Diffraction lateral shift

Lateral shifts are also due to depth penetration and refer to a shift in the exit location of an X-ray at the crystal surface. This results in a transverse shift at the detector, typically 10%-100% of refractive index corrections [20]. While ray-tracing can adequately describe geometrical effects outside the crystal, the effects of depth penetration and lateral shifts require full dynamical diffraction theory. 

The presence of the two gratings in the path of the optical wavefront generates a lateral shift or shearing or optical differentiation of the front. For example, the diffracted beam Ei o, denoted as S xi, X2 + to), is shifted... 

Finally, we emphasize that the lateral shift is not the only manifestation of diffraction on the step-profile planar waveguide. Taken alone, it is insufficient for describing propagation on low- V waveguides. We next investigate another diffraction phenomenon to better appreciate the departure of electromagnetic theory from the ray methods of Part I. 

Thus the modal and ray transit times are equal only when tj - 1. This condition is satisfied only by those rays belonging to modes well above cutoff, i.e. when Vp U, or, equivalently, when 0 < 0c- Hence is inaccurate for arbitrary values of 9. This inaccuracy arises because the ray transit time ignores diffraction effects, which were discussed in Chapter 10. The step-profile planar waveguide is a special case, however, because all diffraction effects can be accounted for exactly by including the lateral shift at each reflection, together with recognizing the preferred ray directions. TWs was carried out in Section 10-6, and for rays, or local plane waves, whose electric field is polarized in the y-direction in Fig. 10-2, leads to the modified ray transit time of Eq. (10-13). If we use Table 36-1 to express 0, and 0(.in terms of U, Vand Wand substitute rj for TE modes from Table 12-2, we find that Eqs. (10-13) and (12-8) are identical since 0 = 0. It is readily verified that the same conclusion holds for TM modes and local plane waves whose magnetic field is polarized in the y-direction of Fig. 10-2. 

When V is small, only low-order modes can propagate. The term in s in Eq. (36-29) is retained to account for diffraction effects, as discussed in Section 10-4, and the complete expression for T in Eq. (36-30) is now required. However, we can still give a simple physical interpretation. We recall from Section 10-6 that the effect of the lateral shift is to increase the ray half-period from Zp to Zp.+ s, corresponding to the addition ST to the path in Fig. 36-3(b). If we introduce an effective core half-width, Pefr>... 

Later on, the role of each effect was examined more precisely by high-pressure neutron diffraction measurements on KDP and DKDP [13,14]. The linear relationship between Tc and Rq-q was confirmed in both KDP and DKDP for Tc > 50 K and the same slope dTc/dJ o-o was found in both crystals. However, the line in DKDP was found to be shifted from the line in KDP by about 40 K toward higher values. This result indicates that only part of 40 K 37%) of the whole isotope effect - Tf = 107 K) is caused by... 

In order to determine the spatial resolution of the system, various sized polystyrene beads were imaged at a Raman shift of 2850 cm-. This experimental condition was achieved by choosing a signal-idler pair at wavelengths of 924 nm and 1254 nm. The characteristic lateral (xy) and longitudinal (z) resolutions were found to be diffraction limited to approximately 420 nm and -1.1 J,m (FWHM), respectively. 

The sizing methods involve both classical and modem instrumentations, based on a broad spectrum of physical principles. The typical measuring systems may be classified according to their operation mechanisms, which include mechanical (sieving), optical and electronic (microscopy, laser Doppler phase shift, Fraunhofer diffraction, transmission electron miscroscopy [TEM], and scanning electron microscopy [SEM]), dynamic (sedimentation), and physical and chemical (gas adsorption) principles. The methods to be introduced later are briefly summarized in Table 1.2. A more complete list of particle sizing methods is given by Svarovsky (1990). 

Proton NMR cannot be used as an indication of the position occupied by hydrides in HNCC in solution as the range of chemical shifts observed is enormous (441). For example, all fully characterized carbonyl clusters that contain interstitial hydrides are listed in Table II, with chemical shifts from 23.2 6 in [Co6(CO)isH]- to -24(5 in [Nii2(CO)2iH] -. The octahedral [Rue(CO).8H]- was the first reported cluster for which an interstitial hydride was assigned on the basis of X-ray (30, 31) and solid-state infrared spectroscopy studies (33). However, because of the extremely low field position of the NMR signal (16.4 S), it was suspected to be of the formyl type (417). Its interstitial position was later unequivocally established by neutron diffraction studies (32). The observation of the satellites in the... 

Figure 4 shows the hydropathy plots for the L-, M- and H-polypeptides of Rb. sphaeroides R-26, using a moving window of 19 amino-acid residues for each scan. The plots for the L- and M-polypeptides [Fig. 4 (A) and (B)] are very similar, showing that both polypeptides have five hydrophobic segments. Each of these hydrophobic segments contains enough amino acids to form a membrane-spanning a-helix. Note that the residue-number scale strictly applies only to the L- and H-polypeptides that for the M-polypep-tide has been shifted in order to maximize the coincidence of its hydrophobic regions with those of the L-polypeptide. The hydropathy plot for the H-polypeptide [Fig. 4 (C) ] shows that it has only one hydro-phobic region, indicating the presence of just one a-helix. Thus the presence of eleven transmembrane helices in the L-, M- and H-subunits as predicted by hydropathy plots is in accord with conclusions drawn from previous studies by circular dichroism and polarized infrared spectroscopy and later confirmed by X-ray diffraction studies.

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