Average is bad! At many places children are taught to try their best, at school, at sports and later in life also at their jobs and in scientific research. People want to keep improving themselves. Average is never considered good. If you don’t stand out people do not notice you and how then can you get on in life? In science this is the same. Often only the best results get presented and published. Average results are frowned upon.
But are there also cases where being average can actually be good? In the world of EBSD analysis that is certainly the case. For example in EBSD deformation analysis people have been using Kernal Average Misorientation (KAM) maps for many years to illustrate and investigate subgrain structures. This takes the orientation of a pixel and calculates the average of the misorientation with its 6 neighbours (fig. 1). This tool is highly effective in visualising subgrain structures and lattice bending and takes full advantage of the unique hexagonal scanning grid that is used in the EDAX EBSD software (fig. 2). Without averaging – no results!
With this in mind another type of averaging has recently been introduced in the EDAX TEAM™ software: NPAR. This stands for Neighbour Pattern Averaging and Reindexing. Similar to KAM, NPAR takes an EBSD point and then considers the 6 points in the hexagon around it. But in this case the orientation is not used. Now the original 7 patterns are put together and averaged onto the single pattern in the middle which gets indexed (fig. 3).
The averaging is then repeated for every pixel in the map. This procedure dramatically reduces any pixel intensity noise in the patterns and allows even very weak patterns to be properly identified and indexed. An obvious drawback of this would be that you lose a lot of detail in your EBSD maps as you are still averaging pixels, right? Wrong!
Well OK, a little bit right. In some cases you indeed lose information, especially if you are investigating narrow lamellae with the pixels on either side having the same orientation and the lamella in question only has very few pixels across. The averaging will then suppress the information coming from the lamella and it will indeed disappear from the map (fig. 4). But in general things are not as bad as might seem at first glance.
So, where else would you lose detail? You would expect it at grain boundaries and in heavily deformed areas. First let’s take a close look at a boundary. When you average a point next to a grain boundary, you will get patterns from different orientations being averaged together. The good news is that initially only 2 or 3 points will show diffraction bands from the second grain while 4 or 5 contributing points still contain the bands from the original host grain (fig. 5). This will cause the bands from the host grain to be brighter in the averaged pattern. And here a little known property of the triplet voting indexing algorithm comes into play, the intensity ranking of the triplets. The ranking will ensure that any triangles constructed from these brighter bands will be given higher importance in the orientation determination and bias the orientation towards that of the brighter pattern. Therefore typically the orientation of the majority of the contributing patterns will prevail. In effect there will be only minimal shifting of the grain boundary position in the resulting map because of this, but a clear improvement in indexing success may result (fig. 6).
An even more visible effect will occur in the Image Quality maps. IQ values are related to the intensity of the bands with respect to the average pattern brightness. Any pixel noise in the patterns will effectively decrease the contrast and therefore reduce the sharpness in the IQ maps. NPAR dramatically reduces this pattern noise and improves the grain definition in the IQ maps (fig. 7).
The nature of the NPAR pattern processing also acts as a smoothing filter for intensity gradients in your patterns that are caused by topographic variations in your sample. An application there would be to reduce the pattern intensity gradients introduced by curtaining on FIB or ion-milled specimens.
So far so good! Now let’s take a look at how NPAR would affect the measurement of deformation features such as lattice bending. Here the observed contrast improvement in the patterns has another neat advantage. The band detection in the patterns becomes more consistent which effectively reduces the error in orientation determination. This actually improves the orientation precision for routine mapping to 0.1 – 0.2 degrees (fig. 8).
This improvement is clearly visible in figure 9 which shows a local orientation spread (LOS) map of the deformation around two nano-indents (the black areas) collected with 50 nm steps on a W SEM.
The NPAR reprocessing does not blur the structure as you might suspect, instead it sharpens it. This can be explained by considering the volume in the sample from which the EBSD patterns originate. The lateral resolution of EBSD is typically recognised by the smallest grains with a distinct orientation that may be identified, which is in the order of 25-50 nm depending on the material. However this is not the same as the actual information volume. The latter can be estimated from the distance to a boundary when a contribution from the second grain becomes visible in the pattern. This is in the order of 150 nm in many materials. Normally we don’t care too much about this distance as the contribution of the second pattern will not yet switch the orientation to that of the second grain, but it will deteriorate the orientation precision and thereby the determination of the misorientation between the grains.
Now, if diffraction information from a second grain already becomes visible over a distance of 150 nm, it is to be expected that this information volume is also valid in subgrain- or dislocation networks inside a grain. But here the effect is not as obvious as at a high-angle grain boundary. EBSD patterns generated in deformed areas already look unsharp where the degree of fuzziness is determined by the density of lattice defects in the interaction volume. So inherently, if you collect maps with stepsizes below 150 nm in deformed materials, you already lose orientation detail without realising it as the unsharp patterns contain information originating from a 150-200 nm source volume.
And now back to NPAR averaging; considering the information limit of 150 nm, you may want to consider scanning a material with stepsizes of 50-100 nm steps, record all the patterns and then apply NPAR reprocessing. This will average the patterns within the effective information volume and as described before it will improve the orientation precision. This allows a good representation of the deformation microstructure. If you are scanning a material with larger stepsizes, then applying NPAR will artificially increase the information volume and smooth out any orientation gradients that may be present. Whether or not this smoothing is acceptable for your analysis depends on the feature size and the properties that you need to determine from your scan. On recrystallized materials with limited deformation structures the stepsize is not so important and applying NPAR may improve the indexing rates without harming the structure determination.
So on average, averaging may actually help a lot in improving your results!
Thanks for sharing. This really informative. But when I choose to use a square grid instead of hexagonal ones, how many neighbors the OIM software will use to calculate the KAM?
Hi Hans Sheng,
For square grids the OIM ANalysis software uses the 8 neighbouring pixels