From a4fb767d6196bee3ab8fcbafe6b6b75b368d8821 Mon Sep 17 00:00:00 2001
From: Valentin Boettcher <valentin@boettcher.cf>
Date: Mon, 27 Jan 2020 16:48:18 +0100
Subject: [PATCH] more pet

---
 PET/auswertung/Untitled.ipynb                 | 272 +++++++++---------
 PET/auswertung/figs/calibration/all_times.pdf | Bin 24279 -> 24279 bytes
 PET/auswertung/figs/calibration/comp.pdf      | Bin 174711 -> 174711 bytes
 .../figs/calibration/lenght_det.pdf           | Bin 25850 -> 25850 bytes
 .../figs/calibration/mid_over_channel.pdf     | Bin 88104 -> 88104 bytes
 .../figs/calibration/mid_over_energy.pdf      | Bin 80619 -> 80619 bytes
 .../figs/calibration/time_range.pdf           | Bin 37396 -> 37396 bytes
 PET/auswertung/out/figlist.txt                |  36 +++
 PET/protokoll/protokoll.tex                   |  23 +-
 9 files changed, 183 insertions(+), 148 deletions(-)

diff --git a/PET/auswertung/Untitled.ipynb b/PET/auswertung/Untitled.ipynb
index 5ab858b..ac272cd 100644
--- a/PET/auswertung/Untitled.ipynb
+++ b/PET/auswertung/Untitled.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 1,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 2,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 3,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -79,7 +79,7 @@
        "7000"
       ]
      },
-     "execution_count": 46,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -94,7 +94,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 4,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -111,7 +111,7 @@
        "array([False, False, False, ..., False, False, False])"
       ]
      },
-     "execution_count": 47,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 5,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -151,7 +151,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 6,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -168,7 +168,7 @@
        "(array([ 970, 1140]),\n (array([46.81285, 55.02385]), array([0.02728758, 0.02979973])))"
       ]
      },
-     "execution_count": 49,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -179,7 +179,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 7,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -199,7 +199,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 8,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -216,7 +216,7 @@
        "(array([2800, 3600]), array([582.2, 725.4]))"
       ]
      },
-     "execution_count": 51,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -227,7 +227,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 9,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -244,7 +244,7 @@
        "(array([1600, 2300]), array([452., 606.]))"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -255,7 +255,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 10,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -310,7 +310,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 11,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -353,7 +353,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 12,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -387,7 +387,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 13,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -427,7 +427,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 14,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -466,7 +466,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 15,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -483,7 +483,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 16,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -500,7 +500,7 @@
        "2.175378970759084"
       ]
      },
-     "execution_count": 59,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -511,7 +511,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 17,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -528,7 +528,7 @@
        "0.6162102374593533"
       ]
      },
-     "execution_count": 60,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -539,7 +539,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 18,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -556,7 +556,7 @@
        "(326.08110436268794, 92.36759086635159)"
       ]
      },
-     "execution_count": 61,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -567,7 +567,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 19,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -584,7 +584,7 @@
        "0.28959951442800036"
       ]
      },
-     "execution_count": 62,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -595,7 +595,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 20,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -612,7 +612,7 @@
        "0.3185594658707989"
       ]
      },
-     "execution_count": 63,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -623,7 +623,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 21,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -640,7 +640,7 @@
        "0.2606395629852018"
       ]
      },
-     "execution_count": 64,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -663,7 +663,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 22,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -682,7 +682,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 66,
+   "execution_count": 23,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -699,7 +699,7 @@
        "(8.211000000000006, 0.040405893134541654)"
       ]
      },
-     "execution_count": 66,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -710,7 +710,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 67,
+   "execution_count": 24,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -727,7 +727,7 @@
        "(8.211000000000006e-09, 4.040589313454165e-11)"
       ]
      },
-     "execution_count": 67,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -738,7 +738,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 25,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -762,7 +762,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 26,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -779,7 +779,7 @@
        "166492800.0"
       ]
      },
-     "execution_count": 69,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -790,7 +790,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 27,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -807,7 +807,7 @@
        "0.07828398077800745"
       ]
      },
-     "execution_count": 70,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -818,7 +818,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 28,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -835,7 +835,7 @@
        "(1.2875574074648669e-09, (647, 2))"
       ]
      },
-     "execution_count": 71,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -846,7 +846,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 29,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -863,7 +863,7 @@
        "333481.7538834827"
       ]
      },
-     "execution_count": 72,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -874,7 +874,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": 30,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -891,7 +891,7 @@
        "0.01"
       ]
      },
-     "execution_count": 78,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -902,7 +902,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 31,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -919,7 +919,7 @@
        "166492800.0"
       ]
      },
-     "execution_count": 73,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -930,7 +930,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 32,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -948,7 +948,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 33,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -965,7 +965,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 34,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -982,7 +982,7 @@
        "(422.7496136012365, 1.5365950819791954)"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -993,7 +993,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 35,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -1012,7 +1012,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 36,
    "metadata": {
     "autoscroll": false,
     "collapsed": false,
@@ -1029,7 +1029,7 @@
        "422.7496136012365"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1040,7 +1040,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 37,
    "metadata": {
     "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,
diff --git a/PET/auswertung/figs/calibration/all_times.pdf b/PET/auswertung/figs/calibration/all_times.pdf
index d5099290a6226cc8d95c67938023604a0d97f978..d83f0371ec083e140a545af7e8fc99031633903a 100644
GIT binary patch
delta 22
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delta 22
dcmcb<m+|^u#to@a>?TGAMrK9^n{%SFSpaDy2k8I+

diff --git a/PET/auswertung/figs/calibration/comp.pdf b/PET/auswertung/figs/calibration/comp.pdf
index 97ac1ec8fab8ba759cc90df136d9ef00cd5c657d..1d0041a4c76ed06d8e417fe5cdfe879c3fc6469b 100644
GIT binary patch
delta 26
icmex<h3oqju7(!IElep(*~|?M42(>+XDwyoWd#76feC#8

delta 26
icmex<h3oqju7(!IElep(*-Q*AO-zioXDwyoWd#76-3f;P

diff --git a/PET/auswertung/figs/calibration/lenght_det.pdf b/PET/auswertung/figs/calibration/lenght_det.pdf
index 653d82d959bc34d157441dd61dcea2ede280d31b..a9ad80bdf3c6864cf6eb7ab254008e11920c9a37 100644
GIT binary patch
delta 22
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delta 22
ecmex$lJVC`#tkpx*-eZLjLeJ-H@}bPW(5Fw=m_}$

diff --git a/PET/auswertung/figs/calibration/mid_over_channel.pdf b/PET/auswertung/figs/calibration/mid_over_channel.pdf
index 6dec6d056f4ac219c4649d1f7cd61499a2cbf3b4..6923e5b4540c681be4d47b52b717026104e33f9a 100644
GIT binary patch
delta 25
hcmZ3nfpx_O)`l&Ni-OtB4Gj#8j10D~3}&on0RVg92!8+o

delta 25
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diff --git a/PET/auswertung/figs/calibration/mid_over_energy.pdf b/PET/auswertung/figs/calibration/mid_over_energy.pdf
index 35b3e9ab5086d74a47f33c2d2dcc089ff7affa5d..009578e6585a2ec67a2aa3b765673fb38cb41c3d 100644
GIT binary patch
delta 25
hcmaF;mF4wUmWC~iqGs&oh6V;khGyGk%oxwJ004(B2#x>%

delta 25
hcmaF;mF4wUmWC~iqGs$SMg~S^hUVL4%oxwJ004(l2$KK+

diff --git a/PET/auswertung/figs/calibration/time_range.pdf b/PET/auswertung/figs/calibration/time_range.pdf
index e59c872c1e8116453bf9bb2886b317029e5dd7bb..3c4c0f488ef7f036da43da9ca6aaf64887c98242 100644
GIT binary patch
delta 22
ecmbQTglWnWrVXch+06|N42+D7Hec*@W&r?YL<l(m

delta 22
ecmbQTglWnWrVXch*-eZLjLZxzH(%^^W&r?YfCxhX

diff --git a/PET/auswertung/out/figlist.txt b/PET/auswertung/out/figlist.txt
index efe760e..a161727 100644
--- a/PET/auswertung/out/figlist.txt
+++ b/PET/auswertung/out/figlist.txt
@@ -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}
     
\ No newline at end of file
diff --git a/PET/protokoll/protokoll.tex b/PET/protokoll/protokoll.tex
index 54fa936..b357c15 100644
--- a/PET/protokoll/protokoll.tex
+++ b/PET/protokoll/protokoll.tex
@@ -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