Coherent Backscattering from Multiple Scattering Systems - KOPS ...
Coherent Backscattering from Multiple Scattering Systems - KOPS ...
Coherent Backscattering from Multiple Scattering Systems - KOPS ...
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2 Theory<br />
Figure 2.6: <strong>Scattering</strong> in the presence of a single boundary. All photon paths A → B<br />
that are lost because they run partially outside the samples can be described by their<br />
image paths A → B ′ . The (virtual) scatterer P is the point where a photon path leaves<br />
the sample.<br />
2.4 The influence of boundaries<br />
Eqns. 2.6 and 2.8 describe the photon density distribution in infinitely extended samples. In<br />
reality however, this distribution is strongly influenced by the borders of the system, where<br />
photons are inserted and released, absorbed and reflected.<br />
There are two different approaches to describe the influence of boundaries on a multiple<br />
scattering system. The more intuitive one is the image point method, which uses symmetry<br />
properties of the density distribution to describe the scattering in terms of the density distribution<br />
in infinite space [38]. The other approach is in the framework of radiative transfer theory,<br />
which describes a field of radiation by the intensity flux through area elements. This makes<br />
it possible to compare the flux through an area element at the sample surface with an area<br />
element inside the sample and derive theoretical descriptions for the various experimental<br />
situations [58].<br />
2.4.1 Image point method<br />
To describe multiple scattering in a finite sample in terms of scattering in infinite space one<br />
can make use of the symmetry properties of the density distribution: The photon density at<br />
any point B in an infinite sample is equal to the density at its image point B ′ with respect<br />
to any mirror plane that contains the starting point P of the photon cloud. Therefore we can<br />
describe photon paths A → P → B by paths A → P → B ′ that end at the image point of B<br />
with respect to P. If P is the endpoint of a photon step that leads the path out of the sample,<br />
the path A → P → B is not possible in the presence of the boundary, and its contribution is<br />
missing <strong>from</strong> the free space photon density in B.<br />
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