Tru-I Indexing

Tru-I indexing is the name given to the whole Electron Backscatter Diffraction (EBSD) pattern indexing process in AZtecHKL, from band detection to solution. This page provides some background information into the ways these processes work, from details about the band detection process (including the concept of weighted band detection and the “Optimized Band Detection” option that is available in the software), as well as the basics of the indexing process (referred to as “Class Indexing”).

There are also additional indexing techniques within AZtecHKL that are dedicated to providing improved solutions for specific application cases. These include:

Details on all of these above processes can be found below.

Band detection is a fundamentally important aspect of EBSD analysis and is critical in terms of data quality. Improvements in band detection can increase the number of correctly indexed points (and thus reduce the reliance on post-acquisition clean up processes), especially for materials that produce weak diffraction patterns with indistinct Kikuchi bands. This will benefit the characterisation of highly strained materials, complex phases (such as many minerals) and also applications with unusual projection geometries, such as off-axis transmission Kikuchi diffraction (TKD).

The standard process of band detection using the Hough transform has been introduced in the EBSD Explained section (see here), and this process underpins the standard band detection approach within AZtecHKL. However, there are 2 additional developments within AZtecHKL that ensure high quality band detection, even on challenging EBSD patterns, thus ensuring robust and reliable indexing. These are described below.

Weighted Band Detection

In AZtecHKL, the system will automatically determine which of the detected Kikuchi bands in each pattern are best used for the indexing process. This involves applying a weighting function based on the band’s average intensity and the position of the band within the “area of interest” (the user-defined area used for band detection). A higher priority is given to those bands at or near the centre of the area of interest: these bands will usually be more reliably detected, thus making the indexing process more robust. The weighted band detection process is illustrated in the example below.

Example EBSD pattern collected from a silicate mineral

Example EBSP from a silicate mineral.

EBSD pattern showing the detected bands using a standard band detection approach

Standard (non-weighted) band detection. Note detection of Kikuchi bands at the edge of the area of interest (red area).

EBSD pattern showing the detected bands using a weighted band detection approach

Weighted band detection. Preference is given to more reliably detected Kikuchi bands closer to the centre of the EBSP (blue area).

Optimised Band Detection

With the introduction of transmission Kikuchi diffraction, TKD, in the years 2010-2012, it became clear that the unusual projection geometry that was required for off-axis TKD measurements caused issues with standard EBSD band detection algorithms. Since the diffraction pattern was projected from the underside of an electron transparent sample, the pattern centre (i.e. the closest point to the beam-sample interaction point on the plane of the phosphor screen) would often be located off the top edge of the phosphor screen. This had the effect of making Kikuchi bands in the lower part of the EBSP appear unusually broad: in the Hough image, such bands would be almost indistinguishable as single peaks, and the band detection algorithm would often incorrectly identify the excess line (the bright upper edge of the Kikuchi bands) as the band centre. This would lead, at best, to slight orientation errors in the indexing and, at worse, to completely incorrect solutions or no solution at all. An example TKD pattern from a deformed Al alloy is shown below, along with the results using a standard band detection process.

Example band detection on a TKD pattern from an Al sample, using a conventional Hough-based band detection process
Example transmission Kikuchi diffraction pattern from a nanocrystalline Al sample

Example transmission Kikuchi diffraction pattern from a nanocrystalline Al sample

Hough transform image from the standard band detection of an Al TKD pattern

Hough image highlights 3 “peaks” that have been identified incorrectly as individual Kikuchi bands

Al TKD pattern showing the results of a standard band detection, with poorly detected band marked with arrows

Detected band image, shows that these 3 peaks correspond to the bright upper edges (the excess lines) of broad Kikuchi bands, marked with the red arrows

Although the unusual geometry of TKD patterns will cause more frequent problems due to conventional band detection processes, these problems will also be apparent in standard EBSD analyses, especially with phases that produce unusually broad Kikuchi bands or materials that suffer from significant excess and deficit lines in the diffraction patterns (such as diamond).

In response to this problem, Oxford Instruments developed a new optimised band detection routine. The algorithm follows these steps:

  • For each phase used for indexing, the software will calculate the broadest and narrowest Kikuchi bands expected in the pattern, taking into account the projection geometry
  • Following initial peak detection via the Hough Transform process, the software will perform a secondary peak search using a localised increased Hough resolution. This peak search will be asymmetric, extending further down the Hough space, since the darker deficit lines at the lower edge of Kikuchi bands are more likely to be missed in the initial peak detection
  • The algorithm will search for the greatest contrast changes (associated with the Kikuchi band edges) and will determine the band centre as being located in between the 2 edge locations

The example below shows how this optimised band detection process delivers more reliable results using the same TKD pattern as shown above.

Example band detection on a TKD pattern from an Al sample, using the optimised band detection process
Example transmission Kikuchi diffraction pattern from a nanocrystalline Al sample

Example transmission Kikuchi diffraction pattern from a nanocrystalline Al sample

Hough transform image from the optimised band detection of an Al TKD pattern

Hough image highlights the same 3 “peaks” that have were identified incorrectly using a standard band detection process

Al TKD pattern showing the results of optimised band detection, with all bands reliably detected

Detected band image, shows that all the Kikuchi band positions in this pattern have been reliably detected, resulting in precise and robust indexing

The benefits of the optimised band detection routine extend to all types of EBSD analysis. Not only does it provide more robust indexing results but, due to the localised higher resolution peak search in the Hough image, it improves the angular precision of the indexing. The graph compares the effect of changing Hough resolution on the angular precision of EBSD indexing for conventional band detection and for optimised band detection, as measured using kernel average misorientation values from maps of a single crystal Si sample. For conventional band detection (black lines), the angular precision improves with increasing Hough resolution, as expected. However, for optimised band detection (coloured lines) the angular precision is unaffected by the Hough resolution, and in all cases, is better than for conventional band detection, even when using a very low Hough resolution value (e.g. 30 or 40). This demonstrates the power of the optimised band detection algorithm – not only does it provide more robust band detection and hence more reliable indexing, but the angular precision is not affected by Hough resolution, so that high speed EBSD analyses with a low Hough resolution can also have a high angular precision.

Graph showing the impact on angular precision of Hough Resolution using standard and optimised band detection

Graph comparing the variation in Kernel Average Misorientation values with varying Hough resolution, as measured from single crystal Si maps collected using standard band detection (black curves) and optimised band detection (coloured curves). The labels indicate the Hough resolution, as defined in AZtecHKL (note that the true Hough resolution = 2 x (HR as defined in AZtecHKL) +1)

The indexing routine is critical in achieving accurate data. The challenge for an EBSD system is to achieve a high validated hit rate without generating false positive solutions, where EBSPs are solved but with the wrong solution. Automated routines can be very sensitive to non-fitting bands, such as those occurring at grain boundaries where the imaged diffraction pattern is actually a superposition of 2 different diffraction patterns, corresponding to the grains on either side of the boundary. The indexing algorithm must be robust enough to handle any inaccuracies arising from the band detection. The relative advantages and disadvantages of pattern matching techniques, such as Dictionary Indexing or Spherical Indexing, have been discussed in the “Techniques for Indexing” page, but here we focus on conventional Hough-transform based indexing.

AZtecHKL uses a robust indexing method termed “Class Indexing”. This utilises groups of 4 bands at a time (it could also be referred to as “Quadruplet Indexing”) and considers the band coherence (where the measured bands and reference crystal reflectors are in agreement) and non-coherence (where the measured bands and the reference crystal reflectors are not in agreement). These 4-band combinations enable the indexing routine to break the solutions into smaller blocks, which are then the foundations of the indexing. Using this method, the routine is far more robust and can find the correct solution, even when one or more bands are non-coherent.

Why use 4 band groups?

The use of groups of 4-bands, unlike other algorithms that use 3-bands, is simply a question of maths. The number of permutations of 3-band and 4-band groups (triplets and quadruplets) that can be derived for a set number of bands detected is shown in the table below.

Bands: 5
6
7
8
9
10
11
12
Quadruplets: 5 15 35 70 126 210 330 495
Triplets:
10 20 35 56 84 120 165 220

For any EBSP in which more than 7 Kikuchi bands are detected, there are more 4-band permutations than 3-band permutations. This means that there will be less noise in the indexing and a greater chance of a robust and reliable solution.

How many bands to detect?

The user interface in AZtecHKL allows the number of detected bands to be set from a minimum of 6 to a maximum of 12. As can be seen in the table in the previous section, detecting a higher number of bands will give more 4-band groups for the software to consider and will typically result in more accurate and robust solutions. Therefore, it is recommended to set the band detection to somewhere between 10 and 12 bands to give the best results and the greatest benefit from the Class indexing approach.

However, in some materials, the EBSPs may be of a poor quality, and the reliable detection of a high number of bands may be difficult; in such cases, it may be beneficial to lower the number of bands detected. It is worth noting that, for a certain number of detected bands, AZtecHKL will only accept solutions that have a minimum number of bands that match with the final solution, and this minimum band value will vary according to the number of detected bands as follows:

No. of bands detected:
6 7 8 9 10 11 12
No. of bands needed to match the solution:
5 6 6 6 6 6 7

Therefore, by detecting a higher number of bands, the software will permit a greater number of these not matching with the final solution, providing better indexing along the grain boundaries (as shown in the following section).

Grain Boundary Resolution

In EBSD datasets, most unindexed points lie along grain boundaries where the indexing algorithm was unable to deconvolve the Kikuchi bands belonging to the diffraction patterns of the 2 orientations. The Class indexing method is much better at accommodating overlapping patterns, and generally, the solution from the dominant group of bands (i.e. from one side of the boundary) supersedes the wrong four-band combinations, including representative bands from either side of the boundary. As a result, grain boundaries are more accurately resolved, and there are fewer non-indexed points, as illustrated in the following figure.

EBSD orientation map collected using conventional indexing, showing non indexed points along grain boundaries

Orientation map collected using a conventional indexing approach that considers each detected Kikuchi band individually. Note the loss of indexing at grain boundaries (black pixels)

EBSD orientation map collected using class indexing, showing well indexed points along grain boundaries

Orientation map collected from the same set of EBSPs using Class indexing with 4-band permutations. Note the high indexing rates along grain boundaries.

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