Exact formulas for a thin-lens system with an arbitrary number of lenses

AbstractWe present an angular thin-lens formula giving the angle of refraction β for arbitrary values of the angle of incidence α. With this formula, we find analytical results for the focal length f of a thin-lens system. The number of lenses n and their focal lengths f1,f2,…,fn are abitrary, as are the mutual distances D12,…,D(n−1)n between the lenses. All these results are exact, i.e. not restricted to small or even paraxial angles. In the literature, the 2-lens and 3-lens versions (the last one without proof or derivation) are known [1]. We present the general result for n lenses and for (the positions of) its principal planes

The Right (Angled) Perspective: Improving the Understanding of Road Scenes Using Boosted Inverse Perspective Mapping

Many tasks performed by autonomous vehicles such as road marking detection, object tracking, and path planning are simpler in bird's-eye view. Hence, Inverse Perspective Mapping (IPM) is often applied to remove the perspective effect from a vehicle's front-facing camera and to remap its images into a 2D domain, resulting in a top-down view. Unfortunately, however, this leads to unnatural blurring and stretching of objects at further distance, due to the resolution of the camera, limiting applicability. In this paper, we present an adversarial learning approach for generating a significantly improved IPM from a single camera image in real time. The generated bird's-eye-view images contain sharper features (e.g. road markings) and a more homogeneous illumination, while (dynamic) objects are automatically removed from the scene, thus revealing the underlying road layout in an improved fashion. We demonstrate our framework using real-world data from the Oxford RobotCar Dataset and show that scene understanding tasks directly benefit from our boosted IPM approach.Comment: equal contribution of first two authors, 8 full pages, 6 figures, accepted at IV 201

Direct profiling of III/V semiconductor nanostructures at the atomic level by cross-sectional scanning tunneling microscopy

By means of modern epitaxial growth techniques it is possible to fabricate semiconductor structures that are faster, cheaper and more complicated. They find their implementation in e.g. quantum dot or quantum well lasers. To obtain extra functionality, these devices have to be made so small, that within these structures charge carriers are confined in 2 or 3 dimensions. This results in discrete energy levels, which enable new applications and may solve several problems in the contemporary technologies. The first chapter will give an introduction in which is explained why cross-sectional Scanning Tunneling Microscopy (XSTM) is a very suitable technique to investigate semiconductor nanostructures, as nanostructures can be investigated at the atomic level by this technique. The differences in the chemical and electrical properties of the various species of atoms, of which the semiconductor materials consist of, can be used to discriminate between them. This can be used to obtain a better insight in the way these structures work. Furthermore, the growth processes involved in the fabrication of these structures can be better understood and optimised. In chapter 2, a short description of two epitaxial growth techniques, Molecular Beam Epitaxy (MBE) and Chemical Beam Epitaxy (CBE) is given. The differences, the advantages and disadvantages of these growth techniques are briefly discussed. Also a method is discussed by which a desired bandgap of the semiconductor can be obtained by choosing the proper materials. Furthermore, the formation of 3D structures by Stranski- Krastanov growth is briefly described. By growing materials with a different lattice constant on top of each other, strain can be introduced in the material. This strain influences the electronic band structure and can therefore be used to modify the band structure of a semiconductor as desired. During STM measurements the local density of states of the surface is imaged. Also the density of states of the STM tip plays a very important role in the imaging mechanism. Not only the topography of the surface under investigation, but also the electronic properties of both the surface and the tip have a large influence on the STM image. The big question therefore often remains: what is actually imaged during an STM measurement? Therefore the tunnel process needs some extra consideration, in order to be able to interpret the STM images in a proper way. In chapter 3, the tunnel process and the influence of the STM tip are described in more detail. Also the possibility of imaging the wavefunctions at the surface of a semiconductor, using I(V) spectroscopy during STM measurements, is briefly explained. Furthermore, the influence of bandbending upon the tunnel current is dealt with. After that the behaviour of a cleaved surface is described, as the outermost atoms of a surface, which are probed during STM measurements, behave in a different way than the atoms in the bulk material. Finally, the relaxation of cleaved surfaces is treated. If in a structure a strained 2D layer, like a quantum well, is present, this layer will relax outward or inward, after it has been cleaved perpendicular to this layer. By investigation of the resulting relaxation profile, the concentration profile inside the layer can be calculated in an analytical way. In chapter 4, the used experimental methods are given. The STM unit itself and the ultrahigh vacuum system with active damping system are described. Also the procedures followed during tip- and sample preparation are given some closer attention. Finally a short description of how STM and spectroscopy measurements are performed is given. In a semiconductor structure, layers with a different lattice constant can be grown on top of each other. This results in strain in the structure. If such a structure is cleaved, this strain will cause a relaxation of the surface. By analysing this relaxation the concentration profile of these layers can be determined. Therefore an exact determination of this relaxation is necessary. During STM measurements, not only topography, but also an electronic component is imaged. In order to be able to separate these two contributions, the height contrast in STM measurements is investigated in detail in chapter 5. Numerical calculations have been performed in order to investigate the electronic contrast as a function of applied tunnel voltage, for an InGaAs layer in a GaAs matrix. From these calculations it has become clear that at high tunnel voltages the electronic contrast can be suppressed very effectively, especially when imaging the filled electron states. These simulations have been compared with measurements that have been performed on an InGaAs quantum well. From voltage dependent measurements it has been concluded that the conclusions from the numerical simulations are indeed correct. It is thus possible to obtain STM images that only contain topographical information. From relaxation and lattice constant profiles obtained from such images, it is possible to determine the concentration profile, by using the theory from chapter 3. The concentration profile of the investigated quantum well has been accurately determined by X-ray diffraction, photoluminescence measurements and by counting atoms in STM images. By comparing the used analytical model with these measurements, it is shown that they agree. Several causes can be indicated for the fact that the calculations do not agree 100% with the measurements. In modern telecommunications there is a large demand for lasers that operate in the 1.3 and 1.55 µm wavelength range. InGaAsN compounds, which can be grown on InP without introducing any strain, are very interesting in this respect. They can be used in e.g. Vertical Cavity Surface Emitting Lasers (VCSEL) and very efficient solar cells. InGaAsN and InGaAs layers have been investigated by X-STM and have been compared to each other in chapter 6. The nitrogen atoms are clearly visible in the InGaAsN layers, and the formation of pairs of nitrogen atoms is observed. From the STM measurements the nitrogen concentration is estimated to be about 1.2%. After a thermal treatment, nitrogen rich clusters are formed, which behave like quantum dots. The existence of such quantum dots has already been expected from optical measurements that have been performed on similar annealed structures. By suppression of the electronic contrast, images have been obtained that show only real topographic information. From the relaxation profile the presence of nitrogen in the InGaAsN layers is demonstrated. Furthermore, they show that after annealing, when the nitrogen quantum dots have been formed, the remaining InGaAsN layer is almost completely depleted from nitrogen. Finally, the influence of extreme annealing temperatures is investigated. Both the InGaAs as the InGaAsN layers are damaged by this and no quantum dot formation takes place. The optical and electrical properties of quantum dots are dependent on their shape, size and composition. If quantum dots are covered with another material, their structural properties will change. Therefore it is necessary to investigate buried dots as well, and not only dots that are uncovered. In chapter 7, the dimensions and the shape of InAs quantum dots within a GaAs matrix have been determined. These dots were grown at an extremely low growth rate, i.e. 0.01 monolayer/sec. As one cannot tell from an STM image at which position the dot has been cleaved, the height vs. base length distribution of an ensemble of quantum dots has been determined. From this it is deduced that the dots have the shape of a truncated 109 pyramid, with a base length of 18 nm and a height of 5 nm. This is in agreement with previous optical measurements and theoretical calculations. By measuring the outward relaxation and the lattice constant profile of the cleaved dot, the concentration profile inside the dot was determined by numerical simulations. In the dots a linear indium gradient from 60% to 100% from bottom to top is present, which is again in agreement with previous optical measurements. By means of Current Imaging Tunneling Spectroscopy (CITS) it was attempted to image the wavefunction of the electrons that are confined within the cleaved dot. This was not possible for the "holes" in the quantum dots. By using a numerical model it is possible to simulate the CITS measurements (current distribution) for the electron wavefunctions. In the model, the shape, the composition, the fact that the dot is cleaved, the strain fields and the band bending underneath the tip are taken into account. By means of these simulations, a better insight is obtained in the energy separation of the various electron states and the positions of the maxima in the CITS measurements. Next, samples were investigated that contained InAs quantum dots grown at a much larger growth rate (0.1 monolayer/sec). In this sample the amount of deposited InAs per quantum dot layer was varied as well. After deposition of 1.5 monolayers of InAs, no quantum dot formation was observed. After the deposition of 2.0 and 2.5 monolayers of InAs, however, quantum dots had been formed. Although the 2.5 monolayer quantum dots are slightly larger than the 2.0 monolayer dots, the larger deposition amount of InAs meanly leads to a higher dot density, rather than larger dots. These dots are lens-shaped and thus do not have the shape of a truncated pyramid. This is due to the higher deposition rate, which leads to a larger aspect ratio of the dots before they are capped with GaAs. This also causes that the dots do not have an indium gradient, which results in dots that consist of InGaAs with a constant indium concentration. This has been determined from the relaxation profiles of the cleaved quantum dots. Even at deposition amounts that are smaller than 1.7 monolayers, which is the critical layer thickness, dot nucleation centers can already be formed due to inhomogeneities at the growth surface. This results in small quantum dots that consist of almost pure InAs. The density of these dots is, however, very low. Finally, the formation of the wetting layers has been studied. From relaxation profiles of the wetting layer between the quantum dots, it is concluded that the wetting layer does not change if the amount of deposited InAs is enlarged. After formation of the wetting layer, i.e. after the deposition of 1.7 monolayers of InAs, the wetting layer remains stable and all the surplus of material is incorporated in the quantum dots. By means of the relaxation profile and numerical calculations, the width and composition profile of the wetting layer has been determined. The width found in these calculations agrees well with the width that is observed in the XSTM measurements. The indium concentration seems to decrease exponentially in the growth direction. Furthermore, the calculated average indium concentration inside the wetting layer is exactly what one would expect if 1.7 monolayers of InAs are incorporated in a layer with the calculated and observed thickness. Finally, stacks of quantum dots have been investigated in chapter 8. If the distance between the quantum dot layers is not too large (<25 nm), the quantum dots will form on top of each other, thus forming a stack. This is an advantage, as in this way the local dot density can be enlarged. From these dots, a higher uniformity is expected as well. From lattice constant profiles it was concluded that these dots have a similar indium concentration profile as the low-growth-rate quantum dots from chapter 7, which is hardly surprising, as the growth conditions were almost identical. Several stacks of quantum dots have been investigated by X-STM. Higher in the stack, the quantum dots get deformed, as the dots become more wing-shaped and terrace growth occurs. From analysis of the growth speed the quantum dot material and the surrounding GaAs matrix it is concluded that the deformation is caused by changes in growth speed of the GaAs matrix. This is due to the fact that the 2D GaAs growth is very sensitive to local lateral strain fluctuations. Furthermore, the growth speed of the InAs quantum dot material remains constant throughout the entire stack. This results in quantum dots that all have the same volume in spite of the deformation. Therefore the consequences of the deformation upon the optoelectronic properties of the dots are expected to be small

Modeling Li I and K I sensitivity to Pleiades activity

We compare schematic modeling of spots and plage on the surface of cool dwarfs with Pleiades data to assess effects of magnetic activity on the strengths of the L II and K I resonance lines in Pleiades spectra. Comprehensive L II and K I NLTE line formation computation is combined with comparatively well-established empirical solar spot and plage stratifications for solar-like stars. For other stars, we use theoretical constructs to model spots and plage that portray recipes commonly applied in stellar activity analyses. We find that - up to B-V = 1.1 | neither the L 670.8 nm nor the K I 769.9 nm line is sensitive to the presence of a chromosphere, in contrast to what is often supposed. Instead, both lines respond to the effects of activity on the stratification in the deep photosphere. They do so in similar fashion, making the K I line a valid proxy to study L II line formation without spread from abundance variations. The computed effects of activity on line strength are opposite between plage and spots, differ noticeably between the empirical and theoretical solar-like stratifications, and considerably affect stellar broad-band colors. Our results indicate that one can neither easily establish, nor easily exclude, magnetic activity as major provider of K I line strength variation in the Pleiades. Since L II line formation follows K I line formation closely, the same holds for L II and the apparent lithium abundance

Canonical lossless state-space systems: Staircase forms and the Schur algorithm

A new finite atlas of overlapping balanced canonical forms for multivariate discrete-time lossless systems is presented. The canonical forms have the property that the controllability matrix is positive upper triangular up to a suitable permutation of its columns. This is a generalization of a similar balanced canonical form for continuous-time lossless systems. It is shown that this atlas is in fact a finite sub-atlas of the infinite atlas of overlapping balanced canonical forms for lossless systems that is associated with the tangential Schur algorithm; such canonical forms satisfy certain interpolation conditions on a corresponding sequence of lossless transfer matrices. The connection between these balanced canonical forms for lossless systems and the tangential Schur algorithm for lossless systems is a generalization of the same connection in the SISO case that was noted before. The results are directly applicable to obtain a finite sub-atlas of multivariate input-normal canonical forms for stable linear systems of given fixed order, which is minimal in the sense that no chart can be left out of the atlas without losing the property that the atlas covers the manifold