Efficient iterative atmospheric tomography reconstruction from LGS and additional tip/tilt measurements

Adaptive Optics systems for the new generation of extremely large telescopes require fast mathematical methods for the computation of the shape of the deformable mirrors. MCAO or MOAO systems use laser guide stars for the reconstruction of the turbulent atmosphere. However, measurements from laser guide stars contain no information on the tip/tilt of the incoming wavefronts. Assuming that additional tip/tilt measurements of wavefronts from natural guide stars are available, we present an iterative Kaczmarz reconstructor that computes the turbulent atmospheric layers from the wavefronts of both the laser and natural guide stars. We show in particular that the resulting algorithm meets the quality and speed requirements for ELTs.