Advances in Crystallographic Image Processing for Scanning Probe Microscopy: Unambiguous identification of the translati
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Advances in Crystallographic Image Processing for Scanning Probe Microscopy: Unambiguous identification of the translation symmetry of a 2D periodic image Taylor T. Bilyeu, Jack C. Straton, Axel Mainzer Koenig, and Peter Moeck* Nano-Crystallography Group, Department of Physics, Portland State University, Portland, OR 972070751, U.S.A, *corresponding author’s email: [email protected] ABSTRACT A statistically sound procedure for the unambiguous identification of the underlying Bravais lattice of an image of a 2D periodic array of objects is described. Our Bravais lattice detection procedure is independent of which type of microscope has been utilized for the recording of the image data. It is particularly useful for the correction of Scanning Tunneling Microscope (STM) images that suffer from a blunt scanning probe tip artifact, i.e. simultaneously recording multiple mini-tips. The unambiguous detection of the type of translation symmetry presents a first step towards making objective decisions about which plane symmetry a 2D periodic image is best modeled by. Such decisions are important for the application of Crystallographic Image Processing (CIP) techniques to images from Scanning Probe Microscopes (SPMs). INTRODUCTION CIP is well established in the electron microscopy community, having been utilized for the analysis and enhancement of high-resolution transmission electron microscope images of crystals and quasi-2D periodic arrays of membrane proteins. The technique has recently been adapted to the processing of 2D periodic images from SPMs [1-9]. A novel procedure for the unambiguous identification of the underlying Bravais lattice of an experimental or simulated image of a 2D periodic array of objects (e.g. molecules or atoms and their respective electron density distribution functions) is part of these adaptations [7]. This procedure is described briefly in this paper and constitutes a partial solution to an unresolved issue in CIP. That unresolved issue is the complete quantification of the deviations of 2D periodic images from the space group symmetries that are allowed in the Euclidian plane so that unambiguous decisions can be made about which plane symmetry a 2D periodic image is best modeled by. The outlook section of this paper will briefly outline a way to fully resolve this issue in future work. METHODS Crystallographic image processing and traditional plane symmetry deviation quantifiers In order to determine the plane symmetry to which a 2D periodic image most likely belongs, one traditionally utilizes Fourier coefficient (FC) amplitude (Ares) and phase angle (ϕres) residuals [3,10]. These values quantify how much an unprocessed image deviates from a symmetrized (fully CIP processed) one, and thus serve as figures of merit for determining which plane symmetry group best models the image (and the sample being imaged). There is, however, no fully objective way to use these two residuals to assign the correct plane symmetry group to an image. This is because higher symmetric plane groups (such as p4mm) pos
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