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 />
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Figure 2.10: Speckles. Random interferences of the photons emerging <strong>from</strong> a multiple<br />
scattering medium result in a random distribution of high and low light intensities.<br />
Still, interference is possible between equally oriented components of the light waves. The<br />
interference pattern observed on a multiple scattering sample results <strong>from</strong> the coherent addition<br />
of the corresponding components of the waves that emerge <strong>from</strong> the ends of the light<br />
paths in the sample. To first order it is therefore the superposition of the interference patterns<br />
of the photons on all pairs of light paths in the sample.<br />
This implies of course that a certain pair of light paths is not only theoretically possible,<br />
but actually has photons traveling on it. The interference pattern of a infinitely extended<br />
incoming wave will therefore differ in some way <strong>from</strong> that of a spatially restricted incoming<br />
wave. Likewise, the interference pattern of multiply scattered light with restricted spatiotemporal<br />
coherence will be only a modified version of the interference pattern of light with<br />
infinite temporal and spatial coherence length.<br />
2.6.1 Speckles<br />
Most of the light paths in the sample are completely unrelated, so that their interference results<br />
in a random speckle pattern of high and low light intensities (fig. 2.10). The speckle pattern<br />
is therefore a subtle image of the positions of the scatterers inside the sample, and is unique<br />
for every sample and every lighting and imaging situation. It is also extremely sensitive to<br />
motions of the scattering particles. Even sub-wavelength movements of the particles lead<br />
to significant variations in the overall phaseshift of the photons and to fluctuations of the<br />
speckles. Averaging over speckle fluctuations or a sample average lead to a detected light<br />
intensity approximately proportional to the cosine of the scattering angle θ, as described by<br />
Lambert’s well-known emission law [33].<br />
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