The far-field diffraction of a plane wave on a system of randomly and in average periodically located point scatterers: the Debye-Waller factor

The description of the superposition field of a system of point sources with a random and, on average, periodic structure is considered. The description is given in the far field and the point sources are considered as centers of secondary sphere waves generated by an external plane wave. In contrast to the traditional approach, where description of the diffraction pattern is given on the base of wave field averaging, here the intensity is averaged. In the framework of the suggested approach the analytic formula of dependence of the average intensity on the direction observation is found. The influence of disorder on the values of intensity of main maximums of a periodic structure is investigated. It is shown that this influence depends on the ordinal numbers of the maximum and in the case of central main maximum this influence vanishes. The question of applicability of the Debye-Weller factor for describing of the statistic of diffracted field is discussed.