EDM Quantification of Diffraction Patterns: Noise Response
In order to analyze the robustness of the Diffraction Pattern Quantification algorithms in EDM, a sample diffraction pattern (below, left) was used to test the response of the program to artificially-added Poisson noise (right). This was carried out varying (one at a time) the main parameters in the Expert Button menu.
For a given set of
parameter values, the program was first run on the original pattern,
yielding a set of measured (and indexed) reflections and their corresponding intensities.
Then this was repeated on the modified pattern. The reflections were paired up and compared:
for each index, a relative change in intensity
ΔI/Ipure (where ΔI=Inoise-Ipure) was calculated
(see figure on the right for a typical distribution
as a function of Ipure). ΔI/Ipure and its magnitude
|ΔI/Ipure| were averaged over all indices
and used as a measure of how well EDM handled the noise in each case. A perfect program would
give zero in both cases.
As an
alternative way of measuring the noise response,
a plot of Inoise versus Ipure was created for
each set of parameter values (a typical plot is shown). Then
a linear fit (which we refer to as the "y=mx+c" kind) was applied and the
slope m and intercept c were extracted. Naturally, a perfect program would
yield m=1 and c=0.
Similarly, a linear fit with m and c set to their ideal values (unity and
zero) was applied; we refered to this as the "y=x" fit. While there are no
degrees of freedom here, the R2 of the
fit gives a measure of how close to ideal the noise response is.
The dependence of the noise response on each individual parameter can be found in detail here: