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Correcting scan-positional errors is critical in achieving electronptychography with both high resolution and high precision. This is a demandingand challenging task due to the sheer number of parameters that need to beoptimized. For atomic-resolution ptychographic reconstructions, we foundclassical refining methods for scan positions not satisfactory due to theinherent entanglement between the object and scan positions, which can producesystematic errors in the results. Here, we propose a new protocol consisting ofa series of constrained gradient descent (CGD) methods to achieve betterrecovery of scan positions. The central idea of these CGD methods is to utilizea priori knowledge about the nature of STEM experiments and add necessaryconstraints to isolate different types of scan positional errors during theiterative reconstruction process. Each constraint will be introduced with thehelp of simulated 4D-STEM datasets with known positional errors. Then theintegrated constrained gradient decent (iCGD) protocol will be demonstratedusing an experimental 4D-STEM dataset of the 1H-MoS2 monolayer. We will showthat the iCGD protocol can effectively address the errors of scan positionsacross the spectrum and help to achieve electron ptychography with highaccuracy and precision.

An Integrated Constrained Gradient Descent (iCGD) Protocol to Correct  Scan-Positional Errors for Electron Ptychography with High Accuracy and  Precision