{"paper":{"title":"Weighted Least Squares Fit of an Ellipse to Describe Complete or Spotty Diffraction Rings on a Planar 2D Detector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Michael Drakopoulos, Michael L. Hart","submitted_at":"2013-11-21T14:55:55Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5430","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}