A two-dimensional imaging theory of surface discontinuities with the scanning acoustic microscope

Abstract

This paper discusses theoretical aspects of the V(z) response of the scanning acoustic microscope (s. a. m.) when used to examine specimens with lateral discontinuities. The problem is introduced in terms of a simple ray model to establish a physical picture of the processes involved. An approximate Green function is then developed which enables use of a modified form of the Fourier optical formulations to calculate V(z) for a cylindrical lens. These calculations explain two different types of contrast observed when imaging specimens in the reflection s. a. m., such as (i) the ability to image fine discontinuities and display them with enhanced contrast and an apparent width determined by the acoustic wavelength; and (ii) to give a quantitative account of the amplitude of periodic ripple often observed running parallel to cracks on acoustic micrographs. Both these types of contrast may be predicted by using the same model and arise naturally from variation of the reflection and transmission properties of the discontinuity, the relative value of these parameters determines which type of contrast predominates. At an interface between media with different elastic properties, the contrast is affected not only by the scattering properties of the boundary but also by the very fact that surface waves must propagate in media with different elastic properties. This effect alone can provide a powerful contrast mechanism which enables one to understand the light to dark contrast reversals often observed at grain boundaries in polycrystalline specimens at different values of defocus.