XCF Peak Height as a Quality Metric

The height of the XCF (cross correlation) peak can be used as a measure of how similar the contents of the ROI are in the 2 EBSD patterns under comparison. The height of the XCF peak will be reduced if the test pattern has diffuse Kikuchi bands while the reference pattern has sharp bands. The height of the XCF peak is dependent on several other factors and, therefore, a normalised value is used to permit comparisons between different ROIs. During normalisation, the XCF peak height is divided by the height of the XCF peak of the autocorrelation of the reference pattern (i.e. the contents of the reference pattern ROI cross correlated with itself). This means perfect cross correlation will have a value of 1.This is called the Mean Angular Error (MAE) map where a quantity is designed to give a quantitative measure of the degree of error in the HREBSD calculation of the distortion matrix.

Theoretically, it is possible to find  negative values representing an anti-correlation but this does not happen in practice. It is also possible to find  values greater than 1 if the test pattern is brighter than the reference patter due to, for example, variation in the beam current .

In CrossCourt, we take the geometrical mean of the XCF peak measured across all the ROIs to have an overall indication of the quality of the cross-correlation.

Limitations

The XCF function only tracks the translation of the EBSD pattern across the ROI; it does not measure any pattern rotation or zooming. The crystal rotation is abstracted subsequently via the calculated distortion matrix. Zooming of the pattern occurs when the pattern is recorded at a point on the specimen which is at a different height (and hence at a different detector distance) from the height  at which the reference pattern was recorded. This variation?  is accounted for by knowledge of the difference between the two beam positions when the measurements were made and the tilt of the specimen.

Furthermore, if the contents of the ROIs are not largely similar , this means  the position of the largest XCF peak may not relate to the true pattern shift. Therefore,  in the case where one pattern is displaced in the x and or y directions by a significant fraction of the width of the ROI, 25% for example, there is then insufficient overlap of the two patterns for a reliable cross correlation to be performed. The effect will be evident by the very low value of the XCF peak height.