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

TL;DR

The paper tackles slow focus errors in laser guide star adaptive optics by leveraging focal plane wavefront sensing (FPWFS) with Keck I's TRICK near-infrared tip-tilt sensor. It compares three single-image phase retrieval algorithms—Gerchberg-Saxton (GS), Linearized Focal Plane Technique (LiFT), and Gaussian fit (Gf)—across simulations, bench tests, and on-sky experiments, assessing linearity, computation, and resilience to residuals. GS emerges as the most robust and stable under AO residuals, guiding on-sky deployment; on-sky closed-loop tests show GS can compensate for introduced focus errors even in challenging conditions, indicating improved sky coverage and faster focus updates. The results support extending FPWFS-based slow focus sensing to other 8-10 m class telescopes and future ELTs, where high-S/N, full-pupil measurements can substantially reduce lag and improve AO performance.

Abstract

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 for that error. Our goal is to develop and operationalize a focal plane wavefront sensing (FPWFS) technique for slow focus tracking for the Keck I telescope, which can significantly increase sky coverage and allow slow focus tracking at higher frequencies, reducing the lag error. We develop, characterize, and compare three different FPWFS algorithms, namely Gerchberg-Saxton (GS), linearized focal plane technique (LiFT), and Gaussian fit (Gf). These algorithms were 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). 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. On-sky tests showed promising results, with GS successfully compensating for purposely introduced focus errors, even under the presence of high turbulence conditions. 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.

Figures (17)

• Figure 1: a) Phase retrieval scheme (Adapted from roddier1999adaptive). b) Example from the NIR TT sensor at Keck I (TRICK), illustrating how the presence of astigmatism (0º) as phase diversity causes the focal plane image to stretch in perpendicular directions depending on the focus sign, thereby resolving the focus sign ambiguity.
• Figure 2: Keck I LGS-AO system scheme (wizinowich2006wm, van2006wm. The high-order (all modes expect TT) loop is operated with the light coming from the LGSs, while the low-order loop is operated with NGS light. In the low-order loop, the TT and slow focus ($Z_4$) sensing can be both performed using images provided by TRICK. The current approach for slow focus sensing is to use the LBWFS. The measured focus values are then used to compensate for the focus error by moving the FCS. OSIRIS is the science camera.
• Figure 3: Lag error ($\sigma_{\epsilon}$) according to the correction cadence ($\Delta t_{CC}$). Perfect correction is assumed, i.e., only the temporal error is taken into account. The values of $\sigma_{\epsilon}$ are proportional to $\sqrt{\Delta t_{CC}}$.
• Figure 4: Focus ramp simulation under ideal conditions (no noise or high-order residuals). Results presented for H band, with the angular pixel size of the simulated images being 50 mas.
• Figure 5: Focus ramp simulated under the same conditions as the one presented in Fig. \ref{['focus_ramp__fov_8_ideal_simulation']}, but with a smaller FoV (4x4 pix.).