We analyze the coherence singularities that occur in the far field that is generated by a broad class of partially coherent sources. It is shown that for rotationally symmetric planar quasihomogeneous sources the coherence singularities form a two-dimensional surface in a reduced three-dimensional space. We illustrate our results by studying the topology of the coherence singularity of a partially coherent vortex beam. We find that the geometry of the phase singularity can be associated with conic sections such as ellipses, lines, and hyperbolas.
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