Accurate and Robust Calibration of the Uniform Affine Transformation Between Scan-Camera Coordinates for Atom-Resolved In-Focus 4D-STEM Datasets

Abstract

Accurate geometrical calibration between the scan coordinates and the camera coordinates is critical in four-dimensional scanning transmission electron microscopy (4D-STEM) for both quantitative imaging and ptychographic reconstructions. For atomic-resolved, in-focus 4D-STEM datasets, we propose a hybrid method incorporating two sub-routines, namely a J-matrix method and a Fourier method, which can calibrate the uniform affine transformation between the scan-camera coordinates using raw data, without a priori knowledge of the crystal structure of the specimen. The hybrid method is found robust against scan distortions and residual probe aberrations. It is also effective even when defects are present in the specimen, or the specimen becomes relatively thick. We will demonstrate that a successful geometrical calibration with the hybrid method will lead to a more reliable recovery of both the specimen and the electron probe in a ptychographic reconstruction. We will also show that, although the elimination of local scan position errors still requires an iterative approach, the rate of convergence can be improved, and the residual errors can be further reduced if the hybrid method can be firstly applied for initial calibration. The code is made available as a simple-to-use tool to correct affine transformations of the scan-camera coordinates in 4D-STEM experiments.

Applications of Transmission Electron Microscopy in Phase Engineering of Nanomaterials

“…In addition to the advantages discussed above, ptychography reconstruction also has the capability to correct a variety of imperfections in imaging, including scan shift, specimen drift, and zone-axis deviation. − As an emerging technology in electron microscopy imaging, 4D-STEM ptychography holds substantial promise for the phase engineering of nanomaterials. This stems from its superior resolution, high adaptability to various material types and imaging conditions, and its three-dimensional resolving power.…”

4D-STEM Ptychography for Electron-Beam-Sensitive Materials

“…The redundancy of the 4D-STEM dataset allows the correction of experimental imperfections and aberrations through reconstruction. For example, position correction , and zone-axis correction have been realized using modified algorithms. In addition, the multislice , and mixed-state methods, , which can be integrated into iterative algorithms (e.g., ePIE and ML algorithms), have been developed to address the problems of multiple scattering associated with thick specimens and the partial incoherence of electron beams, respectively.…”

“…The ability of various existing algorithms to manage ultra-low-dose large-defocus data should be explored, and new algorithms that can meet these requirements should also be developed. Several methods for scanning coordinate correction , and zone-axis correction have been developed to tolerate imperfect experimental conditions to a certain extent. These methods are potentially valuable for highly beam-sensitive materials that require rapid operation without time to perfect the imaging conditions.…”

Atomic Resolution Cryogenic 4D-STEM Imaging via Robust Distortion Correction

“…Loh et al have explored the possibility of using the reciprocal space information contained within a 4D-STEM data set to quantify linear distortions. 21 Subsequently, they demonstrated that ptychography can be used as a followup to correct fine (<30 pm) probe positioning errors, although it is emphasized that ptychography is not suitable for correcting large scan position errors. Wang et al developed a method to correct a 4D-STEM data set suffering from sample drift during its acquisition when the sample's structure is known beforehand.…”

“…Methods correcting 4D-STEM data sets acquired at room temperature were recently reported, mainly focused on scanning distortions, as it is the primary distortion in room temperature 4D-STEM. Loh et al have explored the possibility of using the reciprocal space information contained within a 4D-STEM data set to quantify linear distortions . Subsequently, they demonstrated that ptychography can be used as a followup to correct fine (<30 pm) probe positioning errors, although it is emphasized that ptychography is not suitable for correcting large scan position errors.…”