Complete representation of a correlation singularity in a partially coherent beam.

An understanding of phase singularities of correlation functions is important in optical coherence theory and imaging science, but to date such singularities have only been theoretically studied in a single transverse plane, at most. In this Letter we evaluate the complete structure of a correlation singularity of a partially coherent Laguerre-Gauss beam, describing it in both the transverse and the propagation directions. These results agree with previously found solutions, and introduce new aspects of correlation singularities.