Argand-plane mappings induced by complex scalar wavefields
thesisposted on 02.03.2017, 02:02 authored by Freda, Werdiger
In this thesis, an analysis of two-dimensional complex scalar wavefields associated with electromagnetic radiation is presented. The particular tool of analysis is the Argand-plane mappings that are induced by such wavefields. The analysis is carried out over three distinct but interconnected studies, each accompanied by a published body of work. The first study involves the simulation of a visible-light speckle field that is littered with vortices. The Argand-plane mappings induced by this field reveal caustic-like structures that are singularities of the mapping. It is found that these singularities, called vorticity singularities, are induced by lines of zero vorticity in the physical wavefield, and their connection to vortices is investigated. The second body of work contains an experimental realisation of vorticity singularities, done by generating a speckle field using visible light. Various vorticity singularities - the fold, cusp, and elliptic umbilic - are reconstructed using experimental data, and the lines of zero vorticity that induce them are observed. The third study moves from the domain of visible light into x-ray radiation. Here, the Argand-plane is used as a tool for investigating x-ray diffraction. Three objects, having been illuminated by hard x-rays, are imaged using propagation-based phase contrast imaging; a straight edge, cylinder and a sphere embedded within a cylinder. The full information of the propagated wavefield is recovered using a combination of phase retrieval and virtual optics. The associated Argand-plane mappings reveal structures known as generalised Cornu spirals that are induced by the diffraction of the incident radiation around the object in question. Each object is associated with a particular generalised Cornu spiral that is explained using the Geometrical Theory of Diffraction. The body of work constituting the present thesis indicates that the Argand plane is an interesting tool for the analysis of the complex scalar wavefield associated with optical fields, possessing features that are singularities of the mapping to the Argand plane that can be used to study various phenomena in the physical field. The applications for Argand-plane analysis may be numerous, going beyond the context of optical fields.