Spectral analysis and minimization of moire patterns in color separation

Undesired moire patterns may appear in color printing for various reasons. One of the most important reasons is interference between the superposed halftone screens of the different primary colors, due to an improper alignment of their frequencies or orientations. We explain the superposition moire phenomenon using a spectral model that is based of Fourier analysis. After examining the basic case of cosinusoidal grating superpositions we advance, step by step, through the cases of binary gratings, square grids, and dot screens, and discuss the implications on moires between halftone screens in color separation. Then, based on these results, we focus on the moire phenomenon from a different angle , the dynamic point of view: We introduce the noire parameter space and show how changes in the parameters of the superposed layers vary the moire patterns in the superposition. This leads us to an algorithm for moire minimization that provides stable moire-free screen combinations for color separation

Supraconductivité et ordre de charge dans les bicouches de graphène moirées

Abstract: The recent discovery of a correlated insulating state and superconductivity in twisted bilayer graphene (TBG) has opened a new platform for studying unconventional superconductivity. superconductivity appears for TBG at an angle ∼ 1.08◦ for a very low carrier density of about 1011 cm−2, with a Tc of 1.7 K. The misalignment of the two layers of graphene at the magic angle creates a periodic lattice called the moiré lattice. The effective model we use to describe this system is based on the moiré lattice and was proposed by Kang and Vafek. This model includes four Wannier orbitals located at the honeycomb lattice sites. In addition to hopping terms between these orbitals, we also add intra-orbital and inter-orbital interactions to the Hamiltonian and use a Hubbard or extended Hubbard model to describe the system. Our calculations are based on quantum cluster methods. To investigate the superconductivity we tile the lattice by the four site clusters immersed among six bath orbitals and use the CDMFT method. In the study of the correlated insulating phase, we use the VCA method and select clusters consisting of 12 Wannier orbitals so that we can define inter-orbital interactions in a cluster. We obtain a non-zero p±ip order parameter for superconductivity in a wide range of carrier densities, which is consistent with the experimental observations. Experimental measurements show that the system has a gap in the vicinity of n = 0.5 and n = 1.5 and behaves like a Mott insulator. So we expect that the superconductivity to be suppressed or eliminated in these ranges of densities, which is confirmed by our calculations. d±id is another nonzero superconductor order parameter that we found. The size of this singlet order parameter is smaller than the p ± ip. By calculating the Patthoff functional for two kinds of superconductors, we conclude that p±ip superconductivity has a lower free energy and therefore is the dominant phase between the two. In addition to the superconducting phase, the study of the strongly correlated insulating phases observed in the experiment was another objective of this thesis. Our calculations confirm the existence of these phases at quarter-, half- and three-quarter filling. Further computations show that the insulating phase at quarter-filling is not a charge density wave and that the insulating phase at half-filling is not antiferromagnetic.La découverte récente d’un état corrélé isolant et de la supraconductivité dans la bicouche de graphène moirée (TBG) a ouvert un nouveau canal dans l’étude de la supraconductivité non conventionnelle. Dans ce système, la supraconductivité apparaît à un angle de torsion ∼ 1.08◦ et à très faible densité de porteurs de 1011 cm−2, avec une Tc de 1.7 K. Le défaut d’alignement des deux couches de graphène crée un super-réseau appelé réseau moiré. Le modèle effectif utilisé pour décrire ce système est basé sur ce réseau moiré et a été proposé par Kang et Vafek. Ce modèle comporte 4 orbitales de Wannier centrées sur les sites d’un réseau en nid d’abeille. En plus des termes de saut entre ces orbitales, nous ajoutons des interactions (intra- et inter-orbitales) et utilisons le modèle de Hubbard étendu pour modéliser ce système. Nos calculs reposent sur les méthodes d’amas quantiques. Pour étudier la supraconductivité, nous utilisons un dallage du réseau par des amas de quatre sites couplés à six sites de bain dans la théorie du champ moyen dynamique sur amas (CDMFT). Pour l’étude des phases isolantes, nous utilisons plutôt la méthode de l’amas variationnel (VCA) sur un amas de douze sites, de sorte que les interactions étendues peuvent être comprises minimalement dans l’amas. Pour une large gamme de densités, cohérente avec les observations, nous trouvons un état supraconducteur de type p ± ip. Les expériences montrent que le système possède un gap spectral au voisinage de n = 0.5 et n = 1.5 et se comporte comme un isolant de Mott. On s’attend donc à ce que la supraconductivité soit atténuée ou éliminée près de ces densités, ce qui est confirmé par nos calculs. On trouve aussi un état supraconducteur d ±id comme solution secondaire, avec un paramètre d’ordre plus petit. Un calcul de la fonctionnelle de Potthoff dans ces deux solutions nous permet d’affirmer que l’état p±ip a une énergie plus basse et constitue donc la phase dominante. L’étude des phases isolantes était un deuxième objectif de cette thèse. Nos calculs démontrent l’existence de phases isolantes de Mott au quart remplissage et au demi-remplissage. Des calculs additionnels montrent que l’état isolant à quart rempli n’est pas une onde de densité de charge et que l’état isolant au demi-remplissage n’est pas antiferromagnétique

Electron-electron interaction effects in the optical and transport properties of 2D materials beyond graphene

This Thesis studies optical, plasmonic, and transport phenomena in two-dimensional materials. In particular, optical and plasmonic properties in twisted bilayer graphene are analyzed in the first part of the Thesis, whereas transport phenomena in twodimensional topological insulators are left for the second part. A common element of the physical systems studied here are electron-electron interactions, whose presence is pivotal for many of the results presented. The first Chapter of the manuscript is devoted to a review and critical analysis of the experimental results that motivated our work. Among these results, I emphasize recent experimental work carried out at ICFO on MIT samples on the plasmonic properties of twisted bilayer graphene whose theoretical interpretation was accomplished mostly thanks to the original theory presented in this Thesis. The first Chapter is also devoted to present some of the necessary theoretical concepts and tools forming the basis of this manuscript. The second Chapter of the thesis presents a theory of twisted bilayer graphene, an atomically-thin heterostructure which in early 2018 was showed to host a plethora of exotic quantum phases of matter. This Chapter also includes a technical Section where the details of the numerical codes developed for our study of twisted bilayer graphene are thoroughly discussed. These numerical codes are planned to be fully released and openly available for the scientific community in the near future. The third Chapter contains original results on the optical and plasmonic properties of twisted bilayer graphene. These results are obtained for a large variety of different parameter configurations, in the spirit of giving as much information as possible for a material (twisted bilayer graphene) whose actual physical properties are to a large extent still unknown. This Chapter is concluded by the presentation of preliminary results on the density-density response function of twisted bilayer graphene, which is essential to understand its dielectric properties, and hence how and how much the electron-electron interactions are screened. The fourth Chapter is about the theory of two-dimensional topological insulators, a class of materials hosting very interesting transport phenomena that are related to to the topological nature of their non-interacting bands and eigenstates. A Section of this Chapter is also devoted to the theory of ballistic electron transport, which is essential to understand many properties of two-dimensional topological insulators. In the fifth and last Chapter of the Thesis, we present an original result on the interplay between electron-electron interactions and localized defects in two-dimensional topological insulators. The theory presented in this Chapter provides a straightforward conceptual framework to explain experimental results on the transport properties of two-dimensional topological insulators, especially those in atomically thin crystals, plagued by short-range edge disorder

Topics in Adaptive Optics

Advances in adaptive optics technology and applications move forward at a rapid pace. The basic idea of wavefront compensation in real-time has been around since the mid 1970s. The first widely used application of adaptive optics was for compensating atmospheric turbulence effects in astronomical imaging and laser beam propagation. While some topics have been researched and reported for years, even decades, new applications and advances in the supporting technologies occur almost daily. This book brings together 11 original chapters related to adaptive optics, written by an international group of invited authors. Topics include atmospheric turbulence characterization, astronomy with large telescopes, image post-processing, high power laser distortion compensation, adaptive optics and the human eye, wavefront sensors, and deformable mirrors

Effective field theories for strongly correlated fermions - Insights from the functional renormalization group

'There are very few things that can be proved rigorously in condensed matter physics.' These famous words, brought to us by Nobel laureate Anthony James Leggett in 2003, summarize very well the challenging nature of problems researchers find themselves confronted with when entering the fascinating field of condensed matter physics. The former roots in the inherent many-body character of several quantum mechanical particles with modest to strong interactions between them: their individual properties might be easy to understand, while their collective behavior can be utterly complex. Strongly correlated electron systems, for example, exhibit several captivating phenomena such as superconductivity or spin-charge separation at temperatures far below the energy scale set by their mutual couplings. Moreover, the dimension of the respective Hilbert space grows exponentially, which impedes the exact diagonalization of their Hamiltonians in the thermodynamic limit. For this reason, renormalization group (RG) methods have become one of the most powerful tools of condensed matter research - scales are separated and dealt with iteratively by advancing an RG flow from the microscopic theory into the low-energy regime. In this thesis, we report on two complementary implementations of the functional renormalization group (fRG) for strongly correlated electrons. Functional RG is based on an exact hierarchy of coupled differential equations, which describe the evolution of one-particle irreducible vertices in terms of an infrared cutoff Lambda. To become amenable to numerical solutions, however, this hierarchy needs to be truncated. For sufficiently weak interactions, three-particle and higher-order vertices are irrelevant at the infrared fixed point, justifying their neglect. This one-loop approximation lays the foundation for the N-patch fRG scheme employed within the scope of this work. As an example, we study competing orders of spinless fermions on the triangular lattice, mapping out a rich phase diagram with several charge and pairing instabilities. In the strong-coupling limit, a cutting-edge implementation of the multiloop pseudofermion functional renormalization group (pffRG) for quantum spin systems at zero temperature is presented. Despite the lack of a kinetic term in the microscopic theory, we provide evidence for self-consistency of the method by demonstrating loop convergence of pseudofermion vertices, as well as robustness of susceptibility flows with respect to occupation number fluctuations around half-filling. Finally, an extension of pffRG to Hamiltonians with coupled spin and orbital degrees of freedom is discussed and results for exemplary model studies on strongly correlated electron systems are presented

The quantitative analysis of transonic flows by holographic interferometry

This thesis explores the feasibility of routine transonic flow analysis by holographic interferometry. Holography is potentially an important quantitative flow diagnostic, because whole-field data is acquired non-intrusively without the use of particle seeding. Holographic recording geometries are assessed and an image plane specular illumination configuration is shown to reduce speckle noise and maximise the depth-of-field of the reconstructed images. Initially, a NACA 0012 aerofoil is wind tunnel tested to investigate the analysis of two-dimensional flows. A method is developed for extracting whole-field density data from the reconstructed interferograms. Fringe analysis errors axe quantified using a combination of experimental and computer generated imagery. The results are compared quantitatively with a laminar boundary layer Navier-Stokes computational fluid dynamics (CFD) prediction. Agreement of the data is excellent, except in the separated wake where the experimental boundary layer has undergone turbulent transition. A second wind tunnel test, on a cone-cylinder model, demonstrates the feasibility of recording multi-directional interferometric projections using holographic optical elements (HOE’s). The prototype system is highly compact and combines the versatility of diffractive elements with the efficiency of refractive components. The processed interferograms are compared to an integrated Euler CFD prediction and it is shown that the experimental shock cone is elliptical due to flow confinement. Tomographic reconstruction algorithms are reviewed for analysing density projections of a three-dimensional flow. Algebraic reconstruction methods are studied in greater detail, because they produce accurate results when the data is ill-posed. The performance of these algorithms is assessed using CFD input data and it is shown that a reconstruction accuracy of approximately 1% may be obtained when sixteen projections are recorded over a viewing angle of ±58°. The effect of noise on the data is also quantified and methods are suggested for visualising and reconstructing obstructed flow regions

X-ray Phase Contrast Tomography : Setup and Scintillator Development

X-ray microscopy and micro-tomography (μCT) are valuable non-destructive examination methods in many disciplines such as bio-medical research, archaeometry, material science and paleontology. Besides being implemented at synchrotrons radiation sources, laboratory setups using an X-ray tube and high-resolution scintillation detector routinely provide information on the micrometre scale. To improve the image contrast for small and low-density samples, it is possible to introduce a propagation distance between sample and detector to perform propagation-based phase contrast imaging (PB-PCI). This contrast mode relies on a sufficiently coherent illumination and is characterised by the appearance of an additional intensity modulations (‘edge enhancement fringes’) around interfaces in the image. The strength of this effect depends on hardware as well as geometry parameters. This thesis describes the development of a laboratory setup for X-ray μCT with a PB-PCI option. It contains the theoretical and technical background of the setup design as well the characterization of the achieved performance.Moreover, the optimization of the PB-PCI geometry was explored both theoretically as well as experimentally for three different setups. A simple rule for finding the optimal magnification to achieve high phase contrast for edge features was deduced. The effect of the polychromatic source spectrum und detector sensitivity was identified and included into the theoretical model.Besides application and methodological studies, the setup was used to test and characterise new X-ray scintillator materials. Recently, metal halide perovskite nanocrystals (MHP NCs) have gained attention due to their outstanding opto-electronic performance. The main challenge for their use and commercialization is their low long-term stability against humidity, temperature, and light exposure. Here, a CsPbBr3 scintillator comprised of an ordered array of nanowires (NW) in an anodized aluminium oxide (AAO) membrane is presented as a promising new scintillator for X-ray microscopy and μCT. It shows a high light yield under X-ray exposure which improves with smaller NW diameter and higher NW length. In contrast to many other MHP materials this scintillator shows good stability under continuous X-ray exposure and changing environmental conditions over extended time spans of several weeks. This makes it suitable for tomography, which is demonstrated by acquiring the first high-resolution tomogram using a MHP scintillator with the presented laboratory setup

Light Induced Dynamics in Quantum Matter

This thesis presents studies of different schemes to probe and manipulate quantum matter using light with an aim to discover novel routes to efficiently control the properties of quantum materials. A special focus is placed on developing new schemes utilizing light-matter interactions (1) to modify exchange interactions in magnetic insulators, and (2) to probe and modify band topology in quantum matter. In part II, new schemes are presented to probe local band topology of Bloch bands. First, we study the effects of time-dependent band topology on adiabatic evolution of a Bloch wavepacket. We find that it results in an electric-field analog in semi-classical equation of motion, and can be demonstrated in a honeycomb lattice by varying the sublattice offset energy. We then extend these methods to include non-adiabatic processes, and found interesting connections between the anomalous drift during band excitation and a quantum geometric quantity known as shift-vector. We generalize the concept of shift-vector to include different kinds of band transition protocols beyond light-induced dipole transitions. The idea of electric-field analog and the shift-vector are then combined to develop a novel charge pumping scheme. Motivated by these interesting consequences of band topology in non-adiabatic processes, we study shift-current response in moiré materials, and find that the highly topological nature of flat bands along with their very large unit cells significantly enhances these shift-vector related effects. This response also displays a strong dependence on interaction-induced changes in the band structure and quantum geometric quantities. These results suggest that shift-current response can possibly serve as a very reliable probe for interactions in twisted bilayer graphene. In addition to studying consequences of band topology on single-particle transport, we also consider Berry curvature effects on exciton transport. We find that the non-trivial band topology of underlying electron and hole bands allows us to manipulate excitons with a uniform electric field. We examine the conditions necessary to observe such transport and propose that transition metal dichalcogenide heterobilayers with moiré structure can prove an ideal platform for these effects. In part III, we propose novel drive protocols based on manipulating orbital and lattice degrees of freedom in quantum materials with light. We found that light induced changes in orbital hybridization and their electronic energies results in a significant change in exchange interactions in quantum magnets. We also accounted for the role of ligands in periodically driven quantum magnets, and found that the predictions made by the minimal model based on direct-hopping can be wrong in certain regimes of drive parameters. This understanding of light induced modifications in ligand-mediated exchange interactions was used to explain the phase shift observed in coherent phonon oscillations of CrSiTe₃ upon the onset of short-range spin correlations. We also demonstrate that light induced coherent lattice vibrations can provide a new route to realize space-time symmetry protected topological phases. Our results suggest that manipulating additional degrees of freedom (not included in commonly employed minimal models of periodically driven systems) with light can provide novel routes for ultrafast control of quantum materials.</p