If this rule is broken, such as the mode in
FIT2D that smooths patterns by pixel-splitting) then one introduces
correlation between points in the pattern
Hi Brian, your comment has triggered me it seems :-)
For SAXS and PDF it could be better to under-sample the data (see end),
but for profile fitting I find this story is causing more headaches than
it solves. Splitting pixels was (and still is?) a pragmatic way to
address the following:
- To fit peak positions and widths for strain you need >3 points within
the FWHM. Output bins may be required as smaller than pixel sizes.
- Detector pixels may fall halfway between two output bins, so which
output bin should they go into? If a bunch of pixels "jump" from one bin
to another suddenly, so do your results. Your colleague, with a tiny
change in calibration, might get wildly different answers to you.
Fitting the (raw) 2D images also overcomes that but runs into other
problems: what are the weights for pixels with zero counts? Binning
makes it is easier to look at a fit with ~5 points within a FWHM
compared to 5000. Note that pixel splitting convolutes the pixel (or
bin) shapes into the final peak shape, so you come out with broader and
smoother peaks that tend to be more robust to numerical issues.
Serial correlation in the final fit remains a problem whether you split
pixels or not, from a long time ago, e.g.:
Berar and Lelann: J. Appl. Cryst. (1991). 24, 1-5
https://doi.org/10.1107/S0021889890008391
Note that pixels from some detectors do not arrive as statistically
independent quantities anyway. When spatial corrections have been done
for you the patterns are obvious, but less so when a single X-ray photon
is spread over several CCD pixels.
Is someone aware of a Rietveld example where "not splitting is better"
while keeping the same bin size? I see the point for statistical
analysis of the noise in SAXS and PDF data, but I do not get it when
fitting strong peaks where the signal is greater than the noise level
anyway. The reality for a lot of 2D detector data is that you counted
way too many photons. Systematic errors in the fit are much larger than
the statistical noise anyway.
Best,
Jon
===
PS: The SAXS argument against splitting pixels is here:
"Correlation Map, a goodness-of-fit test for one-dimensional X-ray
scattering spectra"
Daniel Franke, Cy M Jeffries & Dmitri I Svergun
Nature Methods 12, 419–422 (2015)
https://doi.org/10.1038/nmeth.3358
The PDF case is here:
"On the estimation of statistical uncertainties on powder diffraction
and small-angle scattering data from two-dimensional X-ray detectors"
X. Yang, P. Juhás and S. J. L. Billinge
J. Appl. Cryst. (2014). 47, 1273-1283
https://doi.org/10.1107/S1600576714010516
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Please do NOT attach files to the whole list <alan.he...@neutronoptics.com>
Send commands to <lists...@ill.fr> eg: HELP as the subject with no body text
The Rietveld_L list archive is on http://www.mail-archive.com/rietveld_l@ill.fr/
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
