D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson et al., science, vol.254, pp.1178-1181, 1991.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-zaiat, Optics communications, vol.117, pp.43-48, 1995.

A. Dubois, L. Vabre, A. Boccara, and E. Beaurepaire, Applied optics, vol.41, pp.805-812, 2002.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, Journal of biomedical optics, vol.7, pp.457-464, 2002.

A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre et al., Applied optics, vol.43, pp.2874-2883, 2004.

K. Grieve, A. Dubois, M. Simonutti, M. Paques, J. Sahel et al., Optics Express, vol.13, pp.6286-6295, 2005.

B. Pova?ay, A. Unterhuber, B. Hermann, H. Sattmann, H. Arthaber et al., Optics Express, vol.14, pp.7661-7669, 2006.

T. Bonin, G. Franke, M. Hagen-eggert, P. Koch, and G. Hüttmann, Optics letters, vol.35, pp.3432-3434, 2010.

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, Optics express, vol.19, pp.3044-3062, 2011.

H. W. Babcock, Publications of the Astronomical Society of the Pacific, vol.65, pp.229-236, 1953.

J. W. Hardy, Adaptive optics for astronomical telescopes, vol.16, 1998.

J. M. Beckers, Annual review of astronomy and astrophysics, vol.31, pp.13-62, 1993.

R. Tyson, Principles of adaptive optics, 2010.

B. Platt and R. V. Shack, Newsletter, vol.5, p.15, 1971.

L. Sherman, J. Ye, O. Albert, and T. Norris, Journal of microscopy, vol.206, pp.65-71, 2002.

N. Ji, D. E. Milkie, and E. Betzig, Nature methods, vol.7, p.141, 2009.

O. Azucena, J. Crest, S. Kotadia, W. Sullivan, X. Tao et al., Optics letters, vol.36, pp.825-827, 2011.

P. Vermeulen, E. Muro, T. Pons, V. Loriette, and A. Fragola, Journal of Biomedical Optics, vol.16, p.76019, 2011.

S. A. Rahman and M. J. Booth, Applied optics, vol.52, pp.5523-5532, 2013.

C. Bourgenot, C. Saunter, G. Love, and J. Girkin, Journal of the European Optical Society : rapid publications, vol.8, p.13027, 2013.

S. Tuohy and A. G. Podoleanu, Optics express, vol.18, pp.3458-3476, 2010.

J. Wang, J. Léger, J. Binding, A. C. Boccara, S. Gigan et al., Biomedical optics express, vol.3, pp.2510-2525, 2012.

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, Optics express, vol.16, pp.9290-9305, 2008.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nature photonics, vol.6, p.283, 2012.

I. M. Vellekoop and A. P. Mosk, Opt. Lett, vol.32, pp.2309-2311, 2007.

C. Prada, F. Wu, and M. Fink, J. Acoust. Soc. Am, vol.90, pp.1119-1129, 1991.

C. Prada and M. Fink, Wave motion, vol.20, pp.151-163, 1994.

C. Prada, S. Manneville, D. Spoliansky, and M. Fink, J. Acoust. Soc. Am, vol.99, pp.2067-2076, 1996.

C. W. Beenakker, Reviews of modern physics, vol.69, p.731, 1997.

S. Rotter and S. Gigan, Reviews of Modern Physics, vol.89, p.15005, 2017.

H. Ammari, J. Garnier, W. Jing, H. Kang, M. Lim et al., Mathematical and Statistical Methods for Multistatic Imaging, pp.145-161, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00934743

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara et al., Phys. Rev. Lett, vol.104, p.100601, 2010.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nature Comm, vol.1, pp.1-5, 2010.

J. Pendry, Physics, vol.1, p.20, 2008.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld et al., Physical review letters, vol.111, p.153902, 2013.

M. Tanter, J. Thomas, and M. Fink, The Journal of the Acoustical Society of America, vol.108, pp.223-234, 2000.

A. Aubry and A. Derode, J. Appl. Phys, vol.106, p.44903, 2009.

A. Aubry and A. Derode, Phys. Rev. Lett, vol.102, p.84301, 2009.

S. Shahjahan, A. Aubry, F. Rupin, B. Chassignole, and A. Derode, Applied Physics Letters, vol.104, p.234105, 2014.

S. M. Popoff, A. Aubry, G. Lerosey, M. Fink, A. Boccara et al., Physical review letters, vol.107, p.263901, 2011.

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, Inverse Problems, vol.28, p.125008, 2012.

T. Zhang, K. Unger, G. Maire, P. C. Chaumet, A. Talneau et al., Optics express, vol.26, pp.26093-26105, 2018.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink et al., Science advances, vol.2, p.1600370, 2016.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang et al., Nature Photonics, vol.9, p.253, 2015.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang et al., Nature communications, vol.8, p.2157, 2017.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nature physics, vol.11, p.684, 2015.

Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari et al., Physical review letters, vol.111, p.243901, 2013.

J. Mertz, Introduction to optical microscopy, vol.138, 2010.

R. R. Anderson and J. A. Parrish, Journal of investigative dermatology, vol.77, pp.13-19, 1981.

A. Badon, A. C. Boccara, G. Lerosey, M. Fink, and A. Aubry, Optics Express, vol.25, pp.28914-28934, 2017.

M. Marvin, Microscopy apparatus, p.467, 1961.

M. Rajadhyaksha, R. R. Anderson, and R. H. Webb, Applied optics, vol.38, pp.2105-2115, 1999.

J. W. Goodman, Statistical optics, 2015.

W. Drexler and J. G. Fujimoto, Optical coherence tomography : technology and applications, 2008.

M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, Optics express, vol.11, pp.2183-2189, 2003.

R. K. Wang, Applied Physics Letters, vol.90, p.54103, 2007.

F. Zernike, Physica, vol.5, pp.785-795, 1938.

J. W. Goodman, Introduction to Fourier optics, 2005.

J. Zhang and J. Dainty, Journal of Modern Optics, vol.39, pp.2383-2404, 1992.

D. R. Neal, J. Copland, and D. A. Neal, Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, vol.4779, pp.148-161, 2002.

J. C. Dainty, A. V. Koryabin, and A. V. Kudryashov, Applied optics, vol.37, pp.4663-4668, 1998.

R. J. Noll, JOsA, vol.66, pp.207-211, 1976.

C. Sheppard and T. Wilson, Journal of microscopy, vol.124, pp.107-117, 1981.

T. Wilson and C. Sheppard, Theory and practice of scanning optical microscopy, vol.180, 1984.

B. Hermann, E. Fernández, A. Unterhuber, H. Sattmann, A. Fercher et al., Optics letters, vol.29, pp.2142-2144, 2004.

A. Roorda, F. Romero-borja, W. J. Donnelly, I. , H. Queener et al., Optics express, vol.10, pp.405-412, 2002.

P. Xiao, M. Fink, and A. C. Boccara, Journal of biomedical optics, vol.21, p.121505, 2016.

P. Xiao, M. Fink, and A. C. Boccara, Optics letters, vol.41, pp.3920-3923, 2016.

T. ?i?már and K. Dholakia, Nature communications, vol.3, p.1027, 2012.

P. Hougne, M. Fink, and G. Lerosey, Nature Electronics, vol.2, p.36, 2019.

O. Dorokhov, 30 Years Of The Landau Institute-Selected Papers, pp.234-237, 1996.

J. Pendry, A. Mackinnon, and A. Pretre, Physica A : Statistical Mechanics and its Applications, vol.168, pp.400-407, 1990.

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, Physical review letters, vol.113, p.173901, 2014.

S. Popoff, A. Goetschy, S. Liew, A. D. Stone, and H. Cao, Physical review letters, vol.112, p.133903, 2014.

I. Freund, M. Rosenbluh, and S. Feng, Physical review letters, vol.61, p.2328, 1988.

A. Badon, Approche matricielle de l'imagerie optique des milieux diffusants, Theses, 2016.

T. ?i?már and K. Dholakia, Opt. Exp, vol.19, pp.18871-18884, 2011.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, New Journal of Physics, vol.13, p.123021, 2011.

K. Creath, Progress in optics 26, pp.349-393, 1988.

J. Mertz, H. Paudel, and T. G. Bifano, Applied optics, vol.54, pp.3498-3506, 2015.

J. Robert and M. Fink, J. Acoust. Soc. Am, vol.123, pp.866-877, 2008.

R. G. Ghanem and P. D. Spanos, Stochastic finite elements : a spectral approach, Courier Corporation, 2003.

G. E. Fasshauer and M. J. Mccourt, SIAM Journal on Scientific Computing, vol.34, pp.737-762, 2012.

A. Aubry, J. De-rosny, J. Minonzio, C. Prada, and M. Fink, The Journal of the Acoustical Society of America, vol.120, pp.2746-2754, 2006.

S. Provencher, The Journal of Chemical Physics, vol.64, pp.2772-2777, 1976.

F. Gori and C. Palma, Journal of Physics A : Mathematical and General, vol.8, p.1709, 1975.

L. Jost, Oikos, vol.113, pp.363-375, 2006.

O. Roy and M. Vetterli, 2007 15th European Signal Processing Conference, pp.606-610, 2007.

L. Wang, J. Math. Study, vol.50, pp.101-143, 2017.

J. Robert, M. Burcher, C. Cohen-bacrie, and M. Fink, The Journal of the Acoustical Society of America, vol.119, pp.3848-3859, 2006.

J. Robert, Estimation de fonctions de green dans les milieux complexes par décomposition de l'opérateur retournement temporel : application à l'imagerie médicale et à la correction d'aberration, vol.7, 2007.

J. Robert and M. Fink, The Journal of the Acoustical Society of America, vol.127, pp.2904-2912, 2010.

S. Yun, G. Tearney, B. Bouma, B. Park, and J. F. De-boer, Optics express, vol.11, pp.3598-3604, 2003.

J. F. De-boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney et al., Optics letters, vol.28, pp.2067-2069, 2003.

E. Beaurepaire, A. C. Boccara, M. Lebec, L. Blanchot, and H. Saint-jalmes, Optics letters, vol.23, pp.244-246, 1998.

J. Binding, J. B. Arous, J. Léger, S. Gigan, C. Boccara et al., Optics express, vol.19, pp.4833-4847, 2011.

J. Schwider, O. R. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Optical Engineering, vol.32, pp.1883-1886, 1993.

G. Stoilov and T. Dragostinov, Optics and Lasers in Engineering, vol.28, pp.61-69, 1997.

A. Dubois, , vol.18, 1972.

V. N. Mahajan, JOSA, vol.72, pp.1258-1266, 1982.

E. Knop and N. Knop, Immune Response and the Eye, vol.92, pp.36-49, 2007.

A. Daxer, K. Misof, B. Grabner, A. Ettl, and P. Fratzl, Investigative Ophthalmology and Visual Science, vol.39, pp.644-647, 1998.

V. Ntziachristos, Nature methods, vol.7, p.603, 2010.

W. Kutzelnigg and D. Mukherjee, The Journal of chemical physics, vol.107, pp.432-449, 1997.

. Résumé,

, Initialement développées en astronomie, des méthodes d'optique adaptative ont été transposées en microscopie afin de compenser les effets dues aux aberrations. Celles-ci reposent principalement sur la mesure du front d'onde et sur la correction en boucle fermée des aberrations à l'aide de dispositifs de contrôle du front d'onde. Ces méthodes sont toutefois limitées par les cadences de mesure et de correction, Les techniques de microscopie interférométrique présentent une sensibilité aux aberrations qui limite leurs pouvoirs de résolution et de pénétration dans les tissus biologiques

, matricielle innovante reposant sur l'étude d'un nouvel opérateur, la matrice distorsion, permettant de quantifier localement les paramètres liés aux aberrations et à la diffusion, et de corriger les aberrations sur l'ensemble du champs de vision même en présence de plusieurs aires d'isoplanétisme. En parallèle, nous présentons un formalisme mathématique permettant d'expliquer la manifestation des aberrations en OCT plein champ et étendons le champ d'application de la méthode matricielle à de vastes champs de vision au moyen d'un dispositif expérimental de mesure de la matrice de réflexion

. Mots-clés,

. Matrice-de-réflexion, O. Optique, and F. Oct-plein-champ, Most of them rely on the measurement of the wave front and on a close-loop correction of the aberrations using wave-front control devices. These methods are nevertheless limited by the rates of measurement and correction and can only compensate for low-order aberrations. The purpose of this thesis is to present an innovative matrix approach relying on the analysis of a new operator, the distorsion matrix, allowing to locally quantify the scattering and aberration parameters, and to compensate for the aberrations over the whole field of view for different isolanatic areas. Besides, we introduce a mathematical formalism in order to describe the effects of aberrations in full-field OCT and we extend the scope of the matrix approach to very large fields of view thanks to an experimental setup of reflection matrix measurement inspired by this technique of imaging