Analytic results for spatial coherence and information entropy of an optical vortex field

Optical vortex fields have applications in information processing and storage and in the manipulation of microscopic particles. We present analytic results for quantities describing the extent of spatial coherence and entropy of one-dimensional projections of a vortex field. Sums of squares of values of certain Jacobi polynomials are important in the analysis. A family of summation identities is presented that provides the moments of an associated discrete probability distribution.