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Probability theory provides a uniquely valid set of rules for plausible reasoning. This enables us to apply this mathematical formalism of probability, also known as Bayesian, with greater flexibility to problems of scientific inference. In this thesis, we are concerned with applying this method to the analysis of visibility data from radio interferometers. Any radio interferometry observation can be described using the Radio Interferometry Measurement Equation (RIME). Throughout the thesis, we use the RIME to model the visibilities in performing the probabilistic analysis. We first develop the theory for employing the RIME in performing Bayesian analysis of interferometric data. We then apply this to the problem of super-resolution with radio interferometers by performing model selection successfully between different source structures, all smaller in scale than the size of the point spread function (PSF) of the interferometer, on Westerbork Synthesis Radio Telescope (WSRT) simulations at a frequency of 1.4 GHz. We also quantify the change in the scale of the sources that can be resolved by WSRT at this frequency, with changing signal-to-noise (SNR) of the data, using simulations. Following this, we apply this method to a 5 GHz European VLBI Network (EVN) observation of the flaring blazar CGRaBS J0809+5341, to ascertain the presence of a jet emanating from its core, taking into account the imperfections in the station gain calibration performed on the data, especially on the longest baselines, prior to our analysis. We find that the extended source model is preferred over the point source model with an odds ratio of 109 : 1. Using the flux-density and shape parameter estimates of this model, we also derive the brightness temperature of the blazar (10¹¹-10¹² K), which confirms the presence of a relativistically boosted jet with an intrinsic brightness temperature lower than the apparent brightness temperature, consistent with the literature. We also develop a Bayesian criterion for super-resolution in the presence of baseline-dependent noise and calibration errors and find that these errors play an important role in determining how close one can get to the theoretical super-resolution limit. We then proceed to include fringe-fitting, the process of solving for the time and frequency dependent phase variations introduced by the interstellar medium and the Earth's atmosphere, in our probabilistic approach. Fringe-fitting is one of the first corrections made to Very Long Baseline Interferometry (VLBI) observations, and, by extending our method to include simultaneous fringefitting and source structure estimation, we will be able to perform end-to-end VLBI analysis using our method. To this end, we estimate source amplitude and fringe-fitting phase terms (phase offsets and delays) on 43 GHz Very Long Baseline Array and 230 GHz Event Horizon Telescope (EHT) simulations of point sources. We then perform model selection on a 5 μas extended Gaussian source (one-fourth the size of the PSF) on a synthetic 230 GHz EHT observation. Finally we incorporate turbulent time-varying phase offsets and delays in our model selection and show that the delays can be estimated to within 10-16 per cent error (often better than contemporary software packages) while simultaneously estimating the extended source structure.

The Large Binocular Telescope Interferometer (LBTI) is a versatile instrument designed for high angular resolution and high-contrast infrared imaging (1.5-13 mu m). In this paper, we focus on the mid-infrared (8-13 mu m) nulling mode and present its theory of operation, data reduction, and on-sky performance as of the end of the commissioning phase in 2015 March. With an interferometric baseline of 14.4 m, the LBTI nuller is specifically tuned to resolve the habitable zone of nearby main-sequence stars, where warm exozodiacal dust emission peaks. Measuring the exozodi luminosity function of nearby main-sequence stars is a key milestone to prepare for future exo-Earth direct imaging instruments. Thanks to recent progress in wavefront control and phase stabilization, as well as in data reduction techniques, the LBTI demonstrated in 2015 February a calibrated null accuracy of 0.05% over a 3 hr long observing sequence on the bright nearby A3V star beta Leo. This is equivalent to an exozodiacal disk density of 15-30. zodi for a Sun-like star located at 10 pc, depending on the adopted disk model. This result sets a new record for high-contrast mid-infrared interferometric imaging and opens a new window on the study of planetary systems.

As the global demand for energy and natural resources continues to increase so does our interaction with Earth's near surface through resource extraction and waste injection. In monitoring these interaction, seismology plays a central role. The focus of this work is on improving the detection and localization of seismic sources, a fundamental problem in seismology. After discussing the strengths and limitations of existing methods for source detection and localization, I develop a solution based on a beamforming approach that uses cross-correlation functions in a maximum likelihood search for sources of seismic energy. I call this method InterLoc, short for `interferometric locator', and apply it to data recorded at two active underground mines to demonstrate its effectiveness in monitoring both impulsive sources and persistent sources. Next, I demonstrate how persistent seismic sources, typically seen as contaminants, can be used directly to measure small changes in the medium between a source and either source-station pairs. This method relies on the ability to locate and monitor source activity and then use this information to identify and select cross-correlation functions to isolate each source of interest. From the resulting cross-correlations, it is possible to measure small temporal changes in the waveforms. To demonstrate this method, I show how ore-crushers can be used to track the growth of a block cave by measuring changes in traveltimes due to ray paths having to circumvent the growing cave. In the final chapter I focus on the development of a processing framework for the detection and location of microseismic events recorded on dense (or large-N) surface arrays. The proposed framework involves: (1) data reduction; (2) dividing the array into smaller sub-arrays; (3) waveform processing within fixed time windows; (4) stacking of time windows selected based on each potential origin time and source location; and (6) combining the output from all sub-arrays to infer detections and locations of sources. This methodology is validated with synthetic data built to emulate a real dataset from a 10,050 node survey to evaluate the suitability of land for carbon sequestration. Based on the presence of very strong coherent contaminating sources and low rock quality, I am only able to detect sources with moment magnitude greater than -0.5. In the five hours of data processed there is no positive detections suggesting this could be a good site for carbon storage. More work is needed to improve the detection threshold and quantify risk based on event location and magnitude. In summary, my work demonstrates how the interference (via cross-correlation) and stacking of seismic waveforms can be combined in different ways to create effective solutions for problems faced by today's industries.

This project was born out of the work performed by a group of researchers at the New Jersey Institute of Technology (NJIT) [1] [2] [3] working on interferometric imaging with a spiral array. Their investigation stopped at two dimensional imaging with a two dimensional array. In this thesis, their idea was developed further into the significantly more complex imaging with a three dimensional array. The general design of the NJIT [1] [2] [3] experiment was reproduced, studied, and modified in a manner that was theorized to enhance the experiment with the added ability to perform three dimensional imaging. The NJIT team [1] [2] [3] has developed their experiment to where they were able to accurately perform two dimensional imaging of two sources of equal intensity located at different distances from a spiral array. In this thesis, the equations used for two dimensional imaging are extrapolated into a three dimensional array application. This three dimensional imaging concept is simulated with MATLAB and the results presented and compared to the NJIT experimental results. [1] [2] [3] A proof of concept physical experiment is conducted and the results are compared to the MATLAB simulation. The results show that additional spatial information can be obtained from a three dimensional array that can enhance the information gleaned from images. / Master of Science

Fiber optic sensors have been utilized as corrosion sensors by depositing metal coatings to the surface of the sensors. Three types of fiber optic sensors were investigated as candidates for corrosion detection: the extrinsic Fabry-Perot interferometer (EFPI), the absolute extrinsic Fabry-Perot interferometer (AEFPI), and the long period grating (LPG) fiber optic sensor. The corrosion monitoring technique used with the EFPI and AEFPI sensors exploits the ability of a thick coating of metal to maintain strain information in fiber optic strain sensors. The sensors are placed under tensile stress, and while in the resulting strained position, a thick coating of metal is applied. Due to an increase in the quantity of material, the sensor does not return to its original position upon release, and strain is maintained within the sensor element. As the metal thickness decreases due to corrosion, this residual strain is released, providing the sensing mechanism for corrosion detection. LPG fiber optic sensors have demonstrated their ability as bandstop filters, by coupling the fundamental guided mode to circularly symmetric cladding modes. The cladding modes are extremely lossy due to the fiber jacket and bending along the fiber. Losses at discrete wavelengths can be monitored to determine the onset and progress of metal corrosion. Background theory and experimental results are discussed and reported for EFPI, AEFPI, and LPG fiber optic corrosion sensors. The study is preceded with an overview of different corrosion sensor designs and methods which are used in the area of non-destructive evaluation. / Master of Science

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This thesis considers the use of Interferometric Synthetic Aperture Radar (InSAR) for surveying temporal fluctuations in the velocity of glaciers in the Arctic region. The aim of this thesis is to gain a broader understanding of the manner in which the flow of both land- and marine-terminating glaciers varies over time, and to asses the ability of InSAR to resolve flow changes over timescales which provide useful information about the physical processes that control them. InSAR makes use of the electromagnetic phase difference between successive SAR images to produce interference patterns (interferograms) which contain information on the topography and motion of the Earth's surface in the direction of the radar line-of-sight. We apply established InSAR techniques (Goldstein et al., 1993) to (i) the 925 km2 LangjÖkull Ice Cap (LIC) in Iceland, which terminates on land (ii) the 8 500 km2 Flade Isblink Icecap (FIIC) in Northeast Greenland which has both land- and marine-terminating glaciers and (iii) to a 7 000 km2 land-terminating sector of the Western Greenland Ice Sheet (GrIS). It is found that these three regions exhibit velocity variations over contrasting timescales. At the LIC, we use an existing ice surface elevation model and dual-look SAR data acquired by the European Remote Sensing (ERS) satellite to estimate ice velocity (Joughin et al., 1998) during late-February in 1994. A comparison with direct velocity measurements determined by global positioning system (GPS) sensors during the summer of 2001 shows agreement (r2 = 0.86), suggesting that the LIC exhibits moderate seasonal and inter-annual variations in ice flow. At the FIIC, we difference pairs of interferograms (Kwok and Fahnestock, 1996) formed using ERS SAR data acquired between 15th August 1995 and 3rd February 1996 to estimate ice velocity on four separate days. We observe that the flow of 5 of the 8 outlet glaciers varies in latesummer compared with winter, although flow speeds vary by up to 20 % over a 10 day period in August 1995. At the GrIS, we use InSAR (Joughin et al., 1996) and ERS SAR data to reveal a detailed pattern of seasonal velocity variations, with ice speeds in latesummer up to three times greater than wintertime rates. We show that the degree of seasonal speedup is spatially variable and correlated with modeled runoff, suggesting that seasonal velocity changes are controlled by the routing of water melted at the ice sheet surface. The overall conclusion of this work is that the technique of InSAR can provide useful information on fluctuations in ice speed across a range of timescales. Although some ice masses exhibit little or no temporal flow variability, others show marked inter-annual, seasonal and even daily variations in speed. We observe variations in seasonality in ice flow over distances of ~ 10 km and over time periods of ~10 days during late-summer. With the aid of ancillary meteorological data, we are able to establish that rates of flow in western Greenland are strongly moderated by the degree of surface melting, which varies seasonally and secularly. Although the sampling of our data is insufficiently frequent and spans too brief a period for us to derive a general relationship between climate and seasonality of flow, we show that production of meltwater at the ice surface and its delivery to the ice bed play an important role in the modulation of horizontal flow speeds. We suggest that a similarly detailed investigation of other ice masses is required to reduce the uncertainty in predictions of the future Arctic land-ice contribution to sea level in a warming world.

Context. Extended circumstellar emission has been detected within a few 100 milli-arcsec around >= 10% of nearby main sequence stars using near-infrared interferometry. Follow-up observations using other techniques, should they yield similar results or non-detections, can provide strong constraints on the origin of the emission. They can also reveal the variability of the phenomenon. Aims. We aim to demonstrate the persistence of the phenomenon over the timescale of a few years and to search for variability of our previously detected excesses. Methods. Using Very Large Telescope Interferometer (VLTI)/Precision Integrated Optics Near Infrared ExpeRiment (PIONIER) in H band we have carried out multi-epoch observations of the stars for which a near-infrared excess was previously detected using the same observation technique and instrument. The detection rates and distribution of the excesses from our original survey and the follow-up observations are compared statistically. A search for variability of the excesses in our time series is carried out based on the level of the broadband excesses. Results. In 12 of 16 follow-up observations, an excess is re-detected with a significance of >2 sigma, and in 7 of 16 follow-up observations significant excess (>3 sigma) is re-detected. We statistically demonstrate with very high confidence that the phenomenon persists for the majority of the systems. We also present the first detection of potential variability in two sources. Conclusions. We conclude that the phenomenon responsible for the excesses persists over the timescale of a few years for the majority of the systems. However, we also find that variability intrinsic to a target can cause it to have no significant excess at the time of a specific observation.