Dynamic Mode Decomposition for Aero-Optic Wavefront Characterization

TL;DR

This paper demonstrates how optimized Dynamic Mode Decomposition (opt-DMD) can effectively forecast wavefront aberrations caused by aero-optical turbulence, improving adaptive optics control for airborne systems.

Contribution

It introduces the application of opt-DMD to aero-optic wavefront prediction, enabling long-term forecasting and better structural understanding of wavefront dynamics.

Findings

opt-DMD provides robust long-term wavefront forecasts

Eigenvalue spectrum is optimally de-biased with imaginary eigenvalues

Exact DMD loses structural information due to modal decay

Abstract

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.