Circular Hough transform diffraction analysis: A software tool for automated measurement of selected area electron diffraction patterns within Digital Micrograph™

A software tool (script and plugin) for computing circular Hough transforms (CHT) in Digital Micrograph™ has been developed, for the purpose of automated analysis of selected area electron diffraction patterns (SADPs) of polycrystalline materials. The CHT enables the diffraction pattern centre to be determined with sub-pixel accuracy, regardless of the exposure condition of the transmitted beam or if a beam stop is present. Radii of the diffraction rings can also be accurately measured with sub-pixel precision. If the pattern is calibrated against a known camera length, then d-spacings with an accuracy of better than 1% can be obtained. These measurements require no a priori knowledge of the pattern and very limited user interaction. The accuracy of the CHT is degraded by distortion introduced by the projector lens, and this should be minimised prior to pattern acquisition. A number of optimisations in the CHT software enable rapid processing of patterns; a typical analysis of a 1k×1k image taking just a few minutes. The CHT tool appears robust and is even able to accurately measure SADPs with very incomplete diffraction rings due to texture effects. This software tool is freely downloadable via the Internet.