\section{The EUDET telescope}
\label{sec:telescope}

The EUDET telescope is a six-layer silicon sensor device which is available
as a multi-purpose facility. The telescope was developed as part of the
EUDET project~\cite{ref:telescope:eudet} and details of the 
telescope design can be
found in~\cite{ref:telescope:telescope}. A description of the main features of
the telescope relevant to this paper are given below.

\subsection{Sensors}
MIMOSA-26 CMOS pixel sensors~\cite{ref:telescope:mimosa}.
Fabricated with 0.35\,$\mu$m AMS process. Thickness of 700\,$\mu$m (CHECK!)
with 15\,$\mu$m epitaxial layer. Pixel regular array of 
$1152 \times 576$ pixels with a pixel pitch of 18.4\,$\mu$m, giving a total
active area of $21.1 \times 10.6$\,mm$^2$.
Readout is performed using a rolling shutter with a frame period of 110\,$\mu$s
and for each event, data from two contiguous full rolling shutter frames
are kept. For the studies presented here, no selection is made using
the frame time so hits from the full two frames are used.

EPI LAYER UPSTREAM OR DOWNSTREAM?

\subsection{Telescope layout}

Two arms, each of three sensors. Sensors in the two arms spaced XXX\,mm apart.
Space between two arms was set to the minimum of YYY\,mm. This was
as close as was possible, given the mechanical structure of the telescope.

Triggering was performed using two scintillators, each $2 \times 1$\,cm$^2$,
and hence matched to the sensor size, and 3\,mm thick. These were mounted
mounted 6\,mm in front of the first sensor. The trigger required both
scintillators to fire at the same time.
Two other scintillators were mounted
behind the back telescope arm. These were not included in the trigger
requirement for any of the data taken as this would have required 
rear leakage for the shower data and hence would have led to a bias.

A tungsten stack for creating electromagnetic showers was
optionally inserted between the two arms. The stack was made of a number
of plates of tungsten, each $5 \times 5$\,cm$^2$ wide and 3\,mm thick.
This size was significantly larger than the sensors and so could be easily
placed to cover the
full active region of the telescope without requiring accurate alignment.
Tungsten radition length $X_0 = 3.5$\,mm so each plate corresponds
to $0.86X_0$. The tungsten plates were held in place by an aluminium support
made of a sheet of aluminium 1\,mm thick. This was in place for all data
taken, even when no tungsten sheets were present. The aluminium support
and its mount were mechanically separate from the telescope arm mounts.
This allowed the tungsten sheets to be inserted and removed without
causing a major disturbance to the sensor alignment.

Figure~\ref{fig:telescope:layout} shows the layout of the apparatus in the
beam line. The $z$ axis was defined to be along the nominal beam direction
and the $y$ axis was vertically up, with the $x$ axis defined to form a
right-handed coordinate system. The $x$ and $y$ coordinates were defined
to be centred on the most upstream sensor of the telescope (layer~0) while
$z=0$ was defined as the downstream surface of the aluminium mount, which
was equivalent to the upstream face of the tungsten stack when tungsten sheets
were present.
%
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=8cm]{telescope/layout.png}
\hspace{1cm}
\includegraphics[width=4cm]{telescope/layoutPhoto.jpg}
\caption{\sl 
Left: Schematic diagram of the layout of the telescope sensors, scintillators
and tungsten sheets (not to scale). The $z$ coordinates are shown in mm and the
layer numbering defines the convention used in this paper.
Right: Photograph of the telescope viewed from upstream. 
The last of the front arm
sensor boxes and all three of the back arm sensors boxes are visible. The thin
aluminium window indicating the position of the sensor within the box 
is also visible for the first back telescope box, layer~3.
The tungsten stack aluminium support is shown between the arms. 
No tungsten sheets were present at the time of the
photograph.
}
\label{fig:telescope:layout}
\end{center}
\end{figure}

\subsection{Data acquisition}

The readout is digital, so each pixel reports either a hit or not.
Data taken with several thresholds. Programmable in arbitrary units;
data taken with values between 6 and 10.5 units.

\subsection{Data taken}
Beam data were taken with positive hadrons and with positrons.
The hadron data were all taken with a beam momentum of 120\,GeV,
for which the beam mainly consists of pions. All the
hadron data used for this analysis were taken with no tungsten
inserted within the telescope. 

The beam ws delivered in 10\,s spills with a period of 45\,s. For
the 120\,GeV hadron beam, the intensity was high enough that the event rate
was limited by the telescope DAQ rate. This was approximately 700\,Hz
within the spill and hence around 160\,Hz on average. The event size
for these events was on average 1\,kByte per event. 
The total amount of hadron beam data taken was 1.3 million events.

The positron data
were taken with beam momenta between 10 and 100\,GeV and with 
the amount of tungsten varied between 0 and 16 sheets, equivalent
to 0 to $14X_0$. 
In contrast to the hadron beam, the positron
beam was much less intense, particularly for low momentum.
This limited the event rate, giving 
average rates as low as 10\,Hz at 10\,GeV. Due to showering in
the tungsten, the event sizes were larger than for the hadron data,
varying between 1 and 2\,kBytes per event, depending on the configuration.
Table~\ref{tab:telescope:dataset}
shows the numbers of events taken
for each combination of beam energy and tungsten thickness.
A total of 2.2 million positron events were taken.
%
\begin{table}[ht!]
\begin{center}
\caption{\sl 
Numbers of positron beam events (in thousands) taken for each combination of
tungsten sheets/thickness (in radiation lengths) and
beam momentum (in GeV).
}
\label{tab:telescope:dataset}
\bigskip
\begin{tabular}{cc|cccccc}
\hline
\multicolumn{2}{c|}{Tungsten} & \multicolumn{6}{|c}{Beam Momentum}  \cr
Sheets & Thickness ($X_0$) & 10\,GeV & 20\,GeV & 40\,GeV & 60\,GeV & 80\,GeV & 100\,GeV \cr\hline
0 & $\phantom{1}0.0$ &    &    &    & 50 &     &  48 \cr
2 & $\phantom{1}1.7$ &    &    & 31 & 61 &  81 & 102 \cr
4 & $\phantom{1}3.4$ & 22 & 19 & 40 & 70 & 100 & 106 \cr
6 & $\phantom{1}5.1$ &  5 & 17 & 26 & 60 &  62 &  58 \cr
8 & $\phantom{1}6.9$ &  9 & 24 & 35 & 53 &  84 & 101 \cr
10 & $\phantom{1}8.6$ & 11 & 20 & 29 & 60 &  82 &  92 \cr
12 & $10.3$ & 13 & 23 & 30 & 61 &  84 & 102 \cr
14 & $12.0$ &    & 31 & 31 & 61 &  81 & 102 \cr
16 & $13.7$ &    &    &    &    &     & 104 \cr\hline
\end{tabular}
\end{center}
\end{table}
