Forecasting Wavefront Corrections in an Adaptive Optics System

Abstract: We use telemetry data from the Gemini North ALTAIR adaptive optics system to investigate how well the commands for wavefront correction (both Tip/Tilt and high-order turbulence) can be forecasted in order to reduce lag error (due to wavefront sensor averaging and computational delays) 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) in RMS wavefront error can be achieved by using a "forecasting filter" based on a linear auto-regressive model 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 filter 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 (Long-Short Term Memory and dilated convolutional 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