Using compound kinoform hard-x-ray lenses to exceed the critical angle limit

We have fabricated and tested a compound lens consisting of an array of four kinoform lenses for hard x-ray photons of 11.3 keV. Our data demonstrate that it is possible to exceed the critical angle limit by using multiple lenses, while retaining lens function, and this suggests a route to practical focusing optics for hard x-ray photons with nanometer scale resolution and below.