Scattering from large spheres

For some typical modes of scattering from large spherical particles (f >5), simple formulations of phase functions can be obtained. These modes include scattering from a specularly reflecting sphere, scattering from a diffuse reflection sphere, and scattering by diffraction from a sphere. 

In Section 5.2.2 it was shown that at large q the intensity I(q) of scattering from a sphere decays as q A, from a thin disk as q 2, and from a thin rod as q l. The power-law exponent at large q is therefore seen to be related to the dimensionality of the scattering object. There are, however, many cases in which the intensity varies as an unexpected or even fractional power of q. In the case of a Gaussian model of a polymer chain, the intensity was seen to decrease as q 2 even though a chain obviously is a three-dimensional object. The inverse power-law exponents that differ from 1, 2, or 4 can be explained in terms of the concept of a fractal. 

It follows from (7.3) that the scattering efficiency of a large sphere can be written... 

To account for the total directional scattering from a large sphere, effects of both diffraction and reflection must be considered. When a spherical particle is in the path of incident radiation, the diffracted intensity may be obtained from Babinet s principle, which states that the diffracted intensity is the same as that for a hole of the same diameter. The phase function for diffraction by a large sphere is given by [Van de Hulst, 1957]... 

Fjg. 7. Scattering from spheres having various values of m and a. The value of E approaches 2 for large <% ... 

Csca and Cabs have a different dependence from the sphere radius (f and R, respectively) for small spheres the absorption will be larger than the scattering, while the opposite is true for large R. However for a large particle retardation effects cannot be neglect. Thus the above formulas are valid only for R < X. 

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