Transmission electron tomography: quality assessment and enhancement for three-dimensional imaging of nanostructures

Nanotechnology has revolutionised humanity's capability in building microscopic systems by manipulating materials on a molecular and atomic scale. Nan-osystems are becoming increasingly smaller and more complex from the chemical perspective which increases the demand for microscopic characterisation techniques. Among others, transmission electron microscopy (TEM) is an indispensable tool that is increasingly used to study the structures of nanosystems down to the molecular and atomic scale. However, despite the effectivity of this tool, it can only provide 2-dimensional projection (shadow) images of the 3D structure, leaving the 3-dimensional information hidden which can lead to incomplete or erroneous characterization. One very promising inspection method is Electron Tomography (ET), which is rapidly becoming an important tool to explore the 3D nano-world. ET provides (sub-)nanometer resolution in all three dimensions of the sample under investigation. However, the fidelity of the ET tomogram that is achieved by current ET reconstruction procedures remains a major challenge. This thesis addresses the assessment and advancement of electron tomographic methods to enable high-fidelity three-dimensional investigations. A quality assessment investigation was conducted to provide a quality quantitative analysis of the main established ET reconstruction algorithms and to study the influence of the experimental conditions on the quality of the reconstructed ET tomogram. Regular shaped nanoparticles were used as a ground-truth for this study. It is concluded that the fidelity of the post-reconstruction quantitative analysis and segmentation is limited, mainly by the fidelity of the reconstructed ET tomogram. This motivates the development of an improved tomographic reconstruction process. In this thesis, a novel ET method was proposed, named dictionary learning electron tomography (DLET). DLET is based on the recent mathematical theorem of compressed sensing (CS) which employs the sparsity of ET tomograms to enable accurate reconstruction from undersampled (S)TEM tilt series. DLET learns the sparsifying transform (dictionary) in an adaptive way and reconstructs the tomogram simultaneously from highly undersampled tilt series. In this method, the sparsity is applied on overlapping image patches favouring local structures. Furthermore, the dictionary is adapted to the specific tomogram instance, thereby favouring better sparsity and consequently higher quality reconstructions. The reconstruction algorithm is based on an alternating procedure that learns the sparsifying dictionary and employs it to remove artifacts and noise in one step, and then restores the tomogram data in the other step. Simulation and real ET experiments of several morphologies are performed with a variety of setups. Reconstruction results validate its efficiency in both noiseless and noisy cases and show that it yields an improved reconstruction quality with fast convergence. The proposed method enables the recovery of high-fidelity information without the need to worry about what sparsifying transform to select or whether the images used strictly follow the pre-conditions of a certain transform (e.g. strictly piecewise constant for Total Variation minimisation). This can also avoid artifacts that can be introduced by specific sparsifying transforms (e.g. the staircase artifacts the may result when using Total Variation minimisation). Moreover, this thesis shows how reliable elementally sensitive tomography using EELS is possible with the aid of both appropriate use of Dual electron energy loss spectroscopy (DualEELS) and the DLET compressed sensing algorithm to make the best use of the limited data volume and signal to noise inherent in core-loss electron energy loss spectroscopy (EELS) from nanoparticles of an industrially important material. Taken together, the results presented in this thesis demonstrates how high-fidelity ET reconstructions can be achieved using a compressed sensing approach.

Original sin: divine and symbolic violence in the turn to the Apostle Paul

When we take a step back from the imposing figure of physical violence, it becomes possible to examine other structurally violent forces that constantly shape our cultural and political landscapes. One of the driving interests in the “turn to Paul” in recent continental philosophy stems from wrestling with questions about the real nature of contemporary violence. Paul is positioned as a thinker whose messianic experience began to cut through the violent masquerade of the existing order. The crucifixion and resurrection of the Messiah (a slave and a God co-existing in one body) exposed the empty grounding upon which power resided. The Christ-event signifies a moment of violent interruption in the existing order which Paul enjoins the Gentiles to participate in through a dedication of love for the neighbour. This divine violence aims to reveal and subvert the “powers,” epitomised in the Roman Empire, in order to fulfil the labour of the Messianic now-time which had arrived. The impetus behind this research comes from a typically enigmatic and provocative section of text by the Slovene philosopher, cultural critic, and Christian atheist Slavoj Žižek. He claims that 'the notion of love should be given here all its Paulinian weight: the domain of pure violence… is the domain of love' (2008a, 173). In this move he links Paul’s idea of love to that of Walter Benjamin’s divine violence; the sublime and the cataclysmic come together in this seemingly perverse notion. At stake here is the way in which uncovering violent forces in the “zero-level” of our narrative worldviews aids the diagnosis of contemporary political and ethical issues. It is not enough to imagine Paul’s encounter with the Christ-event as non-violent. This Jewish apocalyptic movement was engaged in a violent struggle within an existing order that God’s wrath will soon dismantle. Paul’s weak violence, inspired by his fidelity to the Christ-event, places all responsibility over creation in the role of the individual within the collective body. The centre piece of this re-imagined construction of the Pauline narrative comes in Romans 13: the violent dedication to love understood in the radical nature of the now-time. 3 This research examines the role that narratives play in the creation and diagnosis of these violent forces. In order to construct a new genealogy of violence in Christianity it is crucial to understand the role of the slave of Christ (the revolutionary messianic subject). This turn in the Symbolic is examined through creating a literary structure in which we can approach a radical Nietzschean shift in Pauline thought. The claim here, a claim which is also central to Paul’s letters, is that when the symbolic violence which manipulates our worldviews is undone by a divine violence, if even for a moment, new possibilities are created in the opening for a transvaluation of values. Through this we uncover the nature of original sin: the consequences of the interconnected reality of our actions. The role of literature is vital in the construction of this narrative; starting with Cormac McCarthy’s No Country for Old Men, and continuing through works such as Melville’s Bartleby the Scrivener, this thesis draws upon the power of literature in the shaping of our narrative worlds. Typical of the continental philosophy at the heart of this work, a diverse range of illustrations and inspirations from fiction is pulled into its narrative to reflect the symbolic universe that this work was forged through. What this work attempts to do is give this theory a greater grounding in Paul’s letters by demonstrating this radical kenotic power at the heart of the Christ-event. Romans 13 reveals, in a way that has not yet been picked up by Critchley, Žižek, and others, that Paul opposed the biopolitical power of the Roman Empire through the weak violence of love that is the labour of the slaves of Christ on the “now-time” that had arrived.