Rayleigh angle

There are two particular discontinuities in R(t) that are of great importance for materials in which Rayleigh waves are excited. The first occurs at t0 = 1 /n, because beyond that value Q(f) changes discontinuously to zero. The second is at fR = cos r/tt, because around the Rayleigh angle 6r there is a phase change of 2n in R 6), cf. Fig. 6.3(b)i, and hence in Q(t). The Fourier relationship gives oscillations in V u) of periodicity... 

There is a direct analogy with the fringe pattern that is seen in a Young s double slit experiment, in which the diffraction pattern from two slits produces periodic fringes whose spacing varies inversely with the separation of the slits. The oscillations can also be interpreted in terms of the distortions of the reflected wavefronts in Fig. 7.2 at the Rayleigh angle (Atalar 1979). 

Rayleigh angle as usual. The value of (7.45) has the form of a ratio of impedances multiplied by a ratio of velocities, and it provides a means of relating Rayleigh wave attenuation (due to radiation into the fluid) to the density of the specimen. With the approximation of (7.45), the term in the large curly brackets in (7.42) becomes... 

If R(d) in Fig. 8.3 is compared with the calculated reflectance for a similar material, it is apparent that the phase change at the Rayleigh angle is the feature that is reproduced by far the most faithfully. This must be because this feature corresponds to the strongest interaction of the acoustic waves in the acoustic microscope with the specimen itself. 

Finally, there may be a small systematic error associated with the lens used. The origin of this is not fully understood, but it may depend on how components around the Rayleigh angle are weighted by the pupil function. Each lens may be calibrated on a well defined reference material to correct for such systematic errors. 

Rayleigh angle, and hence the Rayleigh velocity, by the formulae given in eqns (7.7) and (7.8). 

Bertoni, H. L. and Tamir, T. (1973). Unified theory of Rayleigh angle phenomena for acoustic beams at liquid-solid interfaces. Appl. Phys. 2,157-72. [139]... 

Nagy, P. B. and Adler, L. (1989). On the origin of increased backward radiation from a liquid-solid interface at the Rayleigh angle. J. Acoust. Soc. Am. 85,1355-7. [116] Narita, T., Miura, K., Ishikawa, I., and Ishikawa, T. (1990). Measurement of residual thermal stress and its distribution on silicon nitride ceramics joined to metals with scanning acoustic microscopy. /. Japan. Inst. Metals 54,1142-6. [148]... 

---