X-ray beam reflection on bounded multilayer diffraction grating

The paper briefly presents the main provisions of the dynamic theory of diffraction of a monochromatic X ray beam on a lamellar multilayer grating (LMG) with a finite number of periods. The application of the Kotelnikov’s theorem allowed to present integro differential diffraction equations in a simple matrix form. The solution of these equations by the method of numerical integration allows us to find the intensity of the reflected wave from the LMG. The angular distribution of the scattering intensity is represented in the form of reciprocal space mapping (RSM). Using the conclusions of the theory, a numerical experiment was carried out for Ni/C LMG in two configurations. In the first configuration, the incident wave is entirely highlighted by a finite number of periods of LMG. In the second configuration, a narrow beam was reflected on a ratherwide LMG. The RSM and their sections along the qzaxis of these two configurations are analyzed and their differences are shown. We consider the traditional LMG produced by lithographic method with etching.