Angular spectrum based formulation of rough surface scattering with applications to surface characterization

The roughness of material surfaces may be characterized ultrasonically by insonification with an acoustic field whose wavelengths represent a significant fraction of the roughness height. Hence, the scattering behavior of such surfaces is primarily determined by the surface roughness. A classical approach for modeling the scattered field is based on the Kirchhoff approximation. An alternative formulation, using the angular spectrum representation of field quantities, is developed and evaluated in this work. The motivation is partly to develop a computationally efficient modeling tool for rough surfaces which is also able to incorporate the diffraction effects of rough surfaces of finite size, and partly to produce numerical modeling results that can identify measurement strategies suitable for rough surface characterization. Simulation results are presented in terms of surface roughness parameters and acoustic parameters. Comparisons are made between scattering behavior determined with the angular spectrum and with the Kirchhoff approximation. Experimental results are presented for comparison.