Angular spectrum-based statistical formulation of ultrasound scattering by rough surfaces

The determination of the field which is scattered from a rough interface is an area of considerable interest in both ultrasonics and optics. The effects of surface roughness can be dominant in the total scattered field and thus it is important to quantify these effects for the deterministically or statistically described surface. Applications of the scattering from rough surfaces include nondestructive evaluation of surface quality, characterization of surface irregularities such as cracks and flaws, and sample differentiation based on surface properties.;It has been the goal of this research to develop an accurate modeling tool for predicting the scattered field from a deterministic or stochastic surface. A classical approach for determining scattering effects is Kirchhoff theory. An alternative approach, using the angular spectrum representation of field quantities, is compared with classical Kirchhoff theory for accuracy, validity, and computational efficiency considerations. The Kirchhoff and angular spectrum representations of the field scattered from a deterministic irregular surface form the foundation for this research. Simulations using both of these representations of the field scattered from deterministic surfaces of one- and two-dimensional roughness were completed to evaluate the effects of surface descriptors including the correlation function, correlation length, surface height distribution, and the RMS surface height. Both Kirchhoff and angular spectrum theories have been extended to predict the magnitude of the field which is scattered from a one- or two-dimensional stochastic surface. These statistical field estimates are based on specified rough surface statistics.;The scattered field magnitude provides insight into the nature of the rough surface statistics, but the phase of the scattered field is of at least equal importance when differentiating surface characteristics using a pulse echo system. The distribution of the scattered phase has been characterized for surfaces of increasing surface roughness.;An experimental verification of the theoretical formulations developed in this research is possible using a linear FM scheme for measuring the received signal amplitude versus frequency and incident angle from arbitrary surfaces. Experimental results are compared with the numerical modeling results.