Reconstruction of orbital angular momentum eigenstates of light.

Vortex beams, carrying orbital angular momentum (OAM), have found widespread applications in modern optics. However, they are highly susceptible to obstruction during propagation, degrading their reliability in practical scenarios. Although self-healing beams have been desired to address this challenge, their performance is limited by finite diffraction-free zones. Here we show an active reconstruction scheme, vortex reconstructor, combining bidirectional coordinate transformation with spatial filtering on the sorted plane to suppress the broadened profile and recover the original helical wavefront. The performance of the reconstructor is theoretically analyzed, demonstrating 79.6% azimuthal occlusion tolerance. Based on the above, the reconstruction elements are fabricated and the reconstructor is implemented in a dual-directional optical setup. An average mode fidelity of 94.865% is achieved in reconstructing a vortex under 52.316% of the beam area obstructed by complex objects. This approach enables reconstruction independent with diffraction-free zones, advancing OAM applications in occlusion scenarios.