A machine-learning approach to measure 3D sample properties from 2D Transmission Electron Microscopy images

Transmission Electron Microscopy (TEM) is a powerful tool for the characterization of materials at the nanoscale; however, its inherent two-dimensional (2D) nature poses significant challenges to accurately measure three-dimensional (3D) properties. We introduce a supervised machine-learning model that predicts 3D structural information, such as sample thickness and curvature, from a series of conventional 2D TEM images. The model, a U-Net convolutional neural network, is trained on a large synthetic dataset generated from dynamical diffraction simulations that model TEM's complex, nonlinear image formation, accounting for sample thickness and curvature. This physically realistic framework enables exploration of a broad parameter space impractical to sample experimentally. We demonstrate that the trained model has accurate predictions for experimental single-crystal silicon samples, achieving performance comparable to established measurement techniques. This work highlights the critical role of robust, simulation-based training in overcoming the limitations of real-world imaging artifacts and inconsistent sample geometries. By integrating machine learning with numerical simulations, we offer an efficient and scalable framework for quantitative TEM analysis, paving the way for more sophisticated 3D characterization of complex materials.