Second Order Local Analysis for 3D Reconstruction of Specular Surfaces

We analyze the problem of recovering the shape of a mirror surface. A calibrated scene composed of lines passing through a point is assumed. The lines are reflected by the mirror surface onto the image plane of a calibrated camera, where the intersection, orientation and curvature of such reflections are measured. The relationship between the local geometry of the surface around the point of reflection and the measurements is analyzed. We extend the analysis in [13, 14], where we recovered positions and normals and second order local geometry of a specular surface up to one unknown parameter. We show that, provided that we work in a neighborhood of a surface whose third order surface terms can be neglected, the second order parameter ambiguity can be solved by equating the curvatures observed for the reflected lines with those computed from analytical differentiation followed by a perspective projection

Programmable unitary spatial modes manipulation

Free space propagation and conventional optical systems such as lenses and mirrors all perform spatial unitary transforms. However, the subset of transforms available through these conventional systems is limited in scope. We present here a unitary programmable mode converter (UPMC) capable of performing any spatial unitary transform of the light field. It is based on a succession of reflections on programmable deformable mirrors and free space propagation. We first show theoretically that a UPMC without limitations on resources can perform perfectly any transform. We then build an experimental implementation of the UPMC and show that, even when limited to three reflections on an array of 12 pixels, the UPMC is capable of performing single mode tranforms with an efficiency greater than 80% for the first 4 modes of the TEM basis

Cavlectometry: Towards Holistic Reconstruction of Large Mirror Objects

We introduce a method based on the deflectometry principle for the reconstruction of specular objects exhibiting significant size and geometric complexity. A key feature of our approach is the deployment of an Automatic Virtual Environment (CAVE) as pattern generator. To unfold the full power of this extraordinary experimental setup, an optical encoding scheme is developed which accounts for the distinctive topology of the CAVE. Furthermore, we devise an algorithm for detecting the object of interest in raw deflectometric images. The segmented foreground is used for single-view reconstruction, the background for estimation of the camera pose, necessary for calibrating the sensor system. Experiments suggest a significant gain of coverage in single measurements compared to previous methods. To facilitate research on specular surface reconstruction, we will make our data set publicly available

Forcing nonperiodicity with a single tile

An aperiodic prototile is a shape for which infinitely many copies can be arranged to fill Euclidean space completely with no overlaps, but not in a periodic pattern. Tiling theorists refer to such a prototile as an "einstein" (a German pun on "one stone"). The possible existence of an einstein has been pondered ever since Berger's discovery of large set of prototiles that in combination can tile the plane only in a nonperiodic way. In this article we review and clarify some features of a prototile we recently introduced that is an einstein according to a reasonable definition. [This abstract does not appear in the published article.]Comment: 18 pages, 10 figures. This article has been substantially revised and accepted for publication in the Mathematical Intelligencer and is scheduled to appear in Vol 33. Citations to and quotations from this work should reference that publication. If you cite this work, please check that the published form contains precisely the material to which you intend to refe

Texture, twinning and metastable "tetragonal" phase in ultrathin films of HfO₂ on a Si substrate

Thin HfO<sub>2</sub> films grown on the lightly oxidised surface of (100) Si wafers have been examined using dark-field transmission electron microscopy and selected area electron diffraction in plan view. The polycrystalline film has a grain size of the order of 100 nm and many of the grains show evidence of twinning on (110) and (001) planes. Diffraction studies showed that the film had a strong [110] out-of-plane texture, and that a tiny volume fraction of a metastable (possibly tetragonal) phase was retained. The reasons for the texture, twinning and the retention of the metastable phase are discussed

Dynamir: optical manipulations using dynamic mirror brushes

Mirror surfaces are part of our everyday life. Among them, curved mirrors are used to enhance our perception of the physical space, e.g., convex mirrors are used to increase our field of view in the street, and concave mirrors are used to zoom in on parts our face in the bathroom. In this paper, we investigate the opportunities opened when these mirrors are made dynamic, so that their effects can be modulated to adapt to the environment or to a user's actions. We introduce the concept of dynamic mirror brushes that can be moved around a mirror surface. We describe how these brushes can be used for various optical manipulations of the physical space. We also present an implementation using a flexible mirror sheet and three scenarios that demonstrate some of the interaction opportunities

Controlling molecular broadband-emission by optical confinement

We investigate experimentally and theoretically the fluorescence emitted by molecular ensembles as well as spatially isolated, single molecules of an organic dye immobilized in a quasi-planar optical microresonator at room temperature. The optically excited dipole emitters couple simultaneously to on- and off-axis cavity resonances of the microresonator. The multi-spectral radiative contributions are strongly modified with respect to free (non-confined) space due to enhancement and inhibition of the molecular spontaneous emission (SpE) rate. By varying the mirror spacing of the microresonator on the nanometer-scale, the SpE rate of the cavity-confined molecules and, consequently, the spectral line width of the microresonator-controlled broadband fluorescence can be tuned by up to one order of magnitude. Stepwise reducing the optical confinement, we observe that the microresonator-controlled molecular fluorescence line shape converges towards the measured fluorescence line shape in free space. Our results are important for research on and application of broadband emitters in nano-optics and -photonics as well as microcavity-enhanced (single molecule) spectroscopy

Simulation of waviness in neutron guides

As the trend of neutron guide designs points towards longer and more complex guides, imperfections such as waviness becomes increasingly important. Simulations of guide waviness has so far been limited by a lack of reasonable waviness models. We here present a stochastic description of waviness and its implementation in the McStas simulation package. The effect of this new implementation is compared to the guide simulations without waviness and the simple, yet unphysical, waviness model implemented in McStas 1.12c and 2.0

A new non-arithmetic lattice in PU(3,1)

We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the non-arithmetic Deligne-Mostow lattice in PU(3,1)