Slow focus sensor for the Keck I laser guide star adaptive optics system using focal plane wavefront sensing

Context . Laser guide stars (LGSs) have been deployed for the last 20–30 years in ground-based astronomical telescopes to overcome the limited sky coverage of classical adaptive optics (AO) systems. Unfortunately, slow altitude drifts of the sodium layer compromise focus measurements, generating the so-called slow focus error, and, consequently, a natural guide star (NGS) is needed to compensate that error. The Keck I telescope AO system uses a 20 × 20 Shack-Hartmann (SH) wavefront sensor (WFS) for slow focus tracking (with a 5x5 mode used on fainter stars). This approach is far from optimal due to limited sky coverage, since the available NGSs are usually very faint. Aims . Our goal is to develop a different technique for slow focus tracking and make it fully operational using focal plane wavefront sensing (FPWFS), which can significantly increase sky coverage and allow slow focus tracking at higher frequencies, reducing the lag error. The Keck I near-infrared (NIR) tip-tilt sensor, known as TRICK, is used to obtain the focal plane images without any hardware modifications being necessary. Methods . We develop, characterize, and compare three different FPWFS algorithms, namely Gerchberg–Saxton (GS), linearized focal plane technique (LiFT), and Gaussian fit (Gf). These algorithms are studied for the specific purpose of slow focus sensing in the NIR (H and K bands) using numerical simulations and data collected at Keck in 2025 (bench and on-sky). Results . The three algorithms were studied and characterized against different criteria such as linearity, computational costs, and resistance to low signal-to-noise ratio and/or residuals. From the results obtained, the main candidate for an on-sky deployment was GS, for which the main deciding factor was its higher stability and robustness under the presence of residuals. For that reason, on-sky tests in closed loop were made with GS. Conclusions . On-sky tests showed promising results, with GS successfully compensating for purposely introduced focus errors, even under the presence of high turbulence conditions. These tests represent an important step toward the full operationalization of this tool, expected in the coming months. This work can also be extrapolated to other existing 8–10 m class telescopes, or even future 30–40 m class telescopes, where the use of FPWFS can significantly improve sky coverage and reduce the lag error.