Complete destructive interference of four partially coherent point sources

By using the interference law for partially coherent light, the interference in a four-pinhole interferometer with square symmetry illuminated by partially coherent light is studied. It is found that the complete destructive interference in the four-pinhole interferometer may appear, and there may exist phase singularities of intensity and spectral degree of coherence. A comparison with the interference of two and three partially coherent point sources is made and the results can be physically interpreted in such a way, that in spite of the partial coherence of four point sources, the sum of the fields emerging from two point sources may be fully correlated with the sum of the fields emerging from the other two point sources.