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 this data, including experiment, computational fluid dynamics, and simple phase screen 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 matches 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 un-correlated 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 measured data's temporal power spectrum and other key metrics than do two conventional phase screen generation methods and an existing single time-lag autoregressive model.

Boiling flow parameter estimation from boundary layer data

Atmospheric turbulence and aero-optic effects cause phase aberrations in propagating light waves, thereby reducing effectiveness in transmitting and receiving coherent light from an aircraft. Existing optical sensors can measure the resulting phase aberrations, but the physical experiments required to induce these aberrations are expensive and time-intensive. Simulation methods could provide a less expensive alternative. For example, an existing simulation algorithm called boiling flow, which generalizes the Taylor frozen-flow method, can generate synthetic phase aberration data (i.e., phase screens) induced by atmospheric turbulence. However, boiling flow depends on physical parameters, such as the Fried coherence length r0, which are not well-defined for aero-optic effects. In this paper, we introduce a method to estimate the parameters of boiling flow from measured aero-optic phase aberration data. Our algorithm estimates these parameters to fit the spatial and temporal statistics of the measured data. This method is computationally efficient and our experiments show that the temporal power spectral density of the slopes of the synthetic phase screens reasonably matches that of the measured phase aberrations from two turbulent boundary layer data sets, with errors between 8-9%. However, the Kolmogorov spatial structure function of the phase screens does not match that of the measured phase aberrations, with errors above 28%. This suggests that, while the parameters of boiling flow can reasonably fit the temporal statistics of highly convective data, they cannot fit the complex spatial statistics of aero-optic phase aberrations.

Boiling flow estimation for aero-optic phase screen generation

Aero-optic effects due to turbulence can reduce the effectiveness of transmitting light waves to a distant target. Methods to compensate for turbulence typically rely on realistic turbulence data, which can be generated by i) experiment, ii) high-fidelity CFD, iii) low-fidelity CFD, and iv) autoregressive methods. However, each of these methods has significant drawbacks, including monetary and/or computational expense, limited quantity, inaccurate statistics, and overall complexity. In contrast, the boiling flow algorithm is a simple, computationally efficient model that can generate atmospheric phase screen data with only a handful of parameters. However, boiling flow has not been widely used in aero-optic applications, at least in part because some of these parameters, such as r0, are not clearly defined for aero-optic data. In this paper, we demonstrate a method to use the boiling flow algorithm to generate arbitrary length synthetic data to match the statistics of measured aero-optic data. Importantly, we modify the standard boiling flow method to generate anisotropic phase screens. While this model does not fully capture all statistics, it can be used to generate data that matches the temporal power spectrum or the anisotropic 2D structure function, with the ability to trade fidelity to one for fidelity to the other.