Optical solution to spot elongation in laser guide stars wavefront sensors for Extremely Large Telescopes

Laser guide stars have been proposed to overcome a widely recognized limitation of adaptive optics: the need for bright reference sources for wavefront sensing nearby the scientific field of interest. The laser guide stars foreseen for the future Extremely Large Telescopes are based on the resonant back-scattering of a laser beam by the Sodium atoms concentrated in a similar to 13 km thick layer at about 90 km above the ground. Such an artificial source, observed from a position laterally offset from the laser projector, appears elongated due to the finite thickness of the Sodium layer: on a 40-m class telescope with laser projector located on the primary mirror edge the image elongation may exceed 13 arcsec. In a Shack-Hartmann wavefront sensor, the elongated spots require the use of large detectors to avoid spot truncation and impose demanding requirements in terms of photon flux return with respect to smaller telescopes. We propose an alternative wavefront sensor concept intrinsically insensitive to the spot elongation, measuring the local wavefront slope in the direction orthogonal to the elongation itself; the full 2D slope measurements are retrieved by combining the signals from different laser guide stars, projected from different positions at the edge of the telescope. The performance of the new wavefront sensor is analysed in the framework of a ground-layer adaptive optics application. A possible extension to multiconjugate adaptive optics is also qualitatively described.