In \chaptername~\vref{ch-defs} I explained how we compute efficiency. If a hit occurs in the Large GEM within a given radius (\textit{efficiency radius}) from the projection of the track of the particle, then we say that the chamber has been efficient. If there are no hits within the efficiency radius, the chamber has been inefficient.\\

What happens if we set a wrong efficiency radius? There are two scenarios:
\begin{enumerate}
	\item the radius is too short. In a large-pads area we may not include a whole pad within the radius, and the efficiency-computing algorithm might miss some hits.
	\item the radius is too long. Some noise hits on adjacent pads may be mistaken as efficient hits.
\end{enumerate}

\figurename~\vref{effradscan} shows, for every zone we tested, the fluctuation of the computed efficiency for increasing efficiency radius values. It is clear then that $20mm \leq effrad \leq 30mm$ would be appropriate for every purpose.\\

Actually, all the results discussed here were computed trying to minimize the efficiency radius for each zone of the chamber, in order to include as few noise hits as possible. For each zone, the efficiency radius was set to the minimum length at which the efficiency stops rising.\\

\begin{figure}[tbp]
	\centering
	\includegraphics[width=12cm]{Images/0-60-nocolors}
	\caption{Efficiency radius scan: how changing the radius influences the efficiency-computing algorithm. Large GEM working point: $HV=-5.15kV$, $th=-40ds$}
	\label{effradscan}
\end{figure}
The plot of \figurename~\vref{effradscan} is also satisfying because it shows that the noise level is low for all zones, with the exception of \textit{point M}: the \textit{plateau}s are very flat, which means that stretching the radius does not mean to include much more noise. \textit{Zone M} was probably close to two noisy channels, one at a distance of about $20mm$ and the other, less noisy, about $35mm$ far, as it can be inferred from the plot.\\

Playing with the efficiency radius may provide further precise results. For example, we can take a couple of the \textit{HV scan} data sets shown in \figurename~\vref{hva}, and arbitrarily set wrong \textit{offsets} (see the following section for a deeper explanation). This means that we are looking for hits in a part of the chamber which was not irradiated. In that part, a scan like that of \figurename~\vref{effradscan} will show the contribution of pure noise to the computation of the detector efficiency. Stretching the radius, we indeed allow the software to look for hit channels in a larger region of the chamber, therefore we include more noise. \tablename~\vref{noisecontrib} shows, for each scanned zone:
\begin{itemize}
	\item the best efficiency radius, according to \figurename~\ref{effradscan};
	\item the level of efficiency of that chamber sector, computed with the chosen best efficiency radius;
	\item the contribution of noise to the computation of efficiency, at the same efficiency radius. The noise values are plotted like in \figurename~\vref{fig-noisecontrib}\footnote{\figurename~\vref{noise-a} shows that \textit{zone A} is close to some noisy channels. Indeed, with an efficiency radius of $60mm$ the efficiency grows to significant values; however, $effrad=6mm$ excludes virtually all noise from the scans.}, which show the efficiency of a non-irradiated sector as a function of the efficiency radius.
\end{itemize}
The errors in the efficiency column are statistical: 
$$
\Delta \varepsilon = \dfrac{\varepsilon (1 - \varepsilon )}{\sqrt{n}}
$$
where $n$ is the number of events collected and $\varepsilon$ is the computed efficiency. These errors must be added to those of the following column.\\
\begin{figure}
	\centering
	\subfigure[Zone \textit{A}]
	{\includegraphics[width=6.6cm]{Images/radiography/noise/a}\label{noise-a}}
	\hspace{2mm}
	\subfigure[Zone \textit{P}]
	{\includegraphics[width=6.6cm]{Images/radiography/noise/p}\label{noise-p}}
	\caption{Off-beam efficiency computation: evaluating the contribution of noise}
	\label{fig-noisecontrib}
\end{figure}

\tablename~\ref{noisecontrib} therefore shows how noise must be computed to determine which errors affect the efficiency values. If we made this scan on-beam, these effects would be negligible, because the charge released by incoming particles would dominate.

\begin{table}
\centering
\begin{tabular}{|c|c|c|c|}
\hline \rule[-2ex]{0pt}{5.5ex} \textbf{Zone} & \textbf{Best \textit{effrad}} & \textbf{Efficiency} & \textbf{Contribution of noise}  \\ 
\hline \rule[-2ex]{0pt}{5.5ex} A & $6mm$ & $(99.40 \pm 0) \%$ & $0.5 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} B & $7mm$ & $(73.35 \pm 0.11) \%$ & $0.01 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} C & $8.5mm$ & $(74.60 \pm 0.11) \%$ & $0.01 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} D & $9mm$ & $(94.43 \pm 0.03) \%$ & $0.07 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} E & $9mm$ & $(96.76 \pm 0.02) \%$ & $0.35 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} F & $9mm$ & $(85.21 \pm 0.10) \%$ & $0.03 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} G & $12mm$ & $(74.95 \pm 0.14) \%$ & $0.02 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} H & $12mm$ & $(93.68 \pm 0.04) \%$ & $0.02 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} I & $12mm$ & $(97.73 \pm 0.02) \%$ & $0.13 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} L & $23.5mm$ & $(97.07 \pm 0.02) \%$ & $0.04 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} M & $30mm$ & $(80.28 \pm 0.12) \%$ & $13.38 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} N & $18mm$ & $(86.35 \pm 0.09) \%$ & $0.05 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} O & $12mm$ & $(97.67 \pm 0.02) \%$ & $1.01 \%$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} P & $18mm$ & $(97.66 \pm 0.03) \%$ & $0.43 \%$ \\ 
\hline 
\end{tabular}
\caption{Contribution of noise to the computation of LG efficiency. Efficiency was detected at: $HV=-5,15kV$, $th=-60ds$, $MSPL=4clk$}
\label{noisecontrib}
\end{table}