Nanosecond wavefront shaping to focus through agitated turbid media

Abstract

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.

Figures (3)

• Figure 1: Operation regime and demonstration of closed-loop focusing beyond the vanishing distance. (a) Experimental platform implementing 32 parallel phase-modulated channels at $1.55~\mu$m. The channels are recombined to synthesize the incident wavefront illuminating the turbid sample; the transmitted intensity is detected in the far field. (b) Ballistic and diffuse flux per optical mode as a function of optical thickness, defining the vanishing distance $\ell_v$. The experiment operates at $L \gtrsim \ell_v$, beyond the regime where ballistic contributions dominate. (c) Intensity distribution at maximum agitation, demonstrating maintained focusing in the sub-microsecond decorrelation regime. (d) Measured temporal autocorrelation of the transmitted speckle under dynamic conditions, defining the microsecond-scale decorrelation time.
• Figure 2: Focusing performance versus speckle decorrelation time. (a) Measured intensity enhancement as a function of decorrelation time, tuned via controlled flow velocity. Enhancement decreases progressively as the decorrelation time approaches the correction cycle duration. (b) Measured temporal autocorrelation of the transmitted speckle under dynamic conditions for different time scales with caracteristic times ranging from 1 ms to 1 µs
• Figure 3: Parallel frequency-tagged closed-loop control. (a) Principle of frequency tagging applied to the 32 independently modulated phase channels. (b) Frequency-domain spectrum of the detected intensity signal, showing resolved peaks associated with each controlled degree of freedom and enabling simultaneous gradient extraction within a sub-microsecond correction cycle.