Effects of one-dimensional random rough surfaces on ultrasonic backscatter: Utility of phase-screen and Fresnel approximations

Abstract

The effects of one-dimensional randomly rough surface corrugations on the time-dependent backscatter predicted by a simple model of the interaction of ultrasound with the microstructure of a sample are studied. Changes in the wave field that are due to surface topography, were calculated and compared by three different schemes: (1) the boundary integral element (BIE) method, (2) the phase-screen approximation (PSA), and (3) the PSA combined with the Fresnel approximation (which, as we report, yields an analytic series solution). Although the second and third schemes are easy to implement and accurate in some important cases, they are uncontrolled approximations that do not systematically estimate the resulting errors. The BIE method provides increasingly precise answers for a given model (at the cost of increasingly large numerical calculations) and was used to estimate the range of validity for the approximate methods. It is shown that the time evolution of the backscattered signal is approximately the same for the PSA as for the BIE calculations, aside from an overall time-independent constant. It is also shown that the approximate constant of proportionality depends strongly on the frequency, the correlation length, and the rms height; it is much less affected by the radius or the focal length of the probe. The constant of proportionality is presented both graphically and as a semiempirical formula and can be used to estimate and correct the error of the simpler PSA calculation.