The Phase Gradient Autofocus (PGA) algorithm is widely used in spotlight mode SAR for motion compensation. The Maximum Likelihood PGA (ML PGA) algorithm has been shown to be a superior autofocus method. The PGA is restricted to high altitude aircraft. Since lower altitude SARs have significant range dependencies that cannot be ignored, the PGA could not be used. This thesis eliminates the high altitude restriction and extends the PGA for use with all spotlight SARs. The new algorithm is tested with three images. Each image has a unique quality. A desert image provides a low signal to clutter ratio with no distinct targets and the mountain image has areas with high signal-to-clutter and areas with low signal-to-clutter. Each image was corrupted with a low frequency and high frequency motion induced low altitude phase error. The new Phase Weighted Estimation (PWE) low altitude autofocus method converged to a lower standard deviation than the ML PGA, but required more iterations. Another limitation of the PGA is that it will only work for spotlight SAR. In this thesis, the spotlight PGA is extended to stripmap by using a conversion similar to spotlight mode. With the space frequency relationship an altered PGA is used to extend the PGA to stripmap mode SAR. The stripmap SAR, range dependant PGA allows for focusing of low altitude low cost stripmap SARs. The phase weighted estimation method is extended to range dependent stripmap. The stripmap mode estimator is most successful with high signal-to-noise images.

The method development process in liquid chromatography (LC) involves optimization of a variety of method parameters including stationary phase chemistry, column temperature, initial and final mobile phase compositions, and gradient time when gradient mobile phases are used. Here, a general simulation program to predict the results (i.e., retention time, peak width and peak shape) of LC separations, with the ability to study various complex chromatographic conditions is described. The simulation program is based on the Craig distribution model where the column is divided into discrete distance (Δz) and time (Δt) segments in a grid and is based on parameterization with either the linear solvent strength or Neue-Kuss models for chromatographic retention. This algorithm is relatively simple to understand and produces results that agree well with closed form theory when available. The set of simulation programs allows for the use of any eluent composition profile (linear and nonlinear), any column temperature, any stationary phase composition (constant or non-constant), and any composition and shape of the injected sample profile. The latter addition to our program is particularly useful in characterizing the solvent mismatch effect in comprehensive two-dimensional liquid chromatography (2D-LC), in which there is a mismatch between the first dimension (1D) effluent and second dimension (2D) initial mobile phase composition. This solvent mismatch causes peak distortion and broadening. The use of simulations can provide a better understanding of this phenomenon and a guide for the method development for 2D-LC. Another development that is proposed to have a great impact on the enhancement of 2D-LC methods is the use of continuous stationary phase gradients. When using rapid mobile phase gradients in the second dimension separation with diode array detection (DAD), refractive index changes cause large backgrounds such as an injection ridge (from solvent mismatch) and sloping baselines which can be problematic for achieving accurate quantitation. Use of a stationary phase gradient may enable the use of an isocratic mobile phase in the 2D, thus minimizing these background signals. Finally, our simulator can be used as an educational tool. Unlike commercially available simulators, our program can capture the evolution of the chromatogram in the form of movies and/or snapshots of the analyte distribution over time and/or distance to facilitate a better understanding of the separation process under complicated circumstances. We plan to make this simulation program publically available to all chromatographers and educators to aid in more efficient method development and chromatographic training.

Coherence, which gives the similarity of signals received at two microphone locations, can be a powerful tool for calculating acoustic quantities, particularly active acoustic intensity. To calculate active acoustic intensity, a multi-microphone probe is often used, and therefore coherence between all microphone pairs on the probe can be obtained. The phase and amplitude gradient estimator (PAGE) method can be used to calculate intensity, and is well suited for many situations. There are limitations to this method—such as multiple sources or contaminating noise in the sound field—which can cause significant error. When there are multiple sources or contaminating noise present, the coherence between microphone pairs will be reduced. A coherence-based approach to the PAGE method, called the CPAGE method, is advantageous.Coherence is useful in phase unwrapping. For the PAGE method to be used at frequencies where the probe microphone spacing is larger than half a wavelength (above the spatial Nyquist frequency), the phase of transfer functions between microphone pairs must be unwrapped. Phase differences are limited to a 2π radian interval, so unwrapping—adding integer multiples of 2π radians to create a continuous phase relation across frequency—is necessary to allow computation of phase gradients. Using coherence in phase unwrapping can improve phase gradient calculation, which in turn leads to improved intensity calculation.Because phase unwrapping is necessary above the spatial Nyquist frequency, the PAGE method is best suited to dealing with broadband signals. For narrowband signals, which lack coherent phase information at many frequencies, the PAGE method can give erroneous intensity results. One way to improve calculation is with low-level additive broadband noise, which provides coherent phase information that can improve phase unwrapping, and thereby improve intensity calculation. There are limitations to this approach, as additive noise can have a negative impact on intensity calculation with the PAGE method. The CPAGE method, fortunately, can account for contaminating noise in some situations. A magnitude adjustment—which arises naturally from investigation of the bias errors of the PAGE method—can account for the additional pressure amplitude caused by the contaminating noise, improving pressure magnitude calculations. A phase gradient adjustment—using a coherence-weighted least squares algorithm—can likewise improve phase gradient calculations. Both adjustments depend upon probe microphone coherence values. Though not immune to contaminating noise, this method can better account for contaminating noise. Further experimental work can verify the effectiveness of the CPAGE method.

Structural health monitoring (SHM) of aerospace components is a rapidly emerging field due in part to commercial and military transport vehicles remaining in operation beyond their designed life cycles. Damage detection strategies are sought that provide real-time information of the structure's integrity. One approach that has shown promise to accurately identify and quantify structural defects is based on guided ultrasonic wave (GUW) inspections, where low amplitude attenuation properties allow for long range and large specimen evaluation. One drawback to GUWs is that they exhibit a complex multi-modal response, such that each frequency corresponds to at least two excited modes, and thus intelligent signal processing is required for even the simplest of structures. In addition, GUWs are dispersive, whereby the wave velocity is a function of frequency, and the shape of the wave packet changes over the spatial domain, requiring sophisticated detection algorithms. Moreover, existing damage quantification measures are typically formulated as a comparison of the damaged to undamaged response, which has proven to be highly sensitive to changes in environment, and therefore often unreliable. As a response to these challenges inherent to GUW inspections, this research develops techniques to locate and estimate the severity of the damage. Specifically, a phase gradient based localization algorithm is introduced to identify the defect position independent of excitation frequency and damage size. Mode separation through the filtering technique is central in isolating and extracting single mode components, such as reflected, converted, and transmitted modes that may arise from the incident wave impacting a damage. Spatially-integrated single and multiple component mode coefficients are also formulated with the intent to better characterize wave reflections and conversions and to increase the signal to noise ratios. The techniques are applied to damaged isotropic finite element plate models and experimental data obtained from Scanning Laser Doppler Vibrometry tests. Numerical and experimental parametric studies are conducted, and the current strengths and weaknesses of the proposed approaches are discussed. In particular, limitations to the damage profiling characterization are shown for low ultrasonic frequency regimes, whereas the multiple component mode conversion coefficients provide excellent noise mitigation. Multiple component estimation relies on an experimental technique developed for the estimation of Lamb wave polarization using a 1D Laser Vibrometer. Lastly, suggestions are made to apply the techniques to more structurally complex geometries.