In phase shift interferometry (PSI), several factors affect measurement accuracy, such as piezoelectric transducer (PZT) calibration (i.e. PZT slope error) and PZT nonlinearity, vibration, spurious reflection, source bandwidth, detector nonlinearity, and detector noise. The effects of these error sources on several algorithms to solve the phase of the wavefront are studied. When the simple arctangent formula is used, if the PZT slope is properly adjusted, the error due to the PZT quadratic nonlinearity can be tremendously reduced. An exact solution is derived to remove the error when the PZT quadratic nonlinearity is large. Although Carre's formula is insensitive to PZT slope, this formula is more sensitive to the detector nonlinearity than the simple arctangent formula. For most error sources, the error of the phase solved has a double-frequency characteristic. Thus, averaging two measured phases of two runs, which have a ninety degree phase shift related to each other, can effectively reduce the error. For a small vibration, the phase error has a very simple relation to the vibration amplitude, and a very complex relation to the vibration frequency. Although the error caused by vibration has this double-frequency characteristic, the averaging technique does not apply. The error caused by spurious reflection does not have such a characteristic. A new algorithm is proposed to eliminate the phase error caused by certain types of spurious reflection. When detector noise is concerned, the phase error is inversely proportional to the modulation of the intensity times the square root of the number of steps/buckets. For the shot noise, the phase error is inversely proportional to the fringe contrast times the square root of the total number of photons. In practice, the shot noise is very much smaller than the detector noise. In a practical environment, PZT calibration, vibration, and spurious reflection have much more prominent effects on the PSI than the source bandwidth, detector nonlinearity, and detector noise. When spurious reflection and vibration are under control, and the signal-to-noise ratio is about 20, the PSI has an accuracy of 2 degrees, i.e. 3.3nm at 633nm. Because vibration and detector noise are random error sources, the errors caused by them can be reduced by averaging many measurements. However, the error caused by the other discussed sources cannot be reduced by averaging many measurements.

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This thesis concerns the application of seismic interferometry to surface waves. Seismic interferometry is the process by which the wavefield between two recording locations is estimated, resulting in new recordings at one location as if a source had been placed at the other. Thus, in surface-wave interferometry, surface waves propagating between two receiver locations are estimated as if one receiver had recorded the response due to a source of surface-wave energy at the other receiver. In global and engineering seismology new surface-wave responses can allow for imaging of the subsurface, and in exploration seismology it has been proposed that these new surface-wave responses can allow for the prediction and removal of socalled ground-roll (surface waves that are treated as noise). This thesis presents a detailed analysis of surface-wave interferometry: using a combination of modelling studies, real-data studies, and theoretical analyses the processes involved in the application of interferometry to complex (both multi-mode and scattered) surface waves are revealed. These analyses identify why surface waves are often dominant in the application of interferometry, where errors may be introduced in the application of surface-wave interferometry, and how interferometry may be processed in such a way as to minimise those (and other) errors. This allows for the proposal of new data-processing strategies in the application of seismic interferometry to surface waves, potentially resulting in improved surface-wave estimates. Much of the work in this thesis focuses on the use of seismic interferometry to predict and subtract surface waves in land-seismic exploration surveys. Using insights from the presented analyses it is shown that seismic surface waves can be successfully predicted and removed from land-seismic data using an interferometric approach. However, the work in this thesis is not only limited to applications in exploration seismology. In addition to the ground-roll removal method, improved estimates of higher-mode and scattered surfaces waves may allow for more advanced imaging algorithms to be used in conjunction with seismic interferometry. Also, as a consequence of the analysis presented a Generalized Optical Theorem for Surface Waves is derived. This highlights a link between seismic interferometry and the optical theorem and may allow for further application of optical theorems in seismology.

Orientador: Cláudio Kitano / Banca: Ricardo Tokio Higuti / Banca: Ronny Calixto Carbonari / Resumo: Interferômetros ópticos de saída única são muito sensíveis quando operam nas proximidades do ponto de quadratura de fase da sua curva característica de entrada e saída. Entretanto, as flutuações ambientais de baixa frequência produzem derivas aleatórias entre os caminhos ópticos do interferômetro que desviam o ponto quiescente da quadratura, levando ao fenômeno de desvanecimento de sinal. Através de processamento eletrônico de dois sinais interferométricos de saída, defasados a 90º entre si, consegue-se demodular o sinal independentemente das derivas ambientais. Esses interferômetros chamados de interferômetros de quadratura são amplamente utilizados em laboratórios de metrologia, porém, devido à grande quantidade de componentes ópticos normalmente envolvidos, são de difícil alinhamento e de elevado custo. Neste trabalho estuda-se a interferometria homódina de dois feixes em quadratura e as suas complexidades inerentes. Propõe-se uma nova arquitetura, baseada na configuração de Michelson, de alinhamento mais simples e de baixo custo. Descreve-se matematicamente o processo de obtenção dos sinais em quadratura deste arranjo. Também, se explora uma técnica capaz de obter dois sinais interferométricos em quadratura através da configuração tradicional de Michelson explorando-se a distribuição espacial do padrão de franjas. Desenvolve-se, ainda, um novo algoritmo de phase unwrapping aplicável como método de detecção de fase óptica, capaz de reconstruir a forma de onda de sinais de modulação e fornecer a diferença de fase estática entre os braços do interferômetro, quando o sinal de modulação possui valor médio nulo. Testes computacionais são realizados para corroborar na tarefa de evidenciar o potencial da técnica. Por meio do método de demodulação apresentado, em adição com o interferômetro proposto e da técnica explorada, realiza-se testes experimentais em um atuador piezoelétrico... / Abstract: Optical interferometers with single outputs are very sensitive when operating close to the phase quadrature point of their input-output characteristic curves. However, low frequency environmental fluctuations generate random drifts between the optical paths of the interferometer that deviate the quiescent point from the quadrature condition. This problem causes the phenomenon called signal fading. By electronically processing these two interferometry output signals, shifted by 90º, it is possible to demodulate the signal regardless of environmental drift. These kinds of interferometers, known as quadrature interferometers, are widely used in metrology laboratories, but, due to the large amount of optical components, they are expensive and difficult to design. In this work a low cost homodyne interferometer with two output quadrature beams based on the Michelson configuration is studied, and the procedure to achieve the quadrature signals is mathematically described. Also, a recent technique, not widely known in the literature and that is able to obtain two quadrature signals by using the standard configuration of the Michelson interferometer is explored, exploiting the spatial distribution of the fringe pattern. A new method for optical phase shift demodulation based on phase unwrapping is developed. This approach is able to recover not only the modulation signal waveform, but can also calculate the static phase shift between the interferometer arms when the modulation signal has an average value equal to zero. The method also has the ability to demodulate signals which vary arbitrarily in time. Computational test were done aiming to demonstrate the technique potential. By using this new optical phase shift demodulation method, combined with the proposed interferometer and exploiting the spatial distribution of the fringe pattern, a piezoelectric flextensional actuator is characterized. Displacement versus drive voltage and frequency ... / Mestre