Technical Note - EBSD
Confidence Index
Introduction
In Electron Backscatter Diffraction (EBSD), indexing is the
fundamental process of deriving a material’s crystallographic
orientation from the diffraction pattern. The orientation, in turn,
becomes the foundation for almost everything else that follows
in an EBSD analysis. Figure 1 shows an example of what indexing
is all about. The pattern shown has been collected, the bands
detected via the Hough transform, and the crystallographic
orientation determined using the Triplet Indexing method. The
final orientation is displayed as a unit cell, with a (111) plane
highlighted.
EDAX’s patented Confidence Index (CI) is calculated as an
integral part of the indexing process and does exactly what its
name suggests. It tells you when you can, or can’t, reliably trust
the indexing solution, providing a statistical means to measure the
quality of the data. The CI is used extensively throughout
TEAM™and OIM™, allowing the analyst to easily identify and,
if necessary, further process ambiguous data in a scan data set.
The CI is a powerful tool.
The Foundation: Triplet-voting Indexing
EDAX’s indexing routine takes advantage of our being able to
derive a unique orientation solution from just three Kikuchi bands.
As one typically uses more than three bands, OIM™ successively
analyzes all possible combinations of band triplets, with the
possible combinations shown in Table 1. Each time a possible
orientation is found for a band triplet, the solution receives a vote.
The orientation with the most votes at the end of the process is
chosen as the solution. For a more detailed discussion, see the
Triplet Indexing technical note.
The Confidence Index
The CI is the difference in votes received by the highest and second
highest ranking solutions (V1and V2 respectively) divided by the
number of total possible votes (VIDEAL).
CI = (V1 – V2)/ VIDEAL
Figure 1. Indexing determines a crystal’s orientation from information in the
EBSD pattern.
The CI ranges in value from 0 (good) to 1 (perfect). Low CI data
can be found in areas with very poor pattern quality, such as
scratches. However, a CI = 0 doesn’t always mean a solution is
bad or incorrect. Consider a pattern from a grain boundary region,
containing superimposed patterns from the two neighboring grains.
If, for example, six bands were selected and each grain happened
to contribute three, then it is likely that the respective orientations
for each grain will be equally represented in the solutions. If this
is the case, the confidence index would be (10 – 10)/20 = 0. Either
of the two solutions could be “correct”, but we cannot confidently
say which one. Conversely, the CI does not have to be 1 in order
to consider the indexing to be correct.
Number Bands
Possible Triplet
Combinations
3
1
4
4
5
10
6
20
7
35
8
56
9
84
10
120
Table 1. Possible triplet combinations for number of
bands used.
Technical Note - EBSD
Figure 2 shows the results from an experiment done on aluminum.
It was found that for a CI of 0.1, 95% of the indexing solutions
were correct. By the time the CI is 0.2, indexing is virtually 100%
accurate.
A Simple Example
In this simplified case, the orientation for an austenitic steel pattern
was automatically determined, using just four bands. (In a normal
scan, it is common to use seven or more bands, depending on the
material.) From Table 1, we know that four bands have four
possible triplet combinations. Figure 3 shows the pattern with the
four bands to be used in the indexing process (a), together with the
results. One orientation proved to be a viable solution for every
triplet and received four votes. This orientation is shown in (b), as
well as in Figure 1. Three other possible orientations, (c) to (e),
were found, though only once each. The CI is easily calculated
according to the previous equation: (4-1)/4 = 0.75. Looking at the
three “runner up ” orientations, it is easy to see how they found
their way into the process.
Figure 2. Confidence Index and indexing performance.
Real Life
The CI provides a valuable tool for processing data. Figure 4 (a)
shows an OIM™ image quality (IQ) map of damascene copper
lines in silicon. The dark areas are amorphous silicon and, although
data was collected in them, they have no real orientation data.
Figure 4(b) shows a histogram chart of the CI distribution for the
data set. Roughly 50% of the data have a CI<0.1. Points with
CI<0.05 were selected in the chart and automatically updated the
image, 4(c). Clearly, we do not want these data in our analysis, a
point driven home by the inverse pole figure map in 4(d). The
solution, simply excludes all data below a certain CI level. In this
case, 0.1 was used, resulting in the map seen in 4(e).
a
b
Figure 3. Confidence Index (circled) and indexing results: (a) pattern and
bands to be indexed; (b)-(e) solutions 1 to 4 respectively, with bands colored
according to families of indices (111, 200, etc.)
Conclusion
Obtaining the correct indexing solution is clearly important, but
how does one know if the solution is correct? EDAX’s
Confidence Index provides a numerical measure of indexing
quality and makes it easy to find, highlight and, if necessary,
remove suspect points from a data set as quickly as possible.
c
d
e
Figure 4 - Confidence Index and data analysis. (a) image quality (IQ) map; (b) confidence index distribution; (c) IQ with CI
<0.05 highlighted; (d)-(e) inverse pole figure maps with and without low CI data.
© EDAX Inc., 2013 November