Identification en imagerie Doppler : liens avec la transformée de radon généralisée
The magnetic field plays a major role in the star evolution as weil as its interaction with the circumstellar environment. A consequence of the magnetic activity is the existence of stellar surface structures. Unfortunately, very few stars can be spatially resolved by telescope so that indirect methods are needed. Doppler imaging is one of them. We first begin with a detailed presentation of Doppler imaging. We explain, more briefly, what is tomography or equivalently, classical Radon transform. This enable us to show the analogy between these two methods. Doppler imaging is then express as a generalized Radon transform. It is thus easier to study the identification of this inverse problem. In particular we deduce the existence of some radial functions in the Doppler imaging operator kernel. Efficient numerical code are adapted to our geometry in order to characterize these functions of the kernel precedently deduced. Then we focus on the sampling geometry in Doppler imaging. Again we extend some well known results of efficient sampling in classical tomography to the rotation invariant generalized Radon transform with polynomial weight functions. This result can be applied on two extremely cases in Doppler imaging. Besides, we deal with Doppler imaging astrophysical implications. First, we show some evidence of the stars magnetic activity, in particular for the T Tauri stars. Then we briefly present how magnetic field is part of evolution models. Secondly, we make a short revue of the main methods that help to estimate the magnetic activity and we insist on the specificity of Doppler imaging among these methods. At least, this technique is applied to some real data that we obtained on SU Aurigae from the Observatoire de Haute Provence. Some evidence of surface structures on this T Tauri star is deduced and discussed.