Coherent Backscattering from Multiple Scattering Systems - KOPS ...

5 Experiments
Altogether the teflon backscattering measurements confirm that the newly revised small angle
setup yields reliable results for the transport mean free paths of weakly scattering samples.
The difficulty is rather to properly determine the diffusion coefficient that enters in eqn. 2.7
from which the expected value of l ∗ is calculated. The problem herein is a technical one, as
only samples of a certain size fit into the time of flight setup. If in the future the diffusion
coefficients of other weakly scattering samples are to be measured, an appropriate adaption
of the setup should be considered.
5.2.3 Coherent backscattering on fluidized beds
Parallel to the experiments on weakly scattering solid samples like teflon, another field of application
for the small angle setup arose from a cooperation with the group of Dr. M. Schröter
of the Max Planck Institute (MPI) for Dynamics and Self-Organization in Göttingen. Working
on statistical mechanics of granular media, their interest lies in the granular temperature of
fluidized beds, which is proportional to the average speed of the particles.
The group uses diffusing wave spectroscopy (DWS) to measure the typical timescale of the
movements of the particles in the bed. To obtain a speed, they also needed a length scale for
the transport. This scale is given by the transport mean free path l ∗ , which can for example
be measured in coherent backscattering experiments.
Setup modifications
The small angle setup (fig. 3.5) was originally designed to take up the backscattering from
the horizontal top surface of the sample. This is not possible for fluidized beds, which have
to be accessed from the side through the container walls (fig. 4.5), so that the setup has to be
modified accordingly. Here it is important to position the circular polarizer directly in front of
the container to avoid the polarization to be altered by additional optical components between
beamsplitter and bed. As the light now transmits the container walls before and after being
scattered in the fluidized bed, one has to take into account the refraction and reflection at the
acrylic glass surfaces.
In multiple scattering, the transition from the fluidized bed to the acrylic glass becomes noticeable
in the average penetration depth z 0 = 2/3 · (1 + R)/(1 − R) · l ∗ , where R is the reflectivity
of the sample–glass surface.
In addition, the scattering angle θ CCD measured at the CCD camera has to be corrected for
the refraction at the glass–air surface of the container (fig. 5.16) to be compared with the
theoretical description of the backscattering cone:
( )
nair
θ ms = arcsin · sin θ CCD ≈ n air
· θ CCD (5.8)
n glass n glass
Although the light passes a circular polarizer before and after scattering, the ring structure of
single scattering at Mie particles can also be found on the backscattering images (fig. 5.14).
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