Study on Phase and Tip-tilt Control Using Adaptive SPGD Algorithm for Coherent Beam Combining

Coherent Beam Combining (CBC) is a promising technique for enhancing laser output power by accurately aligning the phase and position of multiple laser beams. The Stochastic Parallel Gradient Descent (SPGD) algorithm is commonly used in CBC systems due to its simplicity and scalability. However, its dependence on fixed control parameters can result in slow convergence rates and diminished control stability. To overcome these challenges, this study introduces an adaptive SPGD algorithm that dynamically adjusts the perturbation amplitude and learning rate based on the real-time value of the objective function. This approach accelerates convergence during the initial stages by increasing control inputs when the objective function value is low, while ensuring stability as the function nears its maximum in later stages. Numerical simulations of 7-channel and 19-channel CBC systems revealed that the adaptive SPGD algorithm reduced average iteration counts by 26.4% and 18.1%, respectively, compared to the basic SPGD. Furthermore, the overall control performance improved, achieving high beam combining efficiency with reduced total computation time. This proposed algorithm serves as a straightforward yet effective enhancement to the conventional SPGD method, improving both convergence speed and stability.