X-ray nanofocusing with back diffracting bent crystal

Focusing performance of cylindrically bent crystal in symmetric Bragg back diffraction geometry was investigated theoretically and simulated numerically. A thin flat crystal was introduced into the setup to separate focal spot from the incident beam. It was shown that in order to achieve an ideal focusing with strongly bent crystal the shape of the crystal surface has to be aspherical. A correction term for the surface displacement function free from spherical aberrations was derived. Numerical simulations demonstrated excellent focusing performance of the setup achieving the focal spot size 2.4 nm. The demonstrated result is not yet fundamentally limited and can be further improved by an order of magnitude.