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Register a new userMPFit: A robust method for fitting atomic resolution images with multiple Gaussian peaks
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Added by
Debangshu Mukherjee
Publication date
2019
fields
Physics
and research's language is
English
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The standard technique for sub-pixel estimation of atom positions from atomic resolution scanning transmission electron microscopy images relies on fitting intensity maxima or minima with a two-dimensional Gaussian function. While this is a widespread method of measurement, it can be error prone in images with non-zero aberrations, strong intensity differences between adjacent atoms or in situations where the neighboring atom positions approach the resolution limit of the microscope. Here we demonstrate mpfit, an atom finding algorithm that iteratively calculates a series of overlapping two-dimensional Gaussian functions to fit the experimental dataset and then subsequently uses a subset of the calculated Gaussian functions to perform sub-pixel refinement of atom positions. Based on both simulated and experimental datasets presented in this work, this approach gives lower errors when compared to the commonly used single Gaussian peak fitting approach and demonstrates increased robustness over a wider range of experimental conditions.
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We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the luminosity function of the sources as a distance indicator.The method is characterised by its robustness. In particular, no assumptions are made concerning the spatial distribution of sources and their luminosity function. Moreover, selection effects in redshift are allowed. Furthermore the inclusion of additional observables correlated with the absolute magnitude -- such as for example rotation velocity information as described by the Tully-Fisher relation -- is straightforward. As an illustration of the method, the predicted IRAS peculiar velocity model characterised by the density parameter beta is tested on two samples. The application of our method to the Tully-Fisher MarkIII MAT sample leads to a value of beta=0.6 pm 0.125, fully consistent with the results obtained previously by the VELMOD and ITF methods on similar datasets. Unlike these methods however, we make a very conservative use of the Tully-Fisher information. Specifically, we require to assume neither the linearity of the Tully-Fisher relation nor a gaussian distribution of its residuals. Moreover, the robustness of the method implies that no Malmquist corrections are required. A second application is carried out, using the fluxes of the IRAS 1.2 Jy sample as the distance indicator. In this case the effective depth of the volume in which the velocity model is compared to the data is almost twice the effective depth of the MarkIII MAT sample. The results suggest that the predicted IRAS velocity model, while successful in reproducing locally the cosmic flow, fails to describe the kinematics on larger scales.
Recording atomic-resolution transmission electron microscopy (TEM) images is becoming increasingly routine. A new bottleneck is then analyzing this information, which often involves time-consuming manual structural identification. We have developed a deep learning-based algorithm for recognition of the local structure in TEM images, which is stable to microscope parameters and noise. The neural network is trained entirely from simulation but is capable of making reliable predictions on experimental images. We apply the method to single sheets of defected graphene, and to metallic nanoparticles on an oxide support.
The high beam current and sub-angstrom resolution of aberration-corrected scanning transmission electron microscopes has enabled electron energy loss spectroscopic (EELS) mapping with atomic resolution. These spectral maps are often dose-limited and spatially oversampled, leading to low counts/channel and are thus highly sensitive to errors in background estimation. However, by taking advantage of redundancy in the dataset map one can improve background estimation and increase chemical sensitivity. We consider two such approaches- linear combination of power laws and local background averaging-that reduce background error and improve signal extraction. Principal components analysis (PCA) can also be used to analyze spectrum images, but the poor peak-to-background ratio in EELS can lead to serious artifacts if raw EELS data is PCA filtered. We identify common artifacts and discuss alternative approaches. These algorithms are implemented within the Cornell Spectrum Imager, an open source software package for spectroscopic analysis.
We present a novel algorithm for generating robust and consistent hypotheses for multiple-structure model fitting. Most of the existing methods utilize random sampling which produce varying results especially when outlier ratio is high. For a structure where a model is fitted, the inliers of other structures are regarded as outliers when multiple structures are present. Global optimization has recently been investigated to provide stable and unique solutions, but the computational cost of the algorithms is prohibitively high for most image data with reasonable sizes. The algorithm presented in this paper uses a maximum feasible subsystem (MaxFS) algorithm to generate consistent initial hypotheses only from partial datasets in spatially overlapping local image regions. Our assumption is that each genuine structure will exist as a dominant structure in at least one of the local regions. To refine initial hypotheses estimated from partial datasets and to remove residual tolerance dependency of the MaxFS algorithm, iterative re-weighted L1 (IRL1) minimization is performed for all the image data. Initial weights of IRL1 framework are determined from the initial hypotheses generated in local regions. Our approach is significantly more efficient than those that use only global optimization for all the image data. Experimental results demonstrate that the presented method can generate more reliable and consistent hypotheses than random-sampling methods for estimating single and multiple structures from data with a large amount of outliers. We clearly expose the influence of algorithm parameter settings on the results in our experiments.
With the advent of atomic-resolution transmission electron microscopy (AR-TEM) achieving sub-{AA}ngstrom image resolution and submillisecond time resolution, an era of visual molecular science where chemists can visually study the time evolution of molecular motions and reactions at atomistic precision has arrived. However, the appearance of experimental TEM images often differs greatly from that of conventional molecular models, and the images are difficult to decipher unless we know in advance the structure of the specimen molecules. The difference arises from the fundamental design of the molecular models that represent atomic connectivity and/or the electronic properties of molecules rather than the nuclear charge of atoms and electrostatic potentials that are felt by the e-beam in TEM imaging. We found a good correlation between the atomic number (Z) and the atomic size seen in TEM images when we consider shot noise in digital images. We propose here Z-correlated (ZC) atomic radii for modeling AR-TEM images of single molecules and ultrathin crystals, with which we can develop a good estimate of the molecular structure from the TEM image much more easily than with conventional molecular models. Two parameter sets were developed for TEM images recorded under high-noise (ZCHN) and low-noise (ZCLN) conditions. The new molecular models will stimulate the imaginations of chemists planning to use AR-TEM for their research.
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