Non-invasive optical gain estimation in pyramid wavefront sensors from telemetry using machine learning

Abstract

Modern adaptive optics (AO) instruments at large-aperture observatories require stable loop operation while delivering high correction performance for imaging, spectroscopy, and high-contrast observing modes. The pyra mid wavefront sensor (PyWFS) is intrinsically nonlinear: its slope response depends on the residual aberration entering the sensor, and therefore changes as atmospheric conditions fluctuate. This sensitivity variation is parameterized by the optical gain, Gopt, defined as the ratio between the WFS command amplitude and the measured sensor response for a test mode. At the Large Binocular Telescope Observatory (LBTO), the SOUL AO system tracks this nonlinearity by continuously demodulating an 80Hz sinusoidal probe injected on a controlled mode. The probe provides a direct calibration signal and supports non-common-path-aberration compensation in seeing-tracking operation. However, during rapidly changing seeing it can introduce reactive jumps in the applied correction, and for advanced observing modes it can also produce a coherent feature that is undesirable for high-contrast post processing. We present a machine-learning approach to forecast Gopt non-invasively from synchronized AO telemetry. The method uses random forests and quantile regression forests with split-conformal calibration to produce both a point forecast and an uncertainty interval. The analysis uses telemetry from SOUL operations spanning 2023 2026, including seeing, Strehl-ratio proxy, guide-star magnitude, frame-rate block, and recent Gopt history. A dedicated 1500–2000Hz model achieves a five-minute-ahead mean absolute error of 0.018 and R2 = 0.940 on held-out nights, while calibrated intervals reach approximately 94% empirical coverage. A rate-limited smoothing layer reduces one-minute Gopt jumps by about 71–82% depending on the percentile. This approach provides an operational path for using telemetry-based optical-gain prediction as a smoothing, validation, or no-probe fallback layer in the real-time AO loop.