Automated Atom-By-Atom 3D FIM Reconstruction 259


Figure 2. a,b: Time-ordered FIM images of the [2,2,2] pole. A Gaussian filter has been applied to remove high fre- quency noise. Intensity maximum points are identified and marked in black dots. a: The intensities of atoms marked in white circles are below the set threshold. b: As the evaporation process progresses, the atoms marked in red circles in (a) have evaporated, and the ones marked in white circles are now imaging with intensities above the identification threshold. c: All atomic coordinates identified on the first 80 images, corresponding to the evaporation of the first crys- tallographic layer. The x–y coordinates are set by the pixel coordinates, and the z coordinate at this stage represents the serial number of the image in which every peak was identified.


detected in the first 80 FIM images, corresponding to the first crystallographic plane to evaporate from the surface of the specimen. To create the plot, the measurement of atomic positions seen in Figures 2a and 2b is repeated across the first 80 images, and the detected atomic coordinates are effec- tively stacked in the 3D plot. The z coordinate in Figure 2c represents the serial number of the image in which the atoms were identified. For clarity only the first plane is shown here.


Figure 2c plots the coordinates that were automatically


Consolidating Contributions From Individual Atoms Across the Sequence Once all intensity peaks have been identified across the sequence of images, the next step is to separate these signals into contributions from distinct atoms. The 3D “point cloud” of information to be analyzed (seen in Fig. 6a) at this stage represents every atom detected across all images, but is not the list of atom coordinates for the final reconstruction. Each atom will typically appear in multiple images from the time that it is first exposed at the surface until it is ultimately evaporated. In fact, the number of images in which each atom appears is dependent on its local field conditions and varies from atom to atom. The association of a collection of identified intensity


positions and their measured position from one image to the next can thus change. The imaging intensity of each atom can also change from image to image, dropping below the threshold for identification at times. These changes (dis- cussed in further detail in the following sections) make it necessary to use an adjustable tracking algorithm to identify and group together intensity points describing the same atom across different images. First, peaks from all images are separated according to


peaks to a specific individual atom is carried out through analysis of the relative position of each peak both within the image plane and across the sequence of images. Under the influence of instantaneous field conditions, the imaged positions of atoms may shift from their original recorded


their x–y spatial coordinates (in the image plane). To take into account the displacement of atoms from image to image, a calibration of the imaged size of atoms in pixels is carried out on each image, for each identified intensity peak coor- dinate. This size is determined here by the edge of a circular area surrounding identified atomic coordinate where peak intensity drops to 0.875 of the respective measured maxi- mum. The defined “resolution” distance (taken as half the atomic diameter) provides a method for accounting for small displacements in the coordinates of the imaged atoms throughout a series of images. Each atomic coordinate is compared, using this calibration distance, with all atomic coordinates found on the consecutive image. Intensity peaks that are found to be positioned within the defined x–y “atom-sized” region will be grouped together at this stage, as demonstrated in Figure 3a. Each color represents a group of intensity points associated to the same atom-sized x–y region on the images. Note that atomic positions are compared between adjacent images, and not with the initial position in which the atom was first recorded. This is because the image of atoms can gradually move a distance that is comparable


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