Emittance minimization for aberration correction I: Aberration correction of an electron microscope without knowing the aberration coefficients.

Precise alignment of the electron beam is critical for successful application of scanning transmission electron microscopes (STEM) to understanding materials at atomic level. Despite the success of aberration correctors, aberration correction is still a complex process. Here we approach aberration correction from the perspective of accelerator physics and show it is equivalent to minimizing the emittance growth of the beam, the span of the phase space distribution of the probe. We train a deep learning model to predict emittance growth from experimentally accessible Ronchigrams. Both simulation and experimental results show the model can capture the emittance variation with aberration coefficients accurately. We further demonstrate the model can act as a fast-executing function for the global optimization of the lens parameters. Our approach enables new ways to quickly quantify and automate aberration correction that takes advantage of the rapid measurements possible with high-speed electron cameras. In part II of the paper, we demonstrate how the emittance metric enables rapid online tuning of the aberration corrector using Bayesian optimization.