Reflectance function

Contrast in an image formed by a SAM for the simplest stmcture of the nanoscaled film system is mathematically expressed as V (z) as follows (see Fig. 9)  

Front Focal Spacimen Surface Plane Plane 

Note that u (r) may be used as a Gaussian function determined by the size of the transducer for the calculation.  

From (34), the contrast depends on the reflection reflectance function of a specimen. The reflectance function is determined by the structure of the specimen. Now, we need to assume two cases, i.e., the system has a good adhesive condition at the interface between the film and the substrate (case I), and the system has a bad adhesive condition (i.e., delamination) at the interface (case II). 

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By measuring V z), which includes examining the reflectance function of solid material, measuring the phase velocity and attenuation of leaky surface acoustic waves at the liquid-specimen boundary, the SAM can be used indetermining the elastic constants of the material. 

Inactivation of the tau gene by homologous recombination results in mice that are largely normal [22], indicating that tau is a nonessential protein. This may reflect functional redundancy. Thus, mice doubly deficient in tau and the microtubule-associated protein MAP IB exhibit nervous system defects that are more severe than those in the MAP IB single knockout line. 

Aside from the cysteine motif, conserved regions in the proteins encoded by WHnl.O and WHul.6 are likely to reflect functional roles. Based on the rules of Von Heijne (70), the N-terminal 16 amino acids may function as a signal peptide for secretion. Recombinant WHbl.O and WHt/1.6 proteins are secreted into the medium of infected insect cells (43)... 

Particulate-Reflectance Functions. Regression parameters for particulate-reflectance relationships are shown in Table III. 

Neuroimaging techniques assessing cerebral blood flow (CBF] and cerebral metabolic rate provide powerful windows onto the effects of ECT. Nobler et al. [1994] assessed cortical CBE using the planar xenon-133 inhalation technique in 54 patients. The patients were studied just before and 50 minutes after the sixth ECT treatment. At this acute time point, unilateral ECT led to postictal reductions of CBF in the stimulated hemisphere, whereas bilateral ECT led to symmetric anterior frontal CBE reductions. Regardless of electrode placement and stimulus intensity, patients who went on to respond to a course of ECT manifested anterior frontal CBE reductions in this acute postictal period, whereas nonresponders failed to show CBF reductions. Such frontal CBF reductions may reflect functional neural inhibition and may index anticonvulsant properties of ECT. A predictive discriminant function analysis revealed that the CBF changes were sufficiently robust to correctly classify both responders (68% accuracy] and nonresponders (85% accuracy]. More powerful measures of CBF and/or cerebral metabolic rate, as can be obtained with positron-emission tomography, may provide even more sensitive markers of optimal ECT administration. 

In the simple form given at the start of this chapter, the ray picture correctly predicts the period of the oscillations in V(z), but it does not enable any other aspect of V(z) to be calculated. To do that it is necessary to look more carefully at the form of the reflectance function (Bertoni 1984 Brekhovskikh and Godin 1990). Writing the expression for the reflectance function in (6.90) explicitly in terms of the wavenumber in the fluid k and the longitudinal and shear wavenumbers in the solid k and ks, and with the tangential component of the wavevector = kx, which, by Snell s law, is the same in both media, and with... 

When kx < k the last term in the numerator and the denominator are real, and the reflectance function is real, so that there is no variation of phase with incident angle. When kx = k all terms except the first term in the numerator and the denominator vanish, and R(kx) = 1. When k square brackets depends only on kx and the properties of the solid. Provided that there is no dissipation in the solid, it vanishes when kx is equal to the Rayleigh wavenumber kR = co/vR, as can be seen by substituting X = (ks/kR)2, Y = (k /ks)2, and comparing with (6.55). 

Anyone who has successfully used a microscope to image properties to which it is sensitive will sooner or later find himself wanting to be able to measure those properties with the spatial resolution which that microscope affords. Since an acoustic microscope images the elastic properties of a specimen, it must be possible to use it to measure elastic properties both as a measurement technique in its own right and also in order to interpret quantitatively the contrast in images. It emerged from contrast theory that the form of V(z) could be calculated from the reflectance function of a specimen, and also that the periodicity and decay of oscillations in V(z) can be directly related to the velocity and attenuation of Rayleigh waves. Both of these observations can be inverted in order to deduce elastic properties from measured V(z). 

Thus, by measuring V(u) and inverse Fourier transforming it, the reflectance function may be deduced. Four practical constraints are immediately apparent from the theoretical formation. 

Equation (8.4) is valid only for 1 > t > cos d0 outside this range Pt(t) in the denominator is zero. No information about the reflectance function can be obtained outside the aperture angle of the lens. 

Fig. 8.2. Fused silica, (a) Magnitude and phase of an experimental V(z) using a curved transducer, 8q = 45°, 10.17 MHz. (b) Magnitude and phase of reflectance function -------deduced from (a) via (8.4),----calculated from (6.90) with vq =...

Fig. 8.3. Reconstruction of the reflectance function of duraluminium from magnitude only V(z) data, measured at 320 MHz. (a) Steps in the reconstruction of P(9)R(9) after (i) 1 (ii) 3 (iii) 10 and (iv) 30 iterations of the phase retrieval algorithm, (b) Reconstructed R 8) (Fright etal. 1989).

Time-resolved techniques are very powerful for examining structures where the useful information is contained in the normally reflected signal. Frequency analysis of a reflected broadband signal can also be used for film characterization (Wang and Tsai 1984 Lee et al. 1985). But in many other problems, especially in materials science, there is a great deal of information contained in the way that the coefficient of reflection changes with angle of incidence. It is therefore important to understand the behaviour of the reflectance function R(d) of a layered structure. 

In (10.12) all the parameters except the Mik refer to the substrate. With the normal impedance of the fluid defined as Z0 = pov0/cosd0 ( 6.4.1), the reflectance function has the familiar form... 

Fig. 10.9. Reflectance function for a layer of gold on 42% Ni-Fe alloy as a function of both the incident angle fland the frequency-thickness product fd. (a) Magnitude, plotted as 1 — (601 to show the sharp minima in the magnitude (b) phase (Tsukahara...

Fig. 10.10. Reflectance function for a 5 pm layer of gold on fused silica at 10.17 MHz (fd = 50.85ms-1), using the same system as in Fig. 8.2. (a) Magnitude (b) phase.

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