This paper is concerned with the analysis of acoustic wave fields encountered in phase-sensitive acoustic microscopy (PSAM) applied to elastically anisotropic solids. We show that the fast Fourier transform technique provides a computationally efficient method of calculating two-dimensional amplitude and phase images of these fields. More importantly, we demonstrate how this technique, applied to complex wave field data, can be used to treat inverse problems such as source reconstruction, image quality assessment, and the determination of elastic constants. Monochromatic and also more general time-dependent excitations, such as tone bursts and short pulses, are treated, and the resulting wave fields described. The evolution of these wave fields with increasing frequency is discussed, and emerging infinite frequency features, such as the ray surface and phonon focusing caustics, are identified. A number of numerical simulations are presented that are in good agreement with measured data from the literature. As an illustration of elastic constant determination, we use the point spread function determination based on our PSAM measurements on the longitudinal mode in silicon to determine the elastic constant ${C}_{11}$ of Si.