Adaptive restoration of wavefront symmetry in turbulent atmospheric optical channels: an applied physics perspective on control algorithms

Atmospheric turbulence acts as a physical symmetry-breaking agent on propagating optical fields, distorting the spatial phase distribution and destroying the radial symmetry essential for efficient focal-plane energy concentration. In free-space optical links, these symmetry violations manifest as asymmetric beam wander, focal-spot broadening, and degraded coupling into receiving apertures, directly impacting signal fidelity and link stability. From the standpoint of applied physics, adaptive optics provides a closed-loop instrumental solution that forcibly restores the wavefront symmetry by applying spatially distributed phase corrections via a deformable mirror, thereby recovering the coherent focusing condition and maximizing energy throughput.

This experimental study compares two physically distinct control paradigms for symmetry restoration in a 45 mm laser beam focused through 20 μm and 10 μm apertures—conditions that model the high aperture sensitivity of practical optical receivers. The photodetector signal behind the aperture serves as the direct metric of focal-region symmetry, with higher transmitted energy indicating better restoration of the ideal, rotationally symmetric focal spot. A deterministic hill-climbing algorithm sequentially adjusts mirror electrodes based on the measured signal gradient. This approach achieves near-complete recovery of focal symmetry, delivering transmission efficiencies of approximately 94% (20 μm) and 90% (10 μm), albeit requiring about 5,800 control steps and 8 minutes of convergence time. In contrast, a stochastic Bernoulli perturbation algorithm, which probes multiple spatial modes simultaneously, converges to a slightly lower symmetry-restoration level (~90% and 82%, respectively) but within only 500 steps and approximately 10 seconds.

These results reveal a fundamental applied-physics trade-off: deterministic control maximizes structural symmetry recovery under quasi-static turbulence conditions, while stochastic methods offer robust, rapid adaptation for dynamically decorrelating channels. This quantitative characterization provides a practical basis for designing adaptive optical instruments that balance correction fidelity against temporal bandwidth, directly addressing the real-world challenges of turbulence mitigation in optical sensing and communication systems.