Feasibility study on characterization of non-Gaussian rough surface by ultrasonic reflection method with the Kirchhoff theory

Abstract

The fundamental study on the ultrasonic characterization of non-Gaussian rough surface of a material is carried out. In this study, a theoretical relationship among ultrasonic reflection coefficient at normal incidence, root mean square roughness Rq, and skewness Rsk (which is the measure of symmetrical level of a height distribution) has been derived. In the derivation, a Gaussian curve fitting to the non-Gaussian height distribution of a rough surface is effectively performed so that the Kirchhoff theory of wave scattering from a rough surface can be utilized. In order to verify the validity of the derived relationship, air-coupled ultrasonic pulse-echo measurements with normal incident configuration at center frequency of 0.35 MHz have been conducted to a series of sandpapers having various Rq and Rsk values. From the measured ultrasonic reflection coefficient of each sandpaper, the Rq values of the sandpapers have been estimated from the derived relationship with known values of skewness of the sandpapers and then compared to those measured by a mechanical stylus profiler. It is found that the Rq values estimated by the ultrasonic method and the stylus profiler almost agree with each other. Thus, the validity of the derived theoretical relationship is demonstrated.

Keywords

• air-coupled ultrasound
• roughness
• skewness
• non-gaussian surfaces
• johnson distribution