Deep learning for simultaneous phase and amplitude identification in coherent beam combination.

Coherent beam combination has emerged as a promising strategy for overcoming the power limitations of individual fibre lasers. This approach relies on maintaining precise phase difference between the constituent beamlets, which are typically established using phase retrieval algorithms. However, phase locking is often studied under the assumption that the power levels of the beamlets remain stable, an idealisation that does not hold always in practical applications. Over the operational lifetime of fibre lasers, power degradation inevitably occurs, introducing additional challenges to phase retrieval. To address this, we propose a deep learning algorithm for single-step simultaneous phase and amplitude identification, directly from a single camera observation of the intensity distribution of the combined beam. By leveraging its ability to detect and interpret subtle variations in intensity interference patterns, the deep learning approach can accurately disentangle phase and power contributions, even in the presence of significant power fluctuations. Using a spatial light modulator, we systematically investigate the impact of power-level fluctuations on phase retrieval within a simulated coherent beam combination system. Furthermore, we explore the scalability of this deep learning approach by evaluating its ability to achieve the required phase and amplitude precision as the number of beamlets increases.