some fine tuning

This commit is contained in:
hiro98 2020-01-24 21:09:12 +01:00
parent ea445ea54c
commit 92b81f841f
25 changed files with 10181 additions and 214 deletions

293
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%% Creator: Matplotlib, PGF backend
%%
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%%
%% Figures using additional raster images can only be included by \input if
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@ -2038,4 +2038,196 @@
\caption{}
\label{fig:theory-rec_filtered}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/mid_over_energy.pgf}
\caption{}
\label{fig:calibration-mid_over_energy}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/mid_over_channel.pgf}
\caption{}
\label{fig:calibration-mid_over_channel}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/time_range.pgf}
\caption{}
\label{fig:calibration-time_range}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/all_times.pgf}
\caption{}
\label{fig:calibration-all_times}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/comp.pgf}
\caption{}
\label{fig:calibration-comp}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/3dplot.pgf}
\caption{}
\label{fig:tom1-3dplot}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/filtered_fit.pgf}
\caption{}
\label{fig:tom1-filtered_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/unfiltered_fit.pgf}
\caption{}
\label{fig:tom1-unfiltered_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/3dplot.pgf}
\caption{}
\label{fig:tom1-3dplot}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/filtered_fit.pgf}
\caption{}
\label{fig:tom1-filtered_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/unfiltered_fit.pgf}
\caption{}
\label{fig:tom1-unfiltered_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/mid_over_energy.pgf}
\caption{}
\label{fig:calibration-mid_over_energy}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/mid_over_channel.pgf}
\caption{}
\label{fig:calibration-mid_over_channel}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/time_range.pgf}
\caption{}
\label{fig:calibration-time_range}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/all_times.pgf}
\caption{}
\label{fig:calibration-all_times}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/source.pgf}
\caption{}
\label{fig:theory-source}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/projection.pgf}
\caption{}
\label{fig:theory-projection}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/convoluted.pgf}
\caption{}
\label{fig:theory-convoluted}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/rec_simple.pgf}
\caption{}
\label{fig:theory-rec_simple}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/rec_filtered.pgf}
\caption{}
\label{fig:theory-rec_filtered}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/source.pgf}
\caption{}
\label{fig:theory-source}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/projection.pgf}
\caption{}
\label{fig:theory-projection}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/convoluted.pgf}
\caption{}
\label{fig:theory-convoluted}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/rec_simple.pgf}
\caption{}
\label{fig:theory-rec_simple}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/rec_filtered.pgf}
\caption{}
\label{fig:theory-rec_filtered}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/source.pgf}
\caption{}
\label{fig:theory-source}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/projection.pgf}
\caption{}
\label{fig:theory-projection}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/convoluted.pgf}
\caption{}
\label{fig:theory-convoluted}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/rec_simple.pgf}
\caption{}
\label{fig:theory-rec_simple}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/theory/rec_filtered.pgf}
\caption{}
\label{fig:theory-rec_filtered}
\end{figure}

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@ -303,7 +303,7 @@ mit der Kantenl\"ange des Detektors
\begin{align}
\label{eq:incidentalrate}
\mathfrak{R}_Z &= \qty[4\tau\cdot A\cdot
\qty(\frac{\Omega_{\min}}{2\pi})]\cdot \mathfrak{R} \pm
\qty(\frac{\Omega_{\min}}{2\pi})]\cdot \mathfrak{R} \pm \mathfrak{R}_Z\cdot
\sqrt{\qty(\frac{\Delta\tau}{\tau})^2 + \qty(\frac{\Delta A}{A})^2 +
\qty(\frac{\Delta\Omega_{\min}}{\Omega_{\min}})^2 +
\qty(\frac{\Delta\mathfrak{R}}{\mathfrak{R}})^2} \\
@ -320,7 +320,7 @@ mit \(P_\beta = 0.90382\pm 0.00021\) zu:
\begin{align}
\epsilon & = \frac{\mathfrak{R}}{P_\beta\cdot A \cdot
\frac{\Omega_{\min}}{2\pi}} \pm \sqrt{\qty(\frac{\Delta A}{A})^2 +
\frac{\Omega_{\min}}{2\pi}} \pm \epsilon\cdot\sqrt{\qty(\frac{\Delta A}{A})^2 +
\qty(\frac{\Delta\Omega_{\min}}{\Omega_{\min}})^2 +
\qty(\frac{\Delta P_\beta}{P_\beta})^2 +
\qty(\frac{\Delta\mathfrak{R}}{\mathfrak{R}})^2} \\
@ -674,9 +674,9 @@ von den Eckpunkten eines perfekten Quadrates.
[\si{\milli\meter}]} \\
\midrule
1 & 11.89 & 0.1 & 65.604 & 0.04 & 35.972 & 0.04 & 4.664 & 0.028 \\
1 & 11.89 & 0.10 & 65.604 & 0.040 & 35.972 & 0.040 & 4.664 & 0.028 \\
2 & 22.49 & 0.11 & 67.971 & 0.022 & 64.842 & 0.022 & 4.639 & 0.016 \\
3 & 14.24 & 0.16 & 94.68 & 0.06 & 65.9 & 0.06 & 5.22 & 0.04
3 & 14.24 & 0.16 & 94.680 & 0.060 & 65.900 & 0.060 & 5.220 & 0.040
\end{tabular}
\caption[Peakpositionen]{Gefitte Peakamplituden, Positionen und
Breiten. Die Abweichungen ergeben sich aus den
@ -693,17 +693,22 @@ Abw. \SI{3}{\percent}).
\begin{equation}
\label{eq:act3today}
A_3 = \SI{19\pm 6}{\kilo\becquerel}
A_3 = \SI{19.1\pm .6}{\kilo\becquerel}
\end{equation}
Damit berechnen sich die in~\ref{tab:peakactivities} aufgelisteten
Aktivit\"aten der beiden anderen Proben wiefolgt.
Aktivit\"aten der beiden anderen Proben wiefolgt durch
verh\"altnissbildung der Peak volumina (\(= 2\pi A\sigma**2\)) die ein
Ma\ss{} f\"ur die Z\"ahlrate geben. Die Abweichungen liegen alle in
der Gr\"o\ss{}enordnung von \SI{3}{\percent} und r\"uhren
haupts\"achlich von der Abweichung der Aktivit\"at \(A_3\) her.
\begin{equation}
\label{eq:relakt}
A_i = \frac{\mathfrak{A}_i}{\mathfrak{A}_3}\cdot
A_3\pm\sqrt{\qty(\frac{\Delta\mathfrak{A}_i}{\mathfrak{A}_i})^2 +
\qty(\frac{\Delta\mathfrak{A}_3}{\mathfrak{A}_3})^2 +
A_i = \frac{\mathfrak{A}_i\cdot\sigma_i^2}{\mathfrak{A}_3\cdot\sigma_3^2}\cdot
A_3\pm
A_i\cdot\sqrt{\qty(\frac{\Delta\mathfrak{A}_i}{\mathfrak{A}_i})^2 + \qty(\frac{2\sigma_i}{\sigma_i})^2 +
\qty(\frac{\Delta\mathfrak{A}_3}{\mathfrak{A}_3})^2 + \qty(\frac{2\sigma_3}{\sigma_3})^2 +
\qty(\frac{\Delta A_3}{A_3})^2}
\end{equation}
@ -713,8 +718,8 @@ Aktivit\"aten der beiden anderen Proben wiefolgt.
\toprule
Peak & {\(A\) [\si{\kilo\becquerel}]} & {\(\Delta A\) [\si{\kilo\becquerel}]} \\
\midrule
Peak 1 & 16 & 5 \\
Peak 2 & 30 & 9
Peak 1 & 12.7 & .5 \\
Peak 2 & 23.8 & .9
\end{tabular}
\caption[Rekonstruierte Quellaktivit\"aten]{Die
aus~\eqref{eq:relakt} berechneten Quellaktivit\"aten.}
@ -1125,11 +1130,15 @@ Es ist zu erkennen, das in beiden Rekonstruktionen die starken Signale
Unterschiede in der Signalst\"arke nicht im urspr\"unglichen
Verh\"altnis stehen. Die gefilterte R\"uckprojektion weist in den
Randfeldern und im mittleren Feld einen h\"oheren Kontrast auf,
erzeugt aber dennoch nur ein geringf\"ugig besseres und in manchen
Bereichen (Ecken) sogar ein schlechteres Bild. Das schwache Signal
\((0,4)\) wurde in beiden F\"allen nicht rekonstruiert. F\"uhrt man
die Rechnung ohne diesen Punkt aus, ergibt sich kaum ein
Unterschied. Schwache Signale werden also nicht gut reproduziert.
erzeugt aber dennoch nur ein geringf\"ugig besseres Bild. Der
angewendete Filter unterdr\"uckt schwache Signale, die zwischen
Starken liegen da die angrenzenden Werte abgezogen werden. Das
schwache Signal \((0,4)\) wurde in beiden F\"allen nicht
rekonstruiert. F\"uhrt man die Rechnung ohne diesen Punkt aus, ergibt
sich kaum ein Unterschied. Schwache Signale werden also nicht gut
reproduziert. In beiden F\"allen schmieren die Starken Quellen auf
ihren jeweiligen Verbindungsachsen aus. Dies kann ein Effekt der
bergrenzten Anzahl von Projektionswinkeln sein.
\newpage
\section{Verzeichnisse}