that the neighboring slits are sufficiently well separated from each other. In most cases $D(u)$ is a slowly varying function of $u$, as opposed to the rapidly changing interference term. For this reason the general pattern  consists of well-separated and narrow interference peaks, the intensities of which are modulated by the diffraction term. It appears, however, that in some cases (for instance, when the linear size of the slits becomes comparable to their separation) the diffraction term also exhibits sharp peaks. In such circumstances the distinction between the diffraction and interference peaks is rather difficult to trace. This may lead to misinterpretation of some features of the pattern , as we shall discuss in our paper.

With the emergence of quantum theories and the discovery of wave properties of matter, the investigation of diffraction and interference phenomena of matter waves became very important from the fundamental as well as the practical point of views. The point being that these phenomena have prompted some unexpected observations and applications (see, e.g., [@VanHove; @Silverman1995; @Silverman2008; @Deymier]), such as in the low-energy [@Peierls1979] or high-energy [@BaronePredazzi] scattering. Another example is the so-called diffraction radiation [@Potylitsyn], which is emitted when charged particles move in vacuum 