Martin Teichmann Atomes de lithium-6 ultra froids dans la ... - TEL

CHAPTER 4. DATA ANALYSIS
the one-dimensional fits in the horizontal direction, these fluctuations
are simply averaged out for the one-dimensional fit.
While using the fit, it is important to check that the fitting algorithm
correctly finds the baseline of the data, as the temperature information
is mostly in the wings of the function which are just misplaced if the
baseline is incorrect. It turns out that in most of the cases, the Fermi fit
is much better at finding the baseline than the Gaussian fit. If this is not
the case, the data is most likely too bad to give any information about
the temperature, since the reason why the baseline could not be found
is that the algorithm could not find the typical sharp wings of the Fermi
function.
At very low temperatures, the shape of the expanded cloud shows no
changes. This makes fitting problematic and casts doubts on its result.
Thus, we tested the algorithm by letting it fit theoretical distributions
where a Gaussian noise was added. The results are shown in figure
4.2. This shows that the one-dimensional fit is reliable below T = 0,7TF,
given reasonable noise levels. The error is around 0,1TF, and as this
becomes slightly bigger for lower temperatures, we are not able to
measure temperatures below 0,15TF, this is also where we stopped the
simulation. At high temperatures, we do not have need for this fit, as
we can take the size of the cloud as a measure for the temperature.
The same simulation performed for the two-dimensional fit appears to
be more stable at first sight, given the much higher noise levels the fit
works at. This appearance is deceptive, since for the one-dimensional fit
we average over one direction, giving us much lower noise levels than
in two dimensions. In practice, the difference between the two fitting
methods is negligible. The noise on the data is normally below 30 % for
the two-dimensional fit, and below 3 % for the one-dimensional.
4.2 Three-dimensional reconstruction
In most of the experiments we have at least one axis of symmetry. This
enables us to deconvolute the data to get the original distribution, not
integrated over the line of sight. In the case of cylindrical symmetry, we
have to cut the image into slices perpendicular to the axis of symmetry,
and deconvolute each slice. In the case of spherical symmetry, we could
do the same, since spherical symmetry is cylindrical symmetry with an
additional symmetry axis. We can make use of this additional axis. We
find the center of the distribution and integrate over same distances
around this central point. This gives a one-dimensional distribution
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