  As a burgeoning technique, out-of-focus electron ptychography offers the
potential for rapidly imaging atomic-scale large fields of view (FoV) using a
single diffraction dataset. However, achieving robust out-of-focus
ptychographic reconstruction poses a significant challenge due to the inherent
scan instabilities of electron microscopes, compounded by the presence of
unknown aberrations in the probe-forming lens. In this study, we substantially
enhance the robustness of out-of-focus ptychographic reconstruction by
extending our previous calibration method (the Fourier method), which was
originally developed for the in-focus scenario. This extended Fourier method
surpasses existing calibration techniques by providing more reliable and
accurate initialization of scan positions and electron probes. Additionally, we
comprehensively explore and recommend optimized experimental parameters for
robust out-of-focus ptychography, includingaperture size and defocus, through
extensive simulations. Lastly, we conduct a comprehensive comparison between
ptychographic reconstructions obtained with focused and defocused electron
probes, particularly in the context of low-dose and precise phase imaging,
utilizing our calibration method as the basis for evaluation.
