The Multi-conjugate Adaptive Optics RelaY (MAORY) is one of the key Adaptive Optics (AO) systems on the Extremely Large Telescope (ELT). MAORY aims to achieve a good wavefront correction over a large field of view, which involves a tomographic estimation of the 3D atmospheric wavefront disturbance. Mathematically, the reconstruction of turbulent layers in the atmosphere is severely ill-posed, hence, it limits the achievable reconstruction accuracy. Moreover, the reconstruction has to be performed in real-time at a few hundred to one thousand Hertz frame rates. In this talk we focus on the iterative Finite Element Wavelet Hybrid Algorithm (FEWHA). The key feature of FEWHA is a matrix-free representation of all underlying operators, which makes the algorithm fast and enables on the fly parameter updates. We show the performance of the algorithm regarding reconstruction quality and run-time for the MAORY instrument via numerical simulations.
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