Scattering by single particles

For the optical particle counter of Fig. 6.5, the sensing volume is 1.5 x 1.5 x mm. Determine the total energy scattered by the air molecules in the volume. Compare this with the scattering by single particles with diameters ranging from 0.05 to 5 / m and a refractive index of 1.5. Assume k = 0.5 m and express your answers in terms of the incident intensity. The temperature is 20 0,... 

The distribution of intensity of scattered radiation in a diffraction pattern is related by a Fourier transformation to the autocorrelation function of scattering density, p r)p(r )), where ( ) indicates an average over the sample. In crystallography the autocorrelation function is known as the Patterson function. It is very useful to factor out contributions to the total intensity from interfering waves scattered by single particles and from interparticle interferences ... 

The fundamental problem under consideration is scattering and absorption by single particles in natural environments, however, we are usually confronted with collections of very many particles. Even in the laboratory, where it is possible to do experiments with single particles, it is more usual to make measurements on many particles. A rigorous theoretical treatment of scattering by many particles is indeed formidable (see, e.g., Borghese et al., 1979). But if certain conditions are satisfied, a collection poses no more analytical problems than does a single isolated particle. 

Scattering by single, or collections of oriented, nonspherical particles may, unlike scattering by spheres, be azimuthally dependent. 

Consider a direct solar beam impinging on the layer shown in Figure 24.1. Assume, for the moment, that the beam is directly overhead, at a solar zenith angle of 0o = 0°. The fraction of the incident beam transmitted through the layer is e x, where x is the optical depth of the layer. The fraction reflected back in the direction on the beam is r = (1 — < T)a>P, where to is the single-scattering albedo of the aerosol, and p is the upscatter fraction, the fraction of light that is scattered by a particle into the upward hemisphere. 

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