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The Multi-conjugate Adaptive Optics RelaY (MAORY) is one of the key AdaptiveOptics (AO) systems on the European Southern Observatory's Extremely LargeTelescope. MAORY aims to achieve a good wavefront correction over a large fieldof view, which involves a tomographic estimation of the 3D atmosphericwavefront disturbance. Mathematically, the reconstruction of turbulent layersin the atmosphere is severely ill-posed, hence, limits the achievablereconstruction accuracy. Moreover, the reconstruction has to be performed inreal-time at a few hundred to one thousand Hertz frame rates. Huge amounts ofdata have to be processed and thousands of actuators of the deformable mirrorshave to be controlled by elaborated algorithms. Even with extensiveparallelization and pipelining, direct solvers, such as the Matrix VectorMultiplication (MVM) method, are extremely demanding. Thus, research in thelast years shifted into the direction of iterative methods. In this paper wefocus on the iterative Finite Element Wavelet Hybrid Algorithm (FEWHA). The keyfeature of FEWHA is a matrix-free representation of all operators involved,which makes the algorithm fast and enables on the fly system updates wheneverparameters at the telescope or in the atmosphere change. We provide aperformance analysis of the method regarding quality and run-time for the MAORYinstrument using the AO software package COMPASS.

Performance of an iterative wavelet reconstructor for the Multi-conjugate Adaptive Optics RelaY of ESO's ELT