Introduction
Pattern indexing is at the core of electron backscatter diffraction (EBSD) analysis. The key to the automation of EBSD was the development of an effective indexing algorithm. This was accomplished in two steps: (1) the detection of the bands in the patterns via the Hough transform1 and (2) comparing the angles between the detected bands against the interplanar angles in the crystal lattice to determine the crystallographic orientation2. This approach has stood up well for many years.
Figure 1. Schematic for Hough-based indexing.
Now, a new generation of indexing has arrived. The key to this new indexing approach is the ability to accurately simulate EBSD patterns using a dynamical diffraction model3, 4. This new indexing approach uses a pattern matching approach where the first step is to build a ‘dictionary’ of patterns or every possible orientation. The actual indexing is performed by comparing an experimental pattern against every pattern in the dictionary to find the best match5. As you might imagine, this can be a rather computer-intensive indexing approach. This technique has been implemented in OIM Analysis™ and coded to use the GPU, making the dictionary indexing technique application doable.
Figure 2. Schematic for dictionary indexing.
Discussion
We are very excited to announce a more efficient approach called spherical indexing6, 7 that has been implemented in OIM Analysis 9. The math behind it is fairly complex, but the concept is not too difficult. Previously, it was mentioned that we calculate a dictionary for all orientations. Of course, this isn’t exactly true. Orientation space is discretized into a finite set of orientations and patterns simulated for this discretization of orientation space. But one way to think of orientation space is as a sphere. Instead of simulating all the patterns at each orientation, a single spherical pattern can be simulated. The next step is to back-project an experimental pattern onto a sphere and find the best fit to the spherical pattern using cross-correlation (e.g., using spherical harmonics). This approach also uses a GPU and can reach indexing speeds rivaling the speed of the current Hough transform/triplet indexing approach but with more robustness over the Hough-based method.
Figure 3. Schematic for spherical indexing.
Spherical indexing is very effective for samples where traditional indexing struggles, such as in highly deformed materials, materials that are weak scatterers, samples with rough surfaces, and others. Figure 4 shows a brief example of a cross-section of a shot-peened aluminum sample. Note the improved indexing performance in terms of the number of points indexed over Hough-based indexing and the continuity of the orientation gradients over that obtained by dictionary indexing (e.g., the pink grain on the right edge of the maps near the bottom).
Figure 4. Orientation maps for a shot-peened aluminum sample after indexing using traditional Hough-based, dictionary, and spherical indexing.
For more details and examples, please see the Overcoming EBSD indexing challenges using spherical indexing and real space refinement in OIM Analysis webinar and Spherical Indexing application note.
References
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