Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle

The distribution of degree of coherence of a partially coherent vortex beam reveals rich information about the vortex phase, and it is known that one can determine the topological charge (or orbital angular moment) of a partially coherent vortex beam from its degree of coherence distribution in the focal plane (or in the far field). In this letter, we demonstrate both numerically and experimentally that the degree of coherence distribution of a partially coherent vortex beam that is blocked by an opaque obstacle can self-reconstruct in the focal plane. Thus, one still can determine the topological charge of an obstructed partially coherent vortex beam from its degree of coherence distribution in the focal plane. Our results can find application in information transmission and recovery.