A Novel Sophia-SPGD (Stochastic Parallel Gradient Descent) Optimization Method for Wavefront Correction in WFS-Less AO (Wavefront Sensorless Adaptive Optics) Systems

In wavefront sensorless adaptive optics (WFS-less AO) systems, stochastic parallel gradient descent (SPGD) is the primary optimization method for correcting wavefront distortions. However, as the intensity of atmospheric turbulence interference increases, the fixed gain coefficient of the SPGD algorithm results in significant decreases in convergence speed and precision. Moreover, the algorithm is inclined to local optima, thus failing to satisfy the requirements for real-time wavefront distortion correction. To address these issues, this paper introduces a new optimization algorithm, Sophia optimized stochastic parallel gradient descent (Sophia-SPGD), which is based on second-order clipped stochastic optimization in deep learning. This algorithm computes the first-order and second-order moments of the performance metrics from its first and second gradients, respectively, and dynamically modulates the gain via a shearing mechanism to increase the convergence speed and diminish the probability of falling into local optima. Numerical simulations and experiments demonstrate that under strong turbulence conditions, the performance of Sophia-SPGD surpasses that of the traditional SPGD algorithm.