Ronchigram
Ronchigram.com Interactive
experimentation is
the best way to build intuition for how aberrations are revealed in a Ronchigram.
Ronchigram.com runs locally in a web browser using only client-side JavaScript including the Math.js package; no installation is required. It runs on any platform (for example, macOS, Windows, Linux), including your phone (for example, iOS, Android). Tus, mobile access provides an on-the-go solution for instant
access to Ronchigrams—
should an emergency arise. A simple interface streamlines calculation and facilitates fast adjustments to parameters. User-selection of the k-space sampling rate is supported, facilitating easy balancing between the desired Ronchigram resolution and computation speed. Fine adjust- ment of the feature size in the speci- men potential structure (Vnoise
(x)) is
also supported.
Ronchigram.com is an educational, open-source proj- ect released under the 3-clause BSD license, free for non-commercial use.
Significance While information on all aber-
Figure 4: Simulated electron Ronchigrams visualizing common aberrations in aberration-corrected STEM. Simu- lations made with
Ronchigram.com at 300 keV. The top-left image shows a well-aligned Ronchigram with minimal lower-order aberrations, giving rise to the large featureless region near the optic axis (white circle), while further from the optic axis residual higher order aberrations result in the six-fold structure (white tick marks). The top-right image has 10 nm of two-fold astigmatism (C12
) and 10 nm of defocus (C10 ) applied, causing the region of high magnification
) and 15 nm of defocus applied, causing the center of the Ronchigram to shift (orange circle). The bottom-right image has 400 nm of three-fold astigmatism (C23) applied resulting in a three-fold structure (white tick marks).
these low-order aberrations can be recognized and corrected by hand, efficiently correcting higher-order aberrations neces- sitates the use of computer automation [14]. Even aſter good alignment, aberrations will always become
large far from the center of the Ronchigram, therefore portions of the beam that contain noticeable aberrations must be blocked by placement of a circular aperture. A larger permitted aperture size improves the diffraction-limited resolution. To optimize micro- scope imaging conditions, the aperture size must be balanced against the inclusion of aberrations. Aberrations refer to the phase shiſt of the electron wave at each position in the diffraction plane and should not exceed roughly ± π
resolution and minimize probe tails [15–17]. Along with an image of the Ronchigram, the π
4 in order to achieve the best
ture size, and diffraction-limited resolution are displayed on Ron-
chigram.com ( Figure 3).
4 phase limit (blue ring), optimal aper- 14
to stretch and streaks to appear across its surface (gold arrows). The bottom-left image has 400 nm of axial coma (C21
rations, including higher orders, is encoded in the Ronchigram, Cowley and his contemporaries could initially only use it to correct 1st and 2nd order aberrations, most notably, two-fold astigmatism and coma. Te potential for multipole elements to negate the positive spherical aberration intrinsic to rotationally symmetric magnetic lenses had been known for a consid- erable time; however, only in the late 1990s was a multipole corrector system effectively realized, initiating the recent
commercialization and the widespread implementation of aberra- tion-corrected STEM imaging [10,18]. Te Ronchigram has been essential to this corrector system, as well as subsequent systems, providing an easy and tractable measurement of the aberration state from which manual or automatic corrections could be made [10,12,19]. In the time since, aberration-correction has revolution- ized scientific measurement, making sub-Angstrom resolution possible and the once obscure Ronchigram commonplace.
Conclusion A Ronchigram simulator has been devised called Ronchi-
gram.com. Tis soſtware, free for non-commercial use, can assist in understanding Ronchigrams and thus helps in under- standing the alignment of aberration-corrected scanning transmission electron microscopes.
www.microscopy-today.com • 2019 May
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