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 an...

It is shown that eigenvalues of the Laplace–Beltrami operator on a compact Riemannian manifold can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In particular, a bounded set of eigenvalues can be determined using a space of such polyharmonic functions with a fixed set of singularities. It also shown that co...