Dynamic mode decomposition for aero-optic wavefront characterization

Abstract

Aero-optical beam control relies on the development of low-latency forecasting techniques to quickly predict wavefronts aberrated by the turbulent boundary layer around an airborne optical system, and its study applies to a multidomain need from astronomy to microscopy for high-fidelity laser propagation. We leverage the forecasting capabilities of the dynamic mode decomposition (DMD) — an equation-free, data-driven method for identifying coherent flow structures and their associated spatiotemporal dynamics — to estimate future state wavefront phase aberrations to feed into an adaptive optic control loop. We specifically leverage the optimized DMD (opt-DMD) algorithm on a subset of the Airborne Aero-Optics Laboratory-Transonic experimental dataset, characterizing aberrated wavefront dynamics for 23 beam propagation directions via the spatiotemporal decomposition underlying DMD. Critically, we show that opt-DMD produces an optimally debiased eigenvalue spectrum with imaginary eigenvalues, allowing for arbitrarily long forecasting to produce a robust future state prediction, while exact DMD loses structural information due to modal decay rates.