Extremely broadband grazing-incidence multilayers for hard-x-ray refle
ction can be obtained by a gradual change of the layer thicknesses dow
n through the structure. Existing approaches for designing similar neu
tron optics, called supermirrors, are shown to provide respectable per
formance when applied to x-ray multilayers. However, none of these app
roaches consider the effects of imperfect layer interfaces and absorpt
ion in the overlying layers. Adaptations of neutron designs that take
these effects into account are presented, and a thorough analysis of t
wo specific applications (a single hard-x-ray reflector and a hard-x-r
ay telescope) shows that an improved performance can be obtained. A mu
ltilayer whose bilayer thicknesses are given by a power law expression
is found to provide the best solution; however, it is only slightly b
etter than some of the adapted neutron designs. (C) 1995 Optical Socie
ty of America