Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses

In response to the conjecture that the numerical aperture of x-ray optics is fundamentally limited by the critical angle of total reflection [Bergemann et al., Phys. Rev. Lett. 91, 204801 (2003)], the concept of adiabatically focusing refractive lenses was proposed to overcome this limit [Schroer and Lengeler, Phys. Rev. Lett. 94, 054802 (2005)]. We present an experimental realization of these optics made of silicon and demonstrate that they indeed focus 20 keV x rays to a 18.4 nm focus with a numerical aperture of 1.73(9) × 10−3 that clearly exceeds the critical angle of total reflection of 1.55 mrad.