On the image of a cylindrical inclusion in the scanning acoustic microscope

An analysis is made of the image produced in the scanning acoustic microscope with a cylindrical lens by a cylindrical inclusion in an elastic half-space. The theory is developed in the Rayleigh approximation in which the characteristic wavelengths in the solid are large relative to the diameter of the cylinder, and when scattered waves can be expressed by the leading terms in a multipole expansion concentrated on the axis of the cylinder. A formula is derived for the acoustic contrast when the inclusion is rigid (but movable) and in fully lubricated contact with the solid. The results are illustrated by consideration of an inclusion in aluminum with water as the coupling fluid. The contrast decreases rapidly when the depth of the inclusion within the solid exceeds the Rayleigh wavelength, in accordance with current views concerning the importance of these waves in subsurface imaging.