An integrated constrained gradient descent (iCGD) protocol to correct scan-positional errors for electron ptychography with high accuracy and precision

Correcting scan-positional errors is critical in achieving electron ptychography with both high resolution and high precision. This is a demanding and challenging task due to the sheer number of parameters that need to be optimized. For atomic-resolution ptychographic reconstructions, we found classical refining methods for scan positions not satisfactory due to the inherent entanglement between the object and scan positions, which can produce systematic errors in the results. Here, we propose a new protocol consisting of a series of constrained gradient descent (CGD) methods to achieve better recovery of scan positions. The central idea of these CGD methods is to utilize a priori knowledge about the nature of STEM experiments and add necessary constraints to isolate different types of scan positional errors during the iterative reconstruction process. Each constraint will be introduced with the help of simulated 4D-STEM datasets with known positional errors. Then the integrated constrained gradient decent (iCGD) protocol will be demonstrated using an experimental 4D-STEM dataset of the 1H-MoS₂ monolayer. We will show that the iCGD protocol can effectively address the errors of scan positions across the spectrum and help to achieve electron ptychography with high accuracy and precision.