Phase estimation methods and their application to holographic interferometry

Phase of the interference fringe pattern is known to convey important information in optical metrology. Typically, phase measurement using temporal techniques involves incorporating a piezoelectric device (PZT) in one arm of the interferometer for shifting the relative phase between the two interference beams. Although the precision in the measurement of phase achieved by this technique is one hundredth of the wavelength, the error arising due to the phase shifter itself is one of the potential bottlenecks in the successful measurement of the parameter of interest. The measurement process is also very sensitive to other systematic and random sources of errors that we may encounter during the experiment. To address these concerns, several algorithms have been proposed, but they have met with limited success as they allow only a limited number of error sources influencing the measurements to be minimized. The problem is exacerbated further when it comes to accommodating multiple PZTs in an optical configuration, such as, in holographic moiré. Incorporation of two PZTs is essential for the simultaneous estimation of multiple phase information in holographic moiré, such as, those corresponding to out-of-plane and in-plane displacement components. Recent introduction of high resolution methods in holographic moiré for the estimation of multiple phase information has been found to exhibit constraints while operating outside the linear region of the response of the piezoelectric device to the applied voltage. This research thesis thus addresses a significant issue of measuring phase efficiently in the presence of nonlinear response of the PZT to the applied voltage and at the same time contributes to compensating several other systematic sources of errors. For this we have designed methods based on signal processing approaches which have reputation of robust performers in the presence of random noise. The thesis presents simulation and experimental verification of the proposed methods to show their feasibility in practical situations. To the best of our knowledge, this is one of the first times that an attempt has been made to provide a robust signal processing approach for the estimation of multiple phase information in a topic of extreme significance such as that of optical metrology.


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