Using Aberrations to Improve Dose-Efficient Tilt-corrected 4D-STEM Imaging

Tilt-corrected imaging methods in four-dimensional scanning transmission electron microscopy (4D-STEM) have recently emerged as a new class of direct ptychography methods that are especially useful at low dose. The operation of tilt correction unfolds the contrast transfer functions (CTFs) of the virtual bright-field images and retains coherence by correcting aberration-induced spatial shifts. By performing summation or subtraction of the tilt-corrected images, the real or imaginary parts of the complex phase-contrast transfer functions are recovered, producing a tilt-corrected bright field image (tcBF) or a differential phase contrast image (tcDPC). However, the CTF can be strongly damped by the introduction of higher-order aberrations than defocus. In this paper, we show how aberration-corrected bright-field imaging (acBF), which combines tcBF and tcDPC, enables continuously-nonzero contrast transfer within the information limit, even in the presence of higher-order aberrations. In fact, higher-order aberrations can be beneficial, removing oscillations from the acBF CTF. We demonstrate acBF on both simulated and experimental data, showing it produces superior performance to tcBF or DPC methods alone, and discuss its limitations, including estimates for the number of pixels needed on the detector.