Hybrid particle swarm global optimization algorithm for phase diversity phase retrieval.

The core problem of phase diversity phase retrieval (PDPR) is to find suitable optimization algorithms for wave-front sensing of different scales, especially for large-scale wavefront sensing. When dealing with large-scale wave-front sensing, existing gradient-based local optimization algorithms used in PDPR are easily trapped in local minimums near initial positions, and available global optimization algorithms possess low convergence efficiency. We construct a practicable optimization algorithm used in PDPR for large-scale wave-front sensing. This algorithm, named EPSO-BFGS, is a two-step hybrid global optimization algorithm based on the combination of evolutionary particle swarm optimization (EPSO) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Firstly, EPSO provides global search and obtains a rough global minimum position in limited search steps. Then, BFGS initialized by the rough global minimum position approaches the global minimum with high accuracy and fast convergence speed. Numerical examples testify to the feasibility and reliability of EPSO-BFGS for wave-front sensing of different scales. Two numerical cases also validate the ability of EPSO-BFGS for large-scale wave-front sensing. The effectiveness of EPSO-BFGS is further affirmed by performing a verification experiment.