ultrasonores en milieu aléatoire. Le dispositif expérimental consiste en un réseau multi-éléments placé en vis-à-vis d'un milieu désordonné. L'opérateur de propagation est donné par la matrice des réponses inter-éléments mesurées entre chaque couple de transducteurs. En s'appuyant sur la théorie des matrices aléatoires, le comportement statistique de cet opérateur a été étudié en régime de diffusion simple et multiple. Une cohérence déterministe des signaux est ainsi mise en évidence en régime de diffusion simple, cohérence qui disparaît dès que la diffusion multiple prédomine. Cette différence de comportement a permis la mise au point d'un radar intelligent séparant les échos simplement et multiplement diffusés. On peut ainsi extraire l'écho direct d'une cible échogène enfouie dans un milieu hautement diffusant, bien que ce dernier soit source de diffusion multiple et d'aberration. Une deuxième approche consiste, au contraire, à extraire une contribution de diffusion multiple noyée dans une contribution de diffusion simple largement prédominante. L'étude de l'intensité multiplement diffusée permet de mesurer des paramètres de transport (p.ex. la constante de diffusion D) caractérisant la propagation de l'onde multiplement diffusée. Un passage en champ lointain (ondes planes) permet d'obtenir une mesure fiable de D en étudiant le cône de rétrodiffusion cohérente. Un passage en champ proche, via l'utilisation de faisceaux gaussiens, permet d'effectuer des mesures locales de D en étudiant la croissance du halo diffusif. Cette approche a été appliquée au cas de l'os trabéculaire humain autour de 3 MHz.

References

[1] A. Ishimaru. Wave Propagation and Scattering in Random Media. Academic Press, New

York, USA, 1978.

[2] Y. Kuga and A. Ishimaru. Retroreflectance from a dense distribution of spherical particles.

J. Opt. Soc. Am. A, 1 :831, 1984.

[3] P-E Wolf and G. Maret. Weak localization and coherent backscattering of photons in

disordered media. Phys. Rev. Lett., 55 :2696–2699, 1985.

[4] M. van Albada and A. Lagendijk. Observation of weak localization of light in a random

medium. Phys. Rev. Lett., 55 :2692–2695, 1985.

[5] E. Akkermans, P-E.Wolf, and R.Maynard. Coherent backscattering of light by disordered

media : Analysis of the peak line shape. Phys. Rev. Lett., 56 :1471–1474, 1986.

[6] E. Akkermans, P-E. Wolf, R. Maynard, and G. Maret. Theoretical study of the coherent

backscattering of light by disordered media. J. Phys. France, 49 :77–98, 1988.

[7] R. Vreeker, M.P. Albada, R. Sprik, and A. Lagendijk. Femtosecond time-resolved measurements

of weak localization of light. Phys. Lett. A, 132 :51–54, 1988.

[8] D.S. Wiersma, M.P. van Albada, B.A. van Tiggelen, and A. Lagendijk. Experimental

evidence for recurrent multiple scattering events of light in disordered media. Phys. Rev.

Lett., 74 :4193–4196, 1995.

[9] G. Labeyrie, F. de Tomasi, J.-C. Bernard, C.A. M¨uller, and C. Miniatura ans R. Kaiser.

Coherent backscattering of light by cold atoms. Phys. Rev. Lett., 83 :5266–5269, 1999.

[10] G. Labeyrie, C.A. M¨uller, D.S. Wiersma, C. Miniatura, and R. Kaiser. Observation of

coherent backscattering of light by cold atoms. J. Opt. B., 2 :672–685, 2000.

[11] D.V. Kupriyanov, I.M. Solokov, C.I. Sukenik, and M.D. Havey. Coherent backscattering

of light from ultracold and optically dense atomic ensembles. Laser Phys. Lett., 3 :223–

243, 2006.

[12] G. Bayer and T. Niederdr¨ank. Weak localization of acoustic waves in stongly scattering

media. Phys. Rev. Lett., 70 :3884–3887, 1993.

[13] A. Tourin, A. Derode, P. Roux, B.A. van Tiggelen, and M. Fink. Time-dependent backscattering

of acoustic waves. Phys. Rev. Lett., 79 :3637–3639, 1997.

[14] K. Sakai, K. Yamamoto, and K. Takagi. Observation of acoustic coherent backscattering.

Phys. Rev. B, 56 :10930–10933, 1997.

[15] J. de Rosny, A. Tourin, A. Derode, B. van Tiggelen, and M. Fink. Relation between time

reversal focusing and coherent backscattering in multiple scattering media : A diagrammatic

approach. Phys. Rev. E, 70 :046601, 2004.

[16] J. de Rosny, A. Tourin, A. Derode, P. Roux, and M. Fink. Weak localization and time

reversal of ultrasound in a rotational flow. Phys. Rev. Lett., 95 :074301, 2005.

[17] E. Larose, L. Margerin, B.A. van Tiggelen, and M. Campillo. Weak localization of seismic

waves. Phys. Rev. Lett., 93 :048501, 2004.

[18] B.A. van Tiggelen, L. Margerin, and M. Campillo. Coherent backscattering of elastic

waves : Specific role of source, polarization, and near field. J. Acoust. Soc. Am., 110 :1291–

1298, 2001.

[19] L. Margerin, M. Campillo, and B.A. van Tiggelen. Coherent backscattering of acoustic

waves in the near field. Geophys. J. Int., 145 :593–603, 2001.

[20] E. Akkermans and G. Montambaux. Physique m´esoscopique des ´electrons et des phonons.

CNRS Editions, Paris, France, 2004.

[21] J.W. Goodman. Statistical Optics, chapter 5. Wiley & Sons, New York, USA, 1985.

[22] J. Paasschens. Solution of the time-dependent Boltzmann equation. Phys. Rev. E,

56 :1135–1141, 1997.

[23] A. Lagendijk and B.A. van Tiggelen. Resonant multiple scattering of light. Phys. Rep.,

270 :143–215, 1996.

[24] A. Tourin. Diffusion multiple et renversement du temps des ondes ultrasonores. PhD

thesis, Universit´e Paris 7 - Denis Diderot, 1997.

[25] P. Sheng. Introduction to Wave Scattering, Localization and Mesoscopic Phenomena.

Academic Press, New York, USA, 1995.

[26] N. Tr´egour`es and B. van Tiggelen. Quasi-two-dimensional transfer of elastic waves. Phys.

Rev. E, 66 :036601, 2002.

[27] R.L. Weaver and O.I. Lobkis. Enhanced backscattering and modal echo of reverberant

elastic waves. Phys. Rev. Lett., 84 :4942–4945, 2000.

[28] J. de Rosny, A. Tourin, and M. Fink. Coherent backscattering of an elastic wave in a

chaotic cavity. Phys. Rev. Lett., 84 :1693–1695, 2000.

[29] G. Barton. Elements of Green’s functions and propagation. Oxford Science Press, New

York, USA, 1989.

[30] J.H. Page, H.P. Schriemer, A.E. Bailey, and D.A.Weitz. Experimental test of the diffusion

approximation for multiply scattered sound. Phys. Rev. E, 52 :3106–3114, 1995.

[31] S.E. Skipetrov. Information transfer through disordered media by diffuse waves. Phys.

Rev. E, 67 :036621, 2003.

[32] M. Storzer, P. Gross, C.M. Aegerter, and G. Maret. Observation of the critical regime

near Anderson localization of light. Phys. Rev. Lett., 96 :063904, 2006.

[33] L. Margerin, M. Campillo, and B.A. van Tiggelen. Radiative transfer and diffusion of

waves in a layered medium : new insight into coda Q. Geophys. J. Int., 134 :596–612,

1998.

[34] M.M. Haney, K. van Wijk, and R. Snieder. Radiative transfer in layered media and its

connection to the O’Doherty-Anstey formula. Geophysics, 70 :1–11, 2005.

[35] Z.Q. Zhang, I.P. Jones, H.P. Schriemer, J.H. Page, D.A. Weitz, and P. Sheng. Wave

transport in random media : The ballistic to diffusive transition. Phys. Rev. E, 60 :4843,

1999.

[36] J.H. Page, H.P. Schriemer, I.P. Jones, P. Sheng, and D.A. Weitz. Classical wave propagation

in strongly scattering media. Physica A, 241 :64–71, 1997.

[37] H.P. Schriemer, M.L. Cowan, J.H. Page, P. Sheng, Z. Liu, and D.A. Weitz. Energy

velocity of diffusing waves in strongly scattering media. Phys. Rev. Lett., 79 :3166–3169,

1997.

[38] J. Scales and K. Van Wijk. Tunable multiple-scattering system. App. Phys. Lett.,

79 :2294–2296, 2001.

[39] J. Scales and A. Malcolm. Laser characterization of ultrasonic wave propagation in random

media. Phys. Rev. E, 67 :046618, 2003.

[40] J.H. Page, P.Sheng, H.P. Schriemer, I. Jones, X. Jing, and D.A. Weitz. Group velocity

in strongly scattering media. Science, 271 :634, 1996.

[41] M.L. Cowan, K. Beaty, J.H. Page, Z. Liu, and P. Sheng. Group velocity of acoustic waves

in strongly scattering media : Dependence on the volume fraction of scatterers. Phys.

Rev. E, 58 :6626–6636, 1998.

[42] A. Tourin, A. Derode, A. Peyre, and M. Fink. Transport parameters for an ultrasonic

pulsed wave propagating in a multiple scattering medium. J. Acoust. Soc. Am., 108 :503–

512, 2000.

[43] A. Tourin, A. Derode, and M. Fink. Multiple scattering of sound. Waves in random

media, 10 :R31–R60, 2000.

[44] V. Mamou. Caract´erisation ultrasonore d’´echantillons h´et´erog`enes multiplement diffu-

seurs. PhD thesis, Universit´e Paris 7 - Denis Diderot, 2005.

[45] A. Aubry, A. Derode, P. Roux, and A. Tourin. Coherent backscattering and far-field

beamforming in acoustics. J. Acoust. Soc. Am., 121 :70–77, 2007.

[46] A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier. Dynamic coherent backscattering

in a heterogenous medium : Application to human trabecular bone characterization.

Appl. Phys. Lett., 87 :114101, 2005.

[47] A. Derode, V. Mamou, and A. Tourin. Influence of correlations between scatterers on the

attenuation of the coherent wave in a random medium. Phys. Rev. E, 74 :036606, 2006.

[48] S.E. Skipetrov and B.A. van Tiggelen. Dynamics of weakly localized waves. Phys. Rev.

Lett., 92 :113901, 2004.

[49] R. Mallart and M. Fink. The van Cittert-Zernike theorem in pulse echo measurements.

J. Acoust. Soc. Am., 90 :2718–2727, 1991.

[50] A. Derode and M. Fink. Partial coherence of transient ultrasonic fields in anisotropic

random media : Application to coherent echo detection. J. Acoust. Soc. Am., 101 :690–

704, 1997.

[51] A. Aubry and A. Derode. Ultrasonic imaging of highly scattering media from local

measurements of the diffusion constant : Separation of coherent and incoherent intensities.

Phys. Rev. E, 75 :026602, 2007.

[52] R. Nossal. Scattering and Localization of Classical Waves in Random Media. World

Scientific, Singapore, 1990.

[53] P.W. Anderson. Absence of diffusion in certain random lattices. Phys. Rev., 109 :1492–

1505, 1958.

[54] M.C.W. Rossum and T.M. Nieuwenhuizen. Multiple scattering of classical waves : Microscopy,

mesoscopy and diffusion. Rev. Mod. Phys., 71 :313–371, 1999.

[55] P. Sebbah. Waves and Imaging through Complex Media. Kluwer Academic Publishers,

Dordrecht, The Netherlands, 1999.

[56] K. Aki and B. Chouet. Origin of coda waves : Source, attenuation and scattering effects.

J. Geophys. Res., 80 :3322–3342, 1975.

[57] A. Yodh and B. Chance. Spectroscopy and imaging with diffusing light. Physics Today,

48 :33–40, 1995.

[58] R. Choe, A. Corlu, K. Lee, T. Durduran, S. Donecky, M. Grosicka-Koptyra, S. Arridge,

B. Czerniecki, D. Fraker, A. DeMichele, B. Chance, and A. Yodh. Diffuse optical tomography

of breast cancer during neoadjuvant chemotherapy : A case study with comparison

to MRI. Med. Phys., 32 :1128–1139, 2005.

[59] A. Derode, A. Tourin, J. de Rosny, M. Tanter, S. Yon, and M. Fink. Taking advantage

of multiple scattering to communicate with time-reversal antennas. Phys. Rev. Lett.,

90 :014301, 2003.

[60] J. Alda. Encyclopedia of Optical Engineering, chapter Laser and Gaussian Beam Propagation

and Transformation, pages 999–1013. Marcel Dekker, New York, USA, 2003.

[61] A. Aubry, A. Derode, and F. Padilla. Local measurements of the diffusion constant in

multiple scattering media : Application to human trabecular bone imaging. Appl. Phys.

Lett., 92 :124101, 2008.

[62] S. Chaffa¨ı, V. Roberjot, F. Peyrin, G. Berger, and P. Laugier. Frequency dependence

of ultrasonic backscattering cancellous bone : Autocorrelation model and experimental

reults. J. Acoust. Soc. Am., 108 :2403–2411, 2000.

[63] K.A. O’Donnell and R. Torre. Second-harmonic generation from a strongly roughly metal

surface. Opt. Commun., 138 :341–344, 1997.

[64] M. Leyva-Lucero, E.R. Mendez, T.A. Leskova, and A.A. Maradudin. Destructive interference

effects in the second harmonic light generated at randomly rough metal surfaces.

Opt. Commun., 161 :79–94, 1999.

[65] G. Foschini and M. Gans. Wireless Personal Communication, volume 6. Kluwer Academic

Publishers, Dordrecht, The Netherlands, 1998.

[66] A. Moustakas, H. Baranger, L. Balents, A. Sengupta, and S. Simon. Communication

through a diffusive medium : Coherence and capacity. Science, 287 :287–290, 1999.

[67] B.A. Angelsen. Ultrasound Imaging. Waves, Signals and Signal Processing. Emantec,

Trondheim, Norway, 2000.

[68] C. Prada and M. Fink. Eigenmodes of the time-reversal operator : A solution to selective

focusing in multiple-target media. Wave Motion, 20 :151–163, 1994.

[69] C. Prada, S. Manneville, D. Poliansky, and M. Fink. Decomposition of the time reversal

operator : Application to detection and selective focusing on two scatterers. J. Acoust.

Soc. Am., 99 :2067–2076, 1996.

[70] C. Prada and J-L. Thomas. Experimental subwavelength localization of scatterers by

decomposition of the time reversal operator interpreted as a covariance matrix. J. Acoust.

Soc. Am., 114 :235–243, 2003.

[71] J-G. Minonzio, C. Prada, A. Aubry, and M. Fink. Multiple scattering between two elastic

cylinders and invariants of the time-reversal operator : Theory and experiment. J. Acoust.

Soc. Am., 120 :875–883, 2006.

[72] M. Mehta. Random Matrices. Academic Press, Boston, USA, 1991.

[73] T. Brody, J. Flores, J. Franch, P. Mello, A. Pandey, and S. Song. Random-matrix physics :

Spectrum and strength fluctuations. Rev. Mod. Phys., 53 :385–479, 1981.

[74] C. Ellegaard, T. Guhr, K. Lindemann, J. Nygard, and M. Oxborrow. Symmetry breaking

and spectral statistics of acoustic resonances in quartz blocks. Phys. Rev. Lett., 77 :4918–

4921, 2003.

[75] Y. L. Cun, I. Kanter, and S. A. Solla. Eigenvalues of covariance matrices : Application

to neural-network learning. Phys. Rev. Lett., 66 :2396–2399, 1991.

[76] A. Tulino and S. Verd`u. Random matrix theory and wireless communications. Founda-

tions and Trends in Communications and Information Theory, 1 :1–182, 2004.

[77] L. Laloux, P. Cizeau, J-P. Bouchaud, and M. Potters. Noise dressing of financial correlation

matrices. Phys. Rev. Lett., 83 :1467–1470, 1999.

[78] C-N. Nuah, D. Tse, J. Kahn, and R. Valenzuela. Capacity scaling in MIMO wireless

systems under correlated fading. IEEE Trans. Inform. Theory, 48 :637–650, 2002.

[79] A. Moustakas, S. Simon, and A. Sengupta. MIMO capacity trough correlated channels

in the presence of correlated interferers and noise : A (not so) large N analysis. IEEE

Trans. Inform. Theory, 49 :2545–2561, 2003.

[80] A.M. Sengupta and P.P Mitra. Distribution of singular values for some random matrices.

Phys. Rev. E, 60 :3389–3392, 1999.

[81] I. Johnstone. On the distribution of the largest eigenvalue in principal components analysis.

Ann. Stat., 29 :295–327, 2001.

[82] N. El-Karoui. Spectrum estimation for large dimensional covariance matrices using random

matrix theory. arXiv :math/0609418, 2007.

[83] V. Mar˘cenko and L. Pastur. Distributions of eigenvalues for some sets of random matrices.

Math. USSR-Sbornik, 1 :457–483, 1967.

[84] W. Bryc, A. Dembo, and T. Jiang. Spectral measure of large random Hankel, Markov

and Toeplitz matrices. Ann. Probab., 34 :1–38, 2006.

[85] M. Meckes. On the spectral norm of a random Toeplitz matrix. Electron. Commun.

Probab., 12 :315–325, 2007.

[86] M. Haney and R. Snieder. Breakdown of wave diffusion in 2D due to loops. Phys. Rev.

Lett., 91 :093902, 2003.

[87] J. Garnier, C. Gou´edard, and A. Migus. Statistics of the hottest spot of speckle patterns

generated by smoothing techniques. Journal of Modern Optics, 46 :1213–1232, 1999.

[88] J. Garnier. Statistics of the hot spots of smoothed beams produced by random phase

plates revisited. Physics of plasmas, 6 :1601–1610, 1999.

[89] N. Mordant, C. Prada, and M. Fink. Highly resolved detection and selective focusing in

a waveguide using the D.O.R.T method. J. Acoust. Soc. Am., 105 :2634–2642, 1999.

[90] J. F. Lingevitch, H. C. Song, and W. A. Kuperman. Time reversed reverberation focusing

in a waveguide. J. Acoust. Soc. Am., 111 :2609–2614, 2002.

[91] L. Carin, H. Liu, T. Yoder, L. Couchman, B. Houston, and J. Bucaro. Wideband timereversal

imaging of an elastic target in an acoustic waveguide. J. Acoust. Soc. Am.,

115(1) :259–268, 2004.

[92] E. Kerbrat, C. Prada, D. Cassereau, and M. Fink. Imaging the presence of grain noise

using the decomposition of the time reversal operator. J. Acoust. Soc. Am., 113 :1230–

1240, 2003.

[93] C. Gaumond, D. Fromm, J. Lingevitch, R. Menis, G. Edelmann, D. Calvo, and E. Kim.

Demonstration at sea of the decomposition-of-the-time-reversal-operator technique. J.

Acoust. Soc. Am., 119 :976–990, 2006.

[94] C. Prada, J. de Rosny, D. Clorennec, J-G. Minonzio, A. Aubry, M. Fink, L. Berniere,

P. Billand, S. Hibral, and T. Folegot. Experimental detection and focusing in shallow

water by decomposition of the time reversal operator. J. Acoust. Soc. Am., 122 :761–768,

2007.

[95] H. Tortel, G. Micolau, and M. Saillard. Decomposition of the time reversal operator for

electromagnetic scattering. Journal of Electromagnetic Waves and Applications, 13 :687–

719, 1999.

[96] G. Micolau, M. Saillard, and P. Borderies. D.O.R.T method as applied to ultrawideband

signals for detection of buried objects. IEEE Transactions on geoscience and remote

sensing, 41 :1813–1820, 2003.

[97] E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson. Multi-static response matrix of

a 3-D inclusion in a half space and MUSIC imaging. IEEE Transactions on Antennas

and Propagation, 55 :2598–2609, 2007.

[98] E. Iakoleva and D. Lesselier. Multistatic response matrix of spherical scatterers and the

back-propagation of singular fields. IEEE Trans. Antennas Propagat., 56 :825–833, 2008.

[99] D. de Badereau, H. Roussel, and W. Tabbara. Radar remote sensing of forest at low

frequencies : a two dimensional full wave approach. J. Electromagnetic Waves Applic.,

17 :921–949, 2003.

[100] H. Nguyen, H. Roussel, and W. Tabbara. A coherent model of forest scattering and SAR

imaging in the VHF and UHF band. IEEE Trans. Geosci. Remote Sens., 44 :838–848,

2006.

[101] Y. Ziad´e, H. Roussel, M. Lesturgie, and W. Tabbara. A coherent model of forest propagation

- Application to detection and localisation of targets using the DORT method.

IEEE Trans. Antennas Propagat., 56 :1048–1057, 2008.

[102] D. Chambers and A. Gautesen. Time reversal for a single spherical scatterer. J. Acoust.

Soc. Am., 109 :2616–2624, 2001.

[103] J-G. Minonzio, C. Prada, D. Chambers, and M. Fink. Characterization of subwavelength

elastic cylinders with the decomposition of the time-reversal operator. J. Acoust. Soc.

Am., 117 :789–798, 2005.

[104] H. Zhao. Analysis of the response matrix for an extended target. SIAM Journal on

Applied Mathematics, 64 :725–745, 2004.

[105] A. Aubry, J. de Rosny, J.-G. Minonzio, C. Prada, and M. Fink. Gaussian beams and

Legendre polynomials as invariants of the time reversal operator for a large rigid cylinder.

J. Acoust. Soc. Am., 120 :2746–2754, 2006.

[106] L. Pastur. On the universality of the level spacing distribution for some ensembles of

random matrices. Letters in Mathematical Physics, 25 :259–265, 1992.

[107] C.A. Tracy and H. Widom. Level-spacing distributions and the Airy kernel. Commun.

Math. Phys., 159 :151–174, 1994.

[108] C.A. Tracy and H. Widom. On orthogonal and symplectic matrix ensembles. Commun.

Math. Phys., 177 :727–754, 1996.

[109] K. Johansson. Shape fluctuations and random matrices. Commun. Math. Phys., 209 :437–

476, 2000.

[110] N. El-Karoui. Recent results about the largest eigenvalue of random covariance matrices

and statistical application. Acta Physica Polonica B, 36 :2681–2697, 2005.

[111] R. Adamczak. A few remarks on the operator norm of random Toeplitz matrices.

arXiv :math/0803.3111, 2008.

[112] S. Chatterjee. Fluctuations of eigenvalues and second order Poincar´e inequalities.

arXiv :math/0705.1224, 2007.

[113] P. Norville and W.R. Scott. An investigation of time reversal techniques in seismic

landmine detection. In Proceedings of the SPIE : 2004 Annual International Symposium

on Aerospace/Defense Sensing, Simulation, and Controls, Orlando, USA, 2004.

[114] M. Alam, P. Norville, J. H. McClellan, and W. R. Scott. Time-reverse imaging for detection

of land-mines. In Proceedings of the SPIE : 2004 Annual International Symposium

on Aerospace/Defense Sensing, Simulation, and Controls, Orlando, USA, 2004.

[115] E. Larose, J. de Rosny, L. Margerin, D. Anache, P. Gou´edard, M. Campillo, and B. van

Tiggelen. Observation of multiple scattering of kHz vibrations in a concrete structure

and application to monitoring weak changes. Phys. Rev. E, 73 :016609, 2006.

[116] J-M. Bordier, M. Fink, A. le Brun, and F. Cohen-Tenoudji. The influence of multiple

scattering in incoherent ultrasonic inspection of coarse grain stainless steel. Ultrasonics

Symposium, 2 :803–808, 1991.

[117] S. Flax and M.O’Donnell. Phase-aberration correction using signals from point reflectors

and diffuse scatterers : Basic principles. IEEE Trans. Ultrason. Ferroelectr. Freq. Control,

35 :758–767, 1988.

[118] R. Waag and P. Astheiner. Statistical estimation of ultrasonic propagation path parameters

for aberration correction. IEEE Trans. Ultrason. Ferroelectr. Freq. Control,

52 :851–869, 2005.

[119] L. Borcea, G. Papanicolaou, and C. Tsogka. Adapative interferometric imaging in clutter

and optimal illumination. Inverse Problems, 22 :1405–1436, 2006.

[120] J-L Robert, M. Burcher, C. Cohen-Bacrie, and M. Fink. Time reversal operator decomposition

with focused transmission and robustness to speckle noise : Application to

microcalcification detection. J. Acoust. Soc. Am., 119(1) :3848–3859, 2006.

[121] J-L. Robert and M. Fink. Green’s function estimation in speckle noise using the decomposition

of the time-reversal operator : Application to aberration correction in medical

imaging. J. Acoust. Soc. Am., 123 :866–877, 2008.

[122] E. Kerbrat, D. Clorennec, C. Prada, D. Royer, D. Cassereau, and M. Fink. Detection of

cracks in a thin air-filled hollow cylinder by application of the D.O.R.T method to elastic

components of the echo. Ultrasonics, 40 :715–720, 2002.

[123] R.C. Chivers. The scattering of ultrasound by human tissues - Some theoretical models.

Ultrasound. Med. Biol., 3 :1–13, 1977.

[124] C.M. Sehgal and J. Greenleaf. Scattering of ultrasound by tissues. Ultrasonic imaging,

6 :66–80, 1984.

[125] C.M. Sehgal. Quantitative relationship between tissue composition and scattering of

ultrasound. J. Acoust. Soc. Am., 94 :1944–1952, 1993.

[126] F. Padilla, F. Peyrin, and P. Laugier. Prediction of backscatter coefficient in trabecular

bones using a numerical model of three-dimensional microstructure. J. Acoust. Soc. Am.,

108 :2403–2411, 2003.

[127] D. Deligianni and K. Apostolopoulos. Characterization of dense bovine cancellous bone

tissue microstructure by ultrasonic backscattering using weak scattering models. J.

Acoust. Soc. Am., 122 :1180–1190, 2007.

[128] M. Hakulinen, J. Day, J. T¨oyr¨as, H.Weimans, and J. Jurvelin. Ultrasonic characterization

of human trabecular bone microstructure. Phys. Med. Biol., 51 :1633–1648, 2006.

[129] L.A. Chernov. Wave propagation in a random medium. (a) Chapter 4. Dover, New York,

USA, 1960.

[130] S.M. Rytov, Yu. A. Kravtsov, and V.I. Tatarskii. Principle of statistical radiophysics IV :

Wave propagation through random media. Chapter 4. Springer-Verlag, Berlin, Germany,

1989.

[131] S.M. Rytov, Yu. A. Kravtsov, and V.I. Tatarskii. Principle of statistical radiophysics III :

Elements of random fields. Chapter 4. Springer-Verlag, Berlin, Germany, 1989.

[132] C.D. Jones. High frequency acoustic volume scattering from biologically active marine

sediments. PhD thesis, University of Washington (Applied Physics Laboratory), 1999

(http ://handle.dtic.mil/100.2/ADA371341).

[133] M.P. van Albada, B.A. van Tiggelen, A. Lagendijk, and A. Tip. Speed of propagation of

classical waves in strongly scattering media. Phys. Rev. Lett., 66 :3132, 1991.

[134] L. Ryzhik, G. Papanicolaou, and J. Keller. Transport equations for elastic and other

waves in random media. Wave motion, 24 :327–370, 1996.

Table of content

Introduction



I Formation de voies et diffusion multiple

I.1 Introduction

I.2 Intensité multiplement diffusée en régime dynamique

I.2.1 Introduction

I.2.2 Expression générale des intensités simplement et multiplement diffusées

I.2.3 Opérateur de propagation de l’intensité en milieu aléatoire

I.2.4 Champ proche

I.2.5 Champ lointain

I.2.6 Cas des expériences ultrasonores

I.3 Coherent backscattering and far-field beamforming in acoustics

I.3.1 Abstract

I.3.2 Introduction

I.3.3 Principle and Applications

I.3.4 Conclusion

I.4 Ultrasonic imaging of highly scattering media

I.4.1 Abstract

I.4.2 Introduction

I.4.3 Near-field beamforming with Gaussian beam

I.4.4 Separation of coherent and incoherent intensities

I.4.5 Experimental results

I.4.6 Local measurement of the diffusion constant

I.4.7 Experimental results

I.4.8 Conclusion

I.5 Application to human trabecular bone imaging

I.5.1 Abstract

I.5.2 Introduction

I.5.3 Experiment

I.5.4 Discussion

I.6 Conclusion et perspectives



II L’opérateur matriciel de propagation en milieu aléatoire

II.1 Résumé

II.2 Introduction

II.3 Procédure expérimentale

II.4 Régime de diffusion multiple

II.4.1 Configuration expérimentale

II.4.2 Distribution expérimentale des valeurs singulières

II.4.3 Variance des coefficients de la matrice K

II.4.4 Influence des corrélations sur la distribution des valeurs singulières

II.4.5 Conclusion

II.5 Régime de diffusion simple

II.5.1 Cohérence déterministe des signaux simplement diffusés

II.5.2 Distribution des valeurs singulières

II.6 Détection de cible

II.7 Conclusion

II.A Annexes du chapitre II



IIISéparation diffusion simple/diffusion multiple : détection de cible

III.1 Résumé

III.2 Introduction

III.3 Dispositif et protocole expérimental

III.4 Extraction des signaux simplement diffusés

III.4.1 Cohérence spatiale des signaux simplement et multiplement diffusés

III.4.2 Rotation des données

III.4.3 Extraction de la diffusion simple par un filtrage adapté des antidiagonales

III.4.4 Reconstruction d’une matrice filtrée

III.4.5 Illustration de l’action du filtre adapté sur les antidiagonales de K

III.5 Détection et image de la cible

III.5.1 Echographie fréquentielle

III.5.2 Méthode D.O.R.T appliquée à la matrice de réponse

III.5.3 Méthode D.O.R.T appliquée à la matrice préalablement filtrée

III.6 Critère de détection

III.6.1 Etablissement d’un critère de détection : Théorie

III.6.2 Application des critères de détection à l’expérience

III.7 Aberration

III.7.1 Distorsion du front d’onde due à la couche diffusante

III.7.2 Action du filtrage sur les coefficients de distorsion

III.7.3 Extraction de la diffusion simple combinée avec D.O.R.T

III.8 Conclusion

III.A Annexes du chapitre III



IVSéparation diffusion simple/diffusion multiple : milieu faiblement diffusant

IV.1 Résumé

IV.2 Introduction

IV.3 Séparation diffusion simple / diffusion multiple

IV.3.1 Procédure expérimentale

IV.3.2 Filtrage par SVD des matrices A

IV.4 Application à l’étude d’un milieu très faiblement diffusant

IV.4.1 Illustration de la qualité de séparation diffusion simple / diffusion multiple

IV.4.2 Intensité multiplement diffusée

IV.4.3 Caractérisation d’un milieu très faiblement diffusant

IV.5 Application à l’imagerie ultrasonore dans le corps humain

IV.6 Conclusion

IV.A Annexe du chapitre IV



V Lien entre micro-architecture du milieu aléatoire et paramètres diffusants

V.1 Introduction

V.2 Libre parcours moyen élastique

V.2.1 Equation d’ondes en milieu hétérogène

V.2.2 Passage à la moyenne : Notion de milieu effectif

V.2.3 Expression analytique du libre parcours moyen (3D)

V.2.4 Comparaison entre théorie et simulation numérique (2D)

V.3 Libre parcours moyen de transport & coefficient de diffusion

V.3.1 Sections efficaces différentielle et totale de diffusion

V.3.2 Libre parcours moyen de transport (3D)

V.3.3 Confrontation entre la théorie et les expériences menées dans l’os

V.A Annexes du chapitre V



Conclusion 223



Bibliographie 235

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