Thesis (Ph. D.)--Ohio state University, 1929. / Biography. Bibliography: p. [21].

Thesis (Ph. D.)--Ohio state University, 1929. / Biography. Bibliography: p. [21].

Thesis (Ph. D.)--Ohio University, June, 2004. / Includes bibliographical references (leaves 184-187).

Thesis (M.S.)--Brigham Young University. Dept. of Electrical and Computer Engineering, 2004. / Includes bibliographical references (p. 51-52).

Thesis (M.S.)--Brigham Young University. Dept. of Physics and Astronomy, 2007. / Includes bibliographical references (p. 50-54) and index.

No description available.

On temporal, spatial and spectral scales which are small enough, all fields are fully polarized. In the optical regime, however, instantaneous fields can rarely be examined, and, instead, only average quantities are accessible. The study of polarimetry is concerned with both the description of electromagnetic fields and the characterization of media a field has interacted with. The polarimetric information is conventionally presented in terms of second order field correlations which are averaged over the ensemble of field realizations. Motivated by the deficiencies of classical polarimetry in dealing with specific practical situations, this dissertation expands the traditional polarimetric approaches to include higher order field correlations and the description of fields fluctuating in three dimensions. In relation to characterization of depolarizing media, a number of fourth-order correlations are introduced in this dissertation. Measurements of full polarization distributions, and the subsequent evaluation of Stokes vector element correlations and Complex Degree of Mutual Polarization demonstrate the use of these quantities for material discrimination and characterization. Recent advancements in detection capabilities allow access to fields near their sources and close to material boundaries, where a unique direction of propagation is not evident. Similarly, there exist classical situations such as overlapping beams, focusing, or diffusive scattering in which there is no unique transverse direction. In this dissertation, the correlation matrix formalism is expanded to describe three dimensional electromagnetic fields, providing a definition for the degree of polarization of such a field. It is also shown that, because of the dimensionality of the problem, a second parameter is necessary to fully describe the polarimetric properties of three dimensional fields. Measurements of second-order correlations of a three dimensional field are demonstrated, allowing the determination of both the degree of polarization and the state of polarization. These new theoretical concepts and innovative experimental approaches introduced in thiss dissertation are expected to impact scientific areas as diverse as near field optics, remote sensing, high energy laser physics, fluorescence microscopy, and imaging.

The interaction of optical waves with material systems often results in complex, seemingly random fields. Because the fluctuations of such fields are typically difficult to analyze, they are regarded as noise to be suppressed. Nevertheless, in many cases the fluctuations of the field result from a linear and deterministic, albeit complicated, interaction between the optical field and the scattering system. As a result, linear systems theory (LST) can be used to frame the scattering problem and highlight situations in which useful information can be extracted from the fluctuations of the scattered field. Three fundamental problems can be posed in LST regardless of the nature of the system: one direct and two inverse problems. The direct problem attempts to predict the response of a known system to a known input. The problem may be simple enough to admit analytical solutions as in the case of homogeneous materials, phase and amplitude screens, and weakly scattering materials; or the problem may require the use of numerical techniques. This dissertation will focus on the two inverse problems, namely the determination of either the excitation field or the scattering system. Traditionally, the excitation determination problem has relied on designing optical systems that respond to the property of interest in a simple, easily quantified way. For example, gratings can be used to map wavelength onto direction of propagation while waveplates and polarizers can map polarization properties onto intensity. The primary difficulty with directly applying the concepts of LST to scattering systems iv is that, while the outputs are still combinations of the inputs, they are not ``simple'' combinations such as Fourier transforms or spatially dispersed spectral components of the input spectrum. Instead, the scattered field can be thought of as a massive sampling and mixing of the excitation field. This dissertation will show that such complicated sampling functions can be characterized and that the corresponding scattering medium can then be used as an optical device such as a lens, polarimeter, or spectrometer. The second inverse problem, system determination, is often more difficult because the problem itself may be ill-posed. For scattering systems that are dominated by low-order scattering, the statistical properties of the scattered light may serve as a fingerprint for material discrimination; however, in many situations, the statistical properties of the output do not depend on the material properties. Rather than analyzing the scattered field from one realization of the random interaction, several measurement techniques have been developed that attempt to extract information about the material system from modifications of the scattered field in response to changes in either the excitation or the intrinsic dynamics of the medium itself. One such technique is dynamic light scattering. This dissertation includes an extension to this method that allows for a polarimetric measurement of the scattered light using a reference beam with controllable polarization. Another system determination problem relates to imaging the reflectivity of a target that is being randomly illuminated. It will be demonstrated that an approach based on the correlation between the integrated scattered intensity and the corresponding illumination intensity distribution can prove superior to standard imaging microscopy

This thesis reports on the recent results of a continuing, high-precision pulsar timing project, currently focused on the nearby, binary millisecond pulsar, PSR J0437_4715. Pulse arrival time analysis has yielded a remarkable series of constraints on the physical parameters of this system and evidence for the distortion of space-time as predicted by the General Theory of Relativity. Owing to the proximity of the PSR J0437_4715 system, relative changes in the positions of the Earth and pulsar result in both annual and secular evolution of the line of sight to the pulsar. Although the changes are miniscule, the effects on the projected orbital parameters are detectable in our data at a high level of significance, necessitating the implementation of an improved timing model. In addition to producing estimates of astrometric parameters with unparalleled precision, the study has also yielded the first three-dimensional orbital geometry of a binary pulsar. This achievement includes the first classical determination of the orbital inclination, thereby providing the unique opportunity to verify the shape of the Shapiro delay and independently confirm a general relativistic prediction. With a current post-fit arrival time residual RMS of 130 ns over four years, the unrivaled quality of the timing data presented herein may eventually contribute to the most stringent limit on the energy density of the proposed stochastic gravitational wave background. Continuing the quest for even greater timing precision, a detailed study of the polarimetry of PSR J0437_4715 was undertaken. This effort culminated in the development of a new, phase-coherent technique for calibrating the instrumental response of the observing system. Observations were conducted at the Parkes 64-m radio telescope in New South Wales, Australia, using baseband recorder technologies developed at York University, Toronto, and at the California Institute of Technology. Data were processed off-line at Swinburne University using a beowulf-style cluster of high-performance workstations and custom software developed by the candidate as part of this thesis.

In this work, image processing algorithms are presented for an advanced sensor classification known collectively as imaging modulated polarimetry. The image processing algorithms presented are novel in that they use frequency domain based approaches, in comparison to the data domain based approaches that all previous algorithms have employed. Under the conditions on the data and imaging device derived in this work, the frequency domain based demodulation algorithms will optimally reduced reconstruction artifacts in a least squared sense. This work provides a framework for objectively comparing polarimeters that modulate in different domains (i.e. time vs. space), referred to as the spectral density response function. The spectral density response function is created as an analog to the modulation transfer function (or the more general transfer function for temporal devices) employed in the design of conventional imaging devices. The framework considers the total bandwidth of the object to be measured, and then can consider estimation artifacts that arise in both time and space due to the measurement modality that has been chosen. Using the framework for objectively comparing different modulated polarimeters (known as the spectral density response function), a method of developing a Wiener filter for multi-signal demodulation is developed, referred to as the polarimetric Wiener filter. This filter is then shown to be optimal for one extensive test case. This document provides one extensive example of implementing the algorithms and spectral density response calculations on a real system, known as the MSPI polarimeter. The MSPI polarimeter has been published extensively elsewhere, so only a basic system description here is used as necessary to describe how the methods presented here can be implemented on this system.