Wavefront prediction of convective boundary layers using multiple-aperture digital holography

Abstract

A major limiting factor for adaptive-optic systems is the cumulative latency inherent in the control loop. One way to address the latency problem is to use multiple apertures, where upstream wavefront measurements can be used to predict the wavefronts over the main aperture. In this work, the multiple aperture prediction method is extended to a dual-wavelength digital holography sensing system, and machine learning is used to predict downstream turbulent boundary layer wavefronts from upstream measurements. Wavefronts are decomposed using Joint Proper Orthogonal Decomposition (JPOD), and a ridge least squares predictor and a multilayer perceptron (MLP) are trained to predict downstream time coefficients from a window of upstream coefficients. Predictions are compared to a time shift convective baseline across three aperture separations (2.9δ, 3.6δ, and 4.3δ), which target the regime where Taylor’s frozen flow hypothesis breaks down, and at three Mach numbers (0.58, 0.70, and 0.80). Both predictors substantially outperform the time shift baseline across all nine conditions, recovering 64% of the downstream wavefront energy at the easiest condition compared to 30% for time shift, and 34% compared to −21% at the most extreme condition. They also converge to nearly identical predictions, indicating that the flow’s upstream to downstream dynamics are well described by a linear mapping. Analysis of the ridge weight matrix shows that these predictions are largely enabled by the aperture windowing effect, where convecting structures project onto different modes at different lags as they move through the downstream aperture, allowing the predictor to distinguish coherent convecting structures from unpredictable turbulent fluctuations. For a real time predictive controller, retaining approximately 60 modes captures nearly all the predictable energy. The prediction limits that remain appear to stem from the path-integrated nature of the wavefront measurement itself, in which contributions from the opposite wall boundary layer are integrated into the same signal and cannot be resolved.