Differential programming enabled functional imaging with Lorentz transmission electron microscopy

Abstract

Abstract Lorentz transmission electron microscopy is an advanced characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials. Information such as magnetization and electric potentials is carried by the phase of the electron wave, and is lost during image acquisition. Various methods have been proposed to retrieve the phase of the electron wavefunction using intensities of the acquired images, most of which work only in the small defocus limit. Imaging at strong defoci not only carries more quantitative phase information, but is essential to the study of weak magnetic and electrostatic fields at the nanoscale. In this work we develop a method based on differentiable programming to solve the inverse problem of phase retrieval. We show that our method maintains a high spatial resolution and robustness against noise even at the upper defocus limit of the microscope. More importantly, our proposed method can go beyond recovering just the phase information. We demonstrate this by retrieving the electron-optical parameters of the contrast transfer function alongside the electron exit wavefunction.