Single-shot phase retrieval for randomly fluctuated and obstructed vortex beams

Vortex beams with orbital angular momentum play a crucial role in increasing the information capacity in optical communications. The magnitude of orbital angular momentum determines the ability of information encoding. In practice, a vortex beam can encounter random objects or turbulence during free-space propagation, resulting in information damage. Therefore, accurately measuring the orbital angular momentum of a randomly fluctuated and obstructed vortex beam is a considerable challenge. Herein, we propose a single-shot method for the phase retrieval of a randomly fluctuated and obstructed vortex beam by combining the phase-shift theorem and self-reference holography. Experimental results reveal that the sign and magnitude of the initial orbital angular momentum can be simultaneously determined based on their quantitative relation with the number of coherence singularities on the observation plane, thus addressing the effects of random occlusion and atmospheric turbulence. The proposed method considerably improved the accurate decoding of orbital angular momentum information in nonideal freespace optical communications.