Calibrating coordinate system alignment in a scanning transmission electron microscope using a digital twin

Abstract

In four-dimensional scanning transmission electron microscopy (4D STEM) a focused beam is scanned over a specimen and a diffraction pattern is recorded at each position using a pixelated detector. During the experiment, it must be ensured that the scan coordinate system of the beam is correctly calibrated relative to the detector coordinate system. Various simplified and approximate models are used implicitly and explicitly for understanding and analyzing the recorded data, requiring translation between the physical reality of the instrument and the abstractions used in data interpretation. Here, we introduce a calibration method where interactive live data processing in combination with a digital twin is used to match a set of models and their parameters with the action of a real-world instrument.

Figures (9)

• Figure 1: Impact of the rotation calibration on an integrated CoM Lazic2017 reconstruction of a 4D STEM dataset of $\text{SmB}_6$, recorded with a DECTRIS ARINA on a Thermo Fisher Spectra 200: a) The calibration of the scan rotation is off by 90°. b) Correct calibration of the scan rotation.
• Figure 2: Abstract model of the projection with overfocused STEM with the parameters and coordinate axes labeled.
• Figure 3: Visualization of the ray paths in the digital twin. The figure is generated using TEMGYM's visualization routine from the model used in the calculations with the actual dataset (Figures \ref{['fig:miscalibrated']}-\ref{['fig:numerical']}). The overfocus and the scan step are exaggerated by a factor of $10^4$ to make them visible. Note how this model is closer to the physical reality of a scanning transmission electron microscope than the abstract model in Figure \ref{['fig:abstraction']}. TEMGYM Basic translates the parameters of the abstract model into parameters for simulated optical elements such as deflectors and lenses to yield results equivalent to the abstract model.
• Figure 4: Illustration of the superposition of projected shadow images: a) Projection at first scan position. b) Projection at second scan position. c) Projected image from a). d) Projected image from b). e) Incorrect superposition of the projected images: The features don't align. This will lead to blurring if many images from different scan positions are superimposed incorrectly. f) Correct superposition: The features align and the superposition of many images from different scan positions creates a sharp image of the object.
• Figure 5: Starting condition with scale and alignment miscalibrated. Control interfaces for the calibration parameters are shown at the bottom. The field "Blur metric" shows the blurriness of the "OverfocusUDF: shifted_sum" image as calculated by the algorithm by Crete2007. The plot "OverfocusUDF: point" shows the trace of a single detector pixel as a function of scan position. "OverfocusUDF: shifted_sum" is the main adjustment plot that shows all detector images superimposed in specimen coordinates according to the transformation calculated by TEMGYM that is derived from the input parameters below the plots. If the transformation by TEMGYM matches the actual transformation by the microscope, this plot is a sharp image of the specimen. Note that it is blurred here and doesn't show any specimen features, meaning the parameters are not correct yet. "SumUDF: intensity" shows a sum of all untransformed diffraction patterns. The plot "OverfocusUDF: selected" shows the diffraction pattern at the center of the scan grid rotated and scaled to scan coordinates according to the current settings. Structures of the specimen are only recognizable in "OverfocusUDF: point", while "OverfocusUDF: selected" magnifies the frame so much with the current settings that only a few pixels are in the field of view. The sharp image of the beam-forming aperture shows that the pivot point is adjusted correctly since the aperture is at the same position for each scan point. "OverfocusUDF: sum" shows the sum of partially transformed diffraction patterns where only "Scan Rotation" and "Flip Y" are applied, in contrast to "SumUDF: intensity" that shows the sum of the untransformed diffraction patterns where the position of the beam on the detector can be judged.