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auswertung detektorabstand
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
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\pgftext[x=0.169097in,y=1.362465in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 0}%
|
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
||||
}%
|
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
||||
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|
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\pgftext[x=0.169097in,y=0.756771in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 2}%
|
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|
||||
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|
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|
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|
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
BIN
PET/auswertung/figs/theory/projection-img0.png
Normal file
BIN
PET/auswertung/figs/theory/projection-img0.png
Normal file
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|
After Width: | Height: | Size: 410 B |
BIN
PET/auswertung/figs/theory/projection.pdf
Normal file
BIN
PET/auswertung/figs/theory/projection.pdf
Normal file
Binary file not shown.
429
PET/auswertung/figs/theory/projection.pgf
Normal file
429
PET/auswertung/figs/theory/projection.pgf
Normal file
|
|
@ -0,0 +1,429 @@
|
|||
%% Creator: Matplotlib, PGF backend
|
||||
%%
|
||||
%% To include the figure in your LaTeX document, write
|
||||
%% \input{<filename>.pgf}
|
||||
%%
|
||||
%% Make sure the required packages are loaded in your preamble
|
||||
%% \usepackage{pgf}
|
||||
%%
|
||||
%% Figures using additional raster images can only be included by \input if
|
||||
%% they are in the same directory as the main LaTeX file. For loading figures
|
||||
%% from other directories you can use the `import` package
|
||||
%% \usepackage{import}
|
||||
%% and then include the figures with
|
||||
%% \import{<path to file>}{<filename>.pgf}
|
||||
%%
|
||||
%% Matplotlib used the following preamble
|
||||
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|
||||
%%
|
||||
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|
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|
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||||
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|
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
||||
}%
|
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
\end{pgfscope}%
|
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|
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|
||||
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|
||||
BIN
PET/auswertung/figs/theory/rec_filtered-img0.png
Normal file
BIN
PET/auswertung/figs/theory/rec_filtered-img0.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 487 B |
BIN
PET/auswertung/figs/theory/rec_filtered.pdf
Normal file
BIN
PET/auswertung/figs/theory/rec_filtered.pdf
Normal file
Binary file not shown.
454
PET/auswertung/figs/theory/rec_filtered.pgf
Normal file
454
PET/auswertung/figs/theory/rec_filtered.pgf
Normal file
|
|
@ -0,0 +1,454 @@
|
|||
%% Creator: Matplotlib, PGF backend
|
||||
%%
|
||||
%% To include the figure in your LaTeX document, write
|
||||
%% \input{<filename>.pgf}
|
||||
%%
|
||||
%% Make sure the required packages are loaded in your preamble
|
||||
%% \usepackage{pgf}
|
||||
%%
|
||||
%% Figures using additional raster images can only be included by \input if
|
||||
%% they are in the same directory as the main LaTeX file. For loading figures
|
||||
%% from other directories you can use the `import` package
|
||||
%% \usepackage{import}
|
||||
%% and then include the figures with
|
||||
%% \import{<path to file>}{<filename>.pgf}
|
||||
%%
|
||||
%% Matplotlib used the following preamble
|
||||
%% \usepackage{fontspec}
|
||||
%%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{2.000000in}}%
|
||||
\pgfpathclose%
|
||||
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|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\pgftext[left,bottom]{\pgfimage[interpolate=true,width=1.430556in,height=1.430556in]{rec_filtered-img0.png}}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
}%
|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
}%
|
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|
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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BIN
PET/auswertung/figs/theory/rec_simple-img0.png
Normal file
BIN
PET/auswertung/figs/theory/rec_simple-img0.png
Normal file
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|
After Width: | Height: | Size: 488 B |
BIN
PET/auswertung/figs/theory/rec_simple.pdf
Normal file
BIN
PET/auswertung/figs/theory/rec_simple.pdf
Normal file
Binary file not shown.
454
PET/auswertung/figs/theory/rec_simple.pgf
Normal file
454
PET/auswertung/figs/theory/rec_simple.pgf
Normal file
|
|
@ -0,0 +1,454 @@
|
|||
%% Creator: Matplotlib, PGF backend
|
||||
%%
|
||||
%% To include the figure in your LaTeX document, write
|
||||
%% \input{<filename>.pgf}
|
||||
%%
|
||||
%% Make sure the required packages are loaded in your preamble
|
||||
%% \usepackage{pgf}
|
||||
%%
|
||||
%% Figures using additional raster images can only be included by \input if
|
||||
%% they are in the same directory as the main LaTeX file. For loading figures
|
||||
%% from other directories you can use the `import` package
|
||||
%% \usepackage{import}
|
||||
%% and then include the figures with
|
||||
%% \import{<path to file>}{<filename>.pgf}
|
||||
%%
|
||||
%% Matplotlib used the following preamble
|
||||
%% \usepackage{fontspec}
|
||||
%%
|
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
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|
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|
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|
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|
||||
\end{pgfscope}%
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
BIN
PET/auswertung/figs/theory/source-img0.png
Normal file
BIN
PET/auswertung/figs/theory/source-img0.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 390 B |
BIN
PET/auswertung/figs/theory/source.pdf
Normal file
BIN
PET/auswertung/figs/theory/source.pdf
Normal file
Binary file not shown.
454
PET/auswertung/figs/theory/source.pgf
Normal file
454
PET/auswertung/figs/theory/source.pgf
Normal file
|
|
@ -0,0 +1,454 @@
|
|||
%% Creator: Matplotlib, PGF backend
|
||||
%%
|
||||
%% To include the figure in your LaTeX document, write
|
||||
%% \input{<filename>.pgf}
|
||||
%%
|
||||
%% Make sure the required packages are loaded in your preamble
|
||||
%% \usepackage{pgf}
|
||||
%%
|
||||
%% Figures using additional raster images can only be included by \input if
|
||||
%% they are in the same directory as the main LaTeX file. For loading figures
|
||||
%% from other directories you can use the `import` package
|
||||
%% \usepackage{import}
|
||||
%% and then include the figures with
|
||||
%% \import{<path to file>}{<filename>.pgf}
|
||||
%%
|
||||
%% Matplotlib used the following preamble
|
||||
%% \usepackage{fontspec}
|
||||
%%
|
||||
\begingroup%
|
||||
\makeatletter%
|
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|
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|
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|
||||
\begin{pgfscope}%
|
||||
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|
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|
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|
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|
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|
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\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
|
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|
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|
||||
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|
||||
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|
||||
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|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{2.000000in}}%
|
||||
\pgfpathclose%
|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
\pgfsys@transformshift{0.797049in}{1.627778in}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\pgftext[x=0.797049in,y=1.725000in,,bottom]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 1}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
\pgftext[x=1.082882in,y=1.725000in,,bottom]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 2}%
|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
\pgftext[x=1.368715in,y=1.725000in,,bottom]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 3}%
|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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\pgftext[x=1.654549in,y=1.725000in,,bottom]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 4}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
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\pgftext[x=0.201632in,y=1.436667in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 0}%
|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
}%
|
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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\pgftext[x=0.201632in,y=1.150833in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 1}%
|
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|
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|
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|
||||
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|
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|
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|
||||
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|
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|
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|
||||
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|
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|
||||
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
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|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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\pgftext[x=0.201632in,y=0.865000in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 2}%
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
||||
}%
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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\pgftext[x=0.201632in,y=0.579167in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 3}%
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
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|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.368299in}{0.341528in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.201632in,y=0.293333in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 4}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetrectcap%
|
||||
\pgfsetmiterjoin%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.368299in}{0.198611in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.368299in}{1.627778in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetrectcap%
|
||||
\pgfsetmiterjoin%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{1.797465in}{0.198611in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.797465in}{1.627778in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetrectcap%
|
||||
\pgfsetmiterjoin%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.368299in}{0.198611in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.797465in}{0.198611in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetrectcap%
|
||||
\pgfsetmiterjoin%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.368299in}{1.627778in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.797465in}{1.627778in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfpicture}%
|
||||
\makeatother%
|
||||
\endgroup%
|
||||
|
|
@ -113,3 +113,537 @@
|
|||
\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/source.pgf}
|
||||
\caption{}
|
||||
\label{fig:theory-source}
|
||||
\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/source.pgf}
|
||||
\caption{}
|
||||
\label{fig:theory-source}
|
||||
\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/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_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/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/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}
|
||||
|
||||
\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/calibration/mid_over_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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_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/mid_over_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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/mid_over_channel.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_channel}
|
||||
\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/mid_over_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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_energy.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-mid_over_energy}
|
||||
\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/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/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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\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/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[H]\centering
|
||||
\input{../auswertung/figs/calibration/all_times.pgf}
|
||||
\caption{}
|
||||
\label{fig:calibration-all_times}
|
||||
\end{figure}
|
||||
|
||||
|
|
@ -1,8 +1,11 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
from scipy.optimize import root_scalar
|
||||
import matplotlib
|
||||
import matplotlib.ticker as ticker
|
||||
import os
|
||||
from SecondaryValue import SecondaryValue
|
||||
from scipy.optimize import curve_fit
|
||||
|
||||
###############################################################################
|
||||
# Auxiliary #
|
||||
|
|
@ -30,17 +33,25 @@ def energy_b(channel):
|
|||
"""Channel to Energy, one based index."""
|
||||
return 100 + .220*channel
|
||||
|
||||
|
||||
channel_to_time_val = SecondaryValue('a + b*(k-1/2)', defaults=dict(a=(-.014, .0192), b=(.0483, 2e-5)))
|
||||
def channel_to_time(channel, d=0):
|
||||
return channel_to_time_val(k=(channel, d))
|
||||
###############################################################################
|
||||
# Plot Porn #
|
||||
###############################################################################
|
||||
|
||||
matplotlib.rcParams.update({
|
||||
'font.family': 'serif',
|
||||
'text.usetex': False,
|
||||
'pgf.rcfonts': False,
|
||||
})
|
||||
|
||||
def pinmp_ticks(axis, ticks):
|
||||
axis.set_major_locator(ticker.MaxNLocator(ticks))
|
||||
axis.set_minor_locator(ticker.MaxNLocator(ticks*10))
|
||||
return axis
|
||||
|
||||
def set_up_plot(ticks=10, pimp_top=False):
|
||||
def set_up_plot(ticks=10, pimp_top=True):
|
||||
fig = plt.figure()
|
||||
ax = fig.add_subplot(111)
|
||||
|
||||
|
|
@ -86,7 +97,7 @@ def plot_spectrum(counts, offset=1, save=None, **pyplot_args):
|
|||
ax.step(channels, counts, **pyplot_args)
|
||||
|
||||
ax.set_xlabel('Kanal')
|
||||
ax.set_ylabel('Counts')
|
||||
ax.set_ylabel('Ereignisszahl')
|
||||
ax.set_xlim([channels[0], channels[-1]])
|
||||
ax.set_ylim(0)
|
||||
|
||||
|
|
@ -95,6 +106,26 @@ def plot_spectrum(counts, offset=1, save=None, **pyplot_args):
|
|||
|
||||
return fig, ax
|
||||
|
||||
###############################################################################
|
||||
# Time of Flight Analysiss #
|
||||
###############################################################################
|
||||
|
||||
def gauss(x, a, mu, sigma):
|
||||
return a*np.exp(-(x-mu)**2/(2*sigma**2))
|
||||
|
||||
def find_and_plot_peak(counts, ax, label):
|
||||
channels = np.arange(0, counts.size) + 1
|
||||
counts = counts.copy()/counts.max()
|
||||
times, d_times = channel_to_time(channels)
|
||||
|
||||
splot = ax.step(times, counts, label=label, alpha=.4)
|
||||
opt, cov = curve_fit(gauss, channels, counts, p0=(1, counts.argmax(), 100))
|
||||
cov = np.sqrt(np.diag(cov))
|
||||
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)
|
||||
ax.axvspan(t-dt, t+dt, alpha=.2, color=gplot[0].get_color())
|
||||
return channel_to_time(opt[1], opt[2]/10)
|
||||
|
||||
|
||||
###############################################################################
|
||||
File diff suppressed because it is too large
Load diff
File diff suppressed because it is too large
Load diff
File diff suppressed because it is too large
Load diff
0
PET/protokoll/protokoll.bib
Normal file
0
PET/protokoll/protokoll.bib
Normal file
212
PET/protokoll/protokoll.tex
Normal file
212
PET/protokoll/protokoll.tex
Normal file
|
|
@ -0,0 +1,212 @@
|
|||
\documentclass[slug=PET, room=Andreas-Schubert-Bau\,\ K\ 1A, supervisor=Anne-Sophie\ Berthold, coursedate=13.\ 12.\ 2019]{../../Lab_Report_LaTeX/lab_report}
|
||||
|
||||
\title{Postitronenemissionstomographie}
|
||||
\author{Oliver Matthes, Valentin Boettcher}
|
||||
\usepackage{todonotes}
|
||||
\graphicspath{ {figs/} }
|
||||
\usepackage{tikz}
|
||||
\usepackage{pgf}
|
||||
\usepackage[version=4]{mhchem}
|
||||
\usepackage[ngerman]{babel}
|
||||
\usepackage{subcaption}
|
||||
\usepackage{amssymb}
|
||||
|
||||
% bib
|
||||
\addbibresource{protokoll.bib}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\section{Auswertung}
|
||||
\label{sec:ausw}
|
||||
|
||||
\subsection{Theoriebeispiel}
|
||||
\label{sec:theobei}
|
||||
Zur Verbesserung des verst\"andnisses der Projektions- und
|
||||
Rekonstruktionsprozesse, werden diese hier anhand eines einfachen
|
||||
Beispiels nachvollzogen.
|
||||
|
||||
\begin{figure}[htp]
|
||||
\centering
|
||||
\begin{subfigure}[t]{.25\textwidth}
|
||||
\centering
|
||||
\includegraphics[width=.6\textwidth]{../auswertung/figs/theory/source.pdf}
|
||||
\caption{Ausgangsmatrix}
|
||||
\label{fig:theory-source}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.25\textwidth}
|
||||
\centering
|
||||
\includegraphics[width=.6\textwidth]{../auswertung/figs/theory/projection.pdf}
|
||||
\caption{Sinogram}
|
||||
\label{fig:theory-projection}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.25\textwidth}
|
||||
\centering
|
||||
\includegraphics[width=.6\textwidth]{../auswertung/figs/theory/convoluted.pdf}
|
||||
\caption{Gefiltertes Sinogram}
|
||||
\label{fig:theory-convoluted}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.25\textwidth}
|
||||
\centering
|
||||
\includegraphics[width=.6\textwidth]{../auswertung/figs/theory/rec_simple.pdf}
|
||||
\caption{Einfache R\"uckprojektion}
|
||||
\label{fig:theory-rec_simple}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.25\textwidth}
|
||||
\centering
|
||||
\includegraphics[width=.6\textwidth]{../auswertung/figs/theory/rec_filtered.pdf}
|
||||
\caption{Gefilterte R\"uckprojektion}
|
||||
\label{fig:theory-rec_filtered}
|
||||
\end{subfigure}
|
||||
\caption[Graustufendarstellung der
|
||||
Beispielmatrizen]{Graustufendarstellung der Matrizen aus den
|
||||
Teilschritten des Beispiels. Es wurden jeweils die Matrixelemente
|
||||
in das Interval \([0,1]\) reskaliert.}
|
||||
\label{fig:graubei}
|
||||
\end{figure}
|
||||
|
||||
Im ersten Schritt wird die Projektion~\ref{fig:theory-projection} des
|
||||
Ausgangsbildes~\ref{fig:theory-source} aus Verschiedenen Winkeln
|
||||
berechenet. Dabei wurden die diagonalen entsprechend gewichtet.
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:proj}
|
||||
\mathfrak{M}_0 =
|
||||
\begin{pmatrix}
|
||||
0 & 0 & 0 & 0 & 2\\
|
||||
0 & 9 & 0 & 0 & 0\\
|
||||
0 & 0 & 0 & 0 & 0\\
|
||||
0 & 7 & 0 & 8 & 0\\
|
||||
0 & 0 & 0 & 0 & 0\\
|
||||
\end{pmatrix}
|
||||
\implies
|
||||
\left(
|
||||
\begin{array}{ccccc|c}
|
||||
0. & 16. & 0. & 8. & 2 & 0^\circ\\
|
||||
2.73 & 4.95 & 15.47 & 0.68 & 0.28 & 45^\circ\\
|
||||
0. & 15. & 0. & 9. & 2. & 90^\circ\\
|
||||
3.12 & 5.24 & 8.19 & 5.85 & 3.51 & 135^\circ\\
|
||||
\end{array}\right) = \mathfrak{P}_0
|
||||
\end{equation}
|
||||
|
||||
Ein gefiltertes Sinogram~\ref{fig:theory-convoluted} ergibt sich durch
|
||||
Faltung der Zeilen von \(\mathfrak{M}_0\) mit
|
||||
\(F = \mqty(-.1 & .25 & -.1)\).
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:filter}
|
||||
\mathfrak{M}_1 = \mathfrak{M}_0 * F =
|
||||
\begin{pmatrix}
|
||||
-1.6 & 4. & -2.4 & 1.8 & -0.3\\
|
||||
0.188 & -0.583 & 3.304 & -1.405 & 0.002\\
|
||||
-1.5 & 3.75 & -2.4 & 2.05 & -0.4\\
|
||||
0.256 & 0.179 & 0.938 & 0.293 & 0.292\\
|
||||
\end{pmatrix}
|
||||
\end{equation}
|
||||
|
||||
Die R\"uckprojektion des Einfachen sinogramms
|
||||
ergib~\ref{fig:theory-rec_simple}.
|
||||
|
||||
{\footnotesize
|
||||
\setlength{\arraycolsep}{2.5pt}
|
||||
|
||||
\begin{align}
|
||||
\label{eq:simplerepr}
|
||||
\overbrace{\begin{pmatrix}
|
||||
0. & 16. & 0. & 8. & 2.\\
|
||||
0. & 16. & 0. & 8. & 2.\\
|
||||
0. & 16. & 0. & 8. & 2.\\
|
||||
0. & 16. & 0. & 8. & 2.\\
|
||||
0. & 16. & 0. & 8. & 2.\\
|
||||
\end{pmatrix}}^{0^\circ} & + \frac{1}{2}\overbrace{\begin{pmatrix}
|
||||
15.864 & 8.408 & 0.837 & 0.287 & 0.076\\
|
||||
12.636 & 15.864 & 8.408 & 0.837 & 0.287\\
|
||||
6.569 & 12.636 & 15.864 & 8.408 & 0.837\\
|
||||
2.78 & 6.569 & 12.636 & 15.864 & 8.408\\
|
||||
0.737 & 2.78 & 6.569 & 12.636 & 15.864\\
|
||||
\end{pmatrix}}^{45^\circ} \nonumber \\ + \overbrace{\begin{pmatrix}
|
||||
2. & 2. & 2. & 2. & 2.\\
|
||||
9. & 9. & 9. & 9. & 9.\\
|
||||
0. & 0. & 0. & 0. & 0.\\
|
||||
15. & 15. & 15. & 15. & 15.\\
|
||||
0. & 0. & 0. & 0. & 0.\\
|
||||
\end{pmatrix}}^{90^\circ} &+ \frac{1}{2}\overbrace{\begin{pmatrix}
|
||||
0.842 & 3.172 & 7.12 & 9.283 & 8.966\\
|
||||
3.172 & 7.12 & 9.283 & 8.966 & 9.886\\
|
||||
7.12 & 9.283 & 8.966 & 9.886 & 8.003\\
|
||||
9.283 & 8.966 & 9.886 & 8.003 & 3.569\\
|
||||
8.966 & 9.886 & 8.003 & 3.569 & 0.948\\
|
||||
\end{pmatrix}}^{135^\circ}\nonumber \\
|
||||
& = \begin{pmatrix}
|
||||
10.353 & 23.79 & 5.978 & 14.785 & 8.521\\
|
||||
16.904 & 36.492 & 17.845 & 21.902 & 16.087\\
|
||||
6.844 & 26.959 & 12.415 & 17.147 & 6.42\\
|
||||
21.031 & 38.768 & 26.261 & 34.933 & 22.988\\
|
||||
4.852 & 22.333 & 7.286 & 16.102 & 10.406\\
|
||||
\end{pmatrix} = \mathfrak{M}_1
|
||||
\end{align}}
|
||||
|
||||
Aus dem gefilterten Sinogram ergibt sich auf \"ahnliche
|
||||
Weise~\ref{fig:theory-rec_filtered}
|
||||
{\footnotesize
|
||||
\setlength{\arraycolsep}{2.5pt}
|
||||
|
||||
\begin{align}
|
||||
\label{eq:simplerepr}
|
||||
\overbrace{\begin{pmatrix}
|
||||
-1.6 & 4. & -2.4 & 1.8 & -0.3\\
|
||||
-1.6 & 4. & -2.4 & 1.8 & -0.3\\
|
||||
-1.6 & 4. & -2.4 & 1.8 & -0.3\\
|
||||
-1.6 & 4. & -2.4 & 1.8 & -0.3\\
|
||||
-1.6 & 4. & -2.4 & 1.8 & -0.3\\
|
||||
\end{pmatrix}}^{0^\circ} & + \frac{1}{2}\overbrace{\begin{pmatrix}
|
||||
3.165 & 0.261 & -1.305 & -0.012 & 0.001\\
|
||||
1.076 & 3.165 & 0.261 & -1.305 & -0.012\\
|
||||
-0.407 & 1.076 & 3.165 & 0.261 & -1.305\\
|
||||
0.182 & -0.407 & 1.076 & 3.165 & 0.261\\
|
||||
0.051 & 0.182 & -0.407 & 1.076 & 3.165\\
|
||||
\end{pmatrix}}^{45^\circ} \nonumber \\ +
|
||||
\overbrace{\begin{pmatrix}
|
||||
-0.4 & -0.4 & -0.4 & -0.4 & -0.4\\
|
||||
2.05 & 2.05 & 2.05 & 2.05 & 2.05\\
|
||||
-2.4 & -2.4 & -2.4 & -2.4 & -2.4\\
|
||||
3.75 & 3.75 & 3.75 & 3.75 & 3.75\\
|
||||
-1.5 & -1.5 & -1.5 & -1.5 & -1.5\\
|
||||
\end{pmatrix}}^{90^\circ} &+ \frac{1}{2}\overbrace{\begin{pmatrix}
|
||||
0.069 & 0.258 & 0.351 & 0.646 & 0.972\\
|
||||
0.258 & 0.351 & 0.646 & 0.972 & 0.759\\
|
||||
0.351 & 0.646 & 0.972 & 0.759 & 0.486\\
|
||||
0.646 & 0.972 & 0.759 & 0.486 & 0.295\\
|
||||
0.972 & 0.759 & 0.486 & 0.295 & 0.079\\
|
||||
\end{pmatrix}}^{135^\circ}\nonumber \\
|
||||
&= \begin{pmatrix}
|
||||
-0.383 & 3.86 & -3.277 & 1.717 & -0.214\\
|
||||
1.117 & 7.808 & 0.104 & 3.683 & 2.123\\
|
||||
-4.028 & 2.461 & -2.732 & -0.09 & -3.11\\
|
||||
2.564 & 8.032 & 2.267 & 7.375 & 3.728\\
|
||||
-2.589 & 2.97 & -3.861 & 0.985 & -0.178\\
|
||||
\end{pmatrix} = \mathfrak{M}_2
|
||||
\end{align}
|
||||
}
|
||||
|
||||
Es ist zu erkennen, das in beiden rekonstruktionen die starken Signale
|
||||
\((1,1),\,(3,1),\,(3,3)\) klar zu identifizerien, wenngleich die
|
||||
Unterschiede in der signalst\"arke nicht im urspr\"unglichen
|
||||
Verh\"altniss 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.
|
||||
|
||||
\newpage
|
||||
\section{Verzeichnisse}
|
||||
\label{sec:literatur}
|
||||
|
||||
\listoffigures
|
||||
|
||||
\listoftables
|
||||
|
||||
\printbibliography
|
||||
\end{document}
|
||||
Loading…
Add table
Reference in a new issue