Angle of observation

Based on considerations we have encountered earlier in this chapter, we can anticipate two limiting cases of this function P(0) approaches unity both in the limit of small particles and in the limit of small angles of observation. Interference is absent in both of these cases. 

Since the product srj, appears in Eq. (10.84), there is a trade-off possibility between particle size and the angle of observation. That is, the Debye scattering theory applies with the same level of accuracy to larger molecules at smaller angles and to smaller molecules at larger angles. 

Zimmt has reported the intensity of scattered light at various angles of observation for polystyrene in toluene at a concentration of 2 X 10" ... 

Figure 7.3 shows the radiated intensity S as a function of the observation angle 0 for a dipole 80 nm from the surface. For simplicity, the azimuthal angle of observation is averaged. (This is equivalent to assuming that the excited dipole distribution is azimuthally symmetric about the surface normal.)... 

Another complication in the quantitation of TIRF on cells is the effect of the membrane thickness itself on the profile of the evanescent wave. Reichert and Truskey<105) have calculated that, in theory, the thickness of the membrane should have a negligible effect on the fluorescence and that a simplified theory of three stratified layers (glass/water/cytoplasm) should be adequate. The theory approximates for simplicity that scattering plays a negligible role and that fluorescence intensity versus angle of observation and fluorescence lifetime are not functions of distance to the interface z. Experiments that... 

Ratio of two Rayleigh ratios for different angles of observation, i.e.,... 

The thickness of the compression zone is about 10" cm at atmospheric pressure thus the time for compression is about lO" sec. Since the wave length of visible light is of this order of magnitude, the optical reflectivity method was developed. Experiments were carried out in which the angle of incidence on the shock front was kept constant, and the angle of observation varied. In the case of simple air shock... 

The Rayleigh approximation shows that the intensity of scattered light depends on the wavelength of the light, the refractive index of the system (subject to the limitation already cited), the angle of observation, and the concentration of the solution (which is also restricted to dilute solutions). In the Rayleigh theory, the size and shape of the scatterers (M and B) enter the picture through thermodynamic rather than optical considerations. 

The correction factor is a function of the angle of observation —as implied by the notation P(6) — since it is essentially an interference effect. 

Equation (67) shows clearly that i should be measured as a function of both concentration and angle of observation in order to take full advantage of the Debye theory. The light scattering photometer described in Section 5.4 is designed with this capability, so this requirement introduces no new experimental difficulties. The data collected then consist of an array of i/I0 values (i needs no subscript since it now applies to small and large particles) measured... 

In this technique, one measures i/I0 at 6 = 45° and 0 = 135° for dispersions at several different concentrations. It should be noted that the factor (1 + cos2 0) in Equation (24) has the same value for these two angles of observation. Therefore any deviation of the ratio of the intensities z from unity must measure the ratio of the P(6) values at these two angles [See Equation (47)] ... 

At any given angle of observation, x tends to be an oscillating function of 0. 

For any given value of 0, x varies with the angle of observation 6. The number of oscillations in this curve is greater for larger values of 0 and n. 

Rayleigh scattering is the re-emission by solvent molecules of a small fraction of the excitation radiation. This emission occurs at the same wavelength and is independent of the angle of observation (Fig. 12.6). The Rayleigh scattering intensity varies with the polarisability of solvent molecules. 

Compton effect. A small fraction of the primary X-ray excitation beam is scattered in the form of radiation whose wavelength depends on the angle of observation. This radiation is superimposed on the X-ray fluorescence spectrum. The shift in angstroms between the two wavelengths (excitation and Compton) is given by ... 

A determination of the molecular weight by small-angle x-ray scattering requires, therefore, knowledge of the scattering intensity as a function of protein concentration and angle of observation, as well as of the electron density increment, ( — ), which replaces the refractive index... 

Fig. 18. View of low-energy conformation of gramicidin-S from 80° away from the axis of symmetry, with the side chains included. The apparent asymmetry of the molecule in this figure is due to the angle of observation (Vanderkooi et al., 1966).

Nonlinear Thomson scattering can only be observed for the highest laser intensities, as shown in Fig. 11.7. As expected from the theory, when ao < 1, the nonlinear Thomson scattering vanishes and the collisional radiative processes from the thermal plasma prevail (Bremsstrahlung and radiative recombination). For ao > 1, these latter processes are still effective, as shown by the quadratic dependency on the electronic density of the plasma observed for 9 = 40°. However, this isotropic thermal emission remains less intense than the collimated nonlinear Thomson scattering emission and becomes detectable only at a large angle of observation (> 40°). 

The energy, Eth, of the X-rays produced depends on the interaction angle between the laser and the relativistic electron beam, electron beam direction, 9. It is given by [18] as... 

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