Date of Award

Spring 2020

Degree Type

Thesis

Department

Biological Sciences

Director of Thesis

Peter Binev

Second Reader

Thomas Vogt

Abstract

Electron microscopy is a very exciting field, which has shown huge developments in the last few decades. There is a continuous development of new methods which feature atomic level resolution. One of these methods is the energy dispersive X-ray (EDX) spectroscopy, which allows the researchers to understand the chemical make-up of the sample. It is particularly exciting that we are able to make EDX tomographic reconstructions and view the 3D structure of a nano-object.

This thesis is focused on developing a new methodology for EDX tomography. In a typical EDX set-up, one detects X-rays from the sample with different energies, and each piece of data contains counts of X-rays at thousands of energy levels (ex: 4000). The X-rays emitted from a given chemical element will register with specific energy values. Usually, the accumulated data presents itself as a Gaussian-like bump, concentrated around a known energy level for the element. This process presents two obstacles: the centers of different bumps are often too close and there is a significant amount of unassociated X-rays. One cannot unambiguously identify the source of a single X-ray based on its energy level due to the overlap and the background noise.

The standard way of processing this hyperspectral data is to identify the most likely source for each energy level, ignoring the less significant sources. This process is widely used and gives reasonable results. An accurate reconstruction requires the production of a large amount of X-rays, which is only possible when investing a significant amount of energy into a small volume, which may result in the destruction of the sample. The goal of this thesis is to develop a technique which gives a more robust element identification when there is a lesser amount of X-rays.

The data processing methodology that we propose estimates the number of X-rays emitted from a specific chemical element source. We characterize different sources, energy dispersion levels of the chemical elements or background noise, by modes that represent them in the spectrum. Our goal is to decompose the spectrum into different modes. The intensity of the modes can immediately be related to the number of X- rays emitted for each portion of data.

We identify the modes by looking for bump-like components of the spectrum. The identification of modes is made by processing the entire set of data in a combined spectrum to take advantage of the large amount of X-rays which allows for more sta- tistically significant results. After identifying the main bumps, we consider the rest of the spectrum as background noise. We remain aware that this portion of background noise may contain several insignificant modes which we consider irrelevant.

After the identification of modes, we check the data for consistency by examining the results for portions of the data. Then, we process the modes together with a discrete optimization procedure to create the element maps that show the relative intensities of a chemical element when observed at a specific angle. These element maps are used in the tomography reconstruction which is done through a regularized minimization procedure.

This project is an international collaboration with Peter Binev at the University of South Carolina, Toby Sanders at Arizona State University, Zineb Saghi at CEA- LETI in Grenoble, Sarah Haigh and Yi-Chi Wang from the University of Manchester, UK. This project would not have been possible without the combined efforts of each of these individuals.

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