Rayleigh contribution

Thus, at negative defocus, the amplitude of the Rayleigh ray will vary as exp —2z(ao sec0R — aRtan0R). If the Rayleigh contribution to V(z) is smaller than the geometrical contribution, the amplitude of the oscillations in V(z) will follow the same exponential decay. 

Both the geometrical contribution and the Rayleigh contribution can thus be expressed in terms of material constants and the geometry of the lens, and therefore be directly compared. The complex summation of (7.39) and (7.42) enables V(z) to be computed and leads immediately to oscillations with period... 

In the line-focus beam analysis method, two fundamental assumptions are made regarding (8.21). First, it is assumed that the Rayleigh contribution is a perturbation on the total signal, i.e. that... 

In micro-Raman experiments with charge-coupled device (CCD) detection, a notch filter is commonly used to suppress the Rayleigh contribution. This affects the intensity in the low-frequency part of the spectra. On the other hand, dispersive spectrometers without filters give a strong intensity in the low-frequency region. The use of the reduced R(v) form of the spectrum [20] allows one to establish a better comparison between them. 

The field radiated into the coupling medium by such a distribution of sources may be obtained by means of the well-known Rayleigh integral. The field at the considered point r is computed by a simple integral over the whole radiating surface of the contributions of each elementary source acting as a hemispherical point source. 

We assume that the observed interference is the cumulative effect of the contributions of the individual polymer molecules and that solute-solute interactions do not enter the picture. This effectively limits the model to dilute solutions. This restriction is not particularly troublesome, since our development of the Rayleigh theory also assumes dilute solutions. 

Practical X-ray energies do not exceed 100 keV. The primary beam is mainly attenuated by the photoelectric effect. Scattering, both elastic (Rayleigh) and inelastic (Compton), represents a minor contribution to attenuation at energies below 100 keV. 

Figure 14. Tunneling to the alternative state at energy can be accompanied by a distortion of the domain boundary and thus populating the ripplon states. All transitions exemplified by solid lines involve tunneling between the intrinsic states and are coupled linearly to the lattice distortion and contribute the strongest to the phonon scattering. The vertical transitions, denoted by the dashed lines, are coupled to the higher order strain (see Appendix A) and contribute only to Rayleigh-type scattering, which is much lower in strength than that due to the resonant transitions.

Several authors(22 30) have contributed to developing the formalism with which the effects of an interface on a dipole inside or near a particle can be treated. In the Rayleigh regime (/ > a), Gersten and Nitzan have made several contributions to the theory of molecular decay rates and energy transfer/22 24) Kerker et alP solved the boundary value problem for a dipole and a spherical particle of arbitrary size, and NcNulty et al.,(26) Ruppin,(27) Chew,(28) and Druger and co-workers(29,30) have used the solution to solve some of the problems of interest. 

After the great physicist Clerk Maxwell died in 1879, Lord Rayleigh became his successor at the Cavendish Laboratory, Cambridge. During his professorship the classes increased in size, and women from Girton and Newnham colleges were for the first time admitted on the same terms as the men. Since he was allowed insufficient funds for the purchase of new apparatus, he contributed ,500 of his own money and solicited his friends for similar contributions until he had collected 1500 (3). 

In the case of solutions, concentration fluctuations only contribute to the central elastic part of the scattering spectrum. However, the Brownian movement of solute molecules creates weak frequency displacements that broaden the central peak. This phenomenon is called Rayleigh line broadening or quasielastic scattering [26-28]. This section deals with elastic scattering only. 

Fig. 7.3. Ray model of an acoustic lens with negative defocus aa is an arbitrary ray, which is reflected at such an angle that is misses the transducer (or else hits the transducer obliquely and therefore contributes little to the signal because of phase cancellation across the wavefront) bb is the axial ray, which goes straight down and returns along the same path cc is the symmetrical Rayleigh propagated wave, which returns to the transducer normally and so also contributes to the signal. The wavy arrow indicates the Rayleigh wave.

This equation is, of course, simply a definition of Ro(kx). Its usefulness arises from the explicit separation of the geometrical and Rayleigh components of the reflectance. Moreover, the fraction (k — kfy/ik — k ) in (7.26) contributes significantly only when kx is close to kp. The Rayleigh wavenumber is always greater than the bulk shear wavevector ks by 5-10 per cent or so (Table 6.2), and since R(kx) = 1 for kx > ks, again cf. Fig. 6.3(b)i, the approximation may be made that... 

This, together with the approximation VLI I VgI> means that the lead curve may be subtracted from a curve for the material being studied to give the last term on the right of (8.21), which is the term describing the interference between the Rayleigh ray and the geometrical contribution. To see this, (8.21) may be rewritten... 

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