  Aero-optical beam control relies on the development of low-latency
forecasting techniques to quickly predict wavefronts aberrated by the Turbulent
Boundary Layer (TBL) around an airborne optical system, and its study applies
to a multi-domain 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 -- in
order to estimate future state wavefront phase aberrations to feed into an
adaptive optic (AO) control loop. We specifically leverage the optimized DMD
(opt-DMD) algorithm on a subset of the Airborne Aero-Optics Laboratory
Transonic (AAOL-T) 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 de-biased 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.
