We study the structure of resonance states localized around nonmagnetic impurities in the CuO2 planes of the cuprate superconductors within a potential scattering formalism. In particular we show that strong quantum interference effects arise between several impurities. This interference can be utilized to distinguish the dwave superconducting state from the phase with d-density wave order. This is important if the origin of the pseudo-gap state in the underdoped regime of the High Tc superconductors is caused by preformed Cooper pairs or staggered orbital currents. Furthermore impurity interference can be utilized to reveal subdominant superconducting order parameters and to pose further constraints on the potential scattering scenario.
