mirror of
https://github.com/vale981/fpraktikum
synced 2025-03-04 17:11:41 -05:00
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This commit is contained in:
Valentin Boettcher
parent
c7f86d1db3
commit
a4fb767d61
9 changed files with 183 additions and 148 deletions
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"cells": [
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"7000"
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"execution_count": 46,
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"execution_count": 47,
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"execution_count": 4,
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"array([False, False, False, ..., False, False, False])"
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"execution_count": 47,
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"execution_count": 4,
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"output_type": "execute_result"
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"execution_count": 48,
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"execution_count": 5,
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"metadata": {
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"execution_count": 49,
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"execution_count": 6,
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"metadata": {
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@ -168,7 +168,7 @@
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"(array([ 970, 1140]),\n (array([46.81285, 55.02385]), array([0.02728758, 0.02979973])))"
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]
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"execution_count": 49,
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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{
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"cell_type": "code",
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"execution_count": 50,
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"execution_count": 7,
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"metadata": {
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{
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"cell_type": "code",
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"execution_count": 51,
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"execution_count": 8,
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"(array([2800, 3600]), array([582.2, 725.4]))"
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]
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"execution_count": 51,
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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{
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"cell_type": "code",
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"execution_count": 52,
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"execution_count": 9,
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"metadata": {
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"(array([1600, 2300]), array([452., 606.]))"
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]
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"execution_count": 52,
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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{
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"cell_type": "code",
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"execution_count": 53,
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"execution_count": 10,
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{
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"cell_type": "code",
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"execution_count": 54,
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"execution_count": 11,
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{
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"cell_type": "code",
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"execution_count": 55,
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"execution_count": 12,
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"metadata": {
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{
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"cell_type": "code",
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"execution_count": 56,
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"execution_count": 13,
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"metadata": {
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},
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{
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"cell_type": "code",
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"execution_count": 57,
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"execution_count": 14,
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"metadata": {
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},
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{
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"cell_type": "code",
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"execution_count": 58,
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"execution_count": 15,
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"metadata": {
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{
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"cell_type": "code",
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"execution_count": 59,
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"execution_count": 16,
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"metadata": {
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"2.175378970759084"
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]
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"execution_count": 59,
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"execution_count": 16,
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{
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"cell_type": "code",
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"execution_count": 60,
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"execution_count": 17,
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"0.6162102374593533"
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"execution_count": 60,
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"(326.08110436268794, 92.36759086635159)"
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"execution_count": 61,
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"0.28959951442800036"
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"execution_count": 62,
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"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -1057,7 +1057,7 @@
|
|||
"969"
|
||||
]
|
||||
},
|
||||
"execution_count": 36,
|
||||
"execution_count": 37,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -1066,49 +1066,6 @@
|
|||
"range_t[0] - 1"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 37,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
"ein.hycell": false,
|
||||
"ein.tags": "worksheet-0",
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(0.0577, 0.0018)"
|
||||
]
|
||||
},
|
||||
"execution_count": 37,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"scientific_round(*rand_rate)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 37,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
"ein.hycell": false,
|
||||
"ein.tags": "worksheet-0",
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
}
|
||||
},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 38,
|
||||
|
|
@ -1125,7 +1082,7 @@
|
|||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([0.0136465 , 0.00041789])"
|
||||
"(0.0577, 0.0018)"
|
||||
]
|
||||
},
|
||||
"execution_count": 38,
|
||||
|
|
@ -1133,6 +1090,49 @@
|
|||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"scientific_round(*rand_rate)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 38,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
"ein.hycell": false,
|
||||
"ein.tags": "worksheet-0",
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
}
|
||||
},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 39,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
"ein.hycell": false,
|
||||
"ein.tags": "worksheet-0",
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([0.0136465 , 0.00041789])"
|
||||
]
|
||||
},
|
||||
"execution_count": 39,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"rand_rate/rate[0] * 100"
|
||||
]
|
||||
|
|
@ -1151,7 +1151,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 39,
|
||||
"execution_count": 40,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -1166,34 +1166,6 @@
|
|||
"effectivity = SecondaryValue('rate/(A*omega/(2*pi)*P)')(P=P, A=A0, rate=rate, omega=omega, pi=np.pi)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 40,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
"ein.hycell": false,
|
||||
"ein.tags": "worksheet-0",
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(11.3, 0.8)"
|
||||
]
|
||||
},
|
||||
"execution_count": 40,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"scientific_round((effectivity[0]*100), effectivity[1]*100)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 41,
|
||||
|
|
@ -1210,7 +1182,7 @@
|
|||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"10006.075034502068"
|
||||
"(11.3, 0.8)"
|
||||
]
|
||||
},
|
||||
"execution_count": 41,
|
||||
|
|
@ -1219,7 +1191,7 @@
|
|||
}
|
||||
],
|
||||
"source": [
|
||||
"A0[1]"
|
||||
"scientific_round((effectivity[0]*100), effectivity[1]*100)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1238,7 +1210,7 @@
|
|||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(422.7496136012365, 1.5365950819791954)"
|
||||
"10006.075034502068"
|
||||
]
|
||||
},
|
||||
"execution_count": 42,
|
||||
|
|
@ -1246,13 +1218,41 @@
|
|||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"A0[1]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 43,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
"ein.hycell": false,
|
||||
"ein.tags": "worksheet-0",
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(422.7496136012365, 1.5365950819791954)"
|
||||
]
|
||||
},
|
||||
"execution_count": 43,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"rate"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 43,
|
||||
"execution_count": 44,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
|
|||
Binary file not shown.
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Binary file not shown.
|
|
@ -2230,4 +2230,40 @@
|
|||
\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}
|
||||
|
||||
|
|
@ -44,16 +44,15 @@ Positronen. Diese werden durch \(\beta^+\)~-~Zerfall erzeugt.
|
|||
p^+ \rightarrow n + e^+ + \nu_e
|
||||
\end{equation}
|
||||
|
||||
Wie die Zerfallsgleichung~\eqref{eq:betazerf} zeigt, zerfällt beim
|
||||
\(\beta^+\)~-~Zerfall ein Proton in ein Neutron, das für die PET
|
||||
wichtige Positron und ein Elektron-Neutrino. Weswegen die
|
||||
Tracer-Materialien einen Protonenüberschuss im Kern haben. Neutrinos
|
||||
interagieren nur sehr selten mit Materie, weshalb die beim Zerfall
|
||||
entstehenden einfach durch den Körper durchgehen und somit hier nicht
|
||||
interessant sind. Das Neutron verbleibt im Kern und das Positron
|
||||
propagiert durch das Gewebe des Körpers mit einer Reichweite von
|
||||
wenigen Millimetern und annihiliert dann mit einem Elektron aus der
|
||||
Hülle eines Atoms zu zwei Photonen.
|
||||
Gem\"a\ss{}~\eqref{eq:betazerf} geht beim \(\beta^+\)~-~Zerfall ein
|
||||
Proton in ein Neutron, das für die PET wichtige Positron und ein
|
||||
Elektron-Neutrino \"uber. Dieser Prozess wird durch einen
|
||||
Protonen\"uberschuss im Kern beg\"unstigt. Neutrinos interagieren nur
|
||||
sehr selten mit Materie und sind desshalb f\"ur tomographische Zwecke
|
||||
nicht interessant. Das entstehende Positron allerdings propagiert
|
||||
durch das Gewebe des Körpers mit einer Reichweite von wenigen
|
||||
Millimetern und annihiliert dann mit einem Elektron aus der Hülle
|
||||
eines Atoms zu zwei Photonen.
|
||||
|
||||
\begin{equation}\label{eq:annihi}
|
||||
e^+ + e^- \rightarrow \gamma + \gamma
|
||||
|
|
@ -70,7 +69,7 @@ Photonen einen Winkel von \(180^\circ\) ein, bewegen sich also antiparallel.\\
|
|||
|
||||
Um den Beobachtungsort sind in einem Ring (in diesem Versuch nur zwei
|
||||
gegenüberliegende, die in einer festgelegten Geschwindigkeit um die
|
||||
Quelle herumfahrende, siehe~\ref{fig:aufgau}) Detektoren angebracht,
|
||||
Quelle herumfahrende, siehe~\ref{fig:aufbau}) Detektoren angebracht,
|
||||
die die entstandenen Photonen registrieren. Allerdings können zum
|
||||
Beispiel durch andere Zerfallsprozesse natürlich auch andere Photonen
|
||||
entstehen, die die Messungen stören. Um solche zufällige Koinzidenzen
|
||||
|
|
@ -258,7 +257,7 @@ eingestellten Energie- und Koinzidenzzeitfenster einhalten. Dabei
|
|||
l\"auft die Pr\"ufung des Zeitkriteriums auf einem schnelleren Pfad
|
||||
als die Verarbeitung der Energieinformationen, um eine hohe Z\"ahlrate
|
||||
zu gew\"ahrleisten. Diese Teilung wird durch spezielle NIM Karten in
|
||||
Hardware vorgenommen (siehe~\ref{fig:aufgau}). Die im Detektor
|
||||
Hardware vorgenommen (siehe~\ref{fig:aufbau}). Die im Detektor
|
||||
deponierte Energie wird durch die Summierung der gemessenen
|
||||
Amplituden, die proportional zur Energie sind, ermittelt. Nun werden
|
||||
den Photonen die Kristalle zugeordnet und deren Position auf der
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue