Introduction to the Ronchigram and its Calculation with

Noah Schnitzer,1 Suk Hyun Sung,1 *

Abstract: This article introduces an intuitive understanding of elec- tron Ronchigrams and how they are affected by aberrations. This is accomplished through a portable web application, http://Ronchigram. com. The history of the Ronchigram, the physics which define it, and its visual features are reviewed in the context of aberration-corrected scanning transmission electron microscopy.

Keywords: Ronchigram, scanning transmission electron microscopy, aberration correction, image simulation, software

Introduction In the soupy grist of a Ronchigram exist patterns a trained

electron microscopist can use to immediately assess the qual- ity of the instrument’s alignment. By tuning the currents in a stack of electromagnetic lenses, the shape, texture, and sym- metry of Ronchigrams may be sculpted until a large feature- less region swims like a pool of spit (Figure 1). A well-placed aperture at the center of this pool creates an electron beam that can reveal atomic structure in vivid detail. Te Ronchigram— its structure, etymology, and the physics that describes it—is puzzling to new microscopists yet requisite for high-resolution scanning transmission electron microscopy (STEM).

Historical Development of the Ronchigram Te name Ronchigram honors the Italian physicist Vasco

Ronchi (pronounced [ˈroŋki]), who in 1923 developed a stan- dard test for shaping aberration-free light optical lenses [1,2]. In the eponymous “Ronchi test,” an optical lens focuses light onto a “Ronchi grating” comprised of alternating dark and clear stripes spaced ∼100 × the light’s wavelength (for exam- ple, 10–100 μm). Without this grating, the convergent beam appears as a uniform bright disc. However, with the Ronchi grating in place, the imperfections of the lens are revealed in the interference patterns (Figure 2). Shulz first used the term “Ronchigram” for light optical measurements in 1948 [3]. Constructing Ronchi’s linear grating is not possible in an

electron microscope because the diffracting wavelength is only a few picometers (for example, 2.51 pm at 200 keV). Instead, we use the atomic arrangement in amorphous materials to pro- vide a nearly random assortment of atomic potentials—well approximated as a noisy grating (Vnoise

(x)). Tis amorphous

grating mimics the Ronchi test by providing interference pat- terns that reveal aberrations in electromagnetic lenses. From 1979, Cowley investigated the electron Ronchigram in the convergent beam electron diffraction (CBED) pattern, both coining the term electron Ronchigram [4] and noting its ben- efit for measurement and correction of aberrations in STEM [4–8]. In conventional TEM the Ronchigram is not typically used for alignment because the electron beam is not converged on the sample [9]. Today, the term Ronchigram is popularly

12 doi:10.1017/S1551929519000427

Figure 1: The patterns, shapes, and symmetries in an electron Ronchigram reveal lens aberrations and the quality of microscope alignment. (a) An experi- mental Ronchigram from an electron microscope is shown alongside (b) a simulated Ronchigram at 300 keV beam energy with a 65 mrad semi-angle aperture. Significant defocus adds structure near to the optic axis, while cumu- lative higher-order aberrations give rise to the six-fold shape typical of aberra- tion-corrected electron microscopes. • 2019 May * and Robert Hovden1,2

1Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109 2Applied Physics Program, University of Michigan, Ann Arbor, MI 48109

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