Optimized short kinoform lenses for hard X-ray nano-focusing

An optimized structure of the short kinoform lens (KL) for hard X-ray nano-focusing is presented. By modifying the lower and upper surfaces of the conventional short KL, the focusing performance is improved largely. Unlike the conventional short KLs, whose effective numerical aperture (NA) is limited by the edge diffraction effects and multi-wave scattering, the optimized short KL is capable of achieving diffraction-limited focusing. The Takagi–Taupin description (TTD) of X-ray dynamical diffraction theory is employed to investigate the diffractive properties of the optimized short KL. When the harmonic number equals 1, the optimized short KL could be treated as a diffractive lens, whose effective NA could exceed the critical angle limit. According to their different focusing properties, the lens aperture could be divided into three regions, namely the refraction region, the transition region and the resonance region. As a comparison, with a large harmonic number, the optimized short KL behaves more like a refractive lens and its effective NA is restricted by the critical angle limit. By choosing appropriate harmonic number, maximum duty cycle and maximum propagation ratio, the difficulty in fabricating the proposed lens structure could be alleviated greatly without degrading the focusing performance obviously. This study indicates that, besides the arrangement of lens segments, their shapes are also important. The simulation results demonstrate that a short KL is also a potential candidate for hard X-ray nano-focusing.