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arXiv · 1311.5430

Weighted Least Squares Fit of an Ellipse to Describe Complete or Spotty Diffraction Rings on a Planar 2D Detector

Michael L. Hart·Michael Drakopoulos
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Abstract

We present a procedure for fitting an ellipse to powder diffraction patterns recorded on a planar 2D detector, which uses the peak intensities as weights. This procedure works for complete and spotty diffraction rings. We outline all the steps required: the interpolation of Cartesian pixel data into polar co-ordinates based upon an approximate ellipse centre; the identification of peak locations along each radial direction of a diffraction ring; and the weighted least squares algebraic fit of an ellipse to that diffraction ring. The performance of the procedure is assessed by characterising a complete diffraction ring from a powder standard, and a spotty ring generated from a complete ring of the standard. The fit of an ellipse to a spotty ring from an alkane complex is also shown. Agreement in the calculated parameters for the two rings is good. This procedure is implemented as part of an X-ray beam energy and 2D detector calibration routine which is currently in use at Beamline I12 (Diamond Light Source, UK).

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Michael L. Hart, Michael Drakopoulos. 2013-11-21. Weighted Least Squares Fit of an Ellipse to Describe Complete or Spotty Diffraction Rings on a Planar 2D Detector. https://arxiv.org/abs/1311.5430

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