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Page 2 of 12 Wang et al. Microstructures 2023;3:2023036 https://dx.doi.org/10.20517/microstructures.2023.27

INTRODUCTION
Precession electron diffraction (PED) is a powerful characterization technique used to obtain high-
[4-6]
[1-3]
resolution crystal structure/orientation and elastic strain information about materials at the nanoscale
level. Some notable PED applications include characterizing thin film microstructures [7-10] , nanocrystalline
grain growth behavior [11,12] , material deformation behavior at large strains [13,14] , and submicron and nanoscale
martensite variants [15,16] . When applying PED, the electron beam in the transmission electron microscope
(TEM) is converged to a small probe (~1-3 nm) and rasters on the specimen. Precession (typically 0.3°-0.8°)
is applied to excite higher-order reflections and reduce the dynamical effect [1,17,18] . The experimentally
acquired diffraction patterns from each pixel are compared to the simulated diffraction patterns in a
database to determine the crystal structure and orientation. The information is then used to create phase
(crystal structure) and orientation maps. The PED-based orientation mapping is also termed automated
crystal orientation mapping (ACOM) [2,3,8,10] . Compared to electron backscatter diffraction (EBSD, another
widely used orientation mapping technique, typical resolution ~20-50 nm), PED offers superior spatial
resolution (~3 nm resolution in conventional field-emission gun TEM). In addition, PED offers a larger
field of view compared to high-resolution TEM (HRTEM). HRTEM typically allows examination of lattice
fringes to deduce crystal orientation in a field of view up to 50 × 50 nm², while PED can provide a field of
view up to 6 × 6 μm². Hence, the PED-based orientation mapping fills the length-scale gap between HRTEM
and EBSD.

The quality of PED orientation mapping depends heavily on the quality of the diffraction pattern. Various
factors can affect the diffraction pattern signal, including sample thickness and crystal orientation.
Generally, thinner samples are preferred as longer rel-rods intersect with the Ewald sphere, resulting in
more diffraction spots and accurate template matching between the experimentally acquired and simulated
[19]
diffraction patterns . Diffraction patterns acquired at or close to zone axes are also preferable since they
offer more diffraction spots for template matching. Conversely, diffraction patterns acquired far away from
zone axes have fewer spots, and the intensity of the spots that are not at the exact Bragg condition
diminishes rapidly, potentially leading to poor orientation indexing. While sample thickness can be
controlled by the researcher, it is difficult to control the exact diffraction condition of individual grains in
polycrystalline or deformed single-crystal samples. Therefore, there is a need for a robust and efficient
algorithm to enhance diffraction spot information when it is not ideal for template matching.

Previous work from various research groups has reported that preprocessing PED data is critical to realizing
the full potential of the subsequent algorithms. For example, Bergh et al. demonstrated the importance of
binning and center beam alignment before background removal and diffraction spot identification to
resolve overlapping diffraction patterns . Zhao et al. effectively reduced noise in PED raw data through
[20]
various filters (e.g., Gaussian, non-local means, and Wiener) to enable precise diffraction spot position
identification and strain mapping . Folastre et al. employed sub-pixel adaptive image processing and linear
[4]
filtering to enhance pattern matching for crystal orientation determination and phase recognition .
[21]
However, none of these data preprocessing techniques were specifically designed to amplify the signals of
low-intensity diffraction spots.

In this study, we introduce a new algorithm called “Auto-CLAHE” for enhancing diffraction data in PED.
The name is short for “automatic contrast-limited adaptive histogram equalization”. Auto-CLAHE is based
on a popular image processing technique called CLAHE (contrast-limited adaptive histogram
equalization) [22-24] , which applies histogram equalization to small regions of an image independently to
prevent over-enhancement of local contrast. The amount of enhancement is controlled by a clip limit, with
higher clip limits corresponding to greater enhancement. In our method, the clip limit for each diffraction