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.

Diffraction Patterns







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:

Displacement Tolerance

XCF Motif Base Level

Fractional Motif Size

Fractional Mask Size