\chapter{Fiber Detector}
%sandro is working on the TDR
\label{sec:Fibre}

\chapterresponsible{Sandro}

\nobalance

%\begin{figure}[b!]
%	\includegraphics[width=0.48\textwidth]{Fibres/figures/FibresTimingType}
%	\caption{Fraction of simulated tracks (Michel decays) in which we obtain the
%	dominant timing information for long tracks (>= 6~hits) from the respective detector.}
%	\label{fig:FibresTimingType}
%\end{figure}

To suppress all forms of combinatorial background,
a very thin detector with good spatial and very good timing resolution, very high efficiency,
and high rate capability
is required in the central region of the Mu3e apparatus.
To this aim,
a thin Scintillating Fiber (SciFi) detector
with few 100~ps time resolution, efficiency in excess of 96\%,
spatial resolution around $100~\mu{\rm m}$,
and thickness $< 0.2\%$ of radiation length
has been developed.
Figure~\ref{fig:scifimu3e} shows the SciFi detector inside the Mu3e apparatus.
In particular, the space constraints in the central part of the Mu3e apparatus
impose a very compact design of the SciFi detector.
Moreover the SciFi detector will help resolve the sense of rotation (i.e. the charge)
of the recurling tracks in the central region of the apparatus.

%%%%%
%\begin{figure}[!b]
%   \centering
%   \includegraphics[width=0.48\textwidth]{Fibres/figures/barrel}
%   \caption{Overall view of the SciFi detector.}
%   \label{fig:FibresAll}
%\end{figure}

%%%%%
\begin{figure}[!b]
   \vspace*{-6mm}
   \centering
   \includegraphics[width=0.46\textwidth]{Fibres/figures/scifi_schematics}
   \caption{Open view of the central part of the Mu3e apparatus.
The SciFi arrays are in blue.}
   \label{fig:scifimu3e}
\end{figure}

%Requirements are a detection efficiency close to \SI{100}{\percent} and a time
%resolution below \SI{300}{\pico\second} to allow for the suppression of accidental 
%background in topologies where at least one track never reaches the tile detector
%and a reliable rejection of mis-reconstructed track candidates using the time of flight
%between sub-detector crossings.
%\todo[inline]{Do we need to motivate 350ps in more detail?}
%This allows resolving the sense of rotation from two sub-detector hits of tracks with
%$p>$\SI{20}{MeV/c} which recurl at least $\Phi>90^{\circ}$ better than \SI{95}{\percent}.

%Figure~\ref{fig:FibresTimingType} indicates the role of the timing detectors 
%which provide the time information for simulated long Michel decay tracks within 
%their geometrical acceptance. 
%Displayed is the fraction of tracks which get their timing information from 
%either the fibre detectors, the fibre and tile detectors, or no timing at all.

The SciFi detector is cylindrical in shape,
with a radius of about 6 cm and a length of 300~mm (280 mm in the acceptance / active part).
It is composed of 12 SciFi ribbons 300~mm long and 32.5 mm wide.
The width of the ribbons matches the size of the photo-detector (see later).
The detector is located just below the outer double-layer silicon pixel detector.
During the last two years the design of the fiber detector has significantly evolved.
In particular, the width of the SciFi ribbons has been increased from 16 mm to 32.5 mm, 
reducing thus the number of fiber ribbons by two and the length decreased from 360 mm to 300 mm,
while the radius of the detector did not change.
This reduces the number of components, simplifies the construction of the detector, and finally the installation.

%%%%%
\begin{figure}[!t]
   \centering
   %\includegraphics[width=0.40\textwidth]{Fibres/figures/ribbon}
   \input{Fibres/figures/ribbon}
   \caption{Full SciFi ribbon prototype with preliminary holding structure.}
   \label{fig:scifi}
\end{figure}

We selected the 250~$\mu$m diameter multiclad round fibers from Kuraray, type SCSF-78MJ.
Three SciFi layers are staggered in order to assure continuous coverage and high detection efficiency.
Figure~\ref{fig:scifi} shows a SciFi prototype, 32~mm wide and 300~mm long close to
the final Mu3e design.
The SciFi arrays are coupled at both ends to silicon photomultiplier (SiPM) arrays.
After careful evaluations we selected the 128 ch. LHCb Si-PM array from Hamamatsu, device S13552-HQR
and are read out with a dedicated mixed mode ASIC, the MuTRiG.

%%%%%
\begin{figure}[b!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/suppresionPerTiming}
   \caption{Suppression of Bhabha pair plus Michel accidental background
as a function of fibre detector time resolution if both timing
detectors (blue) are used or only the fibre detector (green) is used.
A tile detector with a time resolution of \SI{60}{\pico\second} is assumed and a
working point with a signal efficiency of \SI{90}{\percent} for the combined
suppression is chosen.
The expected time resolution of the fibre detector is indicated in gray.}
   \label{fig:FibresTimingSuppression}
\end{figure}

%%%%%
\begin{figure}[t!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/bkg-fibers}
   \caption{Reduction of the combinatorial background using the timing information.
The SciFi timing information reduces this background by almost two orders of magnitude.
Also shown is the irreducible background from muon radiative decays.}
   \label{fig:bkg-fibers}
\end{figure}

By far the largest source of background to the $\mu^+ \rightarrow e^+e^-e^+$ search comes from
the accidental combination of positron tracks from muon decays, in which two muons decay very close
in space such that the decay vertices cannot be resolved.
Moreover, if a decay positron undergoes Bhabha scattering
it will eject one electron from the target, simulating the topology of a three prong muon decay.
Such backgrounds can be efficiently suppressed by timing.
Figure~\ref{fig:FibresTimingSuppression} shows the background suppression depending 
on the detector time resolution.
Exploiting only the fibre detector,
with a time resolution of 250~ps and a 90\% overall efficiency,
provides a survival fraction of background 
due to Bhabha electron/positron-pairs plus one Michel positron of 
$\mathcal{O}{(3 \cdot 10^{-2})}$, combining the fibre and tile detectors 
yields $\mathcal{O}{(1.4 \cdot 10^{-2})}$.
\footnote{at a \SI{90}{\percent} signal efficiency working point.}.
For this study, we simulate a Bhabha electron-positron pair and a Michel
positron from the same vertex, but distributed in a \SI{50}{ns} time window
for a beam intensity of $10^8$ stopping $\mu^+$ per second (Phase~I).
The three tracks are required to pass the kinematic signal selection cuts 
described in chapter~\ref{sec:SensitivityStudy}.
By combining both detector systems, backgrounds can be reduced below the aimed sensitivity
of $2 \times 10^{-15}$ as illustrated in Figure~\ref{fig:bkg-fibers}.
As can be noticed in Figure~\ref{fig:bkg-fibers}, the vertexing alone is not sufficient to suppress
the background.
The timing information from the SciFi detector with a conservative time resolution of 500~ps
suppresses this background by almost 2 orders of magnitude in the signal region
(down to a $10^{-18}$ level) making this measurement feasible.

Figure~\ref{fig:FibresChargeId} shows the time of flight of reconstructed track candidates
between two consecutive SciFi detector crossings for recurling tracks. 
The time of flight in relation with the reconstructed trajectory's length allows one to reject
mis-reconstructed track candidates with either wrong charge assignment or confused
particle turns of recurling particles. 

%%%%%
\begin{figure}[t!]
   \centering
   \includegraphics[width=0.38\textwidth]{Fibres/figures/chargeID2}
   \caption{Rejection of mis-reconstructed track candidates by multiple fibre detector hits. 
Correct (blue) and mis-reconstructed (red) 8-hit track candidates with at least two hits in the fibre detector
are shown.
(top) Correlation between the length of the trajectory of a track candidate
between the two fibre hits and the time difference between them.
The different branches correspond to the combination of different segments of recurling tracks.
(bottom) Corresponding velocity $v=\text{distance}/\Delta t$ in terms of speed of light $c$
of the track candidates.
The different branches in the top plot correspond to the peaks in the bottom spectrum.
Track candidates with $\Delta t<0$, respectively $v<0$, have a wrong charge assignment;
hence the wrong rotation direction.}
   \label{fig:FibresChargeId}
\end{figure}

The fibre detector consists of the scintillating fibre ribbons as the active part,
silicon photomultiplier (SiPM) arrays for light detection, a readout ASIC (the \mutrig chip),
further readout electronics and the support mechanics and cooling. 
These elements will be discussed in the following sections.

%%%%%%%%%%
\section{Fibre Ribbons}
\label{sec:FibreRibbons}
The surrounding pixel detector sets the dimensions of the fibre detector.
The minimal active length of 280~mm is dictated by the acceptance 
of the pixel detector for tracks originating from the target.
The SciFi detector is located in the central barrel right below the third pixel-based tracking layer
at a radius of 61~mm.
This particular value is set by the size of the photo-detector.
The detector is segmented azimuthally into 12 SciFi ribbons each with a width of 32.5~mm,
matching the size of the photo-detector.
Each ribbon consists of three layers of 250~$\mu$m staggered SciFi (128~fibres per layer)
with a length of 300~mm.
Figures \ref{fig:scifi} and \ref{fig:fibres:ribbon:front} show a fibre ribbon prototype
with dimensions very close to final ribbons in the experiment.

%%%%%
\begin{figure}[tb!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/ribbon_front}
   \caption{Front view of a SciFi ribbon prototype with 120$\times$3 fibres.}
   \label{fig:fibres:ribbon:front}
\end{figure}

%%%%%
\subsection{Fibres}
\label{sec:Fibres}

%\begin{figure}[t!]
%	\includegraphics[width=0.48\textwidth]{Fibres/figures/FibreScintillatorRoundDeltaT}
%	\caption{
%				Mean time distribution of signals from the two ends of one round fibre inside
%				a ribbon produced without additional titanium dioxide in the glue.
%				The fibre time resolution is found to be $\sigma = $\SI{1.1}{\nano\second}
%				with a threshold of 0.5 photoelectrons.
%				The fit (red) is the sum of two Gaussians with $\sigma_{tails} = $\SI{3.1}{\nano\second} and a fraction of 0.75.
%				Measured with \SI{161}{MeV/c} positrons.
%			}
%	\label{fig:FibreScintillatorRoundDeltaT}
%\end{figure}
%
%\begin{figure}[t!]
%	\centering
%		\includegraphics[width=\linewidth]{Fibres/figures/Run2017_tmean_singlehit}
%		\caption{The mean time distribution for m.i.p. (\SI{115}{MeV/c} positrons) going through a single square fibre inside a ribbon prototype.
%		A timing resolution of  $\sigma = 750 \pm \SI{17}{ps}$ is measured.
%		The time has been extracted using the leading edge with a threshold equal to the half amplitude of one photoelectron fitted with a single Gaussian.
%}
%		\label{fig:LPtiming}
%\end{figure}

The constraints on material budget, and also occupancy and position resolution,
allow only for the thinnest available scintillating fibres (250~$\mu$m) to be used. 
In extensive measurement campaigns, we have performed a detailed comparison of different types
of \SI{250}{\micro\meter} round fibres produced by Kuraray (SCSF-78, SCSF-81, and NOL-11)
and Saint-Gobain (BCF-12) and square cross-section fibres by Saint-Gobain (BCF-12).
Table~\ref{tab:FibresScintillators} summarizes the characteristics of different SciFi types.

%%%%%
\begin{figure}[b!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/lightyield}
   \caption{Light yield of different SciFi ribbons using different scintillating materials.
The number of photoelectrons is the charge sum of all channels in a cluster at one side matched to a track.
The minimal cluster multiplicity is two neighbouring channels with an amplitude of at least 0.5 ph.e.
The histograms are normalised by their integral.
}
   \label{fig:fibres:light}
\end{figure}

%%%%%
\begin{table*}[t!]
   \centering
   \begin{tabular}{l r r r r }
      \toprule
%               & round & square\\
%               \midrule
      company                                 & Saint-Gobain & \multicolumn{2}{c}{Kuraray} & R\&D \\
      type                                    & {\sc BCF-12} & {\sc SCSF-81MJ} & {\sc SCSF-78MJ} & {\sc NOL-11}\\
      \midrule
      emission peak [nm]              & 435  & 437 & 450   &  \\
      decay time [ns]                 & 3.2  & 2.4  & 2.8  & 1.1 \\
      attenuation length [m]  & >2.7 & >3.5 & >4.0 & \\
      light yield     [ph/MeV]        & $\sim$8000 & & high & high\\
      refractive index                & 1.60/1.49/1.42 & \multicolumn{2}{c}{ 1.59/1.49/1.42} & \\
      density [g/cm$^3$]              & 1.05 &  \multicolumn{2}{c}{1.05/1.19/1.43} & \\
%      cladding [\%]                   & 3/1 & \multicolumn{2}{c}{4/2} & ? \\
      available shapes        & round \& square & \multicolumn{2}{c}{round} & round \\
      cladding [\%] round     & 3/1 & \multicolumn{2}{c}{3/3} & \\
~~~~~~~~~~~~~~~~~~square       & 4/2 & - & - & - \\
      trapping [\%] round     & $\geq$5.6 & \multicolumn{2}{c}{5.4} & \\
~~~~~~~~~~~~~~~~~~square       & 7.3 & - & - & - \\
%      capture angle [deg]             & 26.7 & 27.4  \\
      core                                    & \multicolumn{4}{c}{Polystyrene (PS)} \\
      inner cladding                  & \multicolumn{4}{c}{Acrylic (PMMA)} \\
      outer cladding                  & \multicolumn{4}{c}{Fluor-acrylic (FP)} \\
      \bottomrule
   \end{tabular}
   \caption[Scintillating fibre properties.]{Properties of different scintillating fibre types from Kuraray
and Saint Gobain~\cite{KurarayPSFY11, SaintGobainSciFi}.
{\sc NOL-11} is an R\&D fibre with Kuraray involvement.
Its properties are assumed to be very similar to the other Kuraray fibres.
Light yield is only quoted by Saint-Gobain, whereas Kuraray characterises {\sc SCSF-78} and {\sc NOL-11}
as ``high light yield'' fibres. }
   \label{tab:FibresScintillators}
\end{table*}

%%%%%
\begin{figure}[h!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/timeNOL}
   \caption{Time resolution (mean time) obtained with a 4 layer SciFi ribbon using Kuraray NOL-11 fibers.}
   \label{fig:fibres:time}
\end{figure}

%%%%%
\begin{figure}[h!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/attenuation}
   \caption{Light attenuation in different fiber types as a distance of the source.}
   \label{fig:fibres:attenuation}
\end{figure}

Figure~\ref{fig:fibres:light} shows the light yield for a m.i.p. crossing the SciFi ribbon
for different fiber materials.
The light yield is measured with respect to the center of the fiber ribbon (150~mm from the edge).
As can be noticed the Kuraray SCSF-78 and NOL-11 fibers provide the highest light yields.
Figure~\ref{fig:fibres:time} shows the time performance obtained with the NOL-11 fiber;
the achieved resolution on the mean time (i.e. using the timing measurements from both fiber ends)
is around 200~ps (see later).
Figure~\ref{fig:fibres:attenuation} compares the light yield as a function of the distance from the source
(attenuation) of different fibers under the same conditions,
so that the light yields from different fibers, even if not absolutely normalized, can be compared.
The Kuraray fiber types SCSF-78 and NOL-11 are similar with the least attenuation and similar light yields,
while surprisingly the BCF-12 fibers have a rather short attenuation length.
More detailed results can be found in \cite{rutar:phd,damyanova:phd,corrodi:phd}.

Based on their performance with respect to light yield and time resolution, as well as availability,
round double-clad SCSF-78MJ fibres from Kuraray were chosen. 
Novel NOL fibres, based on Nanostructured Organosilicon Luminophores,
give the best performance, but will only become commercially available in the next years. 
Hence, they are a viable option for potential SciFi detector upgrades in the future.

%The round fibres allow for an easier fabrication of ribbons and have less material
%(consequently also less light output) per layer, while the square fibres offer
%a better fill factor and show more light per layer in our measurements.
%
%Figures~\ref{fig:FibreScintillatorRoundDeltaT} and \ref{fig:LPtiming} compare
%the single fibre time resolution inside ribbon prototypes for round and square
%fibres as measured in test beams at PSI.
%The longer average particle path with the resulting larger light production and 
%the better detection fraction in the square fibres
%lead to a better time resolution\footnote{Note that a direct comparison of 
%the single fibre resolution for round and square fibres is not straightforward,
%as path-length effects, light capture and coupling do the SiPM are all different.}
% of $\sigma = 750 \pm \SI{17}{ps}$.
%We thus select the square fibres as a baseline for our simulation studies.
%Recently, there have been exciting development in scintillating materials with
%significantly reduced scintillation times.
%These new materials have the potential to provide even better time resolution and
%will be available first in round fibres; if this development promises a better
%performance and becomes available soon, we will reconsider the fibre choice.

%\subsection{Optical Isolation}
%\todo[inline, author={Simon}]{I don't know how to connect this chapter to the story line.}
%\label{sec:OpticalIsolation}

%\begin{figure*}
%	\begin{center}
%		\begin{tabular}{cc}
%			\includegraphics[width=0.48\linewidth]{Fibres/figures/0199_Crosstalk} &
%			\includegraphics[width=0.48\linewidth]{Fibres/figures/0302_Crosstalk} \\
%            a) without Al &
%		    b) with Al\\
%		\end{tabular}
%		\caption{The correlated charges collected from two adjacent fibres are 
%		plotted one against the other. 
%		The optical cross-talk without (a) and with (b) Al deposit around each fibre of the array.
%		For a), a threshold of half a photoelectron was applied, b) shows all events.}
%		\label{fig:cross-talk}
%	\end{center}
%\end{figure*}
%
%Surface imperfections in the fibres can lead to light propagating into the 
%neighbouring fibre in the ribbon, leading to optical cross-talk.
%An optical isolation of the fibres is thus very important.
%One option for isolation is the admixture of titanium dioxide in the glue used
%to build the fibre ribbons.
%This method is straightforward and efficient, however adds high-$Z$ material in
%the active region of the detector.
%The second investigated option is covering the fibres with $\sim$\SI{100}{\nano\meter}
%of aluminium using vapour deposition. 
%Whilst more technically demanding (the fibres need to be cut before ribbon assembly),
%the aluminium coating adds minimal material and is highly efficient at suppressing
%cross-talk, see figure~\ref{fig:cross-talk} and thus our preferred solution.
%It was demonstrated that applying optical cement (typically BC600) to the fibres
%induces a loss in light yield around 40\%, which can be prevented through the 
%use of aluminisation, see table~\ref{tab:AlMeasurements}, which also shows the 
%effects of Araldite and optical grease application).
%
%\begin{table}
%	\centering
%	\begin{tabular}{l l c c}
%		\toprule
%		material & n & \multicolumn{2}{c}{light loss}\\
%			   &   & bare & aluminised\\
%		\midrule
%		optical cement & 1.56 & $\sim$\SI{40}{\percent} & $\le$\SI{1}{\percent}\\
%		Araldite rapid & $\sim$1.5 & $\sim$\SI{30}{\percent} & $\le$\SI{1}{\percent}\\
%		optical grease & 1.465 & $\sim$\SI{20}{\percent} & $\le$\SI{1}{\percent}\\
%		\bottomrule
%	\end{tabular}
%	\caption{Light loss in \SI{250}{\micro\meter} thick squared fibres covered by given material
%     with respect to air without (bare) and with Al deposit.
%	The loss depends on the refractive index of the used material and can be recovered
%    if the fibres are aluminised.}
%	\label{tab:AlMeasurements}
%\end{table}

%%%%%
\subsection{Number of Layers}
\label{sec:NumberOfLayers}

%%%%%
\begin{figure}[t!]
  \includegraphics[width=0.48\textwidth]{Fibres/figures/FibresScattering}
  \caption{Multiple Scattering $\theta_0$ depending on electron/positron 
momentum and fibre ribbon thickness.
  \textit{r} indicates the thickness of round and \textit{s} of square fibres. }
  \label{fig:FibresScattering}
\end{figure}

A critical point of optimization is the number of fibre layers.
More layers lead to a better timing resolution and a higher efficiency but
deteriorate the momentum resolution of the tracker due to multiple Coulomb scattering.
In addition, more layers lead to
larger cluster size and larger occupancy, which makes it harder to 
associate tracks and clusters of fibre hits.

Using the measured performance characteristics of the fibres, we have performed
extensive simulation studies of the fibre detector resolution, efficiency and
the effects on the track reconstruction and linking.
Details on the complete detector simulation can be found in 
chapter~\ref{sec:Simulation},
the reconstruction algorithm is described in chapter~\ref{sec:Reconstruction} 
and the selection used to determine the performance on signal decays is
detailed in chapter~\ref{sec:SensitivityStudy}.

%%%%%
\begin{figure}[t!]
  \includegraphics[width=0.48\textwidth]{Fibres/figures/trackMomentumResZoom_lf}
  \caption{Momentum resolution for short (outgoing) and long (outgoing and recurling) tracks
as a function of fibre ribbon thickness using simulated Michel decays.
The targeted fibre ribbon thickness of $\sim$\SI{0.9}{\milli\meter} is highlighted.
The momentum resolution of long (6- and 8-hit) tracks is improved over short (4-hit) tracks due to their recurling.
The effect of the fibre detector is more pronounced for 6-hit than 8-hit tracks.
}
  \label{fig:FibreLayerMomentumRes}
\end{figure}

%%%%%
\begin{figure}[h!]
	\includegraphics[width=0.48\textwidth]{Fibres/figures/signalMomentumResAndEff_lf}
  \caption{Signal resolution in terms of invariant mass of the three tracks of a candidate $m_{\text{eee}}$
(top) and the relative reconstruction efficiency with respect to the absence of the fibre detector as a function
of the fibre ribbon thickness.
The planned ribbon thickness $\sim$\SI{0.9}{\milli\meter} is highlighted.
       }
  \label{fig:FibreLayerSignalRes}
\end{figure}

%\begin{figure}[tb!]
%  \includegraphics[width=0.48\textwidth]{Fibres/figures/layersEff.pdf}
%  \caption{Simulated efficiency of the fibre detector for Michel decay tracks
%	reconstructed in the pixel detector.
%	\emph{OR} refers to a signal above threshold (0.5 or 1.5 photoelectron)
%	at either fibre
%	end, \emph{AND} requires a signal above threshold at both ends. 
%	The expectation is for tracks crossing the fibre detector at $z=0$ and no angle.
%	}
%  \label{fig:FibreLayersEff}
%\end{figure}

%\begin{figure}[tb!]
%  \includegraphics[width=0.48\textwidth]{Fibres/figures/layersTimeRes.pdf}
%  \caption{Simulated time resolution per crossing of the fibre detector as a 
%	function of the number of square fibre layers.}
%  \label{fig:FibreLayersTimeReso}
%\end{figure}
%
%\begin{figure}[tb!]
%  \includegraphics[width=0.48\textwidth]{Fibres/figures/layersTimePileUp.pdf}
%  \caption{Simulated pile-up in the fibre detector within \SI{50}{ns} as a function of the
%	number of square fibre layers assuming \num{e8} muon stops per second.
%	Fibre pile-up refers to the same fibre being hit multiple times, cluster pile-up
%	refers to groups of adjacent fibres and recurlers refers to the same track producing
%	an overlapping cluster in a different turn.}
%  \label{fig:FibreLayersPileUp}
%\end{figure}
%
%\begin{figure}[tb!]
%  \includegraphics[width=0.48\textwidth]{Fibres/figures/layersClusterSize.pdf}
%  \caption{Cluster size in columns on the SiPM as a function of the number of
%	square fibre layers at  0.5 and 1.5 photelectron thresholds.
%	The simulation was performed for Michel decays.}
%  \label{fig:FibreLayersClusterSize}
%\end{figure}

The amount of multiple scattering caused by the fibres and the glue in the
ribbons is shown in figure~\ref{fig:FibresScattering}. 
Note that a ribbon of three layers of round \SI{250}{\micro\meter} fibres corresponds
to below \SI{0.3}{\percent} $X/X_0$.
This scattering affects the momentum resolution (see figure~\ref{fig:FibreLayerMomentumRes})
and thus the $\mu^+ \rightarrow e^+e^-e^+$ signal invariant mass resolution and reconstruction efficiency. 
%(see figure~\ref{fig:FibreLayersEff}).

%The detection efficiency and time resolution of the simulated fibre detector are shown in
%figures~\ref{fig:FibreLayersEff} and \ref{fig:FibreLayersTimeReso}.
More fibre layers also lead to larger pile-up, i.e.~hits from different tracks
(or different turns of the same track) producing hits in the same fibre or in the
same cluster of fibres and larger
clusters.%, see figure~\ref{fig:FibreLayersClusterSize}.

As a compromise between the aforementioned constraints,
three layers of \SI{250}{\micro\meter} thick round fibres are chosen.
% coated in vapour 
%deposited aluminium, ending up with a thickness of \SI{0.3}{\percent} $X/X_0$.
With a thinner detector, it would be challenging to fulfill the efficiency
requirements and the time resolution would not be sufficient for a reliable
charge identification, e.g. rejection of mis-reconstructed track candidates.

% This doesn't belong to this chapter
%An operation threshold of 1.5~photoelectrons in an \emph{AND} configuration 
%(requiring signal from both fibre ends) leads
%to a time resolution per pass around \SI{400}{\pico\second}. 
%Particularly the tracks at close to \SI{90}{\degree} to the beam direction which
%do not reach the tile detector pass the fibre detector more than once, thus 
%allowing for an improved time resolution.
%The efficiency of the fibre detector is above \SI{98}{\percent} and pile-up 
%rates are well below \SI{2}{\percent}.

%%%%%%%%%%
\section{Silicon Photomultiplier Arrays}

%%%%%
\begin{figure}[tb!]
        \centering
        \input{Fibres/figures/sipmClose}
\caption[Hamamatsu S13552-HRQ SiPM column array.]{Picture of a Hamamatsu S13552-HRQ SiPM column array (left) and a schematic side view (right).
        All dimensions are given in units of \SI{}{\milli\meter}.
\num{24} such sensors are used in the Mu3e fibre detector.}
        \label{fig:sipmArray}
\end{figure}

%%%%%
\begin{table}
    \centering
        \begin{tabular}{l l}
                \toprule
                characteristic &  value \\
                \midrule
                breakdown                    & \SI{51.0}{\volt} \\
                variation per sensor         & \SI{+-250}{\milli\volt} \\
                variation between sensors    & \SI{+-500}{\milli\volt} \\
                temperature coefficient      & \SI{53.7}{\milli\volt\per\kelvin} \\
                gain                         & \num{3.8e6} \\
                direct crosstalk             & \SI{3}{\percent} \\
                delayed crosstalk            & \SI{2.5}{\percent} \\
                after-pulse                  & \SI{0}{\percent} \\
                peak PDE               & \SI{48}{\percent} \\
                max PDE wavelength     & \SI{450}{\nano\meter} \\
                mean quench resistance $R_Q$ & \SI{490}{\kilo\ohm} at \SI{25}{\celsius} \\
                recovery time $\tau_{\text{recovery}}$ & \SI{68.9+-2.1}{\nano\second} \\
                short component $\tau_{\text{short}}$  & $<\SI{1}{\nano\second}$ \\
                long component $\tau_{\text{long}}$  & \SI{50.1+-4.1}{\nano\second} \\

                \bottomrule
        \end{tabular}
   \caption[Characteristics of used SiPM coloumn arrays.]
{SiPM (S13552-HRQ) characteristics at $\Delta T = \SI{3.5}{\volt}$ and $T=\SI{25}{\celsius}$ from \cite{LPHE-2017-001}.}
   \label{tab:LHCbArrays}
\end{table}

The space constraints between the pixel detector layers and the strong magnetic field
require the use of solid state photon detectors; in fact, the space constraints
are so tight that silicon photomultiplier (SiPM) arrays are the only option.
The compact form factors and moderate high voltage ($\sim$ \SI{60}{\volt}) of
SiPM arrays account for the limited space and they provide the required channel density.
They are insensitive to magnetic fields.
The photon detection efficiency (PDE\footnote{With contributions from quantum 
efficiency and geometrical fill factors.}) up to \SI{50}{\percent}, 
single photon detection and very fast intrinsic time response 
(single photon jitter of approximately  \SI{200}{\pico\second}) are the key 
features for the use in the fibre detector.
The high gain ($\sim \num{e6}$) allows the use of mixed-mode ASICs (like \mutrig) 
without any pre-amplification.
Typical dark-rates of SiPMs are around a few 10~kHz per channel at room temperature,
depending on the SiPM type.

The photons produced in the scintillating fibres are detected on both fibre ends 
in SiPM arrays.
Acquiring the signals on both sides increases the time resolution, helps to 
distinguish between noise and signal and increases the detection efficiency of 
the whole system.
Moreover, by taking the mean time of the two time measurements,
the timing measurements is independent of the hit position
(assuming that light propagates at the same speed to both fiber ends)
and thus no correction is required.

The fibre ends are coupled directly to the surface of SiPMs on both sides.
For easy detector assembly and maintainability, the coupling will be done by using
mechanical pressure (spring loading) of the fibres to the SiPM without the use of glue
or optical grease.
Due to space constraints, no extensive fan-out of fibres to the SiPM array channels is possible.

The Mu3e fibre detector uses the Hamamatsu S13552-HRQ SiPM arrays with a high quenching resistor
(see figure~\ref{fig:sipmArray}).
This sensor was developed for the LHCb experiment.
Different than in LHCb, where the SiPMs are operated around \SI{-40}{\celsius}, 
the Mu3e sensors operate at room temperature but also in a much less intense
radiation field.
We are exploring the possibility to cool the SiPM arrays to \SI{5}{\celsius},
the same temperature of the Mu3e cooling,
in order to further reduce the dark count rate and limit the radiation damage effects.

Each channel of the multi-channel SiPM out of two dies each with \SI{64}{channel} arranged
in a one-dimensional array consists of \SI{104}{pixels} with a size of \SI{57.5 x 62.5}{\micro\meter}
arranged in a $4 \times 26$ grid resulting in a channel area of \SI{230 x 1625}{\micro\meter}.
The pixels are separated by trenches of the fifth generation Hamamatsu low-crosstalk development (LCT5).
The channels have a pitch of \SI{250}{\micro\meter}, and a gap of \SI{220}{\micro\meter} separates
the two dies in the centre of the sensor.
They share a common cathode.
The overall current consumption of one array is expected to be well below 
\SI{1}{\milli\ampere}.
The sensors are delivered wire bonded to a PCB with solder pads on the backside and
covered with a \SI{105}{\micro\meter} thick epoxy resin.
Figure~\ref{fig:sipmArray} shows such an assembly.
Table~\ref{tab:LHCbArrays} summaries the most important features of this sensor.

Figure~\ref{fig:SiPMIVcurves} shows the I-V curves for the SiPM array for each channel of the array.
All breakdown voltages are comprised within $\pm 0.25$~V of the central value of 52.5~V
for this device.
The performance of the photo-detector can be further improved by adjusting individually the
operational voltage for each channel of the array.
This is possible thanks to the MuTRiG ASIC, which allows for the fine tuning of the bias voltage
around a common value.   

%%%%%
\begin{figure}[b!]
   \includegraphics[width=0.48\textwidth]{Fibres/figures/ivcurves}
   \caption{I-V curves for the SiPM array showing the breakdown voltage for each channel of the array.
All breakdown voltages are comprised within $\pm 0.25$~V of the central value of 52.5 V.
   }
  \label{fig:SiPMIVcurves}
\end{figure}

%%%%%
%\subsection{SiPM Radiation Damage}
%\label{sec:SiPMRadiationDamage}
%
%\begin{figure}[tb!]
%        \centering
%       \includegraphics[width=0.48\textwidth]{Fibres/figures/dcrIrrad.pdf}
%        \caption[DCR as a function of \SI{1}{MeV} neutron equivalent fluence.]
%{DCR of Hamamatsu S13360-1350PE as a function of irradiation by a $^{90}$Sr source at room temperature.
%        The presented rate is corrected for temperature variations; the bias voltage is kept constant.
%        At $\sim$\SI{3.2e9}{neq\per\centi\meter\squared} the sensors annealed at room temperature
%  for $\sim$\SI{10}{days}.}
%        \label{fig:irradRate}
%\end{figure}

%\begin{figure}
%	\includegraphics[width=0.48\textwidth]{Fibres/figures/fibreDetecotrSiPMedep}
%	\caption{Simulated energy deposition of positrons and electrons in the thin active layer of the SiPM arrays of the fibre detector.}
%	\label{fig:fibreMppcRadiationEdep}
%\end{figure}
%
%
%\begin{figure}
%	\includegraphics[width=0.48\textwidth]{Fibres/figures/FibresDarkrate}
%	\caption{Dark rate increase of SiPM (Hamamatsu S12571-050P, \SI[product-units = power]{1x1}{\milli\metre} active area, \SI[product-units = power]{50x50}{\micro\metre} pixels) irradiated by \SI{20}{\mega\becquerel} $^{90}$Sr.}
%	\label{fig:FibresDarkrate}
%\end{figure}

%The dark count rate of the SiPM array increases with irradiation.
%Dark counts can be efficiently suppressed by requiring signals from both fibre
%ends; the data acquisition system, however, has to provide enough bandwidth to 
%transport all hits out of the detector to form clusters and then
%bring them into coincidence.

%In the baseline design of phase~I, a positron/ electron flux per 
%\SI{}{\milli\meter\squared} active sensor area inside the thin active SiPM layer 
%of up to $\sim$~\SI{1.6}{\kilo\hertz}, respectively $\sim$~\SI{2.3}{\kilo\hertz} 
%depending on the side, is expected.
%Due to the location of sensors and the experiment's event topologies,
%most of the tracks penetrate the SiPM not perpendicular to the active surface.
%In \SI{1e7}{\second}, corresponding to \SI{116}{\day}, of beam time, roughly one year of operation,
%a dose of \SI{263+-71}{Gy}, respectively \SI{184+-68}{Gy}, is accumulated in the silicon oxide layer.
%In the same time period the neutron equivalent fluence\footnote{integrated flux.} (neq)
%of \SI{3.45+-0.18e10}{neq\per\centi\meter\squared},
%respectively \SI{2.45+-0.07e10}{neq\per\centi\meter\squared}, through the bulk is acquired.

%Figure \ref{fig:irradRate} shows the dark count rate (DCR) in similar Hamamatsu sensor as a function of
%\SI{1}{MeV} neutron equivalent fluence from irradiations with a \SI{}{\mega \becquerel} $^{90}$Sr source.
%The rate is obtained by a discriminator with a fixed threshold at the \SI{0.5}{phe} level
%of the not irradiated sensor.
%A significant, linear DCR increase and no significant loss in signal amplitude is observed.
%After one year of operation at \num{1e8} stopped muon per second on the target a DCR increase
%in the order of \SI{1}{\mega\hertz} per channel is expected.
%\todo[inline]{Lukas: Check and update}

%%Figure~\ref{fig:fibreMppcRadiationEdep} shows the expected spectrum of deposited 
%energy, on average \SI{42}{keV}.
%This sums to an integrated positron flux of \num{0.8e10} (\num{1.4e10}) 
%$\SI{}{e^{+}\per\milli\meter\squared}$ per year;
%\SI{55}{\milli\joule} (\SI{97}{\milli\joule}) 
%corresponding to \SI{24}{Gy} (\SI{42}{Gy}) per year.

%First results from irradiation studies with $^{90}$Sr, as shown in 
%figure~\ref{fig:FibresDarkrate} show a significant 
%increase in the dark rate with irradiation.
%It is to be noted that the different energy spectra prevent a direct translation 
%from irradiation tests with $^{90}$Sr to radiation damage in the experiment.
%A possible recovery due to annealing of the SiPM is currently under investigation.

%\begin{figure*}[tb!]
%	\centering
%	\includegraphics[width=0.55\textwidth]{Fibres/figures/Fibredet.pdf}
%	\caption{CAD view of the fibre detector mounted in the complete Mu3e detector.
%	The central outer pixel layers have been removed for clarity.
%	Light blue are the SiPM arrays, green the SiPM PCBs and the \mutrig PCBs and 
%	golden the flexprints connecting them.}
%	\label{fig:FibreMounting}
%\end{figure*}
%
%\begin{figure*}[tb!]
%	\centering
%	\includegraphics[width=0.55\textwidth]{Fibres/figures/FibreROCADpdf.png}
%	\caption{CAD view of the fibre detector readout region mounted in the complete 
%	Mu3e detector.
%	The outer pixel layers and a segment of the tile detector have been removed for clarity.
%	Light blue are the SiPM arrays, green the SiPM PCBs and the \mutrig PCBs and 
%	golden the flexprints connecting them.
%	The \mutrig PCBs as the main power consumers are in thermal contact with the
%	water-cooled beam-pipe.}
%	\label{fig:FibreROMounting}
%\end{figure*}

%%%%%%%%%%
\section{SciFi Readout Electronics}
The Mu3e scintillating fibre detector requires the digitization of the Time of Arrival (ToA)
at a single photon level where very little space is available.
Furthermore, the readout electronics has to cope with up to \SI{650}{\mega\hertz} signal
from particle crossing the detector in combination with up to several \SI{100}{\mega\hertz} DCR
on a single photo-electron trigger level.
Due to the space constraints, the usage of a mixed-mode ASIC is required.
Although many state-of-the-art ASIC for digitization of SiPM signals exists,
none can handle the required rates.
MuTRiG was developed within the Mu3e collaboration based on STiC to fulfill the detectors requirement
(see chapter~\ref{sec:Mutrig});
the tile sub-detector uses the same SiPM readout chip.

In contrast to the PET applications (usually LYSO crystals as scintillator) for which STiC
was originally designed and the tile sub-detector where signals consist of $\sim 1000$ photons,
the fibre detector readout has to operate with very few photons.
MuTRiG fulfills the fibre detector requirement in a special mode,
where the event validation by a second threshold 
(\textit{energy threshold}) is switched off, and the {\it energy}-time-stamp is reduced to a single flag.

For the readout of the 3000 channels of the fiber detector we plan to use the MuTRiG ASIC:
a mixed signal Silicon Photomultiplier readout ASIC with high timing resolution and gigabit data link.
The MuTRiG chip comprises 32 input fully differential channels with 50~ps TDC time binning.
4~chips are required for the readout of one SiPM array, and 96 for the full detector.
The analog part is complemented by digital readout logic and a 1.28 Gb/s LVDS serial data link.
When operated with the SiPM arrays two thresholds will be used: a low one for timing
(a time stamp will be generated) and a high one for hit selection. 
Moreover, MuTRiG allows for the fine tuning of each SiPM bias voltage,
which is required for the optimal operation of our SiPM arrays (see Figure~\ref{fig:SiPMIVcurves}).

The analogue signals from each SiPM array (128~channels) are digitized by one SciFi front end board.
Each SiPM array is connected via a flex-print to a front end board hosting 4 MuTRiG chips.
Due to the limited space the design of the front end board is very compact.
The boards sit below the SciFi ribbons (see next section).
In addition to the MuTRiG chips, the front board comprises the clock distribution,
components for the control of the MuTRiG chips, power distribution, and temperature monitoring.
Finally each front end board is connected to readout boards via a very thin set of twisted pair cables. 

%\subsection{The Scintillating Fibre Board}
%\begin{table*}[tb!]
%        \centering
%        \begin{tabular}{l l r r r }
%                \toprule
%                component & comment & area [\SI{}{\milli\meter\squared}] & number \\
%                \midrule
%                \mutrig &   ~ & \num{5.0x5.0} & 8 & \\
%                        & wire bonded & $\sim$\num{15x10} & 8 \\
%                        & packaging   & \num{17x17} & 4 \\
%                LDO \SI{1.8}{V} analogue & TPS7A830 & \num{3.5x3.5} & 2 \\
%                LDO \SI{1.8}{V} digital & TPS7A92 & \num{2.5x2.5} & 2 \\
%                LDO \SI{3.3}{V} digital & TPS7A92 & \num{2.5x2.5} & 1 \\
%                current monitor, LV & LTC2991 & \num{4.0x3.0} & 2 \\
%                voltage and current monitor, HV & LTC4151 & \num{3.0x3.0} & 2\\
%                temperature sensors & ~ & ~ & $\geq$4\\
%                chip select (cs) multiplexing & MAX349 & \num{5.3x7.3} & 2 \\
%                clock fan-out & SI53344 & \num{5.0x5.0} & 1 \\
%                TDC injection & PL138-48 & \num{3.0x3.5} & 2\\
%                LVDS buffer & DS15BR400 & \num{5.0x5.0} & 2\\
%                \bottomrule
%        \end{tabular}
%\caption[Proposed components on the  {\sc SciFi Board}.]{Proposed components on the {\sc SciFi Board}. 
%\emph{LV} stands for low voltage and \emph{HV} for high voltage.
%        The MuTRiG ASICs could be directly wire-bonded or packed in pairs of two.}
%        \label{tab:fibres:scifiboard:components}
%\end{table*}

%The analogue signals from two SiPM arrays ($2\times128$~channels) from two ribbons on one side
%are digitized by one Scintillating Fibre Board ({\sc SciFi Board}).
%Each board hosts \num{8} MuTRiG ASICs and their supplies;
%one {\sc SciFi Board} is connected to one bank of an experiment's front-end FPGA boards
%(see table~\ref{tab:fibres:scifiboard:interface}).
%Table~\ref{tab:fibres:scifiboard:components} summarizes the proposed components of such a board.
%\begin{table*}[tb!]
%        \centering
%        \begin{tabular}{l l l r r r }
%                \toprule
%                group & name & type & direction & rates & lines \\
%               \midrule
%               reference clock & clk      & LVDS & in  & \SI{625}{\mega\hertz} & \num{1x2} \\
%                data            & data     & LVDS & out & \SI{1.25}{Gpbs} & \num{8x2} \\
%                slow control    & sclk     & SPI  & in  & \SI{20}{\mega\hertz} & \num{1} \\
%        & \makecell[l]{cs, cec\_cs, \\ cs\_cs, cec\_cs\_cs} & SPI  & in  & \SI{20}{\mega\hertz} & \num{4} \\
%                                & sdi      & SPI  & in  & \SI{20}{\mega\hertz} & \num{1} \\
%                                & sdo, cec\_sdo & SPI  & out & \SI{20}{\mega\hertz} & \num{2} \\
%                                & \bf total    & \bf SPI & & \bf \SI{20}{\mega\hertz} & \bf \num{7}\\
%                injection       & inj & LVDS & in & \ord(\SI{100}{\kilo\hertz}) & \num{1x2}\\
%                i$^2$c           & scl, sda & i$^2$c & inout & \SI{}{\mega\hertz} & \num{2} \\
%                reset$\dagger$  & rst &  ~ & in & ???  & \num{1x2}\\
%                sensor temp     & ~       & 1-wire & inout & ~ & \num{2} \\
%                \it trigger     & \it trg & ~ & in & ~ & \num{1} \\
%                spare           & ~       & ~ & ~  & ~ & \num{2} \\
%                \bf total       & ~       & ~ & ~  & ~ & \bf \num{34} \\
%                \midrule
%       power, ground   & \makecell[l]{\SIrange{1.4}{6.5}{\volt}, $<$\SI{20}{\watt}} & & in & & \num{2}\\
%                high voltage    & $\sim$\SI{55}{\volt} & & in & & \num{2}\\
%                \bottomrule
%        \end{tabular}
%        \caption[The interface of the {\sc sciFi Board}.]
%{The interface of the {\sc SciFi Board} to one bank of the front-end FPGA board and power distribution.
%        The abbreviation \emph{sensor temp} stands for the temperature sensors at the SiPMs
%on the backside of the flex print cables (see \autoref{sec:integration:tempSensor}).
%        The {\it external trigger} line is optional.
%        The reset of the current \mutrig comprises two single-ended signals.
%        The next version will incorporate a single differential reset.
%        }
%       \label{tab:fibres:scifiboard:interface}
%\end{table*}

%\balance

%%%%%%%%%%
\section{Performance}
%\textbf{comprising \num{4} layers round, double-clad \SI{250}{\micro\meter} thick Kuraray fibres
%from type SCSF-78MJ}
Scintillating fibre ribbon prototypes  coupled to SiPM arrays of the latest version have been tested intensively
in test beams at CERN PS (T9 beamline) and PSI ($\pi$M1 beamline),
and with $^{90}$Sr sources, as well.
Data were recorded using a fast pre-amplifier and readout digitizing electronics based on the DRS4 ASIC.
The recorded waveforms were then processed using timing algorithms close to the MuTRiG functioning
(i.e. 0.5 ph.e. low threshold leading edge discriminator).

%The following distributions are obtained by minimum ionizing particles (MIP)
%crossing the fibre ribbon prototype perpendicular in the centre. 

%%%%%
\begin{figure}[tb!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/cluster_charge2}
   \caption[Spectrum of charge and number of photons.]
{Cluster light yield of a three layered SCSF-78MJ fiber ribbon prepared with clear epoxy.
The integral NPhe is obtained by integrating the charge in a region of $\pm 0.5$ ph.e. around each integer.
A convolution of a Gaussian and Landau is used to fit the data and the
most probable value (MPV) is marked with a line.}
   \label{fig:clCharge}
\end{figure}

%The detected photons of all columns of a cluster from both sides are summed to extract the light yield $Y$ of a ribbon under test.
Figure~\ref{fig:clCharge} shows the light yield of a cluster for a 3-layered SCSF-78MJ fiber ribbon
prepared with clear epoxy.
A cluster consists of all consecutive columns with an amplitude larger than a specific threshold (0.5 ph.e.).
The integral NPhe is obtained by integrating the charge in a region of  $\pm 0.5$ ph.e. around
each integer.
A convolution of a Gaussian and Landau is used to fit the data.
This information, however, will not be accessible in the experiment
since the MuTRiG ASIC provides only the timing information and no charge information.

%%%%%
\begin{figure}[tb!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/cluster_size}
   \caption[Cluster size in the SiPM column arrays.]
{Cluster size of both sides of a \SI{3}{layer} NOL-11 ribbon without any additional coating.}
   \label{fig:clSize}
\end{figure}

The cluster size distribution of a 3-layer NOL-11 ribbon without any additional coating
is shown in figure~\ref{fig:clSize}.
Typical cluster sizes are around 3.5 for a threshold of 0.5 ph.e.
The cluster size can be reduced by increasing the detection threshold to e.g. 1.5 ph.e.
The difference of cluster sizes between both sides is caused by slightly different mappings
of the ribbons to the SiPM arrays.

Figure~\ref{fig:SciFiSummary} summarizes the detection efficiency versus timing resolution
for selected fiber ribbons assembled using different scintillating fibers.
The resolution of the time difference from the two ribbon sides
$\sigma(t_{\text{left}} - t_{\text{right}})$,
obtained with a leading edge algorithm,
corresponds to twice the intrinsic resolution $\sigma_{\text{ribbon}}$ (mean time). 

%%%%%
\begin{figure}[tb!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/scifi_summary}
   \caption[Time Resolution.]
{Detection efficiencies vs their respective time-difference resolutions for selected ribbons.
The efficiency is estimated for an AND configuration (i.e. require hits at both ribbon ends)
and the minimal cluster multiplicity of two neighbouring channels with an amplitude of at least 0.5 ph.e.
Events are considered valid if they fall within the area of $\pm 3 \sigma$ around the centroid
of the time difference Gaussian fit.
The efficiency estimates are conservative and represent a lower limit.
No channel by channel time offset correction is applied in extracting the timing resolution.
Note that the figure shows the time difference resolution.
For the mean time the resolution is half the one reported in the figure.}
   \label{fig:SciFiSummary}
\end{figure}

%%%%%
\begin{figure}[tb!]
     \centering
     \includegraphics[width=0.48\textwidth]{Fibres/figures/n2deltaT_m}
     \caption[Time Resolution of fibre prototype extracted with MuTRiG.]
{Time Resolution of a \SI{4}{layer} SCSF-78MJ ribbon without additional TiO$_{2}$ in the glue
extracted from clusters with at least 2 active columns.
No channel by channel time offset correction is applied.}
   \label{fig:mutrig:deltaT}
\end{figure}

Similar timing performances have been obtained also with the MuTRiG ASIC.
Figure~\ref{fig:mutrig:deltaT} shows an example time difference distribution for clusters
with a minimum size of 2, obtained with a sensor biased at \SI{58.2}{\volt}.
The resolution of the time difference from the two ribbon sides
$\sigma(t_{\text{cl, left}} - t_{\text{cl, right}})$ correspond to twice the intrinsic fibre prototype resolution $\sigma_{\text{cl, ribbon}}$.
It agrees very well with the time resolution extracted by the DRS4-based DAQ of the same ribbon.
For example, the FWHM/2.35 obtained in the MuTRiG measurement of \SI{366+-13}{\pico\second} lies very well inside the uncertainty of \SI{361+-23}{\pico\second} obtained in the full waveform test beam analysis.

%\begin{figure}[tb!]
%        \centering
%        %\begin{subfigure}{0.5\textwidth}
%        \centering
%        \includegraphics[width=0.48\textwidth]           {Fibres/figures/sim_meanCor_deltaT_m}
        %\caption{without propagation time correction}
        %\label{fig:sim:timeRes:mean:without}
    %\end{subfigure}%
    %~  
        %\begin{subfigure}{0.5\textwidth}
    %    \centering
    %    \includegraphics[width=\textwidth]             {sim_meanCor_deltaT_m}
    %    \caption{with propagation time correction}
    %    \label{fig:sim:timeRes:mean:with}
    %\end{subfigure}%
%        \caption[Simulated cluster mean time resolution.]{Simulated cluster mean time resolution
%with respect to the truth interaction time.
%        Note the asymmetrical shape of the distribution due to the decay time of the scintillation process.}
%        \label{fig:sim:timeRes:mean}
%\end{figure}

%The properties extracted by the characterization of the prototypes are used to tune the sub-detector
%response in the main simulation framework.
%The above presented time resolution in the test beam and lab setup corresponds to an expected overall
%sub-detector resolution of FWHM/2.35=\SI{233}{\pico\second}, as shown in %figure~\ref{fig:sim:timeRes:mean}.  

%The cluster time resolution, extracted as described in  \autoref{sec:mutrig:clusterTimeResolution} and \autoref{sec:clusterTimeResolution}, at different \ac{SiPM} array bias voltages are summarized in \autoref{tab:mutrig:timeRes}.
%The extracted time resolutions for all clusters ($cl\geq1$) and for clusters consisting of at least two ($cl\geq2$) column hits per side are quoted.

%\balance

%%%%%%%%%%
\section{Fibre Mechanics}
\label{sec:FibreMechanicsAndCooling}
Three considerations determine the SciFi detector location.
Firstly, no material should be placed outside of the fourth pixel layer
where the main momentum measurement is performed.
Secondly, it has to be in close vicinity to a pixel layer.
The track finding algorithm considers scattering alone in this layers.
And thirdly, the larger the radius is, the smaller the sub-detectors occupancy and resulting pile-up.

%%%%%
\begin{figure}[b!]
   \centering
   \includegraphics[width=0.48\textwidth]{Fibres/figures/SciFiCAD}
   \caption[SciFi detector design.]{Overall view of the fibre detetor.}
   \label{fig:scifi:full}
\end{figure}

Figure~\ref{fig:scifi:full} shows the overall design of the SciFi detector.
The detector is composed of 12 SciFi ribbons, 300~mm long and 32.5~mm wide.
The SciFi ribbons are staggered longitudinally (around 10~mm) in order to reduce dead spaces
between the ribbons.
The ribbons are spring loaded on one side (6 ribbons on one side and the other 6 on the other side)
to compensate for the thermal expansion and to provide sufficient tension to avoid sagging.
For forces larger than \SI{0.3}{\newton} a sag below a mm is observed 
what is believed to be sufficient for this detector.

%%%%%
\begin{figure}[tb!]
   \centering
   \includegraphics[width=0.4\textwidth]{Fibres/figures/SciFiCADside}
   \caption[SciFi detector design side view.]
{Detailed side view of the fibre detector, showing the  fibre ribbon coupled to the SiPM array
and the SciFi front end board connected to the array via a flex-print.
The front end board is fixed on a cooling plate.}
   \label{fig:scifi:side}
\end{figure}

%%%%%
\begin{figure}[tb!]
   \centering
   \includegraphics[width=0.4\textwidth]{Fibres/figures/SciFiCADtop}
   \caption[SciFi detector design top view.]
{Detailed top view of the fibre detector at one fiber end.}
   \label{fig:scifi:top}
\end{figure}

The SciFi ribbons are coupled to the SiPM arrays by simple mechanical pressure
(no grease or other optical interface) and the arrays are connected to front end boards via a flex-print.
The front end boards are fixed to cooling plates to dissipate the heat produced by the MuTRiG ASICS
(around 1~W of heat power is generated by one ASIC,  therefore 50~W have to be dissipated on each
side of the SciFi detector)
Figures~\ref{fig:scifi:side} and~\ref{fig:scifi:side} show a detailed side and top view of this structure.
To facilitate the installation two SciFi ribbons are attached to the same fibre support structure
to form one module.
The two ribbons are offset along the beam direction by 10~mm to accommodate the photo-sensors.

%\begin{figure*}[tb!]
%        \centering
%        \input{Fibres/figures/explosion}
%        \caption[Fibre ribbon coupling to SiPM arrays.]{Schematic overview of the fibre ribbon coupling
%to SiPMs column array readout sensors present on both ribbon sides.
%        The sensors are bonded onto flexprint cables.
%        The assembly is fixed with three screws and a stiffener.}
%        \label{fig:scifi:structure}
%\end{figure*}

%\begin{figure*}[tb!]
%        \centering
%        \input{Fibres/figures/module}
%        \caption[One fibre module inside the experiment's support structure.]
%{A fibre module, consisting of two ribbons, located in the central part of the experiment.
%        The full fibre detector comprises \SI{6}{modules}, respectively \SI{12}{ribbons}.
%        Furthermore the fibre support structure including the support rings and fibre electronic boards
%are shown inside the experiment's support structure.}
%        \label{fig:scifi:module}
%\end{figure*}

%The fibre detector is divided into \SI{6}{modules} which each consists of two ribbons.
%The \SI{32+-0.1}{\milli\meter} wide and \SI{288+-0.5}{\milli\meter} long fibre ribbons
%with one 128-channel SiPM column array attached to each side build the base unit of the detector.
%One side of such a module is shown in \autoref{fig:scifi:structure}.
%The sensors, shipped on a PWB which is soldered to a flex print cable,
%are fixed by three screws directly to the holding structure which is glued onto the fibre ribbons at both ends.

%Two ribbons are attached to the same fibre support structure; They form one module.
%The two ribbons are offset along the beam direction by \SI{4}{\milli\meter} to accommodate the sensors.
%On each side, the flex print cables from both sensors end at the bottom of the support structure,
%where they are connected to the scintillating fibre board ({\sc scifi board}).
%This modular design allows to test and characterize the full fibre ribbon-sensor assembly
%outside of the detector.

%\begin{figure}[tb!]
%        \centering
%        \input{Fibres/figures/supportRing}
%        \caption[Fibre detector support ring.]
%{Fibre detector support ring with one electronic board ({\sc SciFi Board}) and cooling plate per module.
%        The support ring backsides of both detector sides are separated by \SI{330}{\milli\meter}.}
%        \label{fig:fibres:supportRing}
%\end{figure}
%The modules are mounted radially onto fibre support rings which are fixed rigidly to the beam pipe.
%This is possible because the thermal expansion of the modules is handled by the individual spring loading
%of each ribbon.
%The support rings comprise one scintillating fibre readout board ({\sc SciFi board})
%per module per side, which host the readout ASICs.
%The boards are attached to liquid-cooled plates.
%Figure~\ref{fig:fibres:supportRing} shows the support ring of one side.

%%%%%
\subsection{The Electrical Connection}
The electrical connection between the sensors and the readout electronics is realized through the
flex-print cables, which end at the bottom of the module support structure.
First the 128 channel SiPM arrays are soldered to a support PCB with embedded flex-prints,
then the circuit continues to a second PCB hosting the MuTRiG ASICs.
The flexibility is required to compensate for the distance difference caused by the spring loading.
%During radial module insertion onto the support rings a two-dimensional connector, called interposer,
%realizes the electrical connection between the flex print cables and {\sc SciFi board}.
Furthermore, the SciFi front end boards are thermally connected to the cooling plates.
%Figure~\ref{fig:mehcnaic:module} shows the radial insertion of a fibre module.
%Screws fasten the electrical contacts and the module itself through holes
%in the module support exclusively from the radial direction.
This construction is repeated on both ribbons ends and for all ribbons.

%%%%%
\subsection{Cooling Concept}
The cooling of the SciFi detector splits into two parts.
Firstly, the system has to discharge around 50~W per side dissipated by the readout ASICs and LDOs.
This is realised directly through the liquid-cooled plates below the SciFi front end boards,
which are connected to the cooling system of the Mu3e apparatus.
Secondly, the temperature of the SiPM sensors is required to be stabilized,
and possibly cooled down to the lowest possible temperature
($4^\circ$~C is the temperature of the liquid coolant).
This will be implemented by adding an additional thermal contact between
the SiPM PCB and the cooling plates. 
%Depending on the overall experiment temperature,
%cooling is needed to operate them around or below room temperature.

%\subsubsection{Liquid-Cooled Plates}
%The major share of heat dissipation of the fibre detector is caused by the eight \mutrig s
%and subordinately by the \acp{LDO} regulators in the {\sc scifi board}.
%They are located at the bottom side of the board in direct contact with the copper cooling plates
%(see \autoref{fig:mehcnaic:supportRing}).
%
%Per side, six supply tubes with an inner diameter of $\sim$\SI{3}{\milli\meter} provide the liquid coolant.
%The liquid is passed through two modules in series.
%Simulations have shown that a water flow below \SI{1}{\meter\per\second} corresponding to
%\SI{0.3}{\liter\per\minute} at an inlet temperature of \SI{10}{\celsius} is sufficient to keep the
%\ac{ASIC} temperature low.
%
%Under the very conservative assumption of a power dissipation of \SI{24}{\watt} per package and a surrounding helium temperature of \SI{40}{\celsius}, the temperature of the package is below \SI{35}{\celsius}.
%The copper plate's temperature stabilizes at $\sim$\SI{30}{\celsius}, and the water temperature
%at the outlet of the first cooled module is \SI{15}{\celsius}.
%\autoref{fig:integration:cooling} shows the equilibrium temperature of the system.
%
%An Alternative cooling scheme where the \acp{ASIC} are located on the top side of the {\sc scifi board}
%and are cooled from the bottom are considered.

%\subsubsection{Temperature Stabilization of the Sensors}
%\label{sec:integration:tempSensor}
%Two sensors at the backside of the flex print cable at the position where the sensors are soldered
%to monitor the temperature of the SiPMs.
%Depending on the experiment's operating temperatures and gradients over the central barrel,
%additional cooling is required.
%In this case, it is foreseen to build the fibre module support structure out of a good heat conducting material.
%The stiffener at the backside of the sensor assembly is connected flexible and well heat conducting.	