Employment of Crystallographic Image Processing Techniques to Scanning Probe Microscopy Images of Two-Dimensional Periodic Objects

• Main Author: Moon, Bill
• Format: Others
• Published: PDXScholar 2011
• Subjects: Image processing; Point spread function; Thin film arrays; Crystallography; High resolution electron microscopy; Scanning tunneling microscopy
• Online Access: https://pdxscholar.library.pdx.edu/open_access_etds/699; https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=1698&context=open_access_etds

Thin film arrays of molecules or supramolecules are active subjects of investigation because of their potential value in electronics, chemical sensing, catalysis, and other areas. Scanning probe microscopes (SPMs), including scanning tunneling microscopes (STMs) and atomic force microscopes (AFMs) are commonly used for the characterization and metrology of thin film arrays. As opposed to transmission electron microscopy (TEM), SPMs have the advantage that they can often make observations of thin films in air or liquid, while TEM requires highly specialized techniques if the sample is to be in anything but vacuum. SPM is a surface imaging technique, while TEM typically images a 2D projection of a thin 3D sample. Additionally, variants of SPM can make observations of more than just topography; for instance, magnetic force microscopy measures nanoscale magnetic properties. Thin film arrays are typically two-dimensionally periodic. A perfect, infinite two-dimensionally periodic array is mathematically constrained to belong to one of only 17 possible 2D plane symmetry groups. Any real image is both finite and imperfect. Crystallographic Image Processing (CIP) is an algorithm that Fourier transforms a real image into a 2D array of complex numbers, the Fourier coefficients of the image intensity, and then uses the relationship between those coefficients to first ascertain the 2D plane symmetry group that the imperfect, finite image is most likely to possess, and then adjust those coefficients that are symmetry-related so as to perfect the symmetry. A Fourier synthesis of the symmetrized coefficients leads to a perfectly symmetric image in direct space (when accumulated rounding and calculation errors are ignored). The technique is, thus, an averaging technique over the direct space experimental data that were selected from the thin film array. The image must have periodicity in two dimensions in order for this technique to be applicable. CIP has been developed over the past 40 years by the electron crystallography community, which works with 2D projections from 3D samples. Any periodic sample, whether it is 2D or 3D has an "ideal structure" which is the structure absent any crystal defects. The ideal structure can be considered one average unit cell, propagated by translation into the whole sample. The "real structure" is an actual sample containing vacancies, dislocations, and other defects. Typically the goal of electron and other types of microscopy is examination of the real structure, as the ideal structure of a crystal is already known from X-ray crystallography. High resolution transmission electron microscope image based electron crystallography, on the other hand, reveals the ideal crystal structure by crystallographic averaging. The ideal structure of a 2D thin film cannot be easily in a spatially selective fashion examined by grazing incidence X-ray or low energy electron diffraction based crystallography. SPMs straightforwardly observe thin films in direct space, but SPM accuracy is hampered by blunt or multiple tips and other unavoidable instrument errors. Especially since the film is often of a supramolecular system whose molecules are weakly bonded (via pi bonds, hydrogen bonds, etc.) both to the substrate and to each other, it is relatively easy for a molecule from the film to adhere to the scanning tip during the scan and become part of the tip during subsequent observation. If the thin film array has two-dimensional periodicity, CIP is a unique and effective tool both for image enhancement (determination of ideal structure) and for the quantification of overall instrument error. In addition, if a sample of known 2D periodicity is scanned, CIP can return information about the contribution of the instrument itself to the image. In this thesis we show how the technique is applied to images of two dimensionally periodic samples taken by SPMs. To the best of our knowledge, this has never been done before. Since 2D periodic thin film arrays have an ideal structure that is mathematically constrained to belong to one of the 17 plane symmetry groups, we can use CIP to determine that group and use it for a particularly effective averaging algorithm. We demonstrate that the use of this averaging algorithm removes noise and random error from images more effectively than translational averaging, also known as "lattice averaging" or "Fourier filtering". We also demonstrate the ability to correct systematic errors caused by hysteresis in the scanning process. These results have the effect of obtaining the ideal structure of the sample, averaging out the defects crystallographically, by providing an average unit cell which, when translated, represents the ideal structure. In addition, if one has recorded a scanning probe image of a 2D periodic sample of known symmetry, we demonstrate that it is possible to use the Fourier coefficients of the image transform to solve the inverse problem and calculate the point spread function (PSF) of the instrument. Any real scanning probe instrument departs from the ideal PSF of a Dirac delta function, and CIP allows us to quantify this departure as far as point symmetries are concerned. The result is a deconvolution of the "effective tip", which includes any blunt or multiple tip effects, as well as the effects caused by adhesion of a sample molecule to the scanning tip, or scanning irregularities unrelated to the physical tip. We also demonstrate that the PSF, once known, can be used on a second image taken by the same instrument under approximately the same experimental conditions to remove errors introduced during that second imaging process. The preponderance of two-dimensionally periodic samples as subjects of SPM observation makes the application of CIP to SPM images a valuable technique to extract a maximum amount of information from these images. The improved resolution of current SPMs creates images with more higher-order Fourier coefficients than earlier, "softer" images; these higher-order coefficients are especially amenable to CIP, which can then effectively magnify the resolution improvement created by better hardware. The improved resolution combined with the current interest in supramolecular structures (which although 3D usually start building on a 2D periodic surface) appears to provide an opportunity for CIP to significantly contribute to SPM image processing.