Enhancement Caused by Discontinuities

When a specimen includes an elastic discontinuity, such as an edge, a step, a crack, or a joint interface, an acoustic image of the elastically discontinuous and peripheral portions visualized by the SAM shows unique contrast such as fringes or black stripes when the lens is defocused toward the specimen. As a model shown in Fig. 12, this type of contrast appears as an interference effect of surface acoustic waves incident on and reflected from elastic discontinuities. Since the thickness of the film is about 100 nm, the same effect may not be remarkable at the operating frequency ranging from 0.6 to 1 GHz for the discontinuities. However, this technique is useful for enhancing existence of surface microcracks that conventional microscopes may not be able to visualize 

With use of a ray tracing technique, the directions of acoustic waves emitted from the lens onto the specimen having the discontinuity (i.e., vertical crack as f) through a coupling medium are shown in Fig. 13. 

The acoustic fields are expressed by uf or [7 (/ = 0, 1, 2, and 3), where uf is the spatial distribution and Uf is the frequency distribution, where numbers 0, 1, 2, and 3 represent the transducer plane, the back focal plane, the front focal plane, and the surface of the specimen, respectively. The superscripts indicate that the acoustic field travels in the direction from the acoustic lens to the specimen or from the specimen to the acoustic lens. 

The pupil function of the lens is again defined as follows  

In this case, the pupil function may be divided into the following two parts for analysis of its acoustic fields  

---