Optimal LGS pointing with faint tip-tilt NGS

Experience with the current generation of astronomical single laser guide star (LGS) adaptive optics (AO) systems has demonstrated system performance that is often limited by residual tip-tilt errors induced by the paucity of bright tip-tilt natural guide stars (NGS). To overcome this limitation, we are developing a new generation of tip-tilt sensors that will operate at near-infrared wavelengths where the NGS is sharpened to the diffraction limit. To optimize performance, single LGS AO systems utilizing sharpened tip-tilt NGS should generally not point their LGS directly toward their science target. Rather, optimal performance for wide sky coverage is obtained by offsetting LGS pointing along a radius connecting the science target and the tip-tilt NGS. We demonstrate that determination of the jointly optimized LGS pointing angle and tip-tilt wavefront sensor (WFS) integration time can improve performance metrics by factors of several, particularly for faintest NGS operation. We find the LGS offset should be as much as 1/2 the distance to the NGS to maximize Strehl ratio at near-infrared wavelengths and ≈ 1/4 the distance to the NGS to maximize ensquared energy, with lesser off-pointing for brighter NGS. Future AO systems may benefit from predictive determination of optimal LGS offsetting, based upon changing atmospheric conditions and observational geometries.