Angular Intensity Distribution

Figure 13. (a) angular intensity distribution of luminescence for an air environment (b) Angular intensity distribution of luminescence for a water environment. 

Chew and Wang(39) have pointed out the possibility of double resonance, that is, that the frequencies of both the excitation and inelastically scattered radiation are resonant. They presented the results of calculations which indicate that double resonance can have a significant effect on the angular intensity distribution of inelastically scattered radiation. This case is of some practical interest, particularly in Raman studies, where coincidence may lead to anomalous Raman band intensities, if both the excitation and the shifted frequency are resonant. 

Many real angular intensity distribution functions have been found to closely approximate a Gaussian and for the remainder of this paper a Gaussian distribution will be used. It should be noted, however, that the angular deconvolution can be used on patterns from specimens with any form of disorientation function. For a Gaussian distribution, equation (2) becomes... 

The angular intensity distribution of X-rays refracted by fibers or spherical pores has been approximated by Hentschel et al. [3]. Quantitative X-ray refraction analysis is implemented at a constant scattering angle of about two minutes of arc and at a fixed wavelength. The refraction value C is proportional to the absolute internal surface density S. With dp denoting the sample thickness the relationship can be given by ... 

The angular intensity distribution of scattered light l 9,n) at angle 6, for particles of diameter d and refractive index fi is given by Mie scattering theoiy. For a polydisperse distribution ... 

FIGURE 7.5 Schematic of angular intensity distributions leaving an ideal blackbody (/u) and a real surface (h). 

Figure 7-20 Angular intensity distribution of the different scattering modes obtained by geometrical optics for a point receiving aperture (X = 0.6328 pm, 0 = 2.11°, Dp = 30 pm a) m = 0.75, b) m = 1.33, c) m= 1.52)...

The flux direction of cosmic ray secondary particles in the lower atmosphere is distributed symmetrically around an intensity maximum in vertical (i.e., zenith) direction. The angular intensity distribution is given by... 

In general, for larger particles, the angular intensity distribution of the scattered radiation depends on both size and internal structure (reftactive index). With increasing particle size, the scattered radiation is further concentrated in the near forward direction. It is for this reason, we can accurately determine the size of particles by making precise measurements of the angular variation of the scattered intoisity in the forward direction only. This is the basis of the forward... 

Note that the angular divergence of the central diffraction order in the far held is smaller for the annular-ring near-held distribution than that of a circular aperture with the same size as the small mirror of the unstable resonator. However, the higher diffraction orders are more intense, which means that the angular intensity distribution has broader wings. 

Like other optical characterisation techniques, SLS exhibits size-dependent concentration limits. At high concentrations, the suspension may become opaque or multiple scattering may occur which affects the angular intensity distribution. Dilution may solve the problem, but then osmotic concentration effects (virial coefficients, particle interactions) are not accessible. Conversely, very fine, weakly scattering particles may require such a high particle concentration that the mentioned concentration effects cannot be neglected and will complicate the determination of morphological structure parameters. 

Fig. 6. Rhombic Turing patterns, (a) and (b) Patterns with a range of characteristic angles in a band near 60° the region shown is 6 mm x 6 mm. (c) and (d) Close-ups of the regions in the boxes in (a) and (b), respectively, (e) and (f) Angular intensity distribution (in bands centered at an intrinsic wave vector of 6.9 mm ) for the patterns in (c) and (d). The characteristic angle of the patterns in (c) and (d) is 66° and 58°, respectively. The patterns were obtained by a sudden jump in [CH2(COOH)2]o from a value yielding the uniform state, 40 mM, to a value yielding a patterned state, 32 mM. Other control parameters were the same as in Figure 3b. (From [13])...

In the case of uniaxial orientation, determination of orientation requires a series of hkl planes preferably perpendicular to the symmetry direction. In polyethylene, the (110), (200), and (020) reflections are strong and allow ready determination of the orientation of the a- and b-crystallographic axes. Furthermore, cos tj>a and cos 0b may be computed directly from the angular intensity distribution of the (200) and (020) reflections, respectively. Alternatively, cos 0b... 

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