Local difference

This operation gives 4 results based on the difference between the maximum and minimum value inside each detected peak, i.e. the range operation is applied on every detected peak. With the difference values of each peak, the 4 results are calculated:

  • average
  • standard deviation
  • maximum
  • minimum


From the Bloch wave theory, Kikuchi bands are characterized by a bright center and dark edges. [1] The difference between the center of a band and its edges is a measure of the sharpness of the band, and is therefore an estimation of the deformation level. In Hough space, this is translated into an intense peak corresponding to the center of the band and two dark regions corresponding to the dark edges. The difference between the maximum and minimum value inside a peak is therefore equivalent to the contrast between the center and edges of a band. It is important for these calculations that the area of the detected peaks includes both the bright and dark regions of the peak.


The Opening operation can be used to increase the area of the detected peaks.

From the difference values obtained for each detected peak, the average and standard deviation can be used to evaluate the overall diffraction quality. As the deformation level increases, the average difference should decrease as the band sharpness decreases. A similar trend is expected for the standard deviation. For a high quality, undeformed diffraction pattern, the sharpness of the bands will have a large dispersion due to the variation of intensity in the Kikuchi bands. The Kikuchi bands of crystallographic planes with a high diffraction intensity have greater contrast than those of lower symmetry planes. However, for a diffraction pattern from a deformed region, the sharpness of all Kikuchi bands are decreased, thus decreasing the dispersion and lowering the standard deviation. Other quality metrics from these difference values can be the maximum and minimum difference between all the peaks. We shall refer to this group of four quality metrics as the local difference metric.