Achieving sub-Angstrom resolution by aberration correction in an electron microscope requires the precise control of a large set of multipole electron-optical elements very similar to those used in synchrotron ring, with similar challenges in their multidimensional optimization.  We approach this challenge by recognizing the equivalence between aberration correction in electron microscopy and phase space beam emittance minimization in accelerator physics. We show that emittance (the volume of phase space occupied by the beam) as an alternate metric of beam quality is better behaved than the aberration function traditionally used in electron microscopy, which suffers from cusp-like minima that are very unstable. 

We diagnose the lens distortions using electron Ronchigrams, which are diffraction patterns of a convergent electron beam focused on an amorphous material that encode the phase variation of the electron beam in momentum space and should be smooth when the microscope is properly tuned. We show a convolutional neural network (CNN) can be trained to predict beam emittance growth directly from single Ronchigrams, providing a bounded metric that enable Bayesian optimization (BO) for the autonomous aberration correction of the microscope. 

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. We have implemented the optimization method on a range of commercial electron microscopes. Tuning is rapid, taking less than several minutes, gives results as good as the current hand-tuning, and requires no operator experience.

CBB is now applying these techniques to higher orders of aberrations.  Once this is done, the goal is to transfer these methods to microscope companies, so that future microscopes can be automatically tuned, and users can avoid expensive and time-consuming visits by company experts.

Bayesian optimization for alignment of an electron microscope. Top:  Ronchigram showing the phase distribution of the beam in momentum space where a larger uniform region in the center indicates a better beam. Bottom: Modelled real space distribution of the electron beam showing better focusing after tuning. 

References: 

Desheng Ma, Chenyu Zhang, Yu-Tsun Shao, Zhaslan Baraissov, Cameron Duncan, Adi Hanuka, Auralee Edelen, Jared Maxon, David Muller, Physics-informed Bayesian Optimization of an Electron Microscope, Microscopy and Microanalysis, Volume 29, Issue Supplement_1, 1 August 2023, Pages 1875–1877, https://doi.org/10.1093/micmic/ozad067.968

Chenyu Zhang, Zhaslan Baraissov, Cameron Duncan, Adi Hanuka, Auralee Edelen, Jared Maxson, David Muller, Aberration Corrector Tuning with Machine-Learning-Based Emittance Measurements and Bayesian Optimization, Microscopy and Microanalysis, Volume 27, Issue S1, 1 August 2021, Pages 810–812, https://doi.org/10.1017/S1431927621003214