Performance comparison of centroiding algorithms for laser guide star wavefront sensing with extremely large telescopes

Sodium laser guide stars (LGSs) increase the sky coverage of adaptive optics systems but have their own limitations. For Shack–Hartmann wavefront sensors (WFSs), the slow variations of the sodium layer altitude and atom density profile induce changing errors on centroid measurements, especially for extremely large telescopes (ELTs), as the spot elongation increases with the telescope diameter. These LGS-induced aberrations are propagated on the science path and must be filtered out by (i) optimizing the LGS WFS and the centroiding algorithm and (ii) adding a high-pass filter on the LGS path and a low-bandwidth natural-guide-star (NGS) WFS. Within the context of the European Southern Observatory European-ELT project, five different centroiding algorithms, namely, the center-of-gravity (CoG), weighted CoG, matched filter, quad cell, and correlation, have been evaluated in a closed loop on the University of Victoria LGS wavefront sensing test bed. This optical bench reproduces, in the laboratory, both NGS spots and LGS elongated spots with changing sodium profiles and turbulence. Each centroiding algorithm performance is compared and discussed for a central- versus side-launch laser: different fields of view, pixel sampling, and signal-to-noise ratios.