Acoustic signal-to-noise ratio for an inclusion beneath a randomly rough surface and in the presence of microstructure

The effects of surface roughness on the signal-to-noise ratio (SNR) for the phase-sensitive detection of an inclusion in a sample with microstructure is explored in a simple model. It is assumed that a phase-sensitive transducer is used in pulse-echo mode, that the sample is immersed in a water bath, and that the noise is dominated by scattering from the sample's microstructure. Since there is interest in roughness-induced changes in the SNR, calculations are reported of the normalized signal-to-noise ratio (NSNR), i.e., the SNR with the rough surface divided by the SNR with the smooth surface. The dependence of the NSNR on transducer parameters (radius and focal length), on surface parameters (root-mean-square height and autocorrelation length), and on material parameters (scattering strength, average crystalline size) is reported. In this paper, approximate analytic series solutions, previously obtained for the signal and the noise, are combined to estimate the NSNR as a function of the inclusion's depth beneath the surface. It is found that for unfocused transducers even moderately rough surfaces can substantially degrade the NSNR for the most typical case, a relatively large inclusion in a background of small microcrystallites. The calculations predict two other results that initially surprised us. First, surface roughness is predicted to increase the SNR for a relatively small strongly scattering inclusion in a sample with relatively large but weakly scattering microstructure. Second, moderate roughness is predicted to have little effect on the SNR for focused transducers at the focal depth. (C) 1997 Acoustical Society of America.