EDM Quantification of Diffraction Patterns:
Noise Response dependence on Fractional Motif Size



The default value for the fractional motif size in EDM is 0.750. We examined the range from 0.350 to 0.950. This value is a fraction of the distance between spots and determines the size of the motif. Of course, this parameter is very specific to each particular pattern; it is the relative size of the spots with respect to the distance between adjacent spots that determines what value is optimal.

We measured, for each value of fractional motif size, 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. The total number of reflections varies strongly, decreasing with increasing motif size, mostly dropping low intensity spots, which become buried in the background.

All cases shared a total of 219 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, some dependence was observed between the noise response and the fractional motif size. The average relative discrepancies tended to decrease with increasing motif size, although not too dramatically. The other measures fluctuated showed a somewhat similar behavior.

The R2 for the "y=x" fit decreased relatively strongly, suggesting that higher values are more adequate. The slope in the more flexible "y=mx+c" fit snaked more, diverging from unity at low values and approaching it at high values, but with a maximum reached at 0.550. The same qualitative pattern was observed in the extracted intercepts. 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.