# Electron fourier ptychography for phase reconstruction

## TL;DR

This paper introduces a new electron microscopy technique for high-resolution phase reconstruction of materials without requiring special equipment.

## Contribution

Electron Fourier ptychography is introduced as a novel method for phase reconstruction in electron microscopy.

## Key findings

- The method achieves a spatial resolution of 0.63 nm at a fluence of 4.5 × 10² e⁻/nm².
- It works effectively on Cry11Aa protein crystals under cryogenic conditions.
- The technique is compatible with existing data collection software and requires no hardware changes.

## Abstract

Exit wavefunction reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We demonstrate that the phase of the exit wave can be reconstructed to high resolution using a modified iterative phase retrieval algorithm from data collected in an alternative optical geometry. This method achieves a spatial resolution of 0.63 nm at a fluence of 4.5 × 102 e−/nm2, as validated on Cry11Aa protein crystals under cryogenic conditions. Notably, this method requires no instrumental modifications, is straightforward to implement, and can be seamlessly integrated with existing data collection software, providing a broadly accessible alternative approach for structural studies.

The online version contains supplementary material available at 10.1038/s41598-025-21638-7.