The range dependence of normal incidence acoustic backscatter from a rough surface

A theoretical expression for the normal incidence, high‐frequency, backscattering coefficient as a function of range from an isotropic rough surface which has both a Gaussian height distribution and a Gaussian autocorrelation function is presented and its correctness substantiated with a series of experimental measurements. Ideally the backscattering coefficient of a rough surface should be dependent only on properties of the surface. For the usual definition of backscattering coefficient this is shown to be true in the farfield of the surface scattering patch. In the nearfield of the surface, the backscattering coefficient is shown to be independent of all statistical properties of the surface and dependent only on its reflection coefficient. In a range interval between the nearfield and farfield, the backscattering coefficient is shown to depend on both the surface statistics and the measurement geometry.