Topological transformations of speckles

Deterministic control of coherent random light is highly important for information transmission through complex media. However, only a few simple speckle transformations can be achieved through diffusers without prior characterization. As recently shown, spiral wavefront modulation of the impinging beam allows permuting intensity maxima and intrinsic $\pm 1$-charged optical vortices. Here, we study this cyclic-group algebra when combining spiral phase transforms of charge $n$, with $D_3$- and $D_4$-point-group symmetry star-like amplitude modulations. This combination allows statistical strengthening of permutations and controlling the period to be 3 and 4, respectively. Phase saddle-points are shown to complete the cycle. These results offer new tools to manipulate critical points in speckles.Comment: 14 pages, 10 figures, 4 table

Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

The Coldest Place in the Universe: Probing the Ultra-Cold Outflow and Dusty Disk in the Boomerang Nebula

Our Cycle 0 ALMA observations confirmed that the Boomerang Nebula is the coldest known object in the Universe, with a massive high-speed outflow that has cooled significantly below the cosmic background temperature. Our new CO 1-0 data reveal heretofore unseen distant regions of this ultra-cold outflow, out to $\gtrsim120,000$ AU. We find that in the ultra-cold outflow, the mass-loss rate (dM/dt) increases with radius, similar to its expansion velocity ($V$) - taking $V\propto r$, we find $dM/dt \propto r^{0.9-2.2}$. The mass in the ultra-cold outflow is $\gtrsim3.3$ Msun, and the Boomerang's main-sequence progenitor mass is $\gtrsim4$ Msun. Our high angular resolution ($\sim$0".3) CO J=3-2 map shows the inner bipolar nebula's precise, highly-collimated shape, and a dense central waist of size (FWHM) $\sim$1740 AU$\times275$ AU. The molecular gas and the dust as seen in scattered light via optical HST imaging show a detailed correspondence. The waist shows a compact core in thermal dust emission at 0.87-3.3 mm, which harbors $(4-7)\times10^{-4}$ Msun~of very large ($\sim$mm-to-cm sized), cold ($\sim20-30$ K) grains. The central waist (assuming its outer regions to be expanding) and fast bipolar outflow have expansion ages of $\lesssim1925$ yr and $\le1050$ yr: the "jet-lag" (i.e., torus age minus the fast-outflow age) in the Boomerang supports models in which the primary star interacts directly with a binary companion. We argue that this interaction resulted in a common-envelope configuration while the Boomerang's primary was an RGB or early-AGB star, with the companion finally merging into the primary's core, and ejecting the primary's envelope that now forms the ultra-cold outflow.Comment: accepted ApJ, 12 Apr, 201

Reconocimiento automático invariante de sujetadores metálicos e squineros, basado en la transformada de Hough.

The Polar Hough Transform has been used to create a system for rotation, translation and sizescaling automatic invariant pattern recognition of polygonal objects, and it has been successfully applied to the invariant recognition of L-shaped metallic corner-fasteners. Since the performance of the developed system is autonomous it may be applied to automatic quality control and automatic classification in the industry.La Transformada polar de Hough ha sido usada para crear un sistema para reconocimiento invariante automático de objetos poligonales, el cual opera independientemente de la posición, orientación y tamaño de los objetos y, ha sido exitosamente aplicado al reconocimiento de sujetadores metálicos esquineros(forma de L). Como el sistema es autónomo, podría ser aplicado a la automatización del control de calidad y de la clasificación, en la industria

Subdivision surface fitting to a dense mesh using ridges and umbilics

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach

Fast Reliable Ray-tracing of Procedurally Defined Implicit Surfaces Using Revised Affine Arithmetic

Fast and reliable rendering of implicit surfaces is an important area in the field of implicit modelling. Direct rendering, namely ray-tracing, is shown to be a suitable technique for obtaining good-quality visualisations of implicit surfaces. We present a technique for reliable ray-tracing of arbitrary procedurally defined implicit surfaces by using a modification of Affine Arithmetic called Revised Affine Arithmetic. A wide range of procedurally defined implicit objects can be rendered using this technique including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others. We compare our technique with other reliable techniques based on Interval and Affine Arithmetic to show that our technique provides the fastest, while still reliable, ray-surface intersections and ray-tracing. We also suggest possible modifications for the GPU implementation of this technique for real-time rendering of relatively simple implicit models and for near real-time for complex implicit models