Effects of laser beam propagation and saturation on the spatial shape of sodium laser guide stars

The possibility to produce diffraction-limited images by large telescopes through Adaptive Optics is closely linked to the precision of measurement of the position of the guide star on the wavefront sensor. In the case of laser guide stars, many parameters can lead to a strong distortion on the shape of the LGS spot. Here we study the influence of both the saturation of the sodium layer excited by different types of lasers, the spatial quality of the laser mode at the ground and the influence of the atmospheric turbulence on the upward propagation of the laser beam. Both shape and intensity of the LGS spot are found to depend strongly on these three effects with important consequences on the precision on the wavefront analysis.