A Relativistic Adaptive Gradient Descent Enhanced SPGD Algorithm for Wavefront Sensorless Adaptive Optics.

Deformable mirrors (DMs) serve as the core wavefront correction devices in wavefront sensorless adaptive optics (AO) systems, and their performance is predominantly determined by the convergence speed and stability of the control algorithm. Although the stochastic parallel gradient descent (SPGD) algorithm is extensively used for wavefront sensorless AO control, its slow convergence limits real-time wavefront correction. To address this issue, the RAD-SPGD algorithm is put forward by integrating the relativistic adaptive gradient descent (RAD) optimizer into the conventional SPGD algorithm. A wavefront sensorless AO system with a 97-element MEMS deformable mirror was established to evaluate the proposed algorithm under different turbulence levels, and physical experiments were carried out for verification. The convergence performance is evaluated by the number of iterations needed for the Strehl ratio (SR) to reach 80% of its maximum value. Simulation results demonstrate that the proposed algorithm improves the correction speed by approximately 56% on average compared with the conventional SPGD algorithm, while experimental results show an improvement of approximately 28.6%. Moreover, dynamic turbulence experiments demonstrate enhanced turbulence adaptability and correction stability. These results suggest that the proposed algorithm effectively enhances the closed-loop control efficiency of the 97-element MEMS deformable mirror, offering an effective solution for real-time wavefront sensorless adaptive optics systems.