Ideal scatterer

Complex processes are involved in transmittance and reflectance of scattered radiation, which are theoretically described by Schuster [4]. In an ideal scattering medium all fluxes of light can be summed up as components of two vectors. Vector I stands for the light flux in the direction of the incident light, and the vector J describes the light intensity in the antiparallel direction. With k, the absorption coefficient, and 5", the scattering coefficient, the two Schuster equations are as follows ... 

It is always easy to calculate idealized scattering curves for perfect networks. The experimental systems vary from the ideal to a greater or lesser degree. Accordingly, any estimate of the correctness of a theoretical analysis which is based on an interpretation of experiment must be put forth with caution since defects in the network may play a role in the physical properties being measured. This caveat applies to the SANS measurement of chain dimensions as well as to the more common determinations of stress-strain and swelling behavior. 

In an ideal scattering experiment the collisions are assumed to occur at a fixed point in space. In practice the collision volume is finite and the part viewed by the detecting system generally depends on the scattering angle. Care must therefore be taken in relating the scattered particle intensity to the cross section. 

The most convenient approximate solutions have been given by Kubelka and Munk 5 6) (cf. J>). These are valid only in the case of an ideal scattering medium without any regular reflection. While the so-called linear Eq. (3) is only valid at infinite thickness, the so-called hyperbolic solution (4) and (5) is of the greatest utility in TLC and HPTLC with a finite layer thickness d. It must be mentioned that in Eq. (3) is the absolute reflectance, while in optical in situ reflectance measurements in TLC and HPTLC only relative reflectances are accessible. 

The most detailed information on the collision process can be obtained from laser spectroscopy of crossed-beam experiments, where the initial quantum states of the collision partners before the collision are marked, and the scattering angle as well as the internal energy of the reactants is measured. In such an ideal scattering experiment aU relevant parameters are known (Sect. 8.5). 

Figure 2.3 PCH for an ideal scatterer placed at the laser focus. The experimental photon-count distribution (solid circles) is exactly fit by a Poisson function (solid line) with an average number of photon counts = 6.7. Residuals are shown in units of standard deviations. The fit gives = 0.91. A total of 131072...

Figure 3.17 Photon count histogram of an ideal scatterer placed at the laser focus. The collected photon count distribution (circles, normalized) is fitted exactly by a Poissonian function (line) indicating that there are no fluctuations in the detected signal arising from instability of the light source or other instrumentation.

Type of quantity A cumulable quantity, like volume, number, or (ideally) scattering intensity of the particle system, which is used to quantify the frequency (weights) of... 

Different idealized scattering situations can be summarized as in Table 4 (Con-well, 1967) ... 

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