Laser beam shaping simulations for generation of artificial stars constellations

We report the study and analysis of different methods to generate arbitrary patterns of sodium laser guide stars asterisms starting from a single laser beam by using continuous face-sheet deformable mirrors. Two laser beam shaping procedures based on iterative Fourier transform algorithms have been explored. Numerical simulations with realistic parameters have been carried out to highlight the requirements on the phase retrieval algorithm and on the deformable mirrors employed.