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We examine paraxial propagation of recently introduced optical coherence lattices in free space and demonstrate a novel phenomenon of periodicity reciprocity between their intensity and coherence properties. The periodicity reciprocity arises because an aperiodic source intensity profile of an optical coherence lattice evolves into a lattice-like far-field profile, while the periodic spectral degree of coherence at the source becomes aperiodic on free-space propagation. We discuss how thedoi:10.1364/oe.23.001848 pmid:25835938 fatcat:gd6qhtppj5cc3ayxpgypubbtbe