Further improvements to the ptychographical iterative engine

Ptychography is a form of phase imaging that uses iterative algorithms to reconstruct an image of a specimen from a series of diffraction patterns. It is swiftly developing into a mainstream technique, with a growing list of applications across a range of imaging modalities. As the field has advanced, numerous reconstruction algorithms have been proposed, yet the early approaches have not seen major improvement and remain popular. In this paper, we revisit the first such algorithm, the ptychographical iterative engine (PIE), and show how a simple revision and powerful extension can deliver an order of magnitude speed increase and handle difficult data sets where the original version fails completely.