Phase structure function and spatial coherence in underwater Rayleigh–Bénard turbulence: experimental characterization

This study presents the first experimental characterization of the phase structure function (PSF) and the spatial coherence radius of a laser beam propagating through underwater Rayleigh-Bénard (RB) turbulence, using a two-channel moiré-based wavefront sensor. A collimated laser beam (<i>λ</i>=532<i>n</i><i>m</i>, <i>d</i><i>i</i><i>a</i><i>m</i><i>e</i><i>t</i><i>e</i><i>r</i>=33<i>m</i><i>m</i>) was passed horizontally through a temperature-controlled water tank, where convective turbulence was induced by vertical temperature differences (0-6°C). Measurements were performed at multiple vertical (21, 100, and 179 mm) and lateral (21 and 100 mm) positions to examine spatial variations in turbulence. Wavefront phases were reconstructed from moiré fringe patterns, and the PSF was computed in two orthogonal directions transverse to the laser beam's propagation. The results revealed that underwater RB turbulence is both anisotropic and inhomogeneous in the cross-plane transverse to the beam propagation direction. While the turbulence intensity increases with the imposed temperature difference, the anisotropy observed in the PSF becomes more apparent at larger separation distances <i>r</i>. The analytical oceanic turbulence optical power spectrum model showed excellent agreement with the experimental PSF within the inertial subrange. Additionally, the spatial coherence radius was found to decrease with increasing temperature difference and was consistently smaller near the tank boundaries. These findings provide unique experimental validation for underwater turbulence models and offer insights critical to the design of robust underwater optical communication systems.