DeltaCC12

Δcc12 is a quantity, that detects datasets/frames, that are non-isomorphous. As described in Assmann and Diederichs (2016), Δcc12 is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values, but is not influenced by a random number sequence as shown in Karplus and Diederichs (2012).

[math]\displaystyle{ R_{p.i.m.} = \frac{\sum_{hkl} \sqrt \frac{1}{n-1} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}} }[/math]

[math]\displaystyle{ CC_{1/2}=\frac{\sigma^2_{\tau}}{\sigma^2_{\tau}+\sigma^2_{\epsilon}} =\frac{\sigma^2_{y}- \frac{1}{2}\sigma^2_{\epsilon}}{\sigma^2_{\tau}+ \frac{1}{2}\sigma^2_{\epsilon}} }[/math]