Shifts from Bragg's condition for X-UV periodic multilayer mirrors

The paper aims at palliating deficiencies of the ordinary use of optimization conditions for X-UV multilayer mirrors reflectivity. The authors explain clearly the foundation and validity of the Bragg's general condition in the case of metallic multilayers. They deduce both Bragg's general condition and its improvement from the nonoscillatory condition of the reflectivity as a function of periods. The second condition of optimization, numerically solved, fixes the thickness of one of the materials within the previously determined period. These two conditions reveal explicitly the similarity and the difference between periodic multilayers and crystals, as interferential mirrors.