Real-space overlap is not enough: ambiguity in nanobeam iterative ptychography

Abstract

High-resolution iterative ptychography typically relies on a well-aligned, high-convergence-angle electron probe. Here we explore whether it can instead be performed at small convergence angles, relaxing the need for probe correctors and enabling experiments at low accelerating voltages or with a de-excited objective lens, as in Lorentz mode. Through experiments and simulations, we show that once the convergence angle is small enough that no diffracted disks overlap, the resulting reconstruction is ambiguous, posing a significant challenge for robust interpretation of results. This challenge arises because of the lack of interference between Bragg disks in the recorded diffraction pattern intensity, leading to no phase information for each reflection. Reconstructions with these data lead to degenerate objects in which rigid translations of the lattice and reversals of contrast of the object produce the same error between experimental data and the ptychography forward model. Increasing the real-space overlap between probe positions does not lift this degeneracy. An amorphous substrate can supply the missing phase relationships by giving the Bragg beams support in the gaps between disks. This phasing is fragile, however, and survives only where the forward model matches the experiment. At fixed dose, either constraining the object to be a pure phase object or introducing thermal motion into the forward model is enough on its own to make the solution non-unique, highlighting why our experimental reconstructions below the overlap threshold are ambiguous despite ample dose and real-space redundancy. Most troublingly, the lattice spacing and orientation are always recovered correctly, so a non-unique reconstruction looks convincing and can be diagnosed only by repeating the reconstruction from different starting points.