Integrated contrast-transfer-function for aberration-corrected phase-contrast STEM

Highlights: • Proposal of an integrated contrast transfer functions (iCTF) for phase-contrast imaging with a modern aberration-corrected electron microscopy. • The iCTF concept with a thick weak-phase object (tWPO) approximation is applied for unique annular bright-field (ABF) imaging in scanning transmission electron microscopy (STEM). • ABF images essentially reveal different depth dependences between the heavy/light atom sites. We describe the optical conditions that are essentially necessary for phase-contrast imaging with aberration-corrected scanning transmission electron microscopy (STEM), whose depth of field has reached almost comparable to the specimen thickness. For such state-of-the-art STEM, contrast-transfer-function (CTF) should be defined not solely for the projected potential but multiply for each wavefront during the beam propagation across the specimen thickness; an integration of multiple CTFs (iCTF). We show that the iCTF concept explains fairly well characteristic annular-bright-field (ABF) imaging behaviors of heavy/light atom sites against the defocus changes, and also provide notable concerns on possible artifacts that arise from different imaging-depth dependences between the heavy/light atom sites.