Thèse de doctorat en Génie biologique et médical. Optique et traitement de signal
Soutenue en 2003
à Paris 12 .
Mueller's matrices and speckle analysis applied to biomedical applications
This memory is posed in terms of "methods and applications" for the investigation, by optical methods, of scattering media for biomedical applications. It makes the object of two great parts, the polarimetric imagery on the one hand and the field of speckle on the other hand. Polarimetric imagery : the first fourth chapters are dedicated to the analysis and the exploitation of the polarisation of the light for the biomedical imagery. The first chapter exposes the various formailisms used in the studies on the polarization of the light:formalisms of Jones, Stokes-Mueller and Poincaré. The second chapter relates to a thorough analysis of the matrices of Mueller through the study of the matrices known as of "Mueller Jones" or of the matrices of Mueller for the depolarizing media in an anisotropic way. An approach by a commutable multilayer model is proposed to extract the polarimetric parameters from diattenuation, retardance and depolarization. The polarimetric treatment is supplemented by the exploitation of the coherency matrix. These treatments make it possible to code the images in optical or physical properties. The chapter three is devoted to a. Device of acquisition of the matrices of Muai- 1er. The chapter four, presents two examples of applications of the formalism of Mueller in the biomedical field, namely the quantification of the hepatic fibrosis and tEe discrimination of cutaneous tissus having undergone an irradiation. Speckle: The chapters five and six present an original anelysis of the speckle. The chapter five briefly exposes the statistical characteristics of the model speckle before proposing a. Junction with the theory of the Brownian motion. A statistical drift of the experimental speckle requires the adaptation of the theory of the Brownien motion to the fractional Brownian motion. An adjustment between the model and the physical phenomenon is thus possible thanks to this degree of additional freedom. This fractal approach allows the multi-characterization of the figures of speckle starting from three qnantifiable criteria. The chapter six presents the experimental validation of the approach, two applications in biomedical matter encourages us to privilege rather the variational approach than static speckle.