Improving centroiding by super-resolution reconstruction of sodium layer density in Shack-Hartmann wavefront sensors

Adaptive optics in the new generation of large telescopes, over 24 m in diameter, present new challenges. One of them is spot elongation in Shack-Hartmann wavefront sensors when using laser guide stars. The laser brightness depends on the sodium layer density profile, and this is reproduced in the format of an elongated spot. The pattern of the spot is a problem for centroiding techniques, and knowledge of the sodium layer profile is essential for adequate centroiding. In this work, we propose a super-resolution reconstruction technique that combines the information available in various low-resolution elongated spots over the sub-apertures of the sensor to obtain a high-resolution sodium layer density profile that can be used as a reference in centroiding. This is achieved with the information available in the Shack-Hartmann wavefront sensor only, dispensing with external measurements. Finally, we present simulation results of an iterative method that yields a super-resolved sodium layer density profile jointly with improved centroiding.