Electron Fourier ptychography for phase reconstruction

Phase 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 using data collected in an alternative optical geometry. This method achieves a spatial resolution of 0.63 nm at a fluence of $4.5 \times 10^2 \, e^-/\text{nm}^2$, as validated on Cry11Aa protein crystals under cryogenic conditions. Notably, this method requires no additional hardware modifications, is straightforward to implement, and can be seamlessly integrated with existing data collection software, providing a broadly accessible alternative approach to structural studies.