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Page 10 of 17 Hansen et al. Microstructures 2023;3:2023029 https://dx.doi.org/10.20517/microstructures.2023.17

of only 0.412. The Cosine method correctly identified that pattern A has the highest similarity value (0.919),
but the ones from the two VO variants also showed high similarity values (0.907 and 0.903), which may
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lead to crystallographic variant misidentification. Among the three algorithms, the Cosine method yields the
lowest reliability value. This shortcoming of the Cosine method is consistent with the observation made in
the SMA samples [Table 1]. The SSIM algorithm yields a similar trend to the Euclidean distance approach
but shows low similarity values in absolute numbers. Taken together, reducing noise with a Gaussian filter
significantly improved the similarity quantification across the three algorithms.

Reducing noise also improved the crystallographic variant mapping. Figure 7 shows the crystallographic
variant maps generated using the Euclidean distance, Cosine, and SSIM algorithms. All methods produced
good results where the sapphire substrate (red), VO variants (blue and green), and vacuum (black) are
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clearly resolved. A manually drawn baseline map is not provided here because the interface between the two
VO variants is curved and difficult to draw. A careful examination of the diffraction patterns in this dataset
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confirmed that the maps shown in Figure 7 are indeed correct.

Method 2: algorithm-selecting-reference-pattern approach
The previous method, though powerful and efficient in generating the crystallographic variant maps,
requires user input to select all known crystallographic variants. In some cases, the number and location of
the crystallographic variants are unknown. Here, we describe a new method that is built upon the user-
selecting-reference-pattern approach (Method 1) but uses the algorithm to select reference patterns to
generate crystallographic variant maps.

This method starts at a pixel in the PED data (0, 0) by default or a pixel position chosen by the user. The
diffraction pattern corresponding to the pixel is treated as the first reference and is added to a list that will
contain reference patterns in the dataset. Each reference pattern in the list represents a unique
crystallographic variant. The diffraction patterns from the following pixels will be compared to the reference
pattern, and the similarity values (using Euclidean distance, Cosine, or SSIM) will be calculated. The starting
pixel will be compared to all other pixels, and the minimum similarity value will be used as the initial cut-off
value. If the calculated similarity value of the pixel is greater than the cut-off value, the algorithm treats the
pixel the same as the reference pattern variant. If the calculated similarity value is less than the cut-off value,
the algorithm will save the diffraction pattern of the pixel as a new reference. The diffraction patterns from
the following pixels will be compared to the two references to determine which variant they belong to. This
process iterates. If a pixel has one or more similarity values greater than the cut-off, the variant is
determined by the one with the highest similarity. If a pixel has all similarity values less than the cut-off, the
pixel itself will be added to the reference list and serve as a new variant. This process repeats for all pixels.
Once all the pixels have been compared, the cut-off value increases by a step; by default, there are 20 steps
between the initial minimum similarity and the maximum similarity values. The process repeats using the
increased cut-off value and starting with the list of unique crystallographic variants from the previous
iteration.

The above-mentioned mapping method was first used on the SMA dataset to produce a series of similarity
maps at varying cut-off values. In the SMA dataset, the (0, 0) point is located at a boundary between two
variants that may skew the variant identification. A user-selected point in the middle of a large variant,
(116, 168), was used, and the corresponding diffraction pattern serves as the first reference pattern. Figure
shows the SSIM similarity maps with various cut-off values ranging from 0.705 to 0.787. The optional initial
point and comparison method are the only user inputs using this method. Note the small cut-off range
generates very different crystallographic maps. With low cut-off values, such as 0.705, the four predominant