A method for accurate localisation of EBSD pattern centres
Research Highlights
►Numerical and experimental study of measuring the pattern centre of EBSD patterns. ►Advanced moving screen technique coupled with sub-pixel cross-correlation. ►In theory, using simulated patterns, the precision is of the order of 1/100th pixel. ►In practice, the precision is drastically reduced due to camera imperfections. ►Methods of improving camera design for high resolution EBSD are outlined.
Introduction
The Electron Back-Scattered Diffraction (EBSD) technique is nowadays a quasi-standard investigation tool for characterising microtextures (microstructural features in relation to their crystallographic nature and orientation). When coupled with EDX analysis, EBSD also provides powerful phase identification capabilities (see [1] for a recent overview). Since the pioneering work of Wilkinson and co-workers [2], [3], EBSD is also increasingly used for elastic strain measurements at the local scale or plastic deformation analysis via GNDs characterisation.
The relative angular resolution of standard equipments ranges from ∼1.0 down to ∼0.3° according to the pattern quality and indexing strategy setup (e.g. Hough transform resolution, number of bands used for indexing, pattern centre localisation). The pattern centre (PC, or source point position) is the position of the volume source responsible for the diffraction pattern with respect to the coordinate system linked to the camera as shown in Fig. 1. The quality of the geometrical interpretation of the diffraction pattern strongly depends on the precise localisation of the source point. Therefore every EBSD analysis starts with a calibration step aiming at positioning the source point for the given sample/beam/camera setup. In the past, several calibration techniques have been proposed for determining its position, namely
Shadow casting methods (Venables and Bin-Jaya [4], Day [5])
Known crystal orientation (Dingley et al. [6])
Pattern magnification (Hjelen et al. [7], Carpenter [8])
Iterative pattern fitting (Krieger Lassen [9], [10], [11])
Randle and Engler [12] give an exhaustive description of these methods and a discussion of their respective advantages and disadvantages.
However, as reviewed recently by Britton et al. [13] these techniques have PC errors of order 0.5% whereas an accuracy better than 0.05% is required for absolute elastic strain measurement [14]. It is worth mentioning that finding the source point position with good accuracy is also very important for the Kossel X-ray diffraction technique. In fact, some of the methods listed above have previously been developed to analyse Kossel diffraction patterns [15].
With the development of higher angular resolution techniques [13], [14], [16], [17] more precise pattern centre localisation is clearly required. The method presented in this paper makes use of the well-known “pattern magnification” (or “moving screen”) technique, but in contrast with the classical point-clicking way of tracing zone axis displacements, an automatic cross-correlation based algorithm is used to locate the pattern centre with much higher resolution.
This paper first describes the principles of the method and then goes on to apply it to simulated EBSPs and finally to experimental patterns.
Section snippets
Principles
Fig. 1 shows the experimental procedure used: two (or more) EBSD patterns are acquired at two (or more) different camera positions, the so-called “out” and “in” positions. This yields two images of the diffraction pattern, where the “out” image is a zoomed version of the “in” image, the zoom centre (invariant point) being the required pattern centre. During this process, it is important to keep the beam in the same position on the sample surface, and also to keep the camera movement in the same
Application to simulated patterns
The numerical procedure has first been tested on simulated patterns calculated by means of the many beam dynamical theory as explained by Winkelmann et al. [18]. An in-house parallel implementation running on an 80 core cluster has been used to produce high-quality simulated EBSD patterns of germanium. The computation time for a 1344×1024 image is typically below 2 min.
The first numerical experiment has been carried out with two patterns calculated with the following projection parameters
Discussion
The results in the first part of the preceding section dealt with “perfect” patterns where the simulated detector was perfectly linear and perfectly orthogonal to the moving direction. In such an ideal case, the pattern centre was found with a precision better than 0.5 μm.
Unfortunately, such a precision was not obtained in the experiment, using the ideal zoom model. From the work of Mingard et al. [17], it appears that available cameras are not as perfect as the simulated one.
At least three
Conclusions
The moving screen technique to determine the pattern centre of EBSPs has been extended to very high resolution by introducing cross-correlation procedures between images from two or more camera positions.
On synthetic patterns it is shown that this method gives an accuracy better than 0.01 pixel.
On experimental patterns the accuracy is expected to be better than that of current fitting procedures but is still limited by factors such as the lens distortion, the camera rotation and misalignment of
Acknowledgements
We would like to thank Ken Mingard (NPL) and Austin Day (Aunt Daisy Scientific) for their help in calibrating the lens distortion of our NordlysII camera and many fruitful discussions.
This work has been financially supported by the ANR project “SAKE”.
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