# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.08496