High-resolution spatiotemporal reconstruction of complex optical fields enables direct testing of turbulence statistics

Recommended citation: Scherz, Pablo and Peters, Eduardo and Nelson Díaz and Tapia, Jorge and Romero, Bastián and Vera, Esteban and Pérez, Darío G, “High-resolution spatiotemporal reconstruction of complex optical fields enables direct testing of turbulence statistics,” Scientific Reports, 2026. [DOI].

Theoretical descriptions of optical propagation through atmospheric turbulence rest on the assumption that complex phase fluctuations follow Gaussian statistics. Testing this hypothesis requires direct comparison between measured coherence and its Gaussian-theory prediction, which in turn demands reconstruction of the complete complex field–amplitude and phase–at spatiotemporal resolutions finer than the turbulence correlation scales, a capability beyond the reach of phase-only methods. Here we reconstruct such fields at kilohertz rates through real optical turbulence using binary amplitude modulation with Hadamard coded apertures, imposing no statistical prior on the phase distribution. Applied to 24 controlled turbulence conditions ( ), the platform enables direct comparison between measured coherence and its Gaussian-theory prediction, revealing systematic departures that grow with turbulence strength in the weak-scintillation regime—where the Gaussian assumption is expected to hold. These departures extend non-Gaussian behavior previously documented in angle-of-arrival statistics to the full spatial coherence structure, and imply that Gaussian-derived coherence estimates systematically underestimate the coherence radius—a quantity that governs fiber-coupling efficiency, coherent detection performance, and turbulence profiling accuracy in ground-layer optical propagation.

Cite

@article{scherz2026high,
  title={High-resolution spatiotemporal reconstruction of complex optical fields enables direct testing of turbulence statistics},
  author={Scherz, Pablo and Peters, Eduardo and D{\'\i}az, Nelson and Tapia, Jorge and Romero, Basti{\'a}n and Vera, Esteban and P{\'e}rez, Dar{\'\i}o G},
  journal={Scientific Reports},
  year={2026},
  publisher={Nature Publishing Group UK London}
}