High robust spatio-temporal wavefront prediction with mixed graph neural network in adaptive optics

The time-delay problem, which is introduced by the response time of hardware for correction, is a critical and non-ignorable problem of adaptive optics (AO) systems. It will result in significant wavefront correction errors while turbulence changes severely or system responses slowly. Predictive AO is proposed to alleviate the time-delay problem for more accurate and stable corrections in the real time-varying atmosphere. However, the existing prediction approaches either lack the ability to extract non-linear temporal features, or overlook the authenticity of spatial features during prediction, leading to poor robustness in generalization. Here, we propose a mixed graph neural network (MGNN) for spatiotemporal wavefront prediction. The MGNN introduces the Zernike polynomial and takes its inherent covariance matrix as physical constraints. It takes advantage of conventional convolutional layers and graph convolutional layers for temporal feature catch and spatial feature analysis, respectively. In particular, the graph constraints from the covariance matrix and the weight learning of the transformation matrix promote the establishment of a realistic internal spatial pattern from limited data. Furthermore, its prediction accuracy and robustness to varying unknown turbulences, including the generalization from simulation to experiment, are all discussed and verified. In experimental verification, the MGNN trained with simulated data can achieve an approximate effect of that trained with real turbulence. By comparing it with two conventional methods, the demonstrated performance of the proposed method is superior to the conventional AO in terms of root mean square error (RMS). With the prediction of the MGNN, the mean and standard deviation of RMS in the conventional AO are reduced by 54.2% and 58.6% at most, respectively. The stable prediction performance makes it suitable for wavefront predictive correction in astronomical observation, laser communication, and microscopic imaging.