Diffraction is one of the universal phenomena.It affects all classical wave fields without exception.In statistical optics,the coherence function of optical fields found to be propagated according to wave equations.In the past decades,the propagation properties of optical coherence function have received a lot of attentions.Especially the diffraction of partially coherent light described by the van Cittert-Zernike theorem is undoubtedly one of the most important theories of modern optics.Similar to the well-known optical diffraction,the coherence function illuminated by a finite sized incoherent source also causes a coherence energy spreading: the spot size of the coherence pattern is extended during its propagation resulting in a limited distance with high coherence.In this paper,we proposed a novel optical geometry for direct visualization of spatial coherence function.The full-field distribution of the coherence function from an incoherent circular aperture source is experimentally investigated.Meanwhile,on the analogy of the propagation-invariant wave,the coherence function should also have diffraction-free solutions,where the coherence function referred to as a non-diffracting wave with its unique property of unchanged transverse shape during the propagation.The experiments of nondiffracting coherence function from an incoherent circular slit source have also been done.The experimental results show that the coherence function generated by an incoherent circular aperture source is in the form of Fresnel diffraction integral which diffracting during the propagation and the coherence function generated by an incoherent circular slit source is unaltered by propagating in free space.