Hard x-ray wavefront engineering for aberration correction and beam shaping

While modern X-ray microscopes at synchrotron radiation sources and free-electron lasers require X-ray optics of highest quality, these optics often show aberrations due to limitations in fabrication technology. Based on ptychography, we determine these aberrations and fabricate tailor made refractive phase plates to compensate for them. Starting from the aberrated optics, di raction-limited beams can be generated by introducing the phase plate behind these optics. In addition, the wavefront can be modi ed to generate custom beams for special needs, such as donut-shaped beams with orbital angular momentum or for structured-illumination microscopy. The nanofocused beam can be engineered in shape and phase by introducing specially designed phase plates. We introduce a general scheme for wavefront engineering and illustrate it with a numerical example.