Measurement of hard x-ray lens wavefront aberrations using phase retrieval

Measuring the deviation of a wavefront from a sphere provides valuable feedback on lens alignment and manufacturing errors. We demonstrate that these aberrations can be accurately measured at hard x-ray wavelengths, from far-field intensity measurements, using phase retrieval with a moveable structure in the beam path. We induce aberrations on a hard x-ray kinoform lens through deliberate misalignment and show that the reconstructed wavefronts are in good agreement with numerical simulations. Reconstructions from independent data, with the structure at different longitudinal positions and significantly separated from the beam focus, agreed with a root mean squared error of 0.006 waves.