Generation of multi-focus shaping with high uniformity based on an improved Gerchberg–Saxton algorithm

The Gerchberg–Saxton (GS) algorithm has been extensively employed in computational holography and beam shaping with the advantages of quick iteration speed and high energy utilization. However, the GS algorithm is prone to trapping into local optima and not reaching ideal outcomes, leading to poor shaping quality. In this paper, a method of random disturbance superposition (RDS) was proposed to feedback GS amplitude, which could stably and universally achieve over 95% high uniformity shaping of multiple beams without other complex operations. In light of this, this paper also covered how this technique affected energy utilization. It has been discovered that the introduction of perturbation could decrease the energy utilization. By analyzing the mechanism, a phase value replacement (PVR) method was proposed, which could effectively improve energy utilization without reducing uniformity. Finally, the simulation results were experimentally validated and met expectations very well. This method helps to accurately control the energy distribution of multiple beams and has a driving effect on laser precision processing technology.