Revolutionizing OIM Analysis with Spherical Indexing

Pattern indexing is central to electron backscatter diffraction (EBSD) analysis. Creating an effective indexing algorithm was essential in the effort to automate EBSD. There are two steps to accomplishing this: (1) detecting the bands in the patterns through the Hough transform and (2) comparing the angles between the detected bands as opposed to the interplanar angles in the crystal lattice to determine the crystallographic orientation.^1,2 This method has held up well over several years.

Figure 1. Schematic for Hough-based indexing. Image Credit: Gatan, Inc.

Today, the next generation of indexing has appeared. At the core of this new indexing approach is the accurate simulation of EBSD patterns utilizing a dynamical diffraction model.^3,4 This new approach uses a pattern matching method where the first step is building a ‘dictionary’ of patterns with every possible orientation.

The indexing is completed by comparing an experimental pattern against each pattern in the dictionary to discover the closest match.⁵ This can prove to be a very computer-intensive indexing approach. This technique has been instilled in OIM Analysis^™ and coded to use the GPU, which makes the dictionary indexing technique application possible.

Figure 2. Schematic for dictionary indexing. Image Credit: Gatan, Inc.

Discussion

Gatan is thrilled to announce a more efficient approach called spherical indexing, which has been implemented in EDAX OIM Analysis 9.^6,7 The math it is based on is fairly complex, but the concept is more easily understood.

Above, it was mentioned that a dictionary has been calculated for all orientations, which is not completely accurate. Orientation space is discretized into a limited set of patterns and orientations simulated for this discretization of orientation space.

One way to visualize orientation space is as a sphere. Rather than simulating all of the patterns at each orientation, a single spherical pattern can be simulated. The next task is to back-project an experimental pattern onto a sphere and locate the best fit to the spherical pattern using cross-correlation (e.g., spherical harmonics).

This approach uses a GPU and can achieve indexing speeds that rival the quickness of the current Hough transform/triplet indexing approach but are more robust than the Hough-based method.

Figure 3. Schematic for spherical indexing. Image Credit: Gatan, Inc.

Spherical indexing offers great efficacy for samples that struggle with traditional indexing, such as those with high levels of deformity, weak scatterers, rough surfaces, and others.

Figure 4 illustrates a cross-section of a shot-peened aluminum sample. Notice the improved indexing performance regarding the number of points indexed versus Hough-based indexing, as well as the continuity of the orientation gradients versus those obtained by dictionary indexing (e.g., the pink grain on the right side of the maps close to the bottom).

Figure 4. Orientation maps for a shot-peened aluminum sample after indexing using traditional Hough-based, dictionary, and spherical indexing. Image Credit: Gatan, Inc.

References

1. Krieger, C., Jensen, D.J. and K. Conradsen (2021). Image Processing Procedures for Analysis of Electron Back Scattering Patterns. (online) DigitalCommons@USU. Available at: https://digitalcommons.usu.edu/microscopy/vol6/iss1/7/ (Accessed 18 Feb. 2025).
2. Wright, S.I. and Adams, B.L. (1992). Automatic analysis of electron backscatter diffraction patterns. Metallurgical Transactions A, 23(3), pp.759–767. https://doi.org/10.1007/bf02675553.
3. Winkelmann, A., et al. (2007). Many-beam dynamical simulation of electron backscatter diffraction patterns. Ultramicroscopy, 107(4-5), pp.414–421. https://doi.org/10.1016/j.ultramic.2006.10.006.
4. Callahan, P.G. and De Graef, M. (2013). Dynamical Electron Backscatter Diffraction Patterns. Part I: Pattern Simulations. Microscopy and Microanalysis, 19(5), pp.1255–1265. https://doi.org/10.1017/s1431927613001840.
5. Chen, Y., et al. (2015). A Dictionary Approach to Electron Backscatter Diffraction Indexing. Microscopy and Microanalysis, 21(3), pp.739–752. https://doi.org/10.1017/s1431927615000756.
6. Hielscher, R., Bartel, F. and Britton, T.B. (2019). Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross correlation on the sphere. Ultramicroscopy, (online) 207, p.112836. https://doi.org/10.1016/j.ultramic.2019.112836.
7. Lenthe, W.C., Singh, S. and Graef, M.D. (2019). A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns. Ultramicroscopy, 207, p.112841. https://doi.org/10.1016/j.ultramic.2019.112841.

This information has been sourced, reviewed and adapted from materials provided by Gatan, Inc.

For more information on this source, please visit Gatan, Inc.