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Etude de quelques questions mathématiques apparaissant en optique adaptative

Abstract : Adaptive Optics is a technics allowing for the correction in real-time of the evoluting and non-predictive of a wavefront, thanks to a deformable mirror. Perturbations usually appear when optical rays cross the Earth's atmosphere. This work is constituted of the study of four main problems arising in most actual adaptive optics systems : - the reconstruction of the incoming wavefront, from measures here of a Shack-Hartmann sensor. - setting the equations describing the shape of the deformable mirror achieving a perfect correction of the incoming wavefront. - the control and the stabilization of a first mirror model, called bimorph mirror, built by Lenczner and Prieur, are studied. Constituted of three layers, the mirror itself (exible layer), and two layers equipped with respectively piezelectric sensors and piezoelectric actuators. The coupling of two PDEs, very different in nature, leads to a really interesting problem. - Several theorems about strong, exponential and polynomial stabilization of a second model, a beam clamped at an extremity and free at the other, and two piezoelectric cells, are proved.
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Pierre Le Gall. Etude de quelques questions mathématiques apparaissant en optique adaptative. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2006. Français. ⟨NNT : 2006NAN10214⟩. ⟨tel-01754269⟩



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