In scanning transmission electron microscopy (STEM), the highly convergent Å-size electron probe forms convergent beam electron diffraction (CBED) in the back focal plane of the objective lens. In four-dimensional (4D) STEM, a high-speed direct electron camera records a series of these CBED patterns as the beam is scanned. The CBED patterns are extremely rich in information, encoding information about the local electric field and magnetic field, local thickness and orientation, three-dimensional defect crystallography, phonon spectra and more. They are also a fairly large dataset, ranging from 10s of GBs to TBs for one scan of the sample.
Convolution neural networks (CNNs) may offer a computationally efficient, flexible, and accurate approach to identifying features in 4D STEM data sets and extracting meaningful information about the sample. Modern CNNs can classify features in natural images (photographs) when trained against a large data set of images tagged with the features present in each image. In 4D STEM, we can generate tagged training data using multislice simulations from known structures, use it train a CNN, then use the CNN to extract information about the sample from experimental CBED patterns.
As a first step, we propose an approach to measuring sample thickness from 4D STEM data using a CNN. We developed the CNN in Keras (Python) by applying the transfer learning method on a pre-trained VGG-16 model. The training dataset was prepared by performing frozen phonon simulations on a 100 nm SrTiO3 model along  axis, and the simulated CBEDs are categorized in 2 nm steps. Random, Poisson-distributed noise is applied to the simulated CBEDs to imitate the noise in the experiment, and the training dataset was further expanded through image augmentation. Preliminary results suggest that the CNN achieves a >98% accuracy on predicting the sample thickness on the test dataset, similar to the performance achieved by Lebeau using a CNN to analyze position-averaged convergent beam electron diffraction data. An analogous CNN method to determine sample tilt will also be discussed.