Nanosecond wavefront shaping to focus through agitated turbid media

Multiple scattering rapidly scrambles optical fields in fog, snow and turbid water, causing op- timized wavefront corrections to become obsolete on microsecond timescales. Although wavefront shaping enables focusing through static scattering layers, closed-loop control in dynamically evolving media has remained experimentally challenging because the correction bandwidth must approach the intrinsic decorrelation rate of the speckle. Here, we demonstrate closed-loop wavefront shaping with 32 independent degrees of freedom in an agitated turbid medium exhibiting sub-microsecond decorrelation. The medium thickness exceeds the transport mean free path, meaning the far-field speckle autocorrelation is limited to a diffraction-sized grain. Despite the microsecond decorrelation and this multiple-scattering regime, stable focusing is maintained as the correction cycle approaches the intrinsic dynamics of the medium. These results establish an experimentally accessible regime for coherent wave control in rapidly evolving complex media.