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

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 ( \(2.8 D/r_0 9.7\) ), 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.