Phase retrieval of an electron vortex beam using diffraction holography

TL;DR

This paper demonstrates a novel interferometric method using a nanofabricated hologram to retrieve the phase of an electron vortex beam in electron microscopy, overcoming traditional challenges in phase measurement.

Contribution

It introduces a diffraction holography technique with a reference wave for phase retrieval in electron microscopy, applicable to various samples.

Findings

Successful phase retrieval of an electron vortex beam.

Extended interference region enables accurate wavefront measurement.

Method applicable to a wide range of diffracted beams.

Abstract

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.