Design of grazing-incidence multilayer supermirrors for hard-x-ray reflectors

Extremely broadband grazing-incidence multilayers for hard-x-ray reflection can be obtained by a gradual change of the layer thicknesses down through the structure. Existing approaches for designing similar neutron optics, called supermirrors, are shown to provide respectable performance when applied to x-ray multilayers. However, none of these approaches consider the effects of imperfect layer interfaces and absorption in the overlying layers. Adaptations of neutron designs that take these effects into account are presented, and a thorough analysis of two specific applications (a single hard-x-ray reflector and a hard-x-ray telescope) shows that an improved performance can be obtained. A multilayer whose bilayer thicknesses are given by a power law expression is found to provide the best solution; however, it is only slightly better than some of the adapted neutron designs.