Forecasting Wavefront Corrections in an Adaptive Optics System.

We use telemetry data from the Gemini North ALTAIR adaptive optics system to investigate how well the commands to the wavefront correctors (Tip/Tilt and high-order turbulence) can be forecasted in order to reduce lag error and improve delivered image quality. We show that a high level of reduction ($\sim$ 5 for Tip-Tilt and $\sim$ 2 for high-order modes) can be achieved by using a "forecasting module" based on a linear auto-regressive models with only a few coefficients ($\sim$ 30 for Tip-Tilt and $\sim$ 5 for high-order modes) to complement the existing integral servo-controller. Updating this module to adapt to evolving observing conditions is computationally inexpensive and requires less than 10 seconds worth of telemetry data. We also use several machine learning models to evaluate whether further improvements could be achieved with a more sophisticated non-linear model. Our attempts showed no perceptible improvements over linear auto-regressive predictions, even for large lags where residuals from the linear models are high, suggesting that non-linear wavefront distortions for ALTAIR at the Gemini North telescope may not be forecasted with the current setup.