Abstract
We develop an automatic and objective method to measure and correct residual aberrations in atomic-resolution HRTEM complex exit waves for crystalline samples aligned along a low-index zone axis. Our method uses the approximate rotational point symmetry of a column of atoms or single atom to iteratively calculate a best-fit numerical phase plate for this symmetry condition, and does not require information about the sample thickness or precise structure. We apply our method to two experimental focal series reconstructions, imaging a β-Si3N4 wedge with O and N doping, and a single-layer graphene grain boundary. We use peak and lattice fitting to evaluate the precision of the corrected exit waves. We also apply our method to the exit wave of a Si wedge retrieved by off-axis electron holography. In all cases, the software correction of the residual aberration function improves the accuracy of the measured exit waves.
Highlights
Hardware aberration correction for electron beams in transmission electron microscopy (TEM) is widespread, substantially improving the interpretable resolution in TEM micrographs [1,2,3,4]. This technology is enabled by the combination of two factors; the ability to accurately measure optical aberrations in the electron beam, and a system of multipole lenses that can compensate for these measured aberrations
We can estimate the residual aberrations and apply a numerical phase plate to the reconstructed complex wavefunction to produce aberration-free images [19]. These numerical corrections fall into two categories; manual correction, where the operator attempts to determine the aberrations present by trial and error, and automatic correction where the aberrations are directly measured in some manner
We have developed an algorithm for measuring and correcting residual coherent wave aberrations in complex exit waves of crystalline samples, measured in transmission electron microscopy
Summary
Hardware aberration correction for electron beams in transmission electron microscopy (TEM) is widespread, substantially improving the interpretable resolution in TEM micrographs [1,2,3,4]. Many authors have studied the problem of direct aberration measurement, and most solutions involve capturing a Zemlin tableau [5,6,7,8] This method requires a thin, amorphous object that can approximate an ideal weak-phase object. Aberrations must be measured and corrected on an amorphous sample region before micrographs can be recorded on the region of interest During this delay, One possible solution is to reconstruct the complex electron wavefunction via inline holography, by taking a defocus series and employing an exit wave reconstruction (EWR) algorithm such as Gerchberg-Saxton or the Transport of Intensity Equation [10,11,12,13,14,15,16]. While the theory of aberration determination from a thin, amorphous sample is well-understood (and used to calibrate the hardware corrector on a modern TEM) [20,21,22], purely crystalline samples are much
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