Dr. Stuart Wright, Senior Scientist EBSD, EDAX

The city has recently started burying a pipe down the middle of one of the roads into my neighborhood. There were already a couple of troublesome intersections on this road. The construction has led to several accidents in the past couple of weeks at these intersections and I am sure there are more to come.

A question from a reviewer on a paper I am co-authoring got me thinking about the impact of intersections of bands in EBSD patterns on the Hough transform. The intersections are termed ‘zone axes’ or ‘poles’ and a pattern is typically composed of some strong ones where several high intensity bands intersect as well as weak ones where perhaps only two bands intersect.

To get an idea of the impact of the intersections on the Hough transform, I have created an idealized pattern. The intensity of the bands in the idealized pattern is derived from the peaks heights from the Hough transform applied to an experimental pattern. For a little fun, I have created a second pattern by blacking out the bands in the original idealized pattern, leaving behind only the intersections. I created a third pattern by blacking out the intersections and leaving behind only the bands. I have input these three patterns into the Hough transform. As I expected, you can see the strong sinusoidal curves from the pattern with only the intersections. However, you can also see peaks, where these sinusoidal curves intersect and these correspond (for the most part) to the bands in the pattern.

In the figure, the middle row of images are the raw Hough Transforms and the bottom row of images are the Hough Transforms after applying the butterfly mask. It is interesting to note how much the Hough peaks differ between the three patterns. It is clear that the intersections contribute positively to finding some of the weaker bands. This is a function not only of the band intensity but also the number of zone axes along the length of the band in the pattern.

Eventually the construction on my local road will be done and hopefully we will have fewer accidents. But clearly, intersections are more than just a necessary evil 😊