EDM Quantification of Diffraction
Patterns:
Noise Response dependence on Fractional Mask Size
The default value for the fractional mask
size in EDM is 0.750. We examined the range from 0.350 to 0.950. This parameter sets a
fraction of the motif size such that the area outside it is used to calculate the background
signal to be subtracted. This parameter is thus a function of the fractional motif size; in
this case, we used the default fractional motif size of 0.750. One
must try to make this big enough so that no part of the Gaussian-like reflections are counted
as background, but not so close to unity that there is not a statistically relevant sample from
which to estimate said background.
We measured, for each value of fractional mask 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 mask size.
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, the noise response was clearly dependent on the
fractional mask size. The average relative discrepancy was not all that conclusive, but
there was a general trend of lower discrepancy with increasing mask size. The other measures of
noise response were more telling.
The R2 for the "y=x" fit, and the slope and the intercept in the "y=mx+c"
fit all showed clearly better (lower) noise response for fractional motif sizes close to unity.
It must be emphasized though, that setting this strictly equal to 1 would deprive the calculation
of an estimate for the background noise and would not be appropriate.