mirror of
https://github.com/vale981/fpraktikum
synced 2025-03-04 17:11:41 -05:00
pet corrections
This commit is contained in:
parent
794b7fa58f
commit
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17 changed files with 555 additions and 648 deletions
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@ -67,10 +67,10 @@
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|
|
|||
Binary file not shown.
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|
|
@ -2267,3 +2267,315 @@
|
|||
\label{fig:calibration-comp}
|
||||
\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/calibration/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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/lenght_det.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\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}
|
||||
|
||||
|
|
@ -2,7 +2,7 @@
|
|||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 47,
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -34,7 +34,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 48,
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -52,7 +52,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 49,
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -85,7 +85,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 50,
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -115,7 +115,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 51,
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -132,7 +132,7 @@
|
|||
"[([50.17388514220538, 65.68908198786471, 36.93627963994932, 4.650969229553721],\n [0.6505252591427874,\n 0.060298800686361356,\n 0.060298769274691306,\n 0.042637675284470856]),\n ([39.304159661459444,\n 79.31346233940788,\n 66.51806573625299,\n -12.180797677677088],\n [1.2865802111592206,\n 0.39869931030584704,\n 0.39869930573273576,\n 0.28192301086177374])]"
|
||||
]
|
||||
},
|
||||
"execution_count": 51,
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
|
|
@ -155,7 +155,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 52,
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -183,7 +183,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 65,
|
||||
"execution_count": 7,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -204,7 +204,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 66,
|
||||
"execution_count": 8,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -221,7 +221,7 @@
|
|||
"(19.115801602937395, 0.5738039944241058)"
|
||||
]
|
||||
},
|
||||
"execution_count": 66,
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -232,7 +232,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 67,
|
||||
"execution_count": 9,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -249,7 +249,7 @@
|
|||
"(19.1, 0.6)"
|
||||
]
|
||||
},
|
||||
"execution_count": 67,
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -260,7 +260,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 68,
|
||||
"execution_count": 10,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -277,7 +277,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 76,
|
||||
"execution_count": 11,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
@ -315,7 +315,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 77,
|
||||
"execution_count": 16,
|
||||
"metadata": {
|
||||
"autoscroll": false,
|
||||
"collapsed": false,
|
||||
|
|
|
|||
|
|
@ -46,6 +46,10 @@ channel_to_time_val = SecondaryValue('a + b*(k-1/2)',
|
|||
def channel_to_time(channel, d=0):
|
||||
return channel_to_time_val(k=(channel, d))
|
||||
|
||||
def time_to_channel(time):
|
||||
a = -.014
|
||||
b = .0483
|
||||
return ((time - a)/b).astype(int)
|
||||
|
||||
def scientific_round(val, err):
|
||||
"""Scientifically rounds the values to the given errors."""
|
||||
|
|
@ -160,23 +164,27 @@ def plot_spectrum(counts, offset=1, save=None, **pyplot_args):
|
|||
# Time of Flight Analysiss #
|
||||
###############################################################################
|
||||
|
||||
def gauss(x, a, mu, sigma):
|
||||
return a*np.exp(-(x-mu)**2/(2*sigma**2))
|
||||
def gauss(x, a, mu, sigma, o):
|
||||
return a*np.exp(-(x-mu)**2/(2*sigma**2)) + o
|
||||
|
||||
def find_and_plot_peak(counts, ax, label):
|
||||
def find_and_plot_peak(counts, ax, label, time_interval=[40, 70]):
|
||||
channels = np.arange(0, counts.size) + 1
|
||||
counts = counts.copy()/counts.max()
|
||||
times, d_times = channel_to_time(channels)
|
||||
|
||||
interval = time_to_channel(np.array(time_interval))
|
||||
splot = ax.step(times, counts, label=label, alpha=.4)
|
||||
opt, cov = curve_fit(gauss, channels, counts,
|
||||
p0=(1, counts.argmax(), 100))
|
||||
opt, cov = curve_fit(gauss, channels[interval[0]:interval[1]],
|
||||
counts[interval[0]:interval[1]],
|
||||
sigma=np.sqrt(counts[interval[0]:interval[1]]),
|
||||
absolute_sigma=True,
|
||||
p0=(1, counts.argmax(), 100, .3))
|
||||
cov = np.sqrt(np.diag(cov))
|
||||
gplot = ax.plot(times, gauss(channels,*opt), label=f"Fit {label}", color=splot[0].get_color())
|
||||
gplot = ax.plot(times, gauss(channels,*opt), label=f"Fit {label}",
|
||||
color=splot[0].get_color())
|
||||
ax.axvline(channel_to_time(opt[1])[0], color=gplot[0].get_color())
|
||||
t, dt = channel_to_time(opt[1], opt[2]/10)
|
||||
t, dt = channel_to_time(opt[1], cov[1])
|
||||
ax.axvspan(t-dt, t+dt, alpha=.2, color=gplot[0].get_color())
|
||||
return channel_to_time(opt[1], opt[2]/10)
|
||||
return t, dt
|
||||
|
||||
|
||||
###############################################################################
|
||||
|
|
|
|||
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|
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PET/protokoll/figs/radon.png
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|
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|
|
@ -1,4 +1,5 @@
|
|||
\documentclass[slug=PET, room=Andreas-Schubert-Bau\,\ 424A, supervisor=Carsten\ Bittrich, coursedate=10.\ 01.\ 2020]{../../Lab_Report_LaTeX/lab_report}
|
||||
\documentclass[slug=PET, room=Andreas-Schubert-Bau\,\ 424A,
|
||||
supervisor=Carsten\ Bittrich, coursedate=10.\ 01.\ 2020, ngerman]{../../Lab_Report_LaTeX/lab_report}
|
||||
|
||||
\title{Postitronenemissionstomographie}
|
||||
\author{Oliver Matthes, Valentin Boettcher}
|
||||
|
|
@ -391,7 +392,7 @@ durch~\eqref{tab:caltime}.
|
|||
\end{equation}
|
||||
|
||||
Die Aktivität der \ce{^22Na} Kalibrierungsprobe ergibt sich mit
|
||||
\(t=\SI{166492800}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\) und \(A_0
|
||||
\(t=\SI{166492800\pm 86400}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\) und \(A_0
|
||||
= \SI{1.36}{\mega\becquerel}\) (1.10.2014, Abw. \SI{3}{\percent}).
|
||||
|
||||
\begin{equation}
|
||||
|
|
@ -400,8 +401,7 @@ Die Aktivität der \ce{^22Na} Kalibrierungsprobe ergibt sich mit
|
|||
\frac{\ln{2}}{t_{1/2}}\cdot A\cdot\Delta A = \SI{.333\pm.010}{\mega\becquerel}
|
||||
\end{equation}
|
||||
|
||||
Die Z\"ahlate der zuf\"alligen Koinzidenzen ergibt sich aus
|
||||
% \todo{!!!!! GLEICHUNG}
|
||||
Die Z\"ahlate der zuf\"alligen Koinzidenzen ergibt sich aus~\eqref{eq:zufkoinz}
|
||||
mit der Kantenl\"ange des Detektors
|
||||
\(a=\SI{54}{\milli\meter}\) und dem Detektorabstand
|
||||
\(D=\SI{386}{\milli\meter}\) sowie
|
||||
|
|
@ -475,29 +475,32 @@ redundant) so ergibt sich die doppelte Lichtlaufzeit \(\mathfrak{t}\)
|
|||
zwischen den Detektoren
|
||||
(\(t_0 + \mathfrak{t} - (t_0 - \mathfrak{t}) = 2\mathfrak{t}\)).
|
||||
|
||||
Um die Peakpositionen zu erhalten, wurden Gaußfunktionen \"uber die
|
||||
Zeitspektren gefittet. Als Ma\ss{} f\"ur die Peakbreite und damit die
|
||||
(statistische) Unsicherheit wurde \(1/10\) des \(\sigma\) Parameters
|
||||
der Gaußfunktion genutzt (heuristische Absch\"atzung). Nicht explizit
|
||||
betrachtet werden hier der endliche Quellendurchmesser
|
||||
\SI{2.5}{\centi\meter} sowie der Restabstand der Quelle zum Detektor
|
||||
(kleiner \SI{1}{\centi\meter}). Der Prozess wird
|
||||
Um die Peakpositionen zu erhalten, wurden Gaußfunktionen (mit
|
||||
vertikalem offset) \"uber die Zeitspektren im Bereich von
|
||||
\SIrange{40}{60}{\nano\second} (links, mitte) und
|
||||
\SIrange{45}{65}{\nano\second} (rechts )gefittet. Die (statistische)
|
||||
Unsicherheit wurde aus der Fit unsicherheit f\"ur den Mittelwert
|
||||
\"bernommen. Nicht explizit betrachtet werden hier der endliche
|
||||
Quellendurchmesser \SI{2.5}{\centi\meter} sowie der Restabstand der
|
||||
Quelle zum Detektor (kleiner \SI{1}{\centi\meter}). Der Prozess wird
|
||||
in~\ref{fig:calibration-lenght_det} illustriert.
|
||||
|
||||
\begin{figure}[htb]\centering
|
||||
\input{../auswertung/figs/calibration/lenght_det.pgf}
|
||||
\caption[Abstandsbestimmung]{Bestimmung der Peakpositionen der Zeitspektren zwecks der
|
||||
Berechnung des Detektorabstandes. Die farbigen Intervallmarkierungen
|
||||
stellen die gesch\"atzte Abweichung dar.}
|
||||
stellen die Abweichung aus dem Fit dar.}
|
||||
\label{fig:calibration-lenght_det}
|
||||
\end{figure}
|
||||
|
||||
Entsprechend ergibt sich dann der Detektorabstand zu:
|
||||
Entsprechend ergibt sich dann der Detektorabstand zu
|
||||
\begin{align}
|
||||
\label{eq:abst}
|
||||
\mathfrak{t} &= \SI{2.2\pm .6}{\nano\second} \\
|
||||
D &= \frac{\mathfrak{t}}{2c} = \SI{330\pm 90}{\milli\meter}
|
||||
2\mathfrak{t} &= \SI{2.0\pm .6}{\nano\second} \\
|
||||
D &= \mathfrak{t}\cdot c = \SI{310\pm 90}{\milli\meter}.
|
||||
\end{align}
|
||||
Dieses Ergebnis ist kompatibel mit dem Litertaturwert von
|
||||
\SI{386}{\milli\meter}.
|
||||
|
||||
\subsubsection{Schwerpunktsdiagramme}
|
||||
\label{sec:schwpkt}
|
||||
|
|
@ -798,7 +801,7 @@ Ort liegt weit \"uber der mittleren Diffusionsl\"ange der Positronen
|
|||
|
||||
Analog zu~\eqref{eq:acttoday} ergibt sich f\"ur die Aktivität der
|
||||
\ce{^22Na} Quelle zu Peak 3 mit
|
||||
\(t=\SI{313632000}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\)
|
||||
\(t=\SI{313632000\pm 86400}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\)
|
||||
und \(A_0 = \SI{270}{\kilo\becquerel}\) (1.2.2010,
|
||||
Abw. \SI{3}{\percent}).
|
||||
|
||||
|
|
@ -811,8 +814,7 @@ Damit berechnen sich die in~\ref{tab:peakactivities} aufgelisteten
|
|||
Aktivit\"aten der beiden anderen Proben wie folgt durch
|
||||
Verh\"altnisbildung der Peakvolumina (\(= 2\pi A\sigma**2\)), 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.
|
||||
der Gr\"o\ss{}enordnung von \SI{3}{\percent}.
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:relakt}
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue