Contrast Transfer Function-Based Exit-Wave Reconstruction and Denoising of Atomic-Resolution Transmission Electron Microscopy Images of Graphene and Cu Single Atom Substitutions by Deep Learning Framework.

The exit wave is the state of a uniform plane incident electron wave exiting immediately after passing through a specimen and before the atomic-resolution transmission electron microscopy (ARTEM) image is modified by the aberration of the optical system and the incoherence effect of the electron. Although exit-wave reconstruction has been developed to prevent the misinterpretation of ARTEM images, there have been limitations in the use of conventional exit-wave reconstruction in ARTEM studies of the structure and dynamics of two-dimensional materials. In this study, we propose a framework that consists of the convolutional dual-decoder autoencoder to reconstruct the exit wave and denoise ARTEM images. We calculated the contrast transfer function (CTF) for real ARTEM and assigned the output of each decoder to the CTF as the amplitude and phase of the exit wave. We present exit-wave reconstruction experiments with ARTEM images of monolayer graphene and compare the findings with those of a simulated exit wave. Cu single atom substitution in monolayer graphene was, for the first time, directly identified through exit-wave reconstruction experiments. Our exit-wave reconstruction experiments show that the performance of the denoising task is improved when compared to the Wiener filter in terms of the signal-to-noise ratio, peak signal-to-noise ratio, and structural similarity index map metrics.