Phase and coherence singularities generated by the interference of partially coherent fields

A condition for the complete destructive interference of partially coherent fields emerging from pinholes in an opaque screen is derived, with the assumption of symmetry in both their geometric positions and coherence properties. We use this condition to theoretically investigate the simultaneous production of phase singularities of the optical field and of the spectral degree of coherence. We find that in cases where the number of point sources is even, a new type of mixed field/correlation singularity is observed.