Using the frequency-difference autoproduct to regain coherence in rough surface scattering

Abstract

Incident and reflected acoustic waves, with wavenumber k, are coherent in an ideal Lloyd’s mirror environment. However, a random rough surface, characterized by its rms roughness height h, reduces this coherence as kh increases. This presentation describes the ability of the frequency-difference autoproduct to recover reflected-field coherence, albeit at a lower frequency, even in the presence of high kh values. The frequency-difference autoproduct is a quadratic product of complex field amplitudes at different frequencies within the signal bandwidth. Prior work has shown that the frequency-difference autoproduct can mimic a below-band field at the difference frequency. Thus, by choosing a sufficiently-low difference frequency, the apparent surface roughness can be reduced so that a rough-surface scattered field resembles a flat-surface reflected one. For the theory and simulation results presented here, the surface roughness is Gaussian distributed and isotropic, and the Kirchhoff (tangent plane) approximation is used to determine the reflected sound. For 1 < kh < 6, theoretical and numerically simulated autoproducts in a rough-surface environment are compared to acoustic fields at the difference frequency in an ideal Lloyd’s mirror environment. Accompanying experimental results may be provided as well, if available. [Work supported by ONR.]