Adaptive Joint Correction of the Piston and Large Tip/Tilt of Beam Combination Using Dynamic Metric Stochastic Parallel Gradient Descent Algorithm

Phase control is paramount for laser beam combination, requiring sequential tip/tilt and piston error correction. The common stochastic parallel gradient descent (SPGD) phase control algorithm using power metrics can't realize the automatic transition from an initial state of spot separation to phase locking. This paper proposes an adaptive metric SPGD phase control method capable of correcting both large-scale tip/tilt and piston errors, thus enabling automatic phase locking from the state of discrete spots. By framing beam combination as an optimization problem, we define a composite metric incorporating distance, power, and sharpness metrics, which dynamically adapts based on spot conditions. Both simulations and experiments confirm the method's capability for large-scale, high-precision beam combinations with robust phase control. Within 60 seconds (300 iterations), the random tip/tilt errors converge to within a pixel, and pistons are stabilized to λ/10, demonstrating its efficiency and feasibility. Our approach simplifies adjustment procedures with one-click large-scale phase error correction, showcasing the significant potential for phase control in complex multi-element systems.