Design of supermirrors for hard x-ray telescopes

X-ray grazing incidence supermirror which has extremely broad reflection band is a kind of multilayer with different each layer thickness down through the structure. The x-rays with different wavelengths or at different grazing incident angles can be reflected at different position in the supermirror structure and its band or angular response thus can be extended. These supermirrors have been developed and applied widely in many fields, especially in astrophysics. Existing approaches for designing similar neutron 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 and all of them insist on the structure with the ratio of the layer thickness of absorbing material to the bi-layer spacing being a constant of 0.5. Adaptations of neutron designs that take these effects into account are presented in the present paper. In addition, other approaches, such as the method based on the combination of analytical and number methods, also are included and discussed in this paper. Two kinds of supermirrors with broad photon energy band or broad angular response have been designed using these different design methods. The results show that for specific applications, different optimization methods with different initial structures should be chosen accordingly to expect some overall improvement on performance of x-ray supermirrors.