High-speed complex phase retrieval of light propagating through optical turbulence: spatiotemporal characteristics

Optical turbulence distorts beam amplitude and phase, causing spreading, wandering, and irradiance fluctuations. Reconstructing perturbed beams’ complex fields is experimentally challenging due to these dynamic effects. Our complex phase retrieval technique, using binary amplitude modulation with a DMD and high-speed camera, characterizes collimated beams through turbulence and overcomes interferometric limitations. Conventionally, phase retrieval modulates optical fields via random coded apertures (RCA) to recover amplitude and phase without prior knowledge, solving ill-posed problems with phase-lift algorithms. Our previous approach required ≥ 20 apertures, increasing acquisition time and complexity. We designed a new coded aperture, reducing time and enhancing quality over traditional RCA. Then we apply a novel deep-learning phase unwrapping algorithm enabling efficient unwrapping of phases with turbulence-induced branch point singularities manifesting as vortices. This is the first experimental observation of turbulence complex wavefronts reconstructed with high spatial resolution and sampling rate. We discuss observed statistical properties and compare with current models.