Wave-front phase retrieval in transmission electron microscopy via ptychography

There are many different strategies that allow the solving of the well-known phase problem corresponding to the loss of phase information during a physical measurement. In microscopy, and, in particular, in transmission electron microscopy, most of these strategies focus on the retrieval of high-resolution information with the importance of lower resolution data often overlooked. Ptychography offers a means to investigate such data. Ptychography is a robust diffractive imaging technique with fast convergence for phase retrieval but, until now, has not been applied at the nanoscale. In this paper, we use the ptychographical iterative engine to retrieve the phase change at the exit plane of metallic nanoparticles using a conventional transmission electron microscope. Ptychographical reconstructions yielded images with a phase resolution of $\ensuremath{\pi}/10$ and a spatial resolution of 1 nm. These results stand as a first step toward aberration-free lensless imaging. The technique lends itself to be an alternative to off-axis electron holography or focal series reconstruction.