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The reconstruction of a phase surface from the observed principal values is required for a number of applications, including synthetic aperture radar (SAR) and magnetic resonance imaging (MRI). However, the process of reconstruction, called

The reconstruction of a phase surface from the observed principal values is required for a number of applications, including synthetic aperture radar (SAR) and magnetic resonance imaging (MRI). However, the process of reconstruction, called

Noise, vibration and harshness (NVH)levels in the luxury automotive industry are used by customers as a subjective method of determining the vehicle quality. This can be achieved by adjusting the vehicle design, where simulations are used to predict the NVH behaviour. Changes can be expensive and time consuming when made after the design stage has been completed, so it is important to produce accurate simulations of the product. Variability exists to some extent in all products, even those just off the production line, however, if a high level of variability exists then only a small portion of products will meet the predicted behaviour. The aim of the project is to provide information that may lead to the reduction of variability in an automotive vehicle. This is achieved by quantifying the statistical spread of FRFs (frequency response function) in a set of nominally identical vehicles. Once overall levels have been calculated, the location of the most variable sources can be identified. Project also seeks to develop new methods of analysis for the system phase response to determine whether further information may be extracted compared to the magnitude response. There are three main themes that run throughout this thesis, with the first being the quantification of variability due to the measurement taking process which is covered in chapter 3. A novel application of a method to separate the measurement variability from the overall system uncertainty was achieved as well as the quantification of the vehicle to- vehicle variability. The second theme that runs through the study concerns the identification of variability sources. This is realised in chapter 4 and chapter 6 as a set of structural and acoustic tests on a luxury sedan door. The trim was found to be held to the door panel by a series of 11 polymer clips and 4 metal screws. The variability of small changes to a significant boundary condition at the door trim was quantified, showing that the removal of rigid clips had a more significant effect on the overall variability that if a loose clip has been removed. It was also found that clips at the corners were the most sensitive to change. The final theme outlines and tests new analysis methods on the phase and compares the statistical spread of the phase with the equivalent spread of the magnitude. Data taken from the same tests was used and for most of the cases the two results were found to be approximately the same.

Time series analysis of Synthetic Aperture Radar Interferometry (InSAR) data has become an important scientific tool for monitoring and measuring the displacement of Earth’s surface due to a wide range of phenomena, including earthquakes, volcanoes,landslides, changes in ground water levels, and wetlands. Time series analysis is a product of interferometric phase measurements, which become ambiguous when the observed motion is larger than half of the radar wavelength. Thus, phase observations must first be unwrapped in order to obtain physically meaningful results. Persistent Scatterer Interferometry (PSI), Stanford Method for Persistent Scatterers (StaMPS), Short Baselines Interferometry (SBAS) and Small Temporal Baseline Subset (STBAS)algorithms solve for this ambiguity using a series of spatio-temporal unwrapping algorithms and filters. In this dissertation, I improve upon current phase unwrapping algorithms, and apply the PSI method to study subsidence in Mexico City. PSI was used to obtain unwrapped deformation rates in Mexico City (Chapter 3),where ground water withdrawal in excess of natural recharge causes subsurface, clay-rich sediments to compact. This study is based on 23 satellite SAR scenes acquired between January 2004 and July 2006. Time series analysis of the data reveals a maximum line-of-sight subsidence rate of 300mm/yr at a high enough resolution that individual subsidence rates for large buildings can be determined. Differential motion and related structural damage along an elevated metro rail was evident from the results. Comparison of PSI subsidence rates with data from permanent GPS stations indicate root mean square(RMS) agreement of 6.9 mm/yr, about the level expected based on joint data uncertainty.The Mexico City results suggest negligible recharge, implying continuing degradation and loss of the aquifer in the third largest metropolitan area in the world. Chapters 4 and 5 illustrate the link between time series analysis and three-dimensional (3-D) phase unwrapping. Chapter 4 focuses on the unwrapping path.Unwrapping algorithms can be divided into two groups, path-dependent and path-independent algorithms. Path-dependent algorithms use local unwrapping functions applied pixel-by-pixel to the dataset. In contrast, path-independent algorithms use global optimization methods such as least squares, and return a unique solution. However, when aliasing and noise are present, path-independent algorithms can underestimate the signal in some areas due to global fitting criteria. Path-dependent algorithms do not underestimate the signal, but, as the name implies, the unwrapping path can affect the result. Comparison between existing path algorithms and a newly developed algorithm based on Fisher information theory was conducted. Results indicate that Fisher information theory does indeed produce lower misfit results for most tested cases. Chapter 5 presents a new time series analysis method based on 3-D unwrapping of SAR data using extended Kalman filters. Existing methods for time series generation using InSAR data employ special filters to combine two-dimensional (2-D) spatial unwrapping with one-dimensional (1-D) temporal unwrapping results. The new method,however, combines observations in azimuth, range and time for repeat pass interferometry. Due to the pixel-by-pixel characteristic of the filter, the unwrapping path is selected based on a quality map. This unwrapping algorithm is the first application of extended Kalman filters to the 3-D unwrapping problem. Time series analyses of InSAR data are used in a variety of applications with different characteristics. Consequently, it is difficult to develop a single algorithm that can provide optimal results in all cases, given that different algorithms possess a unique set of strengths and weaknesses. Nonetheless, filter-based unwrapping algorithms such as the one presented in this dissertation have the capability of joining multiple observations into a uniform solution, which is becoming an important feature with continuously growing datasets.

Three-dimensional reconstruction of small objects has been one of the most challenging problems over the last decade. Computer graphics researchers and photography professionals have been working on improving 3D reconstruction algorithms to fit the high demands of various real life applications. In this thesis, we implemented a 3D scanner system based on fringe projection method. Two different methods have been implemented and used as the unwrapping solution in fringe projection method. A parameterization tool has been created in order to generate different fringe patterns for distinctive needs in the fringe projection method. Considering our first practical implementation (based on phase shifting and multi wavelength techniques) the number of pictures used in phase shifting method has been decreased and the effects of reducing the fringe patterns on the level of precision of the 3D model have been investigated. Optical arrangement and calibration of the system (fringe projection method) have been studied, and numerous suggestions have been proposed to improve the precision of the system. Also, an evaluation method has been implemented based on calibration techniques. The error rate on both surface and height of the 3D model compare with the object has been calculated.

Modern optical measurement techniques have  developed rapidly in recent years. One of the  measurement technologies  is polarization interferometry that can be used  for roughness evaluation, deformation measurement,  and vibration analysis of objects. based on LabVIEW and MATLAB, this project  introduces the technique of virtual  instruments into the field of modern optical  measurements. The optical phase images  have been captured by LabVIEW and processed  by MATLAB to acquire the surface structures. The main research work in the project involves:  (1) Introduction of the virtual instrument  technique to capture and process optical phase  images; (2) Processing of phase  images acquired with different wavelengths using  MATLAB to reveal show the 2D and 3D  surface structures.

A method for measuring the thickness and surface profiles of soft contact lenses while submerged in a saline solution has been implemented utilizing a low coherence Twyman-Green Interferometer. Although the original measurements demonstrated that features on the contact lens surfaces could be accurately determined, it was believed that the layout of the system also induced surface profile distortions. A new opto-mechanical layout has been implemented which eliminates many of these low frequency distortions. Improvements to the original phase unwrapping algorithms have also been developed to overcome the low visibility output inherent to the measurement allowing for a more complete analysis of the two surfaces of a contact lens.

"3D shape measurements are critical in a range of fields, from manufacturing for quality measurements to art conservation for the everlasting archival of ancient sculptures. The most important factor is to gather quantitative 3D information from measurement devices. Currently, there are limitations of existing systems. Many of the techniques are contact methods, proving to be time consuming and invasive to materials. While non-contact methods provide opportunities, many of the current systems are limited in versatility. This project focuses on the development of a fringe projection based system for 3D shape measurements. The critical advantage of the fringe projection optical technique is the ability to provide full field-of-view (FOV) information on the order from several square millimeters to several square meters. In the past, limitations in speed and difficulties achieving sinusoidal projection patterns have restricted the development of this particular type of system and limited its potential applications. For this reason, direct coding techniques have been incorporated to the developed system that modulate the intensity of each pixel to form a sinusoidal pattern using a 624 nm wavelength MEMS based spatial light modulator. Recovered phase data containing shape information is obtained using varying algorithms that range from a single image FFT analysis to a sixteen image, phase stepping algorithm. Reconstruction of 3D information is achievable through several image unwrapping techniques. The first is a spatial unwrapping technique for high speed applications. Additionally, the system uses an optimized Temporal Phase Unwrapping (TPU) algorithm that utilizes varying fringe frequencies ranging from 4 to 512 pixels per fringe to recover shape information in the time domain. This algorithm was chosen based on its robustness and accuracy for high resolution applications [Burke et al., 2002]. Also, unwrapping errors are minimized by approximately 90% as the number of images used is increased from the minimum to maximum fringe density. Cxoontrary to other systems, the 3D shape measurement system developed in the CHSLT laboratories has unprecedented versatility to accommodate a variety of applications with the z-depth resolution of up to 25.4 µm (0.001 inches) and speeds close to 200 frames per second. Hardware systems are integrated into user-friendly software that has been customized for fringe projection. The system has been tested in two extreme environments. The first is for quantification of cracks and potholes in the surface of roads under dynamic conditions. The second application was digitization of an art sculpture under static conditions. The system shows promising results and the potential for high quality images via algorithm optimization. Most importantly, there is potential to present real time 3D information at video speeds."

The Ground-Based Synthetic Aperture Radar (GB-SAR) is a relatively new technique, which in the last ten years has gained interest as deformation measurement and monitoring tool. The GB-SAR technique is based on an imaging radar-based sensor, which o ers high sensitivity to small displacements, in the region of sub-millimetres to millimetres, long-range measurements, which can work up to some kilometres, and massive deformation measurement capability. These features confer to the GB-SAR technique interesting advantages with respect to other point-wise deformation measurement techniques. The process of estimating deformation from the GB-SAR data is not straightforward: it requires complex data processing and analysis tools. This dissertation is focused on these tools, covering the whole deformation estimation process. This thesis collects the main research results achieved on this topic during my work at the Active Remote Sensing Unit of the Institute of Geomatics. Two di erent approaches for measuring deformation with GB-SAR data are described and discussed. The irst one is the interferometric approach, based on the exploitation of the phase component of the GB-SAR data, which is the commonly used GB-SAR method. The second one is a non-interferometric approach, which exploits the amplitude component of the GB-SAR data, o ering an interesting alternative way to exploit the GB-SAR data. This dissertation has two main objectives. The first one is presenting, step by step, a complete interferometric GB-SAR procedure for deformation measuring and monitoring. The second one is presenting two new algorithms, which represent the most innovative part of this thesis. The first algorithm faces the phase unwrapping problem, providing an automatic solution for detecting and correcting unwrapping errors, which is called 2+1D phase unwrapping. The second algorithm is the base of the above mentioned non- interferometric approach, which overcomes some of the most critical limitation of GB-SAR interferometry, at the expense of getting less precise deformation estimates. The dissertation is divided in 6 chapters. The first one is the introduction, while the second one provides an overview of GB-SAR interferometry, introducing the main aspects that are the basics of the subsequent chapters. Chapter 3 describes a complete GB-SAR processing chain. Chapters 4 and 5 contain the most original part of the dissertation, i.e. the 2D+1 phase unwrapping algorithm, and the non-interferometric approach. Finally, in Chapter 6 the conclusions are discussed and further research is proposed. / El radar terrestre d’obertura sintètica (GB-SAR) és una tècnica relativament nova que, en els últims deu anys, ha guanyat interès com a eina per a mesurar i monitorar deformacions. La tècnica GB-SAR es basa en un sistema radar amb capacitat per proporcionar imatges, que ofereix una alta sensibilitat a petits desplaçaments, d’ordre mil·limètric o submil·limètric, que és capaç de mesurar a llargues distàncies (alguns km) i que té una alta capacitat per fer mesures massives. Aquestes característiques donen a la tècnica interessants avantatges respecte a altres tècniques clàssiques de mesura de deformacions, típicament basades en mesures puntuals. Derivar mesures de deformació a partir de dades GB-SAR no és un procés senzill, ja que requereix uns procediments complexos de processat i anàlisi de dades. Aquesta tesi es centra en aquests processos. Aquesta tesi recull alguns dels resultats més destacats de la investigació que he desenvolupat sobre aquest tema a la unitat de Teledetecció Activa de l'Institut de Geomàtica. Al llarg del document es descriuen dues aproximacions diferents per mesurar deformacions amb GB-SAR. Una es basa en la explotació de la tècnica de la interferometria, és a dir explotant la component de la fase de les imatges GB-SAR: és la tècnica GB-SAR usada habitualment. La segona, anomenada tècnica no-interferomètrica, es basa en la component de l’amplitud de les dades GB-SAR i ofereix una interessant alternativa a la primera. La tesi acompleix dos objectius principals. En primer lloc presenta un procediment complet per la mesura i monitoratge de deformacions mitjançant interferometria GB-SAR. En segon lloc, descriu dos nous algorismes que resolen problemes específics de la interferometria clàssica aplicada al GB-SAR i que representen la part més innovadora d’aquesta tesi. El primer algorisme aborda un dels problemes oberts de la interferometria, el phase unwrapping, proposant un mètode automàtic per detectar-ne i corregir-ne els errors. El segon algorisme proposa un nou mètode per a l'explotació de les dades GB-SAR per mesurar deformacions sense utilitzar la interferometria. La estructura de la tesi consisteix en sis capítols. Després de la introducció, el Capítol 2 proporciona una visió general de la interferometria GB-SAR, introduint els conceptes principals utilitzats en la tesi. En el tercer capítol es descriu una cadena de processament basada en GB-SAR interferomètric. Els capítols quart i cinquè contenen la part més original de la tesi: l'algorisme de phase unwrapping i el mètode no-interferomètric per la mesura de deformacions. Finalment, es discuteixen les conclusions principals i es proposen futures línies d’investigació.