The ptychographical iterative engine (or PIE) is a recently developed phase retrieval
algorithm that employs a series of diffraction patterns recorded as a known illumination
function is translated to a set of overlapping positions relative to a target sample. The
technique has been demonstrated successfully at optical and X-ray wavelengths and has
been shown to be robust to detector noise and to converge considerably faster than support-
based phase retrieval methods. In this paper, the PIE is extended so that the requirement for …