Measurement of Object Displacement Using Phase Stepped, Real-Time Holographic Interferometry.

Phase stepped holographic interferometry is a noncontact method for measuring displacements over a large field of view with a precision of about 5 nm. The whole -field capabilities and high sensitivity of this method make it potentially unrivaled for measuring spatial inhomogeneities, for example, the proposed spatial variation of the piezoelectric coefficient in cortical bone. This dissertation has advanced the capabilities of this technique for the simultaneous, whole-field measurement of two or more components of displacement (1) by providing a detailed analysis of the effect of random and systematic errors on a displacement or strain measurement; (2) by demonstrating that the Carre algorithm, with phase step angles in multiples of pi/4, provides a least squares solution to an over-determined set of phase stepped intensity measurements, minimizes the affect of random and systematic intensity and phase errors and therefore is the best choice for a phase step algorithm; (3) by offering a new method for compensating for spurious systematic drift; (4) by applying of the former method to allow temporal averaging of repeatedly acquired data sets thereby increasing signal-to-noise while maintaining full spatial resolution; (5) by developing a new test procedure for calibrating the apparatus based on displacement of a poled ceramic due to the converse piezoelectric effect and (6) by introducing a two-camera method for measuring two or more components of displacement and strain simultaneously and verifying the methodology for two dimensional displacements of a piezoelectric ceramic. The evidence indicates that this method, which can employ stereo viewing with either two or three cameras, is a promising approach for the simultaneous measurement of two or more components of displacement. The method was also applied to the measurement of displacement in two old samples of dry bovine tibia, held as cantilever beams and subjected to potentials up to 900 V, however, consistent results were not found. The null results indicate either: (1) the samples were no longer piezoelectrically active; (2) the proposed model, which stipulates that the piezoelectric coefficients vary across the bone, is incorrect and/or (3) the appropriate piezoelectric constant is less than 0.001 pm/V.