Natural guide-star processing for wide-field laser-assisted AO systems

Sky-coverage in laser-assisted AO observations largely depends on the system's capability to guide on the faintest natural guide-stars possible. Here we give an up-to-date status of our natural guide-star processing tailored to the European-ELT's visible and near-infrared (0.47 to 2.45 {\mu}m) integral field spectrograph - Harmoni. We tour the processing of both the isoplanatic and anisoplanatic tilt modes using the spatio-angular approach whereby the wave-front is estimated directly in the pupil plane avoiding a cumbersome explicit layered estimation on the 35-layer profiles we're currently using. Taking the case of Harmoni, we cover the choice of wave-front sensors, the number and field location of guide-stars, the optimised algorithms to beat down angular anisoplanatism and the performance obtained with different temporal controllers under split high-order/low-order tomography or joint tomography. We consider both atmospheric and far greater telescope wind buffeting disturbances. In addition we provide the sky-coverage estimates thus obtained.