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We develop an analytical model for the 3D spatial coherence function of speckle fields generated by scattering of vortex and perfect optical vortex beams. The model is general and describes the spatial coherence along both the transversal and the longitudinal directions. We found that, on propagation, the 3D spatial coherence evolves differently for the different types of initially structured beams, which may affect their use in a variety of sensing applications.