# Quality metrics for XCF results

#### XCF Peak Height as a Quality Metric

We can use the height of the XCF (cross correlation) peak as a measure of how similar the contents of the ROI are in the 2 EBSD patterns being compared . If the test pattern has diffuse Kikuchi bands whilst the reference pattern has sharp bands, then the height of the XCF peak will be reduced. The height of the XCF peak is dependent on several other factors so 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). Thus perfect cross correlation will have a value of 1. We call this the Mean Angular Error (MAE) map is a quantity designed to give a quantitative measure of the degree of error in the HR EBSD calculation of the distortion matrix.

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

In CrossCourt we take the geometrical mean of the XCF peak measured across all the ROIs to get 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 that at which the reference pattern was recorded. It is accounted for from a knowledge of the difference between the two beam positions at which the measurements were made and the tilt of the specimen.

Further, if the contents of the ROIs are not similar to a large extent, then the position of the largest XCF peak may not relate to the true pattern shift. Thus 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, then there is 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.