| This dissertation is the product of experiments designed to utilize the phase-sensitive characteristics of ultrasonic piezoelectric transducers to study and characterize the effects magnitude and phase aberrating media have on the propagation of ultrasonic waves. Two specific measurement artifacts were addressed resulting from propagation through magnitude and phase distorting paths: the spatial overlap and therefore interference of two or more ultrasonic waves and phase cancellation occurring at the surface of a phase sensitive receiver.;The study of magnitude and phase distorting media naturally lends itself to Kramers-Kronig analysis. The ultrasonic Kramers-Kronig relations couple the frequency dependent ultrasonic attenuation coefficient and the phase velocity through the fundamental notions of causality, linearity, and finite energy. Experiments demonstrated that even in the presence of phase cancellation artifacts, measurements of apparent attenuation and apparent phase velocity appear to remain causally consistent. A number of forms of the Kramers-Kronig relations found in the acoustics literature are derived, clarified, and related in this dissertation, and are applied to specific data sets to illustrate the utility and the limitations of the individual forms.;Measurements of the attenuation coefficient of cancellous bone have been shown to correlate well with bone mineral density, and ultimately with osteoporotic fracture risk. However, in the context of the Kramers-Kronig relations, published data reporting the attenuation coefficient of cancellous bone do not appear to be causally consistent with the measured dispersion. The cause of this disagreement might, in part, be due to the detection of multiple waves. In this dissertation it was experimentally shown, using a simple phantom capable of supporting multiple waves, that the effects of phase cancellation might be a potential source of the anomalous dispersion observed in studies of cancellous bone.;Artifacts due to phase cancellation at the surface of a phase sensitive receiver can be avoided if one is able to collect data phase insensitively. However, artifacts due to interference in the ultrasonic field can plague both phase sensitive and phase insensitive measurements systems. It was demonstrated that the largest possible phase insensitive receiving transducer should be implemented in order to supress the effects of interference on experimental data. |
