Aberration correction for hard x-ray focusing at the nanoscale

We developed a corrective phase plate that enables the correction of residual aberration in reflective, diffractive, and refractive X-ray optics. The principle is demonstrated on a stack of beryllium compound refractive lenses with a numerical aperture of 0.49 10$^{-3}$ at three synchrotron radiation and x-ray free-electron laser facilities, where we corrected spherical aberration of the optical system. The phase plate improved the Strehl ratio of the optics from 0.29(7) to 0.87(5), creating a diffraction-limited, large aperture, nanofocusing optics that is radiation resistant and very compact