Finite, thickness effect of a zone plate on focusing hard x-rays

Spatial resolution and focusing efficiency are two important properties of a zone plate in x-ray focusing applications. In this paper a general expression of the zone plate equation describing its zone registration is derived from the interference of spherical waves emitted from two mutually coherent point sources. An analytical expression of the focusing efficiency in terms of the zone plate thickness and x-ray refractive indices of the zones is also derived. Validity condition for using this expression is considered. Thickness required for obtaining adequate focusing efficiency is calculated as a function of x-ray energy for several representative materials. The spatial resolution of a finite thickness zone plate is worse than that of an infinitely thin zone plate, which is approximately equal to the smallest zone width of the zone plate. The effect of the finite thickness on the spatial resolution is considered