Global properties of gravitational lens maps in a Lorentzian manifold setting

In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere of the observer (or on part of it) and it takes values in a two-dimensional manifold representing a two-parameter family of worldlines. In this article we use methods from differential topology to characterize global properties of the lens map. Among other things, we use the mapping degree (also known as Brouwer degree) of the lens map as a tool for characterizing the number of images in gravitational lensing situations. Finally, we illustrate the general results with gravitational lensing (a) by a static string, (b) by a spherically symmetric body, (c) in asymptotically simple and empty spacetimes, and (d) in weakly perturbed Robertson-Walker spacetimes.Comment: 26 page

Electrostatic Deflection and Correction Systems

Tato diplomová práce se věnuje prozkoumání možností dynamické korekce vad v elektronové litografii. Pro výpočty byl zvolen elektronový litograf BS600. Práce se zabývá korekcí vad vychýlení třetího řádu: zklenutí pole, astigmatismu a zkreslení. Aberace byly spočteny jak pro současný magnetický vychyolvací systém, tak pro nově navržený elektrostatický deflektor. Vlastnosti a vady obou vychylovacích a korekčních systémů byly porovnány.The aim of this master's thesis is to explore and study dynamic aberration correction options in electron-beam lithography systems. For the calculations, the thesis uses the optical column of the BS600 electron-beam writer. The thesis focuses on corrections of the third order field curvature, astigmatism, and distortion aberrations of the currently used magnetic deflection system and a newly designed electrostatic deflection system. The parameters of the two deflection and correction systems were compared.

Theoretical and experimental studies of femtosecond streak and picosecond framing image tubes

Imperial Users onl

Laser scanning methods and a phase comparison, modulated laser range finder for terrain sensing on a Mars roving vehicle

Two areas of a laser range finder for a Mars roving vehicle are investigated: (1) laser scanning systems, and (2) range finder methods and implementation. Several ways of rapidly scanning a laser are studied. Two digital deflectors and a matrix of laser diodes, are found to be acceptable. A complete range finder scanning system of high accuracy is proposed. The problem of incident laser spot distortion on the terrain is discussed. The instrumentation for a phase comparison, modulated laser range finder is developed and sections of it are tested

Fast Volume Rendering and Deformation Algorithms

Volume rendering is a technique for simultaneous visualization of surfaces and inner structures of objects. However, the huge number of volume primitives (voxels) in a volume, leads to high computational cost. In this dissertation I developed two algorithms for the acceleration of volume rendering and volume deformation. The first algorithm accelerates the ray casting of volume. Previous ray casting acceleration techniques like space-leaping and early-ray-termination are only efficient when most voxels in a volume are either opaque or transparent. When many voxels are semi-transparent, the rendering time will increase considerably. Our new algorithm improves the performance of ray casting of semi-transparently mapped volumes by exploiting the opacity coherency in object space, leading to a speedup factor between 1.90 and 3.49 in rendering semi-transparent volumes. The acceleration is realized with the help of pre-computed coherency distances. We developed an efficient algorithm to encode the coherency information, which requires less than 12 seconds for data sets with about 8 million voxels. The second algorithm is for volume deformation. Unlike the traditional methods, our method incorporates the two stages of volume deformation, i.e. deformation and rendering, into a unified process. Instead to deform each voxel to generate an intermediate deformed volume, the algorithm follows inversely deformed rays to generate the desired deformation. The calculations and memory for generating the intermediate volume are thus saved. The deformation continuity is achieved by adaptive ray division which matches the amplitude of local deformation. We proposed approaches for shading and opacit adjustment which guarantee the visual plausibility of deformation results. We achieve an additional deformation speedup factor of 2.34~6.58 by incorporating early-ray-termination, space-leaping and the coherency acceleration technique in the new deformation algorithm

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integrations of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published versio

Theoretical and experimental studies of femto-second streak and picosecond framing image tubes

Imperial Users onl