ReVAR: a data-driven algorithm for generating aero-optic phase screens

The propagation of light through a turbulent flow field around an aircraft results in optical distortions commonly known as aero-optic effects. The development of methods to mitigate these effects requires large amounts of realistic aero-optic data. However, methods for obtaining these data, including experiment, computational fluid dynamics, and simple phase screen generation algorithms (e.g., boiling flow), each have significant drawbacks such as high cost, high computation, limited quantity, and/or inaccurate statistics. More recently, data-driven algorithms have been proposed that are computationally efficient and can synthesize aero-optic data to match the statistics of measured data, but these approaches still have drawbacks, including limited quality, inaccurate statistics, and the use of complicated algorithms. In this paper, we introduce ReVAR (Re-whitened Vector AutoRegression), a data-driven algorithm for generating synthetic aero-optic data that match the statistics of measured data. A key contribution in this algorithm is long-range autoregression, a linear predictive model that combines a standard autoregression with a set of low-pass filters of the data to fit both short-range and long-range temporal statistics. ReVAR uses long-range AR together with a spatial re-whitening step to convert measured aero-optic data to temporally and spatially uncorrelated white noise. ReVAR can then generate synthetic aero-optic data by reversing this process using white noise input. Using two measured turbulent boundary layer data sets, we demonstrate that ReVAR better matches the temporal power spectrum and other key metrics of the measured data than do two conventional phase screen generation methods and an existing single time-lag autoregressive model.