Weighted ellipse fitting routine for spotty or incomplete Debye-Scherrer rings on a 2D detector

Abstract: We introduce a weighted ellipse fitting routine to measure Debye Scherrer rings acquired on 2D area detectors and demonstrate its use in strain determination. The method is relatively robust against incomplete rings due to low number of grains in the diffraction volume (spotty rings), or strong texture (intensity depletion in some azimuths). The method works by applying an annular mask around each diffraction ring and fitting an ellipse, using all pixel positions and their diffracted intensity as weights in the minimisation. We compare this method to the more popular cake integration method, and show that the weighted ellipse method works when the cake integration method fails or works poorly. The lattice strain sensitivity from spotty diffraction rings is in the order or 2E-5 or better. The algorithm has been made available for public use and works with 2D diffraction patterns acquired in a laboratory scale XRD equipment, TEM or a synchrotron.