Angular dependence of reflectance

Tsukahara, Y., Takeuchi, E Hayashi, E., and Tani, Y. (1984). A new method of measuring surface layer-thickness using dips in angular dependence of reflection coefficients. IEEE 1984 Ultrasonics Symposium, pp. 992-6. IEEE, New York. [214] Tsukahara, Y Nakaso, N., Kushibiki, J., and Chubachi, N. (1989a). An acoustic micrometer and its application to layer thickness measurements. IEEE Trans. UFFC 36, 326-31. [213-215]... 

For the determination of the average thickness of the polyelectrolyte layers the following procedure was applied. At first, the angular dependence of reflectivity (an-... 

Fig. 2. (Left) Excitation of SPR via the Kretschmann geometry. (Right) (A) Fresnel simulation of angular dependence of reflected light intensity and the corresponding relative field intensity. (B) Experimental data of an angular scan of the reflected light intensity and the corresponding fluorescence emission from surface attached Cy5-DNA molecules.

According to the geometrical optics treatment (Bom and Wolf, 1980), the angular dependence of reflectance p,2 at the air/film interface for 5- andp-... 

In the following analysis, we assume that the mixed LB film is a non-absorbing medium for the following two reasons (1) Since the molar ratio of p-carotene to barium stearate is 1 10 in the mixed LB fihn, the number of the barium stearate molecules predominates in the film (2) The angular dependence of reflectance for the mixed LB fihn fits the theoretical curves for the non-absorbing medium calculated using the refractive index of barium stearate (1.462) (Blodgett, 1935). 

For semiconductor and dielectric in the range of their transparency, the angular dependence of reflectance R substantially differs from the analogous dependence for metals (Fig. 1.11). A characteristic property of transparent media is the existence of the polarizing Brewster angle at which the intensity of the reflected component of / -polarized radiation is eqnal to zero (1.4.15°). The value of this angle [Eq. (1.63)] at v = 3000 cm is equal to 55.6°, 73.6°, and 76° for quartz. Si, and Ge, respectively. 

Another issue of interest is the angular dependence of reflection coeflftcient. For some structures, this dependence is very strong and large values of / are obtained only for near-normal incidence, thus furnishing surfaces with very high directivity of reflected light. The other pole are the surfaces offering near-omnidirectional or even fully omnidirectional reflectivity. 

Since then, TXRE has become the standard tool for surface and subsurface microanalysis [4.7-4.11]. In 1983 Becker reported the angular dependence of X-ray fluorescence intensities in the range of total reflection [4.12]. Recent demands have set the pace of further development in the field of TXRE - improved detection limits [4.13] in combination with subtle surface preparation techniques [4.14, 4.15], analyte concentrations extended even to ultratraces (pg) of light elements, e. g. A1 [4.16], spe-dation of different chemical states [4.17], and novel optical arrangements [4.18] and X-ray sources [4.19, 4.20]. 

Figure 36. Angular dependence of the Cu( 111) reflectivity and the normalized T L fluorescence yield. Points represent experimental data curves are least-squares fits. (From Ref. 119, with permission.)...

Figure 2.79 For 0 = 0. (a) The angular dependence of the reflectivity R and relative phase V of the reflected plane wave, (b) The angular dependence of the electric field intensity at =0 and 2 = 2DC for Ej = I. After Bedzyk et at. (1990) and M. J. Bedzyk, Synchrotron Radiation News. 3 (1990) 25, Copyright 1990 Gordon and Breach Science Publishers, S.A.

Fig. 6. Lower part angular dependence of the non-normalized static scattering intensity I(q) observerd with latex particles (R=265 nm). Upper part dependence of r/q =D on the scattering angle in dynamic LS. The sharp downturn at large scattering angles results from a weak back reflection of light on the boundary of the aqueous solution to the index matching bath, that consisted of toluene. This reflection results from the difference in the refractive indices of water (n = 1.333) and toluene (n =1.51). Reprinted with permission from [182]. Copyright [1982] American Society...

Rotational state distributions in fragmentation processes often reflect, in a quite direct manner, the angular dependence of the wave function at the transition state, that is, the 7-dependent distribution of dissociating molecules before they enter the exit channel [9, 10, 55, 56]. In a semiclassical picture, the modulus square of the TS wave function determines the initial conditions... 

The final rotational state distributions of the products in the fragmentation of a polyatomic molecule contain additional clues about the intra- and intermolecular dynamics, especially about the coupling in the exit channel. In realistic as well as model studies it has been observed that the rotational state distributions of the photodissociation products reflect the angular dependence of the wave function at the transition state and the anisotropy of the PES in the exit channel [4, 9, 10]. HO2 is no exception. 

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

---