Wavefront prediction using artificial neural networks for open-loop Adaptive Optics

Latency in the control loop of adaptive optics (AO) systems can severely limit performance. Under the frozen flow hypothesis linear predictive control techniques can overcome this, however identification and tracking of relevant turbulent parameters (such as wind speeds) is required for such parametric techniques. This can complicate practical implementations and introduce stability issues when encountering variable conditions. Here we present a nonlinear wavefront predictor using a Long Short-Term Memory (LSTM) artificial neural network (ANN) that assumes no prior knowledge of the atmosphere and thus requires no user input. The ANN is designed to predict the open-loop wavefront slope measurements of a Shack-Hartmann wavefront sensor (SH-WFS) one frame in advance to compensate for a single-frame delay in a simulated $7\times7$ single-conjugate adaptive optics (SCAO) system operating at 150 Hz. We describe how the training regime of the LSTM ANN affects prediction performance and show how the performance of the predictor varies under various guide star magnitudes. We show that the prediction remains stable when both wind speed and direction are varying. We then extend our approach to a more realistic two-frame latency system. AO system performance when using the LSTM predictor is enhanced for all simulated conditions with prediction errors within 19.9 to 40.0 nm RMS of a latency-free system operating under the same conditions compared to a bandwidth error of $78.3\pm4.4$ nm RMS.