Diffractive optical elements for differential interference contrast x-ray microscopy.

In this paper we introduce phase diffractive optical elements (DOEs) that beside simple focusing, can perform new optical functions in the range of x-rays. In particular, the intensity of the wavefront can be distributed with almost complete freedom. We calculated and fabricated high resolution DOEs that can focus a monochromatic x-ray beam into multiple spots displaced in a single or two planes along the optical axis or can shape the beam into a desired continuous geometrical pattern. The possibility to introduce a specified phase shift between the generated spots, which can increase the image contrast, is demonstrated by preliminary results obtained from computer simulations and experiments performed in visible light. The functionality of the DOEs has been tested successfully in full-field differential interference contrast (DIC) x-ray microscopy at the ID21 beamline of the European Synchrotron Radiation Facility (ESRF) operated at 4 keV photon energy.