Compressive electron backscatter diffraction imaging

Abstract

Electron backscatter diffraction (EBSD) has developed over the last few decades into a valuable crystallographic characterisation method for a wide range of sample types. Despite these advances, issues such as the complexity of sample preparation, relatively slow acquisition, and damage in beam-sensitive samples, still limit the quantity and quality of interpretable data that can be obtained. To mitigate these issues, here we propose a method based on the subsampling of probe positions and subsequent reconstruction of an incomplete data set. The missing probe locations (or pixels in the image) are recovered via an inpainting process using a dictionary-learning based method called beta-process factor analysis (BPFA). To investigate the robustness of both our inpainting method and Hough-based indexing, we simulate subsampled and noisy EBSD data sets from a real fully sampled Ni-superalloy data set for different subsampling ratios of probe positions using both Gaussian and Poisson noise models. We find that zero solution pixel detection (inpainting un-indexed pixels) enables higher-quality reconstructions to be obtained. Numerical tests confirm high-quality reconstruction of band contrast and inverse pole figure maps from only 10% of the probe positions, with the potential to reduce this to 5% if only inverse pole figure maps are needed. These results show the potential application of this method in EBSD, allowing for faster analysis and extending the use of this technique to beam sensitive materials.

Keywords: EBSD; SEM; compressive sensing; electron backscatter diffraction.

FIGURE 1

Operating principles of EBSD imaging. A convergent electron beam is raster scanned across the sample. Backscattered electrons form a pair of cones which intersect the phosphor screen, allowing the EBSD pattern to be read by the detector.

FIGURE 2

Example EBSD maps of Ni‐superalloy. EBSD maps provide crystallographic information about the sample such as (A) the locations of grain boundaries or (B) crystal orientation.

FIGURE 3

Conventional versus compressive EBSD imaging. Probe locations are subsampled and the EBSD patterns acquired are indexed. The incomplete maps formed can then be inpainted.

FIGURE 4

Effect of Gaussian and Poisson noise models on Hough‐based indexing. (A) Hit rate; (B) normalised error between reference and indexed EBSD maps. Due to the high amount of redundancy in EBSD data, the indexing process is robust to moderate noise levels. Data points from 5 and –5 dB are shown in Figure 5.

FIGURE 5

Band contrast and IPF Z maps produced through Hough‐based indexing of noisy EBSD data corrupted by Gaussian and Poisson noise. The indexing quality of these maps are shown in Figure 4.

FIGURE 6

(A) Normalised error of inpainted maps both with and without ZSP detection. (B, C) IPF Z maps with ZSP correction. Examples of these maps without ZSP correction can be found in Figure 5.

FIGURE 7

Image quality of reconstructed subsampled EBSD maps showing the effects of noise on the quality of the images reconstructed. (A) Band contrast; (B) IPF Z maps.

FIGURE 8

Examples of inpainted band contrast and IPF Z maps. These datapoints are taken from Figure 7.

FIGURE 9

SSIM results for band contrast and IPF Z maps with subsampling in comparison to those which have been subsampled and downsampled.