Crystallographic image processing (CIP) is well established in the electron microscopy community, where it is used for the analysis and enhancement of high-resolution transmission electron microscope images of crystals and two-dimensional (2D) arrays of membrane proteins. The technique has recently been adapted to the processing of 2D periodic images from scanning probe microscopes (SPMs) [1]. Within this context, a procedure for the unambiguous identification of the underlying Bravais lattice of an experimental or theoretical image of a 2D periodic array of objects (e.g. molecules or atoms and their respective electron density distribution functions, ...) has been developed [2]. This procedure constitutes a partial solution to a longstanding but unresolved issue in CIP. The unresolved issue itself is the complete quantification of the deviations of 2D periodic images from the plane symmetry groups. A complete solution to this problem will allow for unambiguous decisions as to which plane symmetry best models experimental data when all systematic errors in the acquiring and processing of the image data have been accounted for at a level that systematic rest errors are negligible. Our 2D Bravais lattice identification procedure is independent of which type of microscope has been utilized for the recording of the images. It is based on classification procedures for non-disjoint models from the robotics community and is particularly useful for the correction of scanning tunneling microscope (STM) images that suffer from a blunt scanning probe tip artifact [2]. With the crystallographic processing of two molecular resolution STM images of periodic arrays of tetraphenoxyphthalocyanine on graphite, it is demonstrated how the classical CIP plane symmetry estimation procedures are augmented by our unambiguous translation symmetry identification method. We also apply CIP to an artificial SPM image that features a blunt scanning probe tip artifact, see the figure below.

Scanning probe microscopy (SPM) images can be obscured by signals from blunt and multiple probe tips. We show why crystallographic image processing (CIP) techniques may be utilized to restore obscured images that are periodic in two dimensions. The image-forming current for double tips in scanning tunneling microscopy (STM) is derived in a more straightforward manner than prior approaches. The Fourier spectrum of the tunneling current for p4mm Bloch surface wave functions and a pair of delta function tips reveals the tip-separation dependence. Our analysis clarifies why crystallographic averaging works well in removing such effects from the recorded 2D periodic images and also outlines the limitations of this image processing technique for certain spatial separations of STM double-tips. Classical simulations of double tip effects in STM images (that ignore electron interference effects) may be understood as modeling double tip effects in images that were recorded with other types of SPMs. Appendix A demonstrates how double tip effects on scanning probe microscope images are detected unambiguously.

Crystallographic image processing (CIP) techniques may be utilized in scanning probe microscopy (SPM) to glean information that has been obscured by signals from multiple probe tips. This may be of particular importance for scanning tunneling microscopy (STM) and requires images from samples that are periodic in two dimensions (2D). The image-forming current for double-tips in STM is derived with a slight modification of the independent-orbital approximation (IOA) to allow for two or more tips. Our analysis clarifies why crystallographic averaging works well in removing the effects of a blunt STM tip (that consists of multiple mini-tips) from recorded 2D periodic images and also outlines the limitations of this image-processing technique for certain spatial separations of STM double-tips. Simulations of multiple mini-tip effects in STM images (that ignore electron interference effects) may be understood as modeling multiple mini-tip (or tip shape) effects in images that were recorded with other types of SPMs as long as the lateral sample feature sizes to be imaged are much larger than the effective scanning probe tip sizes.

Crystallographic Image Processing (CIP) is applied to experimental Scanning Tunneling Microscopy (STM) images of regular (2D periodic) arrays of organic molecules on noble metal substrates. The crystallographically averaged (surface) lattices, structural motifs, and plane symmetry groups of the arrays are determined. An assessment of the samples with the goal of utilizing highly symmetric molecular arrays as calibration samples for STM is made. A brief introduction to the CIP procedures is given in an appendix.

Crystallographic image processing (CIP) is a technique first used to aid in the structure determination of periodic organic complexes imaged with high-resolution transmission electron microscopes (TEM). The technique has subsequently been utilized for TEM images of inorganic crystals, scanning TEM images, and even scanning probe microscope (SPM) images of two-dimensional periodic arrays. We have written software specialized for use on such SPM images. A key step in the CIP process requires iii List of Tables vi