In both light optics and electron optics, the amplitude of a wave scattered by an object is an observable that is usually recorded in the form of an intensity distribution in a real space image or a diffraction image. In contrast, retrieval of the phase of a scattered wave is a well-known challenge, which is usually approached by interferometric or numerical methods. In electron microscopy, as a result of constraints in the lens setup, it is particularly difficult to retrieve the phase of a diffraction image. Here, we use a "defocused beam" generated by a nanofabricated hologram to form a reference wave that can be interfered with a diffracted beam. This setup provides an extended interference region with the sample wavefunction in the Fraunhofer plane. As a case study, we retrieve the phase of an electron vortex beam. Beyond this specific example, the approach can be used to retrieve the wavefronts of diffracted beams from a wide range of samples.
Phase retrieval of an electron vortex beam using diffraction holography / Venturi, Federico; Campanini, Marco; Gazzadi, Gian Carlo; Balboni, Roberto; Frabboni, Stefano; Boyd, Robert W.; Dunin-Borkowski, Rafal E.; Karimi, Ebrahim; Grillo, Vincenzo. - In: APPLIED PHYSICS LETTERS. - ISSN 0003-6951. - 111:22(2017), pp. 223101 -1-223101- 5. [10.1063/1.4998595]