Abstract To describe wave interference, a wave function with a direct physical meaning is used. On the contrary the distribution of material particles in an interference pattern is calculated with a probability wave function whose interpretation presents controversial features. Here, a general law is reported which provides a unified explanation of wave and material particle interference. We will show that the wave superposition principle as well as the counterintuitive features such as wave–particle duality, self-interference and wave collapse are not needed to explain observed interference patterns. With the present model, the contestable features regarding the physical meaning of the probability wave are removed. Simulations of experimental results show clearly that the predictive accuracy of our model overcomes that one of the standard optical method. Finally, an original interpretation of the uncertainty principle in connection with the diffraction modulation of interference patterns is also reported.