Automatic calibration of powder diffraction experiments using two-dimensional detectors

Abstract

Calibration of powder diffraction experiments using area detectors is essential to extract high quality one-dimensional powder diffraction pattern. Precise calibration necessitates a sensible characterization of the Debye-Scherrer rings formed on the detector plane. An algorithm, designed and developed to automate this process, is described in this paper. All the parameters required for an experimental calibration are extracted using robust pattern recognition techniques. Several image preprocessing methods are employed, reducing the computational cost but retaining high signal quality. A modified version of a one-dimensional Hough transformation is used to determine the final parameters of the ellipses. After extraction, the parameters are optimized using nonlinear least squares fit. The presented algorithm is insensitive to image artefacts and was successfully applied to a large number of calibration images. The performance of the algorithm is demonstrated by the comparison of results obtained from the presented automatic calibration method and an existing manual method.

Complete elliptical ring geometry provides energy and instrument calibration for synchrotron-based two-dimensional X-ray diffraction

“…For a set of concentric cones the positions of the ellipse centres and the ellipse focal points differ for rings originating from different (hkl) planes. This viewpoint is in contrast to that presented elsewhere (Norby, 1997;Rajiv et al, 2007;Hinrichsen et al, 2008), where it was incorrectly stated that the cone's axis intersects the elliptical conic section at its focal point. Subsequent geometrical expressions involving the focal point were thus incorrectly derived (Rajiv et al, 2007;Hinrichsen et al, 2008).…”

Automatic Debye–Scherrer elliptical ring extractionviaa computer vision approach

“…Since the extraction of the rings is carried out manually, the method is not directly comparable with our automatic method. In Comparison with Rajiv et al (2007). Our algorithm recognizes a number of ellipses higher than their method.…”

“…The work of Rajiv et al (2007) extracts Debye-Scherrer rings for orthogonal detectors only under rather restrictive assumptions using a modified Hough transform. Since a 5D Hough transform for ellipse detection is computationally demanding, the authors suggest to decompose the Hough transform in order to work in 1D only.…”

“…Fig. 17 compares the result of our algorithm on two of the images used by this method (Rajiv et al, 2007). Our algorithm was able to detect all the Debye-Scherrer rings available in the image.…”

“…Pattern recognition techniques were developed to estimate calibration parameters featuring high accuracy along with some degree of automation (Rajiv et al, 2007;Cervellino et al, 2006;. However, these approaches make restrictive assumptions about the diffraction setup and/ or the diffraction rings.…”