\section{Monte Carlo \label{sec:mc}}

\subsection{Charge Signals with Simulated Noise \label{sec:mc:charge}}

\begin{figure}[htp]%%[t!]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_FixW_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_FixW_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_FixW_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_FixW_WithNoise_LoGain.eps}
\caption[Charge per Number of photo-electrons Fixed Windows]{Extracted charge per photoelectron versus number of photoelectrons, 
for fixed window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ChargeDivNphe_FixW}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_SlidW_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_SlidW_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_SlidW_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_SlidW_WithNoise_LoGain.eps}
\caption[Charge per Number of photo-electrons Sliding Windows]{Extracted charge per photoelectron versus number of photoelectrons, 
for sliding window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ChargeDivNphe_SlidW}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_DFSpline_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_DFSpline_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_DFSpline_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_DFSpline_WithNoise_LoGain.eps}
\caption[Charge per Number of photo-electrons Spline and Digital Filter]{Extracted charge per photoelectron versus number of photoelectrons, 
for spline and digital filter extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ChargeDivNphe_DFSpline}
\end{figure}

\begin{figure}[htp]%%[t!]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_FixW_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_FixW_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_FixW_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_FixW_WithNoise_LoGain.eps}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeDivNphevsNphe_FixW_WithNoise_LoGain.eps}
\caption[Bias Fixed Windows]{The measured bias (extracted charge divided by the conversion factor minus the number of photoelectrons) 
versus number of photoelectrons, 
for fixed window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ConversionvsNphe_FixW}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_SlidW_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_SlidW_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_SlidW_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_SlidW_WithNoise_LoGain.eps}
\caption[Bias Sliding Windows]{The measured bias (extracted charge divided by the conversion factor minus the number of photoelectrons) 
versus number of photoelectrons, 
for sliding window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ConversionvsNphe_SlidW}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_DFSpline_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_DFSpline_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_DFSpline_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ConversionvsNphe_DFSpline_WithNoise_LoGain.eps}
\caption[Bias Spline and Digital Filter]{The measured bias (extracted charge divided by the conversion factor minus the number of photoelectrons) 
versus number of photoelectrons, 
for spline and digital filter extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ConversionvsNphe_DFSpline}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_FixW_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_FixW_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_FixW_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_FixW_WithNoise_LoGain.eps}
\caption[Charge Resolution Fixed Windows]{The measured resolution (RMS of extracted charge divided by the conversion factor minus the number of photoelectrons) versus number of photoelectrons, 
for fixed window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ChargeRes_FixW}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_SlidW_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_SlidW_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_SlidW_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_SlidW_WithNoise_LoGain.eps}
\caption[Charge Resolution Sliding Windows]{The measured resolution (RMS of extracted charge divided by the conversion factor minus the number of photoelectrons) versus number of photoelectrons, 
for sliding window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ChargeRes_SlidW}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_DFSpline_NoNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_DFSpline_WithNoise_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_DFSpline_NoNoise_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_ChargeRes_DFSpline_WithNoise_LoGain.eps}
\caption[Charge Resolution Spline and Digital Filter]{The measured resolution 
(RMS of extracted charge divided by the conversion factor minus the number of photoelectrons) versus number of photoelectrons, 
for spline and digital filter extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{ChargeRes_DFSpline}
\end{figure}

\clearpage

\subsection{Charge Signals with and without Simulated Noise \label{sec:mc:chargenoise}}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_Bias_SlidW_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_Bias_FixW_HiGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_Bias_DFSpline_HiGain.eps}
\caption[Bias due to noise high-gain]{Bias due to noise: Difference of extracted charge of same events, with and without simulated noise, 
for different extractor methods in the high-gain region.}
\label{Bias_HiGain}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_Bias_SlidW_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_Bias_FixW_LoGain.eps}
  \vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_Bias_DFSpline_LoGain.eps} 
\caption[Bias due to noise low-gain]{Bias due to noise: Difference of extracted charge of same events, with and without simulated noise, 
for different extractor methods in the low-gain region.}
\label{Bias_LoGain}
\end{figure}

\clearpage

\subsection{Arrival Times \label{sec:mc:times}}

\begin{figure}[htp]%%[t!]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_NoNoise_HiGain.eps}
\vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_WithNoise_HiGain.eps}
\vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_NoNoise_LoGain.eps}
\vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_WithNoise_LoGain.eps}
\caption[Time Resolution Sliding Windows]{The measured time resolution (RMS of extracted time minus simulated time) 
versus number of photoelectrons, 
for sliding window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{TimeRes_SlidW}
\end{figure}

\begin{figure}[htp]
\centering
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_NoNoise_HiGain.eps}
\vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_WithNoise_HiGain.eps}
\vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_NoNoise_LoGain.eps}
\vspace{\floatsep}
  \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_WithNoise_LoGain.eps}
\caption[Time Resolution Spline and Digital Filter]{The measured time resolution (RMS of extracted time minus simulated time) 
versus number of photoelectrons, 
for spline and digital filter window extractors in different window sizes. The top plots show the high-gain and the bottom ones show the 
low-gain regions. Left: without noise, right: with simulated noise.}
\label{TimeRes_DFSpline}
\end{figure}


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