Aberration-free x-ray lenses made of silicon

Brilliant beams of hard x-rays, with geometrical cross-sections below 50×50 nm2, are a standard research tool for synchrotron users. With the advent of lower emittance sources, such as NSLSII, Petra III and Max IV, and planned upgraded lattices, such as APS-2, SPING8-II, ESRF II and DLS II, nanofocusing optics operating in transmission mode will become more competitive than they are currently. In general, they suffer from lower efficiency than reflective optics, however they often have easier set-up and alignment, combined with a smaller footprint. Fabrication and exploitation of ultra-short focal refractive lenses has not witnessed the same progress in the last decade as other optics, such as multilayer mirrors and multilayer Laue lenses. This paper reports on current status of high-resolution lithography for fabricating silicon lenses and on proposed designs for a new class of refractive lenses with zero aberrations and good efficiency. The new designs are created with geometrical parameters matching the spatial resolution achieved by modern lithography and silicon etch technology.