Topological Properties of Spatial Coherence Function

The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures (coherence vortices) of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence
vortices are characterized by the Hopf index and Brouwer degree in
topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.