Vortex beams, characterized by their orbital angular momentum proportional to the topological charge, offer significant potential in optical communication. However, turbulence-induced beam distortion and wandering lead to mode crosstalk and hinder accurate topological charge measurement, resulting in the degradation of transmitted information. While coherence modulation has shown potential in enhancing beam stability under dynamic turbulence, robust measurement of the topological charge remains a significant challenge. To address this, we proposed a robust measurement method that integrates learning-based turbulence compensation with self-reference holography for topological charge measurement of partially coherent vortex beams. Both simulation and experimental results confirm that the proposed compensation neural network effectively corrects distorted beams, thereby enabling stable topological charge measurement over extended periods. Moreover, the proposed framework demonstrates strong generalization capabilities, accurately measuring topological charges for coherence widths beyond those in the training dataset. This work provides a promising solution for non-ideal free-space optical communication systems utilizing vortex beams.
Zhu et al. (2025) studied this question.