An overall goal of this research has been to enhance our understanding of the scientific principles necessary to develop advanced ultrasonic nondestructive techniques for the quantitative characterization of advanced composite structures. To this end, we have investigated a thin woven composite (5-harness biaxial weave). We have studied the effects that variations of the physical parameters of the experimental setup can have on the ultrasonic determination of the material properties for this thin composite. In particular, we have considered the variation of the nominal center frequency and the f-number of the transmitting transducer which in turn address issues such as focusing and beam spread of ultrasonic fields. This study has employed a planar, two-dimensional, receiving pseudo-array that has permitted investigation of the diffraction patterns of ultrasonic fields. Distortion of the ultrasonic field due to the spatial anisotropy of the thin composite has prompted investigation of the phenomenon of phase cancellation at the face of a finite-aperture, piezoelectric receiver. We have performed phase-sensitive and phase-insensitive analyses to provide a measure of the amount of phase cancellation at the face of a finite-aperture, piezoelectric receiver. The pursuit of robust measurements of received energy (i.e., those not susceptible to phase cancellation at the face of a finite-aperture, piezoelectric receiver) supports the development of robust techniques to determine material properties from measure ultrasonic parameters.