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Valentin Boettcher 2020-01-24 19:02:20 +01:00
parent 5ed653f60f
commit 6c47b5031f
58 changed files with 31399 additions and 604 deletions
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CS/auswertung/Untitled.ipynb
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CS/auswertung/figs/calibrate/am_1.pgf
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CS/auswertung/figs/calibrate/am_2.pgf
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\pgfpathclose%
\pgfusepath{stroke,fill}%
\end{pgfscope}%
@ -9936,7 +9936,7 @@
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=4.051327in,y=2.998148in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 3\cdot\sigma\)}%
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\end{pgfscope}%
\end{pgfpicture}%
\makeatother%

BIN
CS/auswertung/figs/winkelmessung/energycurve.pdf
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32
CS/auswertung/figs/winkelmessung/energycurve.pgf
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@ -3559,8 +3559,8 @@
\pgfsetstrokecolor{currentstroke}%
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\pgfusepath{stroke}%
\end{pgfscope}%
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@ -3578,7 +3578,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.687140in}{0.623246in}%
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\pgfsys@useobject{currentmarker}{}%
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@ -3597,7 +3597,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{4.801389in}{0.623246in}%
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\pgfsys@useobject{currentmarker}{}%
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@ -4131,8 +4131,8 @@
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\pgfusepath{stroke}%
\end{pgfscope}%
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@ -4150,7 +4150,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.687140in}{1.022937in}%
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\pgfsys@useobject{currentmarker}{}%
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@ -4169,7 +4169,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{4.801389in}{1.022937in}%
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\pgfsys@useobject{currentmarker}{}%
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@ -4235,8 +4235,8 @@
\pgfsetstrokecolor{currentstroke}%
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\pgfusepath{stroke}%
\end{pgfscope}%
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@ -4254,7 +4254,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.687140in}{1.084428in}%
\pgfsys@transformshift{0.687140in}{1.084429in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
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@ -4273,7 +4273,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{4.801389in}{1.084428in}%
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\pgfsys@useobject{currentmarker}{}%
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@ -4859,8 +4859,8 @@
\pgfsetstrokecolor{currentstroke}%
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\pgfusepath{stroke}%
\end{pgfscope}%
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@ -4878,7 +4878,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.687140in}{1.484119in}%
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\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
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@ -4897,7 +4897,7 @@
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{4.801389in}{1.484119in}%
\pgfsys@transformshift{4.801389in}{1.484120in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%

420
CS/auswertung/out/figlist.txt
View file

@ -904,4 +904,424 @@
\caption{}
\label{fig:crossec-rel_countrates}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/cs.pgf}
\caption{}
\label{fig:calibrate-cs}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_1.pgf}
\caption{}
\label{fig:calibrate-ba_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_2.pgf}
\caption{}
\label{fig:calibrate-ba_2}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_3.pgf}
\caption{}
\label{fig:calibrate-ba_3}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/am_1.pgf}
\caption{}
\label{fig:calibrate-am_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/am_2.pgf}
\caption{}
\label{fig:calibrate-am_2}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/eu_1.pgf}
\caption{}
\label{fig:calibrate-eu_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/energy_fit.pgf}
\caption{}
\label{fig:calibrate-energy_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90.pgf}
\caption{}
\label{fig:hists-am_90}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{}
\label{fig:hists-am_90_0}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/cs.pgf}
\caption{}
\label{fig:calibrate-cs}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_1.pgf}
\caption{}
\label{fig:calibrate-ba_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_2.pgf}
\caption{}
\label{fig:calibrate-ba_2}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_3.pgf}
\caption{}
\label{fig:calibrate-ba_3}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/am_1.pgf}
\caption{}
\label{fig:calibrate-am_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/am_2.pgf}
\caption{}
\label{fig:calibrate-am_2}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/eu_1.pgf}
\caption{}
\label{fig:calibrate-eu_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/energy_fit.pgf}
\caption{}
\label{fig:calibrate-energy_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90.pgf}
\caption{}
\label{fig:hists-am_90}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{}
\label{fig:hists-am_90_0}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90.pgf}
\caption{}
\label{fig:hists-am_90}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{}
\label{fig:hists-am_90_0}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{}
\label{fig:hists-am_90_0}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90.pgf}
\caption{}
\label{fig:hists-am_90}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{}
\label{fig:hists-am_90_0}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90.pgf}
\caption{}
\label{fig:hists-am_90}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{}
\label{fig:hists-am_90_0}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub_fit.pgf}
\caption{}
\label{fig:hists-am_90_sub_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub_fit.pgf}
\caption{}
\label{fig:hists-am_90_sub_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub_fit.pgf}
\caption{}
\label{fig:hists-am_90_sub_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub_fit.pgf}
\caption{}
\label{fig:hists-am_90_sub_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub_fit.pgf}
\caption{}
\label{fig:hists-am_90_sub_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_fit.pgf}
\caption{}
\label{fig:hists-am_90_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/cs.pgf}
\caption{}
\label{fig:calibrate-cs}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_1.pgf}
\caption{}
\label{fig:calibrate-ba_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_2.pgf}
\caption{}
\label{fig:calibrate-ba_2}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/ba_3.pgf}
\caption{}
\label{fig:calibrate-ba_3}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/am_1.pgf}
\caption{}
\label{fig:calibrate-am_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/am_2.pgf}
\caption{}
\label{fig:calibrate-am_2}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/eu_1.pgf}
\caption{}
\label{fig:calibrate-eu_1}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibrate/energy_fit.pgf}
\caption{}
\label{fig:calibrate-energy_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90.pgf}
\caption{}
\label{fig:hists-am_90}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{}
\label{fig:hists-am_90_0}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_sub_fit.pgf}
\caption{}
\label{fig:hists-am_90_sub_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/hists/am_90_fit.pgf}
\caption{}
\label{fig:hists-am_90_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/30.pgf}
\caption{}
\label{fig:winkelmessung-30}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/45.pgf}
\caption{}
\label{fig:winkelmessung-45}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/60.pgf}
\caption{}
\label{fig:winkelmessung-60}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/75.pgf}
\caption{}
\label{fig:winkelmessung-75}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/90.pgf}
\caption{}
\label{fig:winkelmessung-90}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/105.pgf}
\caption{}
\label{fig:winkelmessung-105}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/120.pgf}
\caption{}
\label{fig:winkelmessung-120}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/winkelmessung/energycurve.pgf}
\caption{}
\label{fig:winkelmessung-energycurve}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/crossec/countrates.pgf}
\caption{}
\label{fig:crossec-countrates}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/crossec/rel_countrates.pgf}
\caption{}
\label{fig:crossec-rel_countrates}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/dicke/2.pgf}
\caption{}
\label{fig:dicke-2}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/dicke/4.pgf}
\caption{}
\label{fig:dicke-4}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/dicke/6.pgf}
\caption{}
\label{fig:dicke-6}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/dicke/10.pgf}
\caption{}
\label{fig:dicke-10}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/dicke/20.pgf}
\caption{}
\label{fig:dicke-20}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/dicke/countrate.pgf}
\caption{}
\label{fig:dicke-countrate}
\end{figure}

42
CS/auswertung/utility.py
View file

@ -77,7 +77,7 @@ def set_up_angle_plot(ticks=10):
deg_ax = ax.secondary_xaxis('top', functions=(mu_to_deg, deg_to_mu))
deg_ax.set_xlabel('Winkel')
ax.set_xlabel('$\mu$')
ax.set_xlabel(r'$\mu$')
return fig, ax
@ -124,10 +124,10 @@ def calibrate_peak(spec, start, end, save=None, ret_sigma=False):
opt[0] = np.round(opt[0])
fig, ax = plot_spec(slc, offset=start, label='Gemessen')
ax.plot(chan, gauss_offset(chan, *opt), label='Peak Fit', linestyle='--')
plt.axvline(opt[0], linestyle='-.', color='green', label='$Peak$')
plt.axvline(opt[0], linestyle='-.', color='green', label='Peakzentrum')
if ret_sigma:
ax.axvspan(opt[0]-3*opt[1], opt[0]+3*opt[1], alpha=.2,
label='$3\cdot\sigma$', color='gray', zorder=-10)
label=r'$3\cdot\sigma$', color='gray', zorder=-10)
ax.legend()
if save:
@ -154,7 +154,7 @@ def save_fig(fig, title, folder='unsorted', size=(5, 4)):
+ f'{folder}/{title}.pgf' +
r'''}
\caption{}
\label{fig:''' + folder + '-' + title + '''}
\label{fig:''' + folder + '-' + title + r'''}
\end{figure}
''')
@ -194,3 +194,37 @@ def baseline_als(y, lam, p, niter=10):
z = spsolve(Z, w*y)
w = p * (y > z) + (1-p) * (y < z)
return z
def scientific_round(val, err):
"""Scientifically rounds the values to the given errors."""
val, err = np.asarray(val), np.asarray(err)
if err.size == 1 and val.size > 1:
err = np.ones_like(val)*err
if val.size == 1 and err.size > 1:
val = np.ones_like(err)*val
i = np.floor(np.log10(err))
first_digit = err // 10**i
i = i.astype(int)
prec = (-i + np.ones_like(val) * (first_digit <= 3)).astype(int)
def smart_round(value, precision):
value = np.round(value, precision)
if precision <= 0:
value = int(value)
return value
if val.size > 1:
rounded = np.empty_like(val)
rounded_err = np.empty_like(val)
for n, (value, error, precision) in enumerate(zip(val, err, prec)):
rounded[n] = smart_round(value, precision)
rounded_err[n] = smart_round(error, precision)
return rounded, rounded_err
else:
return smart_round(val, prec), smart_round(err, prec)

68
CS/protokoll/protokoll.tex
View file

@ -254,7 +254,8 @@ Um die Kanallage der Peaks zu bestimmen wird eine Gaußkurve der Form
die Kanallage. Die Unsicherheit der Kanallage ergibt sich aus der
Unsicherheit im Fit. Für die Unsicherheit der H\"ohe der einzelnen
Bins im Histogram wurde gem\"a\ss{} der Poissonverteilung die Wurzel
der Ereigniszahl angesetzt.
der Ereigniszahl angesetzt. Daraus ergibt sich auch die Unsicherheit
der Ereigniszahl im Peak.
Für \ce{^{137}Cs} ist das Resultat in~\ref{fig:calfitcs} dargestellt.
\begin{figure}[h]\centering
@ -317,13 +318,50 @@ durch statistische Schwankungen auch zu N\"agtiven Ereigniszahlen
kommen, die an sich unphysikalisch sind, aber nur bei geringen
Ereignisszahlen auftreten. Die aufgenommen Histogramme sind
in~\ref{fig:am20hist} und~\ref{fig:am20histnull} dargestellt.
\ref{fig:hists-am_90_sub} zeigt das korrigierte Histogram mit
abgezogenem Hintergrund. Es ist zu erkennen, dass der Peak
symmetrischer wirkt und das Histogram die steigende Flanke bei hohen
Kan\"alen verloren hat. Generell schwankt die Z\"ahlrate au\ss{}erhalb
der Peaks einigerma\ss{}en Symmetrisch um die Nullinie, wobei die
Schwankung bei Gro\ss{}en Energien zunehmen und der Mittlwert unter
die Nullinie f\"allt. Da nach der Poissonverteilung zwar der relative
Fehler sinkt, aber der Absolute steigt, ist dieser Unmstand nicht
verwunderlich.
\begin{figure}[h]\centering
Analog zu den Kalibrierungsmessungen wurde
in~\ref{fig:hists-am_90_sub_fit} und~\ref{fig:hists-am_90_fit} das
Zentrum des hohen Peaks bestimmt. Mit abgezogenem Untergrund ergibt
sich \(E_{p}=\SI{51.4\pm 2.1}{\kilo\electronvolt}\) und ohne
\(E_{p}=\SI{53.4\pm 2.1}{\kilo\electronvolt}\). Dahingegen ist der
Theoretisch f\"ur diesen Winkel erwartete Wert
\(E_{pt}=\SI{50.9}{\kilo\electronvolt}\). Es zeigt sich hier also,
dass der Peak ohne Abgezogenen untergrund einen Bias zu h\"oheren
Energien hat. Warscheinlich finden au\ss{}erhalb des Streustabes
andere Streuprozesse unter anderen Winkel mit anderen Charakteristika
statt.
\begin{figure}[htp]\centering
\input{../auswertung/figs/hists/am_90_sub_fit.pgf}
\caption{Fit des \am{} Peaks bei \(\vartheta = 90^\circ\) mit Target und abgezogenen Hintergrund.}
\label{fig:hists-am_90_sub_fit}
\end{figure}
\begin{figure}[htp]\centering
\input{../auswertung/figs/hists/am_90_fit.pgf}
\caption{Fit des \am{} Peaks bei \(\vartheta = 90^\circ\) mit Target und Hintergrund.}
\label{fig:hists-am_90_fit}
\end{figure}
\begin{figure}[htp]\centering
\input{../auswertung/figs/hists/am_90_sub.pgf}
\caption{Histogramm f\"ur \am{} bei \(\vartheta = 90^\circ\) mit Target und abgezogenen Hintergrund.}
\label{fig:hists-am_90_sub}
\end{figure}
\begin{figure}[htp]\centering
\input{../auswertung/figs/hists/am_90.pgf}
\caption{Histogramm f\"ur \am{} bei \(\vartheta = 90^\circ\) mit Target.}
\label{fig:am20hist}
\end{figure}
\begin{figure}[h]\centering
\begin{figure}[htp]\centering
\input{../auswertung/figs/hists/am_90_0.pgf}
\caption{Histogramm f\"ur \am{} bei \(\vartheta = 90^\circ\) ohne
Target. Nullmessung.}
@ -451,15 +489,15 @@ Die Messabweichung ergeben sich gem\"a\ss{}~\eqref{eq::countrate} zu:
&= \frac{1}{t}\sqrt{N_g + N_0} \\
\end{align}
Die ermittelten Zählraten sind in~\ref{fig:countrates}
aufgetragen. Normiert man diese und auch die theoretische Kurve
nach~\eqref{eq::kn} auf den Wert bei \(\theta = 120^\circ\), so ergibt
sich~\ref{fig:rel_countrates}. Man erkennt wiederum eine prinzipielle
\"Ubereinstimmung, wobei sich Abweichungen wie
in~\ref{fig:sigmaknkorrigiert} ergeben. Der dritte Messpunkt ist von
sehr schlechter Qualit\"at, da die Messung ungew\"ohnlich stark
rauschte und liegt deswegen weitab der Theoriekurve. (Siehe
auch~\ref{fig:90})
Die ermittelten Zählraten sind in~\ref{fig:countrates} aufgetragen und
in~\ref{tab:ratedurch1} aufgelistat. Normiert man diese und auch die
theoretische Kurve nach~\eqref{eq::kn} auf den Wert bei
\(\theta = 120^\circ\), so ergibt sich~\ref{fig:rel_countrates}. Man
erkennt wiederum eine prinzipielle \"Ubereinstimmung, wobei sich
Abweichungen wie in~\ref{fig:sigmaknkorrigiert} ergeben. Der dritte
Messpunkt ist von sehr schlechter Qualit\"at, da die Messung
ungew\"ohnlich stark rauschte und liegt deswegen weitab der
Theoriekurve. (Siehe auch~\ref{fig:90})
Zu erkennen ist weiterhin, dass die Theoriekurve bei gro\ss{}en Winkeln
recht gut mit den Messungen \"ubereinstimmt und kleinen Winkeln
@ -484,7 +522,7 @@ gew\"ahlt, um dieses Bild zu provozieren.
120 & 4.04 & .13
\end{tabular}
\caption{Zählrate \(\dot{N}\) in Abhängigkeit vom Winkel.}
\label{tab:ratedurch}
\label{tab:ratedurch1}
\end{table}
@ -523,7 +561,9 @@ in~\ref{fig:dicke-countrate} aufgetragen.
10,2 & 9.88 & .20 \\
20,4 & 8.13 & .19
\end{tabular}
\caption{Zählrate \(\dot{N}\) in Abhängigkeit des Durchmessers \(d\).}
\caption{Zählrate \(\dot{N}\) in Abhängigkeit des Durchmessers
\(d\). Die ungeraden Zahlen wurden so gemessen. Im text wird
auf gerundete Were Bezug genommen.}
\label{tab:ratedurch}
\end{table}

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