Authors: Thierry Fusco, Jean-Marc Conan
The estimation of the turbulent phase from wavefront sensing measurements is a key issue in high resolution imaging. Phase reconstruction is an inverse problem in a rather simple context: direct problem generally assumed to be linear, statistical prior information on the turbulent phase easily derived from physical models. Solving this problem is also very important in order to address the issue of optimal control in Adaptive Optics [AO].
We will first recall the basic concepts of stochastic estimation and inverse problem theory: maximum likelihood, regularization, maximum a posteriori and minimum mean square error estimation. We will then show how these concepts can be used to define an optimal wavefront reconstruction. We will first consider a static open-loop case. Using standard Kalman filtering theory, the approach will be extended to the case of closed-loop dynamic control in AO and MCAO.
AO and MCAO simulations will be presented to illustrate the theoretical developments.
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