Coherent Backscattering from Multiple Scattering Systems - KOPS ...

5 Experiments
is lower than 1 (fig. 5.5). At the wings of the backscattering cone an intensity cutback appears
that balances the intensity enhancement of the cone.
However, the effect of α (B+C)
c is significant only for small kl ∗ . For kl ∗ 10 its influence is negligible,
and the backscattering cone is well described by the cooperon α (A)
c given in eqn. 2.15.
In this regime the diffuson can be found from the large angle wings of the backscattering data
[55]. For small kl ∗ the diffuson is hidden by the intensity cutback, and the proceeding devised
above has to be used to extract the cooperon from the data.
Small kl ∗ however means strongly scattering dense samples, where the scattering particles are
in touching distance. In such systems, near-field effects become important for the scattering
process. Strictly speaking, the random walk model developed for dilute systems and the
deduction of the transport mean free path from the intensity distribution of Mie scattering
and the anisotropy parameter 〈cos θ〉 are no longer valid. The kl ∗ obtained by fitting with the
theory from Akkermans and Montambaux will therefore certainly have the correct order of
magnitude, but might deviate slightly from the real value.
5.1.4 The results of the test experiments
To test the theoretical prediction made above, the coherent backscattering cones of various
samples were measured with the wide angle setup. The diffusion coefficients lay in the range
between 13 m2 /s and 250 m2 /s (see tab. 4.1), so that we expected to observe extremely wide
backscattering cones with kl ∗ close to unity and a distinct intensity cutback as well as narrow
cones with high kl ∗ where no cutback is visible.
As the albedos of the titania samples are basically 1, the albedo mismatch of sample and
reference is mainly given by the albedo of the teflon block. The latter was calculated with
all three diffusion coefficients D = 27500 m2 /s, D = 16500 m2 /s, and D = 13300 m2 /s that can
be derived from time of flight and small angle backscattering experiments, as discussed in
sec. 4.2.2.
The data quality of the wide angle backscattering experiments varies strongly, as the wide
angle setup is extremely sensitive to parasitically scattered light. However, as stated above,
the backscattering cone is evidentially caused by interference, so that the total amount of
backscattered power must be the same both for the coherent and the incoherent addition of
∫ π/2
0
a c (θ) sin θ dθ dφ of the cooperon is
the backscattered intensity, and the integral E = ∫ 2π
0
necessarily zero. E can therefore be used as a criterion to judge the quality of the experimental
data.
Furthermore, it is also possible to substantiate the method to calculate the albedo that was
developed earlier. In fig. 5.6 one observes that the data are approximately centered at E = 0
if the albedo is calculated with D = 16500 m2 /s and D = 13300 m2 /s, but are shifted to E ≈
−0.1 sterad for an albedo calculated with D = 27500 m2 /s. Therefore the data on average
suggest conservation of energy for precisely those values of the diffusion coefficient which
are obtained from the small angle measurements (see sec. 5.2.2). This strongly indicates that
the values for the albedos are correct, although as proof further experiments on samples with
other albedos than teflon or titania are necessary.
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