Microwave interferometry (MI) is a Doppler based diagnostic tool used to measure the detonation velocity of explosives, which has applications to explosive safety. The geometry used in existing MI experiments is cylindrical explosives pellets layered in a cylindrical case. It is of interest to Lawrence Livermore National Labs to measure additional geometries that may be overmoded, meaning that the geometries propagate higher-order transverse electromagnetic waves. The goal of my project is to measure and analyze the input reflection from a novel structure and to find a good frequency to use in an experiment using this structure. Two methods of determining a good frequency are applied to the phase of the input reflection. The first method is R2, used to measure the linearity of input reflection phase. The second is a zero-crossing method that measures how periodic the input reflection phase is. Frequencies with R2 values higher than .995 may be usable for an experiment in the novel structure.

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No / In this work we present the angle of arrival estimation techniques and their comparison at different values of SNR using a 5 element UCA. The techniques that have been considered include phase interferometry, Multiple Signal Classification and covariance. The results show that for very low values of SNR the performance of the covariance matrix based algorithm is the best but for slightly higher values of SNR, MUSIC algorithm outperforms covariance.

The electrical double layer (EDL) is formed due to the accumulation of charge at the interface of a metal surface in contact with an electrolyte. The total charge in the EDL compensates the charge on the metal surface. As EDL is the layer that "connects" the electrode to the "bulk", all electrode mediated transport and redox reaction depends on the structure and dynamics of the ions in the EDL. Thus the ion dynamics in the EDL are critical to a wide range of physical and biological phenomena such as electrochemical reaction, flow in channels of nanofluidic devices, wetting of fluids; to biology, for example, folding and function of proteins, conformation change of DNA and ionic flow through cell membranes. EDL polarization is the ion accumulation or depletion in the EDL due to the potential of the metal surface. The conventional method of measuring the EDL polarization is by monitoring the current flowing through the electrochemical system. Thus, the electrical characteristics of the EDL are inferred indirectly from the total current that is implicitly related to effects such as the impedance of the bulk solution. We have developed a sensitive optical interferometric technique to directly measure the polarization of the metal-electrolyte interface. The key advantage of our method is high sensitivity, and the measurement is specific only to the changes at the metal-electrolyte interface. The ion accumulation in the EDL of a simple salt like NaCl is studied as a function of the frequency and the amplitude of the applied potential on the metal electrode. The amplitude of modulation of the ions is linearly proportional to the amplitude of the applied AC potential. The linearity is observed up to high amplitude (up to 2V) and salt concentration as high as 0.5M. Furthermore, the local segmental dynamics of polyelectrolytes such as polystyrene sulfonate have been measured. Next we extend this novel technique to study electrochemical redox reactions. The oxidation of the widely used redox ion [Fe(CN)6]4- is followed by measuring the response to an AC potential (amplitude ~100mV) as a function of a superimposed saw-tooth potential ramp, at a time period 106 fold slower and amplitude 5-10 fold larger than the AC potential. The sensitivity of the optical method is significantly better than the measurement of the AC current. For a redox process on the electrode, the change in the optical signal is over two orders of magnitude larger than the electrical signal. Using the optical technique, we can separate the kinetic events in redox processes: transport of charged species to the electrode surface and charge transfer across the electrode-electrolyte interface. Because we measure the local electrochemical process, the method can be used to probe redox reaction at multiple spots on the same electrode (i.e., combinatorial electrochemistry). / Ph. D.

The photothermal effect is a way in which chemical contrast can be measured as an optical pathlength or phase change. When a chemical species in a sample absorbs optical energy at a particular wavelength, this absorption raises the temperature at these points in the sample via the photothermal effect. This temperature change changes the local refractive index in the sample. Quantitative phase imaging is an interferometric technique for measuring the optical pathlength of sample features. Quantitative phase imaging is capable of detecting the photothermally-induced refractive index change, and is thus a powerful method for performing photothermal imaging. In this work, a thermal wave model is derived from Fourier's law of conduction in conjunction with a medium's heat capacity to derive the diffusion of temperature in a medium. This diffusion theory is transformed to a thermal wave model by applying a temporally modulated thermal source. Analytical expressions for the temperature field surrounding such a modulated thermal source are derived in multiple dimensions. The thermal wave equation is also simulated using a custom finite difference numerical method, and the simulated results are compared to the theoretical expressions with good agreement. The experimental apparatus for inducing such a thermal point source in a medium of water is described using the quantitative phase imaging system of spectral modulation interferometry. The spectral modulation interferometry system is aligned with a visible light pumping laser in two configurations for point source measurement and cell imaging. Label-free chemical imaging is then performed by pumping a field of cellular samples with wide-field illumination, and the resulting photothermal signal is detected by temporal analysis of the optical pathlength changes, generating the two-dimensional photothermal image. The measured photothermal cell image is qualitatively compared to predicted photothermal image based on the application of the thermal wave model in the spatial frequency domain. The chemical specificity of this technique is also verified by simultaneously pumping absorbing and non-absorbing biological cells in the same field-of-view. / Generating image contrast is a fundamental challenge in optical microscopy. Samples of interest in optical microscopy typically do not have visible absorption contrast without modification. A method of contrast that could provide information about a sample's absorption at different optical wavelengths would be useful for characterizing a sample's chemical content. The photothermal effect is an effect in which the small absorption of light by microscopic samples can be detected as a temperature change. With quantitative phase imaging, this temperature change can be measured by detecting the change in optical density of a sample due to its increase in temperature. Thus, quantitative phase imaging can be used to detect the small absorption of light by microscopic samples and generate two-dimensional images with chemical contrast. This work describes the theory of how thermal energy produced by optical absorption diffuses through a sample immersed in water. A thermal wave model is derived theoretically and compared to a custom simulation of the thermal wave physics with strong agreement. This thermal theory is verified with the quantitative phase imaging system used in this work to characterize the photothermal imaging technique. The photothermal imaging method is then applied to cellular samples, which are pumped with green light. The photothermal image is then generated and compared qualitatively to the image predicted by the thermal theory. The chemical imaging ability of the technique is then demonstrated by simultaneous imaging of absorbing and non-absorbing cells.

A new hybrid method combining moire interferometry, high resolution data-reduction technique, two-dimensional datasmoothing method, and Finite Element Method (FEM) has been successfully developed. This hybrid method has been applied to residual strain analyses of composite panels, strain concentrations around optical fibers embedded in composites, and cruciform composite shear test. This hybrid method allows moire data to be collected with higher precision and accuracy by digitizing overexposed moire patterns (U & V fields) with appropriate carrier fringes. The resolution of the data is ± 20 nm. The data extracted from the moire patterns are interfaced to an FEM package through an automatic mesh generator. This mesh generator produces a nonuniform FEM mesh by connecting the digitized data points into triangles. The mesh, which uses digitized displacement data as boundary conditions, is then fed to and processed by a commercial FEM package. Due to the natural scatter of the displacement data digitized from moire patterns, the accuracy of strain values is significantly affected. A modified finite-element model with linear spring elements is introduced so data-smoothing can be done easily in two dimensional space. The results of the data smoothing are controlled by limiting the stretch of those springs to be less than the resolution of the experimental method. With the full-field hybrid method, the strain contours from moire interferometry can be easily obtained with good accuracy. If the properties of the material are known, the stress patterns can also be obtained. In addition, this method can be used to analyze any two-dimensional displacement data, including the grid method and holography. / Ph. D.

Interferometry in geosciences uses mathematical techniques to image subsurface properties. This method turns a receiver in to a virtual source through utilizing either random noises or engineered sources. The method in seismology has been discussed extensively. Electromagnetic interferometry at high frequencies with coupled electromagnetic fields was developed in the past. However, the problem was not addressed for diffusive electromagnetic fields where the quasi-static limit holds. One of the objectives of this dissertation was to theoretically derive the impulse response of the Earth for low-frequency electromagnetic fields. Applying the theory of interferometry in the regions where the wavefields are diffusive requires volumetrically distributed sources in an infinite domain. That precondition imposed by the theory is not practical in experiments. Hence, the aim of this study was to quantify the important areas and distribution of sources that makes it possible to apply the theory in practice through conducting numerical experiments. Results of the numerical analysis in double half-space models revealed that for surface-based exploration scenarios sources are required to reside in a region with higher diffusivity. In contrast, when the receivers straddle an interface, as in borehole experiments, there is no universal rule for which region is more important; it depends on the frequency, receiver separation and also diffusivity contrast between the layers and varies  for different scenarios. Time-series analysis of the sources confirmed previous findings that the accuracy of the Green\'s function retrieval is a function of both source density and its width. Extending previous works in homogenous media into inhomogeneous models, it was found that sources must be distributed asymmetrically in the system, and extend deeper into the high diffusivity region in comparison to the low diffusivity area. The findings were applied in a three-layered example with a reservoir layer between two impermeable layers. Bayesian statistical inversion of the data obtained by interferometry was then used to estimate the fluid diffusivity (and permeability) along with associated uncertainties. The inversion results determined the estimated model parameters in the form of probability distributions. The output demonstrated that the algorithm converges closely to the true model. / Ph. D.

Virtual source gathers were generated using the principles of seismic interferometry from 135 hours of ambient noise recorded during a controlled-source survey across the Salton Sea Geothermal Field in southern California. The non-uniform nature of the noise sources violated a primary assumption of the method and generated artifacts in the data. The artifacts generated by the high-energy impulsive sources (e.g. earthquakes, shots) were removable using traditional methods of amplitude normalization prior to cross-correlation. The continuous source artifacts generated by the geothermal wells and highways required an unconventional approach of utilizing only normalized impulsive sources to successfully reduce the artifacts. Virtual source gathers were produced successfully that contained strong surface waves at 0.4-2.5 Hz, an order of magnitude below the corner frequency of the geophones, and modest body waves at 22-30 Hz, which are generally more difficult to obtain due to the need for many large, well-distributed subsurface sources. The virtual source gathers compare well to nearby explosive shots and are more densely spaced, but have a much lower signal-to-noise ratio. Analysis of the surface waves was complicated by strong higher-order modes. Spectral analysis of virtual source gathers required utilization of the geothermal plant energy, which produced usable signal at offsets required for mode separation. The virtual source dispersion curve compared well to a dispersion curve from a nearby explosive shot. P-waves were observed on the virtual source gathers. Creation of a low-quality multichannel reflection stack revealed two weak reflectors in the upper 2 km. / Master of Science

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