Defining HRTEM Resolution: Why Young?s Fringes Don?t Determine Resolution

Abstract

Aberration correction of the objective lens in the high-resolution transmission electron microscope (HRTEM) can extend microscope resolution to the linear information limit [1], the upper bound of a HRTEM’s structural resolution. HRTEM resolution is demonstrated canonically in real space when two image peaks (representing atoms) are distinguishable from a single peak – just as Rayleigh's criterion establishes when two sources of light (stars) are distinguishable from a single source [2]. The “A-OK” set of specimens can be employed to measure HRTEM resolutions from 1.6Å to 0.2Å unequivocally in real space [3] and to characterize image resolution quality [4]. Such real-space measurements have established sub-Ångström resolutions of 0.78Å [5-6] and 0.63Å [7]. Despite the straightforward approach of resolution quantification in real space, resolution is often gauged using image intensity spectrum measurements in reciprocal space, probably because resolution |d| requires the corresponding spatial frequency 1/|d| in the TEM image intensity spectrum; however, the mere presence of a 1/|d| frequency does not establish a resolution of |d| [8].