EDM Quantification of Diffraction Patterns:
Noise Response dependence on Displacement Tolerance



The default value for the displacement tolerance in EDM is 4.999 pixels. We examined the range from 2.999 to 6.999 pixels. Much larger values would be too lax on the periodicity condition. As a reference, the dimensions of these images are 2000x2000 pixels.

We measured, for each value of displacement tolerance, the number of peaks measured in both the original and modified patterns. A greater number of peaks will make conclusions more reliable, but we want to avoid spurious peaks. As expected in this case, the number of measured reflections varies strongly and directly with the displacement tolerance.

All cases shared a total of 290 common reflections, which were the only ones used to calculate the average relative discrepancies and other figures of merit, as shown in the plots below.

In the range of values examined, the noise response was rather independent of the displacement tolerance. The average relative discrepancy, however defined, was clearly flat, and the other measures fluctuated slightly.

The R2 for the "y=x" fit was both very small and flat, showing in this range a variation smaller than 10-4. The slope in the more flexible "y=mx+c" fit is almost identical for four of the cases, with only one diverging clearly, but even with it (which is a case of random fluctuation) the total variation is <5x10-3. The intercept also changes very little (NOTE ON UNITS?), with no discernible pattern.