Modal expansion of thin annular sources with Schell-model angular correlation function

"A general procedure is presented for the evaluation of the modes of a thin annular scalar source, whose angular mutual intensity is of the Schell-model type. Starting from the knowledge of the modes, the coherence properties of the field propagated from the source in paraxial conditions can be evaluated. When the propagated field is collimated by a suitable converging lens, presented results apply to the synthesis of propagation-invariant partially coherent beams."