I looked at magnification distortion of data we collected at the end of January 2016 at Janelia (the left Krios with the energy filter). We did not take images of gold crystals, but I do have diffraction from my molecules (much lower resolution than the gold) and from that I obtain ~1% distortion with an angle of ~110 degrees (K2 super resolution pixel size is 0.855 A). These values are similar than in your paper, but of course my estimation is probably much less accurate compared to the 2.4 ring of the gold. Do you know whether anyone recently repeated the gold measurements on this scope? Since the particle diameter is almost 600 A and after reading your paper, I pay now attention to this issue.
Anyway, my question is whether you have a formula for calculating the pixel coordinates of an object after correction, e.g. stretching or shrinking the image? If you scale, does the center or a corner of the image stay in place? For instance, if in the original image a particular particle is located at x_original, y_original what are x_corrected, y_corrected?
All the best, Simon