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\title{
        {\Huge\bf Beam Tests of Final Modules and Electronics of the LHCb Outer Tracker in 2005}
} \maketitle
%
\begin{abstract}
This note presents the results of the beam tests of the mass production 
modules of the LHCb Outer Tracker equipped with final version prototypes of 
the frontend electronics. The tests were performed in March 2005 at DESY,
using a 6~GeV electron beam. 
\end{abstract}
%
\vfill
%
\begin{flushleft}
    \fbox{\begin{minipage}[c]{15cm}
    \vspace{0.25cm}
    {\huge\bf Note}
    \normalsize
    \begin{displaymath}
        \begin{array}{ll}
%            \mbox{Issue} & \mbox{20} \\
%            \mbox{Revision} & \mbox{n} \\ [4ex]
            \mbox{Reference} & \mbox{LHCb 2005-076} \\
%            \mbox{Created} & \mbox{April 7, 2005} \\
%            \mbox{Last Modified} & \mbox{\today} \\[3ex]
            \mbox{Date} & \mbox{\today} \\[3ex]

            \mbox{\bf Prepared by} & \mbox{G.W.~van~Apeldoorn, Th.~Bauer, 
	      E.~Bos, Yu.~Guz\footnote[1]{~On leave from the Institute for 
			High Energy Physics, Protvino, Russia}, T.~Ketel,} \\
            & \mbox{J.~Nardulli, A.~Pellegrino, T.~Sluijk, 
	      N.~Tuning, P.Vankov,} \\
            & \mbox{A.~Zwart} \\
            & \mbox{\it NIKHEF, Amsterdam, The Netherlands} \\[3ex]
	    & \mbox{S.~Bachmann, T.~Haas, J.~Knopf, U.~Uwer, D.~Wiedner}\\ 
            & \mbox{\it Physikalisches Institut, Heidelberg, Germany} \\[3ex]
	    & \mbox{M.~Nedos} \\ 
            & \mbox{\it University of Dortmund, Germany} \\[3ex]
        \end{array}
    \end{displaymath}
    \end{minipage}}
\end{flushleft}

\newpage
\tableofcontents
%\listoftables
\clearpage
\listoffigures
%
\newpage
%=========================
\section{Introduction}
%=========================
The purpose of these studies was to test the final mass-production modules of
the LHCb Outer Tracker (OT)~\cite{ref.OT1,ref.OTbeamtest2000} -- in combination with the final version of the
frontend electronics~\cite{ref.frontend} -- in a beam and to determine the main
performance parameters of the detector, such as efficiency, coordinate resolution and
noise (random and correlated).  The dependence of these quantities on the gas gain and
the preamplifier threshold is investigated. In addition, they may depend on the beam position along
the wire at which the particle crosses the chamber.  In order to study these
dependencies, the data were taken at various combinations of parameter settings
in several beam positions.  In total, more than 10$^7$ events were recorded
during the beam test.

The tests were done in March 2005 in the experimental area~22 of DESY at the
DESYII accelerator, with an electron beam at energies between 1 and 6~GeV.  Most of
the data were taken at 6~GeV to minimize multiple scattering, while in order to
study multiple scattering effects some runs were taken at lower beam energies.
%
\begin{figure}[!b]
  \begin{minipage}[c]{0.65\textwidth}%
    \includegraphics[%
      bb=75bp 275bp 250bp 600bp,clip,height=8.5cm,keepaspectratio]{%
      plots/ot_station.ps}\hfill{}\end{minipage}%
  \hfill{}\begin{minipage}[c]{0.35\textwidth}%
    \hspace{-4.5cm}
    \vspace{-0.0cm}
    \hfill{}\includegraphics[%
      bb=50bp 275bp 550bp 391bp,clip,width=7.5cm,keepaspectratio]{%
      plots/ot_module.ps}\end{minipage}%
%    \PText(-325, 80)(0)[c]{U side}
%    \PText(-325,-40)(0)[c]{L side}
    \PText(-125,40)(0)[c]{panel A}
    \PText(-125,-25)(0)[c]{panel B}
    \PText(-325,-100)(0)[c]{Front view}
    \PText(-125,-100)(0)[c]{Top view}
  \caption[Outer Tracker geometry]{\label{fig:otgeom}  \em
    a) The front view of one half-station of the outer tracker is shown. 
    The short modules that are used in the test are located on the left, above and below
    the future beampipe.
    b) The top view of one module is shown.
    The individual straw tubes are arranged in two mono-layers.}
\end{figure}

The OT uses straw tube technology and 
consists of short modules above and below, and of long modules next to the beampipe,
respectively, as is shown in Fig.~\ref{fig:otgeom}a.
For the test descibed in this document, four ``short'' OT modules were used
with a length of 2.4~m. One of these short modules consists of two mono-layers (A and B), 
as is shown in Fig.~\ref{fig:otgeom}b, and contains $2\times 64$ readout channels.
The length of one straw is 2320~mm, the 
inner diameter of a straw is 4.9~mm, and the straw-to-straw pitch amounts to 5.25~mm.

%=========================
\section{Test Setup}
%=========================
The schematic setup layout is shown in Fig.~\ref{fig:setup}.  The test setup
comprised four short S1U-type OT modules, consisting of two layers with
straws.  The complete setup contained a total of eight monolayers, or planes, of
straws.
Throughout this note the modules and planes will be referred
to according to their position along the beam starting from 1, i.e. modules 1--4
and planes 1--8.  The chambers were installed in vertical position on a
moveable platform.  The gas mixture used in these tests was the LHCb baseline gas of
70\% Ar and 30\% CO$_2$. Each chamber was equipped with a final prototype frontend box, 
as is described in Section~\ref{sec:electronics}.

\begin{table}[!b]
\begin{center}
\footnotesize
\begin{tabular}{|l||r|r|r||r|r|r|r|r|r|r|r|}
  \hline 
          & \multicolumn{3}{c||}{Si} & \multicolumn{8}{c|}{OT} \\
          & \multicolumn{3}{c||}{  } & \multicolumn{2}{c|}{M1} 
                                     & \multicolumn{2}{c|}{M2}   
                                     & \multicolumn{2}{c|}{M3}   
                                     & \multicolumn{2}{c|}{M4} \\
          &  P1 & P2 & P3            & pl 1 & pl 2
                                     & pl 3 & pl 4
                                     & pl 5 & pl 6
                                     & pl 7 & pl 8  \\
  \hline							       		  	  	
  \hline							       		  	  	
  $Z$(mm) &0 &267& 387  & 897& 902.5& 949.5& 955 & 1090 & 1095.5 &1151 & 1156.5 \\  
  \hline							       		  	  	
\end{tabular}
\normalsize
\end{center}
\end{table}
%
\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,125)(0,0)
      \put(20,-20){\includegraphics[bb=0 0 565 270,scale=0.6]{plots/setup_testbeam.eps}}
    \end{picture}
  \end{center}
  \caption[Test setup]{\em A schematic picture of the test setup. 
    Note that module 2 is hang upside-down in order to compare the results
    for particles passing the detector close and far from the frontend electronics.
  }
  \label{fig:setup}
\end{figure}
%

%Each chamber was equipped with a standard frontend box.  The output signals from
%each frontend box were transmitted through an optical line to the data
%acquisition system based on the Texas Instruments TLK2501 receiver and
%de-serializer chip, and an ALTERA Stratix FPGA.

The measurement of the detector parameters, such as efficiency and resolution,
require knowledge on the coordinate at which the beam particle traverses the
detector plane.  In order to have a possibility to independently measure track
parameters, a silicon strip telescope was used~\cite{ref.Moritz}.  It consisted
of three pairs (X and Y) of 32x32 mm$^2$, 0.3 mm thick, single sided silicon
strip detectors, with 25~$\mu$m strip pitch and 50~$\mu$m readout pitch.  The
detectors were mounted inside light tight boxes with 30~$\mu$m thick Al windows.

On the other hand, the total number of OT modules (4 modules, or 8 monolayers)
were sufficient to reconstruct tracks using OT data only.  Therefore part of
studies were done without taking Si-telescope data.
%
The trigger signal, which served also as time reference, was produced by
coincidence of two scintillator counters S4 and S5 installed downstream of the
OT modules.  In runs with the Si-telescope included, additional small
scintillation counters S1, S2 and S3\footnote{% 
The counter S3 was not used for the most part of data, as it was found to give significant 
contribution into multiple scattering of beam particles.}  
with a width of 9~mm and a thickness of 2~mm, mounted on the telescope support,
were used in coincidence.  The beam width in runs with Si-telescope was
therefore significantly less than in runs with OT only.  The OT hit map is shown
in Fig.~\ref{fig:otbeamprof}, with~({\it a}) and without~({\it b}) the
Si-telescope included.
%
\begin{figure}[!t]
  \begin{center}
    \begin{picture}(420,120)(0,0)
      \put(30,-20){\includegraphics[bb=43 54 510 306,width=11cm,height=5.5cm]{%
	  plots/otbeamprof.eps}}
    \end{picture}
  \end{center}
  \caption[Beam profile]{\em
    The OT hit maps for plane 1 (the upstream plane of the first module)
    are shown with ({\it a}) and without ({\it b}) the Si-telescope. 
    Note the difference in the number of illuminated straws.
  }
  \label{fig:otbeamprof}
\end{figure}
%
In the former case the beam illuminates 2--3 straws per OT plane. 
When only OT modules were used, several (5--7) straws were fully illuminated. 
The coordinates and slopes of the tracks measured with the Si-telescope 
are shown in Fig.~\ref{fig:slopes}.
%
\begin{figure}[!t]
  \begin{center}
    \begin{picture}(420,130)(0,0)
    \put(20,-10){\includegraphics[bb=0 0 567 250,scale=0.6]{%
	plots/clust_pos_and_slope_3.eps}}
    \PText(50, 120)(0)[c]{(a)}
    \PText(240, 120)(0)[c]{(b)}
    \end{picture}
  \end{center}
  \caption[Beam as measured with Si]{\em Beam coordinates ({\it a}) 
    and slopes ({\it b}) measured by the Si-telescope.}
  \label{fig:slopes}
\end{figure}
%
\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,90)(0,0)
    \put(-10,-20){\includegraphics[bb=0 30 815 290,scale=0.49]{%
	plots/otdrifttime3.eps}}
    \end{picture}
  \end{center}
  \caption[OT time distribution]{\em %
    Precision of the time reference provided by S4 and S5 ({\it a}); 
    the arrival time distribution of OT hits ({\it b}) 
    and the drift time distribution ({\it c}).} 
  \label{fig:otdrifttime}
\end{figure}

Since the beam was asynchronous with the OTIS chip, unlike in the final experiment at the LHC,
in order to measure the OT drift times, the time reference as provided by the
scintillators was used.  The arrival time of the scintillator signals was
measured by the OTIS TDCs and then subtracted from the arrival times of the OT
signals in order to obtain the drift time:  
\begin{equation}
t_{\mathrm{drift}} = t_{\mathrm{raw~TDC}} - t_{\mathrm{ref}}.
\label{eq:td}
\end{equation}
More specifically, the average time of S4 and S5 was used as the time
reference: $t_{\mathrm{ref}}=(t_{S4}+t_{S5})/2$.  Its precision, evaluated from the
distribution of $t_{diff}=(t_{S5}-t_{S4})/2$, was better than 0.4~ns, see
Fig.~\ref{fig:otdrifttime}{\it a}, which is small enough not to affect the OT
performance.  The raw time distribution of the OT signals is shown in
Fig.~\ref{fig:otdrifttime}{\it b}, showing that it fits well into the 75 ns time
window of the OTIS.  The OT drift time distribution is shown in
Fig.~\ref{fig:otdrifttime}{\it c}, showing that the full drift time distribution
in these conditions (HV=1600~V) is contained within approximately 42~ns.

In this document the performance of the outer tracker detector and its final frontend
electronics will be determined as a function of the high voltage applied,
and as a function of the amplifier threshold setting.
To a lesser extend, also the dependence on the position of the hit along the straw 
is estimated.

\clearpage

%====================================
\section{The Readout Electronics}
%====================================
\label{sec:electronics}
Figure \ref{Elektronikuebersicht} shows a schematic overview of the
final prototype readout electronics used in the beam test. 
The on-detector electronics consisted of the amplifiers, TDCs and
data serializers housed in one FE-box for each detector (half-)
module, and is shown in Fig.~\ref{FE-Box-Pic}.

\begin{figure}[!b]
  \begin{center}
    \epsfig{file=plots/Electronics-overview.eps, scale=0.5, angle=0}
    \caption[Beam Test readout scheme]
	    {\em The beam test readout scheme. Note that the scintillator 
	      time reference is specific for this beam test. In the final experiment the
	      L1 buffer will be located in the TELL1 board, and also the DAQ PC will be different. }
	    \label{Elektronikuebersicht}
  \end{center}
 \end{figure}

\begin{figure}[!t]
  \begin{center}
    \epsfig{file=plots/FE-box-000-small-2.eps, scale=0.5, angle=0}
    \caption[Front end box]
	    {\em A photograph of the final prototype front end box.}
	    \label{FE-Box-Pic}
  \end{center}
\end{figure}

Eight channel amplifiers ASDBLR version 2002 \cite{ASDBLR,ASDBLR-OTIS}
amplified, shaped and discriminated the charge pulse.  If the pulse lay above a
threshold, the amplifier output a digital differential signal used for the time
measurement by the Outer Tracker time Information System (OTIS) TDC
\cite{OTISmanual,DoktorarbeitUweStange,OTISBoard-specs}.  Four
ASDBLR amplifiers situated on two PCBs were connected to one OTIS TDC.

The 32 channel OTIS TDC measured the time of the discriminated signal from the
amplifier with an accuracy of $<$1~ns.  A delay locked loop (DLL) consisting of
64 inverters subdivided the 40 MHz clock period of 25~ns in 64 bins of
390~ps. When an amplifier signal arrived the number of the active bin was
converted to a 6-bit drift time and stored to a pipeline memory.  A 32 bit
header together with 32 drift times of 8 bit each was output for each accepted
event.  In the test beam OTIS version 1.2 was used, which was proven to be fully
functional. One FE-box was modified with three external timing inputs for the
scintillators S4 and S5, in order to obtain a time reference with the same TDC.

Data from four OTIS TDCs, sitting on a separate PCB each, were serialized and
8/10 Bit encoded by a radiation hard Gigabit Optical Link (GOL) chip
\cite{GOLmanual}.  The GOL chip output the serial data at 1.6~Gbit/s to a VCSEL
laser diode. All 128 channels of one half module were read out over one optical
fiber. The GOL chip shares the GOL-Auxiliary-Board \cite{GOLauxboard-IF13-2},
with the QPLL \cite{QPLLmanual} clock filter and three low voltage regulators
for +3~V, -3~V and +2.5~V.

The optical data was transformed into parallel electrical signals on the optical
receiver card (O-RxCard) \cite{O-RxCard-specs-IF14-1}. The de-serializer on the
O-RxCard synchronized the incoming data stream and output the data to a
commercial PCI card \cite{PCI-Stratix-Kit,JanKnopfDiplom}, which employs
the same FPGA as the will be used in LHCb, but has a PCI interface. The data was
stored on a PC at an event rate of up to 1~kHz allowing high statistic runs.

For the operation of the described readout electronics a fast control system
(TFC) and a slow control system (ECS) was necessary in addition.  The Timing and
Fast Control (TFC) system \cite{HowCan?} distributed the 40.0786~MHz LHC clock,
L0 decisions, the bunch counter, the event counter\footnote{The event counter
counts the L0 accepted events.}, plus the reset signals for bunch counter, event
counter and L0 electronics optically.  The L0 decision was derived from a
scintillator coincidence.  Different runs were taken either with a coincidence of all five
scintillators or with the S4, S5 scintillators only.  For the beam test a local
TTC system with a TTCvi \cite{TTCvisoftware}, TTCvx and a RIO CPU was employed.
A TTCrq \cite{TTCrqmanual} module mounted on a two output distribution card
(IF16-0) received the fast control signals.  The TTCrq decoded the serial data
and output clock, L0 accept, bunch count reset, event count reset and L0 reset
on separate lines.  From the IF16-0 service box the TFC signals were
differentially lead to the detector modules via 6~m long SCSI2 cables.
%
Slow control settings as amplifier thresholds, OTIS TDC pipeline
latency etc. were made via I$^2$C, running single ended from a PC to
the front end boxes.

Throughout the note, the ASDBLR amplifier threshold is expressed in mV as set in practice.
The corresponding charge can be obtained to first approximation with:
\begin{equation}
Q(\mathrm{fC}) = e^{-1.25 + 0.0033 \mathrm{Thr(mV)}},
\end{equation}
and is shown graphically in Fig.~\ref{fig:thr_fC}:
%
\begin{figure}[!h]
  \begin{center}
    \begin{picture}(420,160)(0,0)
    \put(100,-15){\includegraphics[bb=15 270 265 520,scale=0.7]{%
	plots/threshold_fC.eps}}
    \end{picture}
  \end{center}
  \caption[Charge(fC) vs threshold(mV)]{\em %
  The approximate correspondance between amplifier threshold and charge is shown.} 
  \label{fig:thr_fC}
\end{figure}


\clearpage

%==================
\section{Analysis}
%==================
The analysis to estimate the performance  of the outer tracker detector 
and its readout electronics, consist of the following basic steps:
\begin{itemize}
\item[1)] Attain the predicted distance of closest approach of the particle to the sense wire.
\item[2)] Establish the relation between the measured drift time and the predicted
  distance to the wire, i.e. the rt-relation.
\item[3)] Convert each measured drift time into position coordinate.
\end{itemize}
%
With the measured position coordinate in hand, the resolution of this measurement
can be obtained by comparing it to the predicted position.
The hit finding efficiency is attained by verifying whether the OT produced a hit 
at the predicted position, within a given window.
Three independent analyses have been carried out to estimate the performance of the
OT and its readout electronics, and have all used a different method to obtain
the rt-relation (also described in~\cite{ref.Rutger}).
The main differences are listed below, and are given in detail later in this section.
%
\begin{itemize}
\item Track prediction given by the silicon telescope, see Section~\ref{sec:si}.
  \begin{itemize}
  \item rt-relation is obtained after correcting for the Si-track uncertainty.
  \item Efficiency  is obtained from the plateau at the center of the cell.
  \end{itemize}
\item Track prediction given by the OT, see Section~\ref{sec:otanal1}.
  \begin{itemize}
  \item The 1$^{st}$ rt-relation is obtained by integrating the TDC spectrum. 
    Subsequently the rt-relation is obtained from a 3$^{rd}$ order polynomial fit
    to the mean $r$ in slices of the drift time.
  \item Efficiency is obtained from the plateau at the center of the cell.    
  \end{itemize}
\item Track prediction given by the OT, see Section~\ref{sec:otanal2}.
  \begin{itemize}
  \item rt-relation is obtained iteratively from the track fit.
  \item Efficiency is obtained from the average efficiency in a layer.
    Subsequently a correction for the dead space between the straws is applied.
  \end{itemize}
\end{itemize}
The procedure of the analyses is explained in this section, whereas the results will be 
given in Section~\ref{sec:results2005}.

%--------------------------------
\subsection{Analysis I: Using Si-telescope for track reconstruction}
%--------------------------------
\label{sec:si}
In studies of the OT modules using the Si-telescope precisely one track per
event was required, with a properly reconstructed $xz$-projection in the
telescope.  For this, events were selected based on the number of clusters
in the Si-detector planes.  Exactly one cluster was required in each of the 
three Si-planes that measure the horizontal coordinate, and 0 or 1 in the planes
that measure the vertical coordinate. The total number of clusters had to be
equal to 5 or 6.  In total 56\% of the events passed this cut.  An additional
cut on the track slopes, $-3<tx<3$~mrad and $-3<ty<3$~mrad, was applied, see
Fig.~\ref{fig:slopes}{\it b}.  This cut reduced the number of events by only 3\%.

\begin{figure}[!h]
  \begin{center}
    \begin{picture}(420,120)(0,0)
    \put(10,-10){\includegraphics[bb=1 550 540 730,scale=0.7]{%
	plots/Si_resolutions_x.eps}}
    \end{picture}
  \end{center}
 \caption[Si-track residual]{%
   \em Distributions of the Si-track residuals in the three Si $x$ planes.}
 \label{fig:siclusterres}
\end{figure}

\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,70)(0,0)
    \put(30,-15){\includegraphics[bb=40 530 555 666,scale=0.65]{%
	plots/fig6gev_mod1.eps}}
    \end{picture}
  \end{center}
  \caption[Drift time versus track position ]{\em %
    The drift time $vs$ predicted distance between wire and track
    reconstructed in the Si-telescope.}
\label{fig:otbeamprof2}
\end{figure}

The intrinsic resolution of the detector planes is better than 3~$\mu$m~\cite{ref.Moritz}.  
The width of the distributions of the track residuals is about 5--20
$\mu$m, see Fig.\ref{fig:siclusterres}, and is almost fully determined by the
multiple scattering in the detector planes. Note that these residuals are biased,
since the clusters are used to construct the track.  As expected, the middle
plane thus has the biggest residual. The residual of the first and third
plane differ, because the second silicon plane is located closer to the third
plane than to the first plane.


Figure~\ref{fig:otbeamprof2} shows the correlation between the drift time
measured in module 1 (planes 1 and 2) and the distance between the wire and the
track reconstructed in the Si-telescope.  The distinct V-shape patterns expected
for drift tubes are clearly seen.  The reconstructed Si-track parameters were
used to calculate the predicted position $x_{\mathrm{OT}}$ for a hit in a plane 
at $z_{\mathrm{OT}}$:
\begin{equation}
x_{\mathrm{OT}} = x_{\mathrm{Si,~P3}} + 
                  tx_{\mathrm{Si}}  (z_{\mathrm{OT}} - z_{\mathrm{Si,~P3}}),
\label{eq:xpred}
\end{equation}
where $tx_{\mathrm{Si}}$ is the the slope of the Si-track in the $xz$-plane.
The detector resolution was then extracted from the comparison of the predicted
track position with the position as determined from the measured hit, 
see Appendix~\ref{app:si_rt}.



%--------------------------------------
\subsection{Analysis II: OT standalone analysis}
%--------------------------------------
\label{sec:otanal1}
Two independent analyses were performed that did not use any information from the
silicon telescope, but performed standalone tracking with the OT.  The
four modules provide potentially eight measurements for a given track, enough
for accurate track reconstruction. 

In order to estimate the efficiency and resolution, 
the tracks were reconstructed using the two outer modules
only, after which the efficiency and resolution were determined from
modules 2 and 3.
The effects from noise were minimized by using only those five straws per layer,
that were fully illuminated by the beam.  Events were selected with
good quality tracks by requiring precisely one hit in each layer of module 1 and
4. No cuts are applied on modules 2 and 3.

The raw TDC spectra of each layer differs due to the variation in the delay in
the various layers.  Figure~\ref{fig:tanja_t0}a shows the drift time spectra for
all layers, as calculated according to Eq.~(\ref{eq:td}).
For each layer a straight line was fitted to the rising edge of the spectrum, after
which the TDC time was corrected.  This corrected TDC spectrum summed for all layers is
shown in Fig.~\ref{fig:tanja_t0}b.
%
\begin{figure}[!t]
  \begin{center}
    \begin{picture}(420,80)(0,0)
    \put(0,-10){\includegraphics[bb=1 1 520 380,scale=0.35,clip=]{%
	Tanja/beforeT0_ns.eps}}
    \put(200,-10){\includegraphics[bb=1 1 520 380,scale=0.35,clip=]{%
	Tanja/afterT0_ns.eps}}
    \PText( 40, 100)(0)[c]{(a)}
    \PText(240, 100)(0)[c]{(b)}
    \PText(145, -10)(0)[c]{t}
    \PText(345, -10)(0)[c]{t}
    \PText(155, -15)(0)[c]{raw}
    \PText(355, -15)(0)[c]{drift}
    \end{picture}
  \end{center}
  \caption[$t_0$ correction]{\em % 
    The TDC spectrum is shown for all layers, before (a) and after $t_0$-correction.
  The TDC spectrum corrected for the $t_0$-correction corresponds to the drift time.} 
  \label{fig:tanja_t0}
\end{figure}

An initial rt-relation was obtained by integrating the driftime spectrum~\cite{ref.Atlas-Muon}.  
Assuming a uniform illumination of the straw tube the relation between the impact point $r$ of the particle
and the corresponding drifttime $t$ can be expressed as:
$$
r(t) \, = \, r_{max} \sum_{i=1}^{n} T(t_i),
$$
where $T(t)$ denotes the drift time spectrum, normalized to unity, 
and with $r_{max}$ the straw radius of 2.45~mm.
For example, the maximal drift time that contains 25\% of all hits,
corresponds to $r=2.45/4$, the maximal drift time that contains 50\% of all hits,
corresponds to $r=2.45/2$, and so further.

The measured radius $r_{meas}$ was then calculated for each hit from this initial
rt-relation.  Subsequently, for each event a straight-line fit of the track was
performed, using these hits.  The left-right ambiguities were solved by pairing
the hits from two neighbouring layers.  For the remaining ambiguities a straight
line was fitted for all combinations by means of the least square method. These
last ambiguities were solved by chosing the solution with the minimal $\chi^2$.

From the resulting rt-distribution as shown in Fig.~\ref{fig:tanja_rt}a, a new
rt-relation was obtained by slicing the distribution in bins of the drift time.
The slices were then fitted with a gauss and their mean values were fitted by a
3$^{rd}$ order polynomial.  The resulting rt-relation is shown in
Fig.~\ref{fig:tanja_rt}b, together with the original rt-relation from the
integration of the TDC spectrum.

\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,120)(0,0)
    \put(-20,-15){\includegraphics[bb=1 1 525 385,scale=0.4,clip=]{%
	Tanja/time_vs_radius2.eps}}
    \put(190,-15){\includegraphics[bb=1 1 525 385,scale=0.4,clip=]{%
	Tanja/compare_rt.eps}}
    \PText( 20, 100)(0)[c]{(a)}
    \PText(240, 100)(0)[c]{(b)}
    \end{picture}
  \end{center}
  \caption[Iterated rt-relation]{\em % 
    (a) The relation between the distance to the wire - as obtained from integrating the TDC spectrum - 
    and the drift time is shown. 
    (b) Both rt-relations are shown: the one obtained from integrating the TDC spectrum, 
    and the one obtained from fitting a $3^{rd}$ order polynomial to time slices of (a).} 
  \label{fig:tanja_rt}
\end{figure}

\clearpage
%--------------------------------------
\subsection{Analysis III: OT standalone analysis}
%--------------------------------------
\label{sec:otanal2}
The setup included a total of eight OT straw planes, which is sufficient to
reliably reconstruct tracks and estimate the detector characteristics.  This OT
standalone analysis was performed in exactly the same way as for testbeam
results used for the OT TDR~\cite{ref.OT1}.

In this third method of determining the rt-relation the so-called auto-calibration 
method was used~\cite{ref.Tolsma,ref.Wouter}.
The method is based on the assumption that the track parameters resulting from a fit
will provide a better estimate of the distance between a track and the wire,
compared to the estimate from the hits themselves.
The tracks are used to predict the distance $r_i$. The difference between the 
reconstructed time $t(r_i)$ and the measured time $t_i$ is then minimized to
obtain $t(r_i)$.
The track fit was performed by minimization of the $\chi ^2$, determined as 
\begin{equation}
\chi^2=\sum_{i=1}^{N_{hits}}\frac{(\tau_i - t(r_i))^2}{\sigma_t^2(r_i)},
\end{equation}
where $N_{hits}$ is the number of hits used in the track fit, 
$\tau_i$ is the measured drift time of hit $i$, 
$r_i$ is the distance between the track and the wire at which the hit $i$ occured, 
$t(r)$ and $\sigma_t(r)$ are the $tr$-relation and time resolution functions 
which were determined iteratively.
The rt-relation is simply the inverse function of $t(r)$.
The resulting $\chi^2$-distribution is shown in Fig.~\ref{fig:chi2}.

A hit was used for the track reconstruction if the drift time was in agreement
with the track prediction within 6$\sigma_t$. Only those tracks were kept which
had at least 4 hits and and had a length along the beam direction of at least 150 mm.  The
event was used for subsequent analysis if it contained precisely one track, which
rejected 5--7\% of the events.

The rt-relation as obtained by either of the three analyses are in good agreement,
as will be shown in Sections~\ref{sec:resolution} and \ref{sec:results2005}.

\begin{figure}[!h]
  \begin{center}
    \begin{picture}(420,80)(0,0)
    \put(20,-20){\includegraphics[bb=30 290 530 534,clip=,width=12cm,height=3.5cm]{%
	plots/chi2_2.eps}}
      \PText(  30,80)(0)[c]{Tracks}
      \PText( 180,-15)(0)[c]{Chi2}
      \PText( 350,-15)(0)[c]{Chi2/n.d.f}
    \end{picture}
  \end{center}
  \caption[$\chi^2$ distribution of OT tracks]{\em %
    Both the $\chi^2$ distribution and the $\chi^2$/n.d.f of the OT tracks is shown.
    The average $\chi^2$/n.d.f is close to unity, indicating that the errors were estimated 
    properly.}   
  \label{fig:chi2}
\end{figure}

\clearpage
%--------------------------------
\subsection{Study of OT position measurement performance}
%--------------------------------
\label{sec:resolution}
\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,300)(0,0)
    \put(20,-20){\includegraphics[bb=0 0 545 555,scale=0.6]{%
	plots/ot-si-comp.eps}}
    \end{picture}
  \end{center}
  \caption[rt-relation and residuals]{\em %
    The correlation between the OT drift time and the track distance to the wire 
    is shown, as determined with OT standalone ({\it a}) and by using the Si-telescope ({\it b}).
    The superimposed curve is the fitted $tr$-relation (see Section~\ref{sec:otanal2}). 
    The corresponding distributions of the track residuals are also shown ({\it c}), ({\it d}). 
  }
  \label{fig:ot-si-comp}
\end{figure}

In both approaches, with the Si-telescope and with OT information standalone,
the coordinate resolution was determined from the distribution of the track
residuals, i.e. from the differences between the measured coordinates in the
detector and those predicted according to reconstructed track parameters.  For
the conversion of measured drift time into distance to the wire the inverse of
the $tr$-relation was used.

In the study where the Si-telescope was used, the $t(r)$ relations was
determined from the correlation between the measured drift time and the
predicted track distance to the wire, see Appendix~\ref{app:si_rt}, whereas in
the OT standalone analysis it was obtained from an iterative calibration
procedure, see Sections~\ref{sec:otanal1} and~\ref{sec:otanal2}.  The final
values for the resolution were obtained from the width of a gaussian fit to the
residual distributions.  Differences in the resolution when only the core of the
residual is fitted, or when a double gaussian was used, are quantifed in
Appendix~\ref{app:si_rt}.  Note also that the coordinate resolution depends
significantly on the distance between track and wire, see
Appendix~\ref{app:dist}.
%The width of the distribution of track residuals in case of uniform illumination represents the
%average resolution of the straw.

Figs.~\ref{fig:ot-si-comp}{\it a,b} show the correlation between the OT drift
time and track distance to the wire for plane 3 in a run in which the
Si-telescope information was available and all the OT modules were operated at
HV=1580 V, $U_{thr}$=700 mV.  The track reconstruction was performed using the
OT data, with plane 3 excluded from the track fit (Fig.~\ref{fig:ot-si-comp}{\it
a}) and using the Si-telescope data (Fig.~\ref{fig:ot-si-comp}{\it b}),
respectively.  In Fig.~\ref{fig:ot-si-comp}{\it c, d} the corresponding
distributions of the track residuals and the superimposed gaussian fits are
shown.

%--------------------------------
\subsubsection{Correction for track bias of residual}
%--------------------------------
\begin{figure}[!b]
 \centerline{\includegraphics[width=0.8\textwidth]{plots/resol_1322.eps} }
 \caption[Resolution corrected for OT track]{\em %
   The resolution studies in the OT standalone analysis. 
   The resolution values for the eight planes were 
   obtained from track residuals for hits included into the track fit 
   (underestimated), excluded from the fit (overestimated) 
   and with correction applied.
   The data of run 1322 are used, with HV=1600 V and $U_{thr}=700$~mV. 
   See Section~\ref{sec:otanal2} for details of the analysis. 
 }
 \label{fig:resids}
\end{figure}
In the OT standalone analysis the resolution values obtained from the track
residuals are biased.  If the hits of the plane under study are excluded from
the track fit, the variance of residuals overestimates the resolution, because
of the finite precision of the track parameter reconstruction in the other OT
planes.  On the other hand, if the hits of the plane are included in the fit,
the variance of residuals for this plane underestimates the true resolution.  In
particular, the resolution of 170~$\mu$m obtained from the fit to the residual
distribution in Fig.~\ref{fig:ot-si-comp}{\it c} is overestimated, because plane
3 was excluded from the track fit.  In order to obtain an unbiased estimate of
resolution, an event-by-event correction was applied based on the covariance
matrix of the track parameters~\cite{ref.Wouter}.  In the remainder of this
note, the values of the resolution determined with the OT standalone analysis
are obtained with this correction.

The size of over- and underestimation for each of the eight planes of the OT
modules is shown in Fig.~\ref{fig:resids}, for HV=1600V. 
Numerical values for the resolution at HV=1550V are given in Table~\ref{tab:tanjares}.
The residuals in the outer planes are larger due to the larger uncertainty in
the track prediction. After correcting the residual for the uncertainty in the
track prediction, approximately equal resolution is obtained for all layers.

\begin{table}[h!]
\begin{center}
\begin{tabular}{|l||c||c|c|}
\hline
layer & intrinsic            &measured            & error track        \\
      &  resolution ($\mu$m) &residual ($\mu$m)   & prediction ($\mu$m)\\
\hline			      			     
\hline			      			     
1     &      168             &  201               &           110     \\
2     &      166             &  197               &           106     \\
3     &      158             &  175               &            75     \\
4     &      159             &  175               &            73     \\
5     &      154             &  170               &            72     \\
6     &      146             &  164               &            74     \\
7     &      157             &  190               &           107     \\
8     &      157             &  193               &           112     \\
\hline
\end{tabular}
\end{center}
\caption{\em %
Resolution for each layer at HV=1550V, $U_{thr}=700$~mV,
including the correction from the error on the track prediction.
The measured resolution is obtained from a gaussian fit to the residual
around $\pm 2 \sigma$ around the mean.
See Section~\ref{sec:otanal1} for details of the analysis.} 
\label{tab:tanjares}
\end{table}

\clearpage
%--------------------------------
\subsubsection{Multiple scattering of Si-tracks}
%--------------------------------
\label{sec:multscat}
\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,210)(0,0)
      \put(60,-25){\includegraphics[bb=0 0 540 560,scale=0.44]{plots/multscatt_1370.eps}}
    \end{picture}
  \end{center}
  \caption[Estimate of multiple scattering with Si-tracks]{\em %
    Resolutions of each OT plane estimated with Si and OT 
    as a function of its {\it z} position ({\it a}); 
    multiple scattering contribution 
    ($\sigma_{MS}=\sqrt{\sigma_{Si}^2-\sigma_{OT}^2}$) ({\it b}). }
  \label{fig:multscatt_1370}
\end{figure}
The resolution obtained from the residual distribution when using the Si-tracks
(Fig.~\ref{fig:ot-si-comp}{\it d}) is overestimated.  The multiple
scattering in the Si-detector planes, and for part of the runs also in the
scintillator S3, smear the distribution of the predicted hit position.

The multiple scattering was studied in two ways. The coordinate resolutions for
each OT detector plane as obtained with the Si-tracks and with the OT standalone
analysis were compared.  Secondly, runs were taken at different beam energies,
so that the multiple scattering contribution could be extracted from the energy
dependence.

\begin{table}
\begin{center}
  \begin{tabular}{|l|l||r|r|r|r|}
    \hline 
    \multicolumn{2}{|l||}{$\sigma_{\mathrm{MS,~6GeV}}$}&\multicolumn{2}{c|}{without S3}&\multicolumn{2}{c|}{with S3}\\
    \multicolumn{2}{|l||}{}                            &  ($\mu$m)   &     (mrad)      &    ($\mu$m)   & (mrad) \\
    \hline							       		  	  	
    \hline	
    Module 2                     & plane 3,4           &   143       &  0.253           &  195          & 0.345  \\ 
    Module 3                     & plane 5,6           &   176       &  0.249           &  246          & 0.348  \\
    \hline							       		  	  	
  \end{tabular}
\end{center}
  \caption[Estimate of multiple scattering contribution to residuals]{\em %
    The contribution to the residual as a result from multiple scattering are
    estimated from the energy dependence of the residual, see Fig.~\ref{fig:escan}.
    Both the contribution to the residual (dependent on the $z$-position of the modules) 
    and the angular spread are given.}
\label{tab:ms}
\end{table}


The result of the comparison of the Si and OT standalone resolutions is shown in
Fig.~\ref{fig:multscatt_1370}{\it a}.  The horizontal axis represents the
$z$-coordinate (along the beam), where the $z$-position of the OT and Si-planes
are indicated.  The difference between the two estimates increases with $z$.
The multiple scattering contribution,
$\sigma_{MS}=\sqrt{\sigma_{Si}^2-\sigma_{OT}^2}$, is shown in
Fig.~\ref{fig:multscatt_1370}{\it b}.  The straight line fit to the points is
superimposed on the plot.  As expected, the main multiple scattering
contribution effectively comes from the last Si-plane: the scattering in the
first two planes is absorbed by the procedure of the track fit in the telescope.
The multiple scattering amounts to about 0.3~mrad.

Alternatively, the amount of multiple scattering was estimated by running at
different beam energies. The resolution was measured with and without the
scintillator S3 between the silicon sensors and the OT.  The results are given
in the table below, and are consistent with the value from
Fig.~\ref{fig:multscatt_1370}{\it b}. These values were used to correct the
residuals in order to obtain the resolution.

After the corrections described above, the Si and OT analyses are compatible,
and the results obtained with both of the techniques are presented in this note.


\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,190)(0,0)
      \put(40,0){\includegraphics[bb=0 0 540 352,clip=,scale=0.55]{%
	  plots/e_scan_note_new_2sigma_sliceing.eps}}
    \end{picture}
  \end{center}
  \caption[Estimate of multiple scattering with different beam energies]{\em %
    Resolutions of the OT as measured at 1600~V and 700~mV using the Si-tracks,
    as a function of the beam energy. The line indicates the fit using  
    $\sigma_{tot}=\sqrt{\sigma_{OT}^2+(\sigma_{MS, 1GeV}/E)^2}$. 
    The point at 1~GeV is not used in the fit.}
  \label{fig:escan}
\end{figure}

\clearpage
%--------------------------------
\subsection{Noise}
%--------------------------------
The fake hits produced by the electronic noise were studied with a random
trigger at several settings of the ASDBLR discriminator threshold.  The measured
quantity is the average noise occupancy $R$ in each frontend module, defined as
the average number of hits per channel per event:
\begin{equation}
  R = \frac{\sum_{\mathrm{evts}} \sum_{\mathrm{ch}} \mathrm{hit}}{%
            N_{\mathrm{evts}}N_{\mathrm{ch}}}.
\end{equation}
The average noise occupancy $R$ is related to  
the noise hit rate per wire $f$ 
as $R=f\cdot 75\mbox{ ns}$. 
The measured dependence of the noise on the amplifier threshold will be shown in 
Fig.~\ref{fig:noisefreq} in Section~\ref{sec:results2005}. 

%--------------------------
\subsection{Cross talk}
%--------------------------
%
\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,90)(0,0)
    \put(10,-15){\includegraphics[bb=0 30 815 290,scale=0.45]{%
	plots/xtplot.eps}}
    \end{picture}
  \end{center}
 \caption[Cross talk]{\em %
  The straw hit map ({\it a}) is shown for those tracks that point to straw 41.
  The time difference distributions for neighbouring ({\it b}) and
  non-neighbouring ({\it c}) channels show that hits in neghbouring channels
  mainly come from crosstalk, while in other channels they are mostly noise.
  This data was taken at HV=1700~V.}
\label{fig:xtalk}
\end{figure}
The cross talk is a consequence of electromagnetic coupling between neighbouring
channels.  Its intensity can be defined as the probability that, if straw~$i$
produces a hit caused by the particle, either of the neighbouring straws also
produces a hit:
\begin{equation}
\mathrm{crosstalk}_{\mathrm{ i}} = \frac{N_{i-1}+N_{i+1}}{N_i}.
\end{equation} 
The strength of crosstalk is an important parameter for the choice of the
working point of the OT detector.

The hit distribution for plane 3 is shown in Fig.~\ref{fig:xtalk}{\it a} for
those events in which the track points to wire~41 {\em and} there is a hit in
this wire that is compatible with the track.  The high voltage at plane 3 in
this run was 1700~V.  The time difference between the crosstalk hits in channels
40 and 42 and the track hit in channel 41 is shown in Fig.~\ref{fig:xtalk}{\it
b}.  The time correlation is evident, which is a clear signature of cross talk.
The distribution of the time difference for other (non-neighbouring) channels is
shown in Fig\ref{fig:xtalk}{\it c}, indicating random noise.

The correction for random noise on the cross talk estimate 
was done by subtracting the average probability
to have a hit in non-neighbouring channels.

%---------------------------
\subsection{Efficiency}
%---------------------------
\label{sec:effmeas}
The efficiency is the probability that a hit is observed if a charged particle
traverses the detector. For a reliable determination of the efficiency, the
predicted position of the hit is obtained from reconstructed tracks.  The track
reconstruction can be performed either with the Si-telescope or with the OT
itself.  In the latter case the layer(s) for which the efficiency is determined
were excluded from the track reconstruction.  The efficiency can be estimated
as the ratio of the number of observed hits to the number of expected hits in
the detector.

The efficiency profile along a OT module is not uniform. The efficiency inside a
straw drops at the edges of the straw, and is fully inefficient in the gap between two
neighbouring straws. In order to show the dependence of the efficiency on the HV
or amplifier threshold, a single number is desireable.  Several definitions can
be made.

%------------------------------------
\subsubsection{Average efficiency }
%------------------------------------
The efficiency can simply be defined as the number of valid hits in the OT
divided by the total number of tracks. Only the hits in those straws are
considered, where the tracks point to, or in one of the two neighbours.  The
efficiency was averaged over all irradiated straws in a given plane, resulting
in the so-called layer-efficiency $\epsilon_{\mathrm{layer}}$:
\begin{equation}
\epsilon_{\mathrm{layer}}=\frac{N_{hit}}{N_{track}},
\end{equation}
where $N_{track}$ is the number of tracks under study (see
Section~\ref{sec:otanal2}), and $N_{hit}$ is the number of events in which a hit
occured in either the straw where the track points to or in one of the two
straws next to it.  The track parameters were estimated using the remaining 7
planes of the OT.

However, the geometry of one OT plane results in a certain amount of dead area.
The inner diameter of a straw is 4.9~mm, whereas the pitch between the straws is
5.25~mm.  The fraction of active area of one OT monolayer hence amounts to
$\frac{4.90}{5.25}\approx 93.3\%$.

By correcting for the dead area between two straws, the average cell-efficiency
is obtained:
\begin{equation}
\epsilon_{\mathrm{cell}}=\epsilon_{\mathrm{layer}} \cdot g\ ,
\end{equation}
where $g$ is the geometrical factor which is equal to the ratio of the wire pitch 
to the straw inner diameter: 
$g=\frac{5.25}{4.90}\approx 1.071$. 

Note that the efficiency estimated in this way is based on the nominal value of
the straw inner diameter and can be biased if the actual diameter differs from
its nominal value (a tolerance of $\pm 50\mu\mbox{m}$ as given by the producer {\em Lamina}
translates into a variation of $\pm 1\%$) or in case of slight deformation of
the straws during the assembly.  Additionally, the small beam width could result
in an erroneous estimation of the {\em fraction} of dead area between the straws, since the
runs with the Si-telescope have an illuminated width of only 9~mm.  The average
efficiency measurements are expected to have up to $\sim$2\% systematic
uncertainty because of the geometrical factor.
%, and could yield values above 100\%.  
This does however not affect the determination of the plateau position.

Finally, the average efficiency is corrected for random noise, using
$\epsilon_{meas}=\epsilon_{true}+(1-\epsilon_{true})R$, where $R$ is the noise
probability.  For reasonably low noise ($<$1\%) and high efficiency ($>$90\%)
this correction can savely be neglected.

%--------------------------------------
\subsubsection{Plateau efficiency }
%--------------------------------------
Alternatively, the efficiency can be evaluated by its plateau value in the
center of the straw, within $|r|<1.6$~mm from the wire. This window is enlarged
to 2.0~mm for the OT standalone analysis, that does not suffer from multiple
scattering effects.  Ideally, the efficiency can be modeled as follows. In a gas
mixture of Ar/CO$_2$-70/30 the average ionisation length $\lambda$ amounts to
about 325~$\mu$m~\cite{ref.Sauli}.  As a result, the probability to create a
cluster is smaller at the edges of the straw, where the path length of the
particle through the straw is limited.  Using Poisson statistics the
cell-efficiency as a function of the distance to the wire, $X$, can be estimated
as:
\begin{equation}
\epsilon_{\mathrm{cell}}(X) = 
\epsilon_{\mathrm{plateau}}\Big( 1 - e^{-2\sqrt{R^2-X^2}/\lambda}\Big),
\label{eq:effprof}
\end{equation}
where $R$ is the radius of the straw (2.45~mm) and $X$ the distance to the wire.
Statistically this results in an integrated efficiency loss of 0.5\%.

The plateau efficiency can in principle deviate from unity due to fluctuations 
in the gain of the avalanche.

The efficiency profile is shown in Figs.~\ref{fig:oteffprof2} and~\ref{fig:oteffprof3}.  
The profile as obtained using the Si-track
prediction (Fig.~\ref{fig:oteffprof2}) is distorted at the edges due to the
imperfect track prediction.  The position of the track is smeared due to the
multiple scattering in the last Si-station, see Section~\ref{sec:multscat}, as shown
by the dashed line. The predicted efficiency from Eq.~(\ref{eq:effprof}) is shown by the full line.

\begin{figure}[!t]
  \begin{center}
    \begin{picture}(420,120)(0,0)
    \put(0,-10){\includegraphics[bb=10 270 515 515,width=13cm,height=6cm]{%
	plots/eff_profile2.eps}}
    \PText(50, 140)(0)[c]{(a)}
    \PText(230, 140)(0)[c]{(b)}
    \end{picture}
  \end{center}
  \caption[Efficiency profile (1)]{\em %
    The straw efficiency profile is shown, as obtained with the analysis
    described in Section~\ref{sec:si}, averaged over module 2 and 3 at HV=1600~V
    and $U_{thr}=700$~mV.  (a) The drop in efficiency at the sides is caused by
    the finite Si-track resolution, see Section~\ref{sec:multscat}.  (b) A
    zoom-in to the plateau region reveals an efficiency of $>$99\% in the region
    $\pm$1.6~mm.}
  \label{fig:oteffprof2}
\end{figure}

\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,120)(0,0)
    \put(0,-10){\includegraphics[bb=1 1 277 216,clip=,scale=0.7]{%
	Tanja/cell_eff_straw.eps}}
    \put(200,-10){\includegraphics[bb=1 1 277 216,clip=,scale=0.7]{%
	Tanja/cell_eff_2mm.eps}}
    \PText( 40,100)(0)[c]{(a)}
    \PText(240,100)(0)[c]{(b)}
    \end{picture}
  \end{center}
  \caption[Efficiency profile (2)]{\em %
    The straw efficiency profile of layer 5 (mod 3) at HV=1550V,
    $U_{thr}=700$~mV (run 316) is shown for the OT standalone analysis
    (Section~\ref{sec:otanal1}), as a function of the predicted track
    position. The sharp drop at $\sim 1.6$~mm is absent, because the track
    prediction is not diluted by multiple scattering.  (a) The efficiency
    plateau is shown, where the detector is defined to be efficient if a hit is
    found in the predicted straw, or in either neighbour.  (b) The hit is
    counted in the efficiency only if it is consistent with the track within
    2.0~mm.
}
  \label{fig:oteffprof3}
\end{figure}




\clearpage
%====================
\section{Available Data Sets}
%====================
The performance of the OT modules was studied when varying the high voltage and
the ASDBLR threshold voltage around their nominal values.  For the measurements
without the Si-telescope, the parameters were varied only in plane 3, while
keeping the other planes at nominal values HV=1580~V and $U_{thr}$=700~mV, in
order to provide good track reconstruction.  In the runs with the Si-telescope,
the parameters in the planes 3--6 were varied simultaneously.

The OT modules were installed on a vertically moveable support, in order to be
able to vary the position of the beam spot along the wire upto a range of 45~cm.
Measurements were done at two vertical positions of the chambers, one with the
beam spot near the end of the wires and another at 45~cm from the end. These
positions will be referred to as ``high'' and ``low'', respectively.  The OT
modules 1, 3 and 4 were installed with the frontend electronics box up, and
module 2 with the electronics box down, see Fig.~\ref{fig:setup}.  Module 2 was
thus studied at distances $y$=0 and 45~cm from the preamplifiers, while the
frontend electronics for the other modules were at a distance from the beam spot
of $y$=225 and 180~cm, respectively, in the ``high'' and ``low'' positions.

The data sets used in the analysis are given in Table~\ref{tab:data}, below.

\begin{table}[!h]
\begin{center}
\footnotesize
 \begin{tabular}{|l||l|l||l|l|l|l|l|l|}
  \hline 
  Runs        & Meas.          & Figure               &  OT      & $U_{thr}$       & HV               & Si-   & S3      & E    \\ 
              &                &                      &  pos.    &  (mV)           & (V)              & tel. &         &(GeV)\\ 
  \hline 						
  301-359    & thresh. scan   & \ref{fig:thrscan2005}&  high         & 400-1540       & 1550             & no     & yes   & 6    \\
  \hline 						
  1201-1219  & hv scan        &                      &  high         & 700            & 1300-1700        & yes    & yes    & 6    \\
  1230-1243  & thresh. scan   &                      &  high         & 575-900        & 1550             & yes    & yes   & 6    \\
  1263-1277  & energy scan    & \ref{fig:escan}      &  high         & 700            & 1600             & yes    & yes   & 1-5 \\
  1279-1283  & energy scan    & \ref{fig:escan}      &  high         & 700            & 1600             & yes    & no    & 1-5 \\
  1286-1312  & hv scan        & \ref{fig:eff2005}b,
                                 \ref{fig:resol2005}b &  high         & 700            & 1300-1700       & yes    & no    & 6    \\
%  1312      &                &                       &  high         & 700            & 1600            & yes    & no    & 6    \\
  \hline
  1320-1330  & hv scan        & \ref{fig:eff2005}a,\ref{fig:resol2005}a,\ref{fig:xt2005} 
                                                      &  high         & 700            & 1200-1700       & no     & no    & 6    \\
  1331-1341  & hv scan        & \ref{fig:eff2005}a,\ref{fig:resol2005}a,\ref{fig:xt2005} 
                                                      &  low          & 700            & 1200-1700       & no     & no    & 6    \\
  1342-1351  & hv scan        & \ref{fig:eff2005}a,\ref{fig:resol2005}a,\ref{fig:xt2005} 
                                                      &  low          & 800            & 1200-1700       & no     & no    & 6    \\
  1362-1368  & noise          &\ref{fig:noisefreq}    &  low          & 645-800        & 1580            & no     & no    & 6    \\
  \hline
  1370        &                &                      &  low          & 700            & 1580            & yes    & no    & 6    \\
  \hline
 \end{tabular}
\caption[Data sets]{\em Available data sets. 
  Note that the HV and the amplifier threshold of the 1$^{st}$ and 4$^{th}$ module is always at 1580 V
  and 700 mV, respectively.}
\label{tab:data}
\end{center}
\end{table}
\normalsize

\clearpage
%====================
\section{Results}
%====================
\label{sec:results2005}

The average noise frequency per wire $f$ as a function of the ASDBLR threshold
is shown in Fig.~\ref{fig:noisefreq}.  The corresponding scale for the noise
occupancy, $R=f\cdot 75\mbox{ ns}$, are given at the right of the plot.  
The first module shows somewhat lower noise rate than the other three.  
Note that the typical occupancy of a B-event is around 4\%. An additonal occupancy of
0.1\% at thresholds higher than 700~mV does not affect the track reconstruction
performance~\cite{ref.robustness}.


\begin{figure}[!h]
  \begin{center}
    \begin{picture}(420,180)(0,0)
      \put(40,-15){\includegraphics[bb=0 0 560 530,clip=,width=11cm,height=7cm]{%
	  plots/noisefreq_note_1.eps}}
    \end{picture}
  \end{center}
  \caption[Noise]{\em The average noise frequency in Hz/wire for the 4 modules.
    The corresponding values of noise occupancy are given at the right. 
  }
  \label{fig:noisefreq}
\end{figure}

The efficiency curves as a function of the applied high voltage, taken at
various ASDBLR threshold settings and various beam positions, are shown in
Fig.~\ref{fig:eff2005}.  The efficiency at the far end, with beam spot at 225 cm
from the preamplifiers, corresponds to the data from module 3.  The efficiency
is higher than at the near end (0 and 45 cm) from module 2 taken at the same
threshold. This is in agreement with the fact that the signal amplitude from
the far end is higher because of the superimposition of direct and reflected
signals~\cite{ref.lhcb-2004-120}.

As expected, the efficiency curve for the higher threshold of 800~mV
undershoots the curve of 700~mV.  The average cell efficiency as obtained with
the OT standalone analysis differs from the plateau efficiency as obtained by the Si
analysis by $\sim 0.5\%$.

In general, the OT detector reaches full efficiency at 1550~V, independent of
the amplifier threshold settings, or beam spot position.

\begin{figure}[!t]
  \begin{center}
    \begin{picture}(420,110)(0,0)
      \put(-10,-22){\includegraphics[bb=0 0 520 380,clip=,width=7cm,height=6cm]{plots/eff2005_3.eps}}
      \put(200,-13){\includegraphics[bb=0 0 540 370,clip=,width=7cm,height=5.95cm]{%
	  plots/eff_HVscan_new_2sigma_sliceing.eps}}
    \PText(40, 130)(0)[c]{(a)}
    \PText(250, 130)(0)[c]{(b)}
    \end{picture}
  \end{center}
 \caption[Efficiency vs HV]{\em The efficiency dependencies on HV 
   at various beam positions and ASDBLR thresholds. Both the average cell efficiency (a)
   and the plateau efficiency is shown (b). The double curves in (b) show the results of both planes separately.}
 \label{fig:eff2005}
\end{figure}

The corresponding coordinate resolution as a function of the HV is shown in
Fig.~\ref{fig:resol2005}, corrected for the track uncertainty or the multiple scattering,
respectively.  The resolution is dependent on the method
with which the rt-relation is obtained, see Sections~\ref{sec:si}-\ref{sec:otanal2}.  
At HV=1400~V the resolution for plane 3 and 4 is very large,
due to the non-gaussian distribution of the residual. Large tails make the
single-gaussian fit unstable. The variation of the resolution for alternative
fits of the residual is discussed in the Appendix~\ref{app:res}.  Nevertheless,
the detector resolution is better than the design value of 200~$\mu$m at high voltages above 1550~V
for both methods~\footnote{%
The drift cell parameters obtained from the calibration procedure for high
voltage of 1600 V and threshold of 800 mV at beam position of 45 cm are given in
the Appendix~\ref{app:dist}.}.
%
\begin{figure}[!h]
  \begin{center}
    \begin{picture}(420,130)(0,0)
      \put(-10,-29){\includegraphics[bb=0 0 530 300,clip=,width=7cm,height=6.cm]{plots/resol2005.eps}}
      \put(200,-12){\includegraphics[bb=0 0 540 370,clip=,width=7cm,height=5.45cm]{plots/res_HVscan_new_2sigma_sliceing.eps}}
    \PText(40, 30)(0)[c]{(a)}
    \PText(250, 30)(0)[c]{(b)}
    \end{picture}
  \end{center}
 \caption[Resolution vs HV]{\em %
   The coordinate resolution as a function of HV 
   at various beam positions and ASDBLR thresholds. }
 \label{fig:resol2005}
\end{figure}


\clearpage
\begin{figure}[!t]
  \begin{center}
    \begin{picture}(420,160)(0,0)
      \put(-10,-22){\includegraphics[bb=0 0 530 300,clip=,width=14cm,height=7.6cm]{plots/xt2005.eps}}
    \end{picture}
  \end{center}
 \caption[Cross talk vs HV]{\em %
   The cross talk as a function of HV: 
   ASDBLR threshold of 700 mV, beam at 0, 45 and 225 cm ({\it a}); 
   ASDBLR thresholds of 700 and 800 mV, beam at 45 cm ({\it b}) }
 \label{fig:xt2005}
\end{figure}

The crosstalk dependencies on HV at the ASDBLR threshold of 700~mV and various
beam positions are shown in Fig.~\ref{fig:xt2005}{\it a}.  The crosstalk is
minimal when the beam spot is close to the readout end and significantly grows
towards the far end.
The crosstalk can be suppressed significantly by increasing the threshold to
800~mV, as is shown in Fig.~\ref{fig:xt2005}{\it b}.  The crosstalk level is
acceptable ($<$10\%) at high voltages below 1650~V.

\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,130)(0,0)
     \put(-10,-15){\includegraphics[bb=14 34 730 540,clip=,scale=0.28]{%
	  Tanja/threshhold_vs_efficency_niels2.eps}}
     \put(190,-15){\includegraphics[bb=14 34 730 540,clip=,scale=0.28]{%
	  Tanja/treshold_vs_resolution_niels2.eps}}
    \end{picture}
  \end{center}
  \caption[Efficiency vs amplifier threshold]{\em %
    The dependence of efficiency ({\it a}) and resolution ({\it b}) 
    on ASDBLR threshold for module 3 (planes 5 and 6)  
    at HV=1550 V. Note that the resolution is obtained from a fit to the residual in 
  a range of $\pm 2\sigma$, resulting in slightly better resolutions, see Section~\ref{app:res}}.
  \label{fig:thrscan2005}
\end{figure}

The crosstalk between the two {\em planes} of module 2 was studied by setting the high
voltage of one of the planes to zero and varying the high voltage of the other
plane.  It was found that at high voltages up to 1700~V the crosstalk between
planes does not exceed 1\%.

The dependencies of efficiency and resolution for modules 2 and 3 (planes 3--6)
on the ASDBLR threshold at HV=1550~V is shown in Fig.~\ref{fig:thrscan2005}. The
OT detector performance does not strongly depend on the ASDBLR threshold in the 
range around 700--800~mV, corresponding to 3--4~fC. The
crosstalk at this voltage was found to be $<$4\% for all thresholds.

Finally, the effect of the length of the readout window on the efficiency is
studied.  By cutting part of the TDC spectrum, hits may be lost. By cutting at
45~ns the efficiency gets reduced by a relative 2\%, see Fig.~\ref{fig:timecut}.\\
\begin{figure}[!h]
  \begin{center}
    \begin{picture}(420,160)(0,0)
     \put(80,0){\includegraphics[bb=7 34 717 530,clip=,scale=0.3]{%
	  Tanja/eff_time.eps}}
    \end{picture}
  \end{center}
  \caption[Normalized efficiency vs OTIS readout window]{\em %
    The dependence of efficiency as a function of OTIS time window,
    at HV=1550 V.}
  \label{fig:timecut}
\end{figure}



\clearpage
%====================
\section{Conclusions}
%====================
The beam test with 6~GeV electrons of four S-type OT modules with final prototype
frontend electronics has demonstrated good OT detector performance. For
an example setting of the parameters at HV=1550~V and amplifier threshold at 800~mV
the following key performance numbers can be quoted:
\begin{itemize}
  \item high efficiency ($\sim 98\%$); 
  \item coordinate resolution better than 200~$\mu$m; 
  \item acceptable noise ($<10$~kHz/wire) and crosstalk level ($<4\%$).
\end{itemize}
These results are confirmed by three different, independent analyses, 
using different methods. 

Within the threshold range of 700--800 mV and high voltage range between
1520--1650 V the detector performance meets the design requirements with
efficiencies higher than 95\% and resolution better than 200~$\mu$m with
reasonable noise and crosstalk level.

The tracking performance in terms of efficiency and ghost rate as a function of 
the OT tracker resolution and cell-efficiency goes beyond the scpoe of this note 
and can be found elsewhere~\cite{ref.robustness}.


\clearpage
%==================================
\appendix
\section{rt-relation}
%==================================
\label{sec:appendix}
%---------------------------------
\subsection{Parabolic parametrization}
%---------------------------------
\label{app:si_rt}
\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,250)(0,0)
      \put(  0,-13){\includegraphics[bb=0 0 360 720,width=4.5cm,height=9cm]{%
	  plots/res_Vshape_run1296.eps}}
      \put(130,-13){\includegraphics[bb=0 0 360 720,width=4.5cm,height=9cm]{%
	  plots/res_Vshape_run1300.eps}}
      \put(260,-13){\includegraphics[bb=0 0 360 720,width=4.5cm,height=9cm]{%
	  plots/res_Vshape_run1303.eps}}
      \PText( 60, 240)(0)[c]{U = 1450 V}
      \PText(200, 240)(0)[c]{U = 1550 V}
      \PText(320, 240)(0)[c]{U = 1650 V}
    \end{picture}
  \end{center}
 \caption[Rt relation for different HV]{%
   \em The rt-relation and the resulting coordinate resolution
   is shown for three values of the applied high voltage. Note that this is the raw residual,
   not corrected for multiple scattering in the last silicon plane, see 
   Section~\ref{sec:multscat}.}
 \label{fig:rt_hv}
\end{figure}
The rt-relation as used in the Si-analysis - as described in Section~\ref{sec:si} -
was obtained by fitting a second order polynomial to the relation between drift time
and predicted track position, see Fig.~\ref{fig:rt_hv}.
The 2d-t(r) histogram was sliced in bins of the predicted track position,
and subsequently the mean drift time was determined with a gaussian fit
around 2$\sigma$ of the peak.
The final t(r)-relation was determined with the fit through the mean drift times per slice,
given by:
\begin{eqnarray}
\label{eq:rtfit}
t(r) = p_0 + p_1(r-p_2)^2 & \textrm{for~} r<0 \\
t(r) = p_0 + p_1(r-p_3)^2 & \textrm{for~} r>0 \nonumber,
\end{eqnarray}
which is a half parabola, mirrored at the wire position 
$r_{\mathrm{wire}}=(p_2+p_3)/2$. The (arbitrary) time offset $t_0$ can be obtained
through:
\begin{equation}
t_0 = p_0 + p_1\Big(\frac{p_2-p_3}{2}\Big)^2.
\end{equation}
The values for $p_{0-3}$, are given in Table~\ref{tab:rtpar}.
The parameters $p_2$ and $p_3$ are very similar by construction, because the plots
were constructed such that the wire position was set at $r=0$.

%
\begin{table}[!t]
  \begin{center}
    \begin{tabular}{|l||r|c||c|c|c|c|}
      \hline 
       U (V)     &  $t_0$ (ns) & $r_{\mathrm{wire}}$ ($\mu$m) & $p_0$ & $p_1$ & $p_2$ & $p_3$ \\ 
      \hline 
      \hline 
      1450       &     4.2 &         16 &            1.0 &   0.33E-05 &       -974 &       1007\\
      1550       &     0.8 &         13 &           -4.5 &   0.28E-05 &      -1356 &       1382\\
      1650       &    -1.3 &          2 &           -8.4 &   0.24E-05 &      -1708 &       1712\\
      \hline 
    \end{tabular}
    \label{tab:rtpar}
    \caption[Rt parameters]{\em The $t(r)$ parameters as obtained from the fit 
      of Eq.~(\ref{eq:rtfit}).}
  \end{center}
\end{table}

%---------------------------------
\subsection{Fit of the residual}
%---------------------------------
\label{app:res}
The coordinate resolution is obtained by fitting a gaussian to the 
residual. However, as is seen in Fig.~\ref{fig:rt_hv}, in some cases
the residual is not well described by a gaussian distribution, due to the
presence of large tails, presumably caused by the fact that the hit is 
not due to the {\em first} cluster.

To show the affect on the resolution, both the results from a  
gaussian fit around the core of the residual within $\pm 1.5\sigma$, as well 
as from a double gaussian fit are presented, see Fig.~\ref{fig:res},
using
$\sigma_{\mathrm{double~gaussian}} \equiv \frac{c_1\sigma_1 + c_2\sigma_2}{c_1 + c_2}$.
%\begin{equation}
%\sigma_{\mathrm{double~gaussian}} \equiv \frac{c_1\sigma_1 + c_2\sigma_2}{c_1 + c_2}
%\end{equation}


\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,80)(0,0)
      \put( 60,-15){\includegraphics[bb=35 25 530 380,scale=0.45]{%
	  plots/resolu_comparison.eps}}
    \end{picture}
  \end{center}
 \caption[Resolution - different definitions]{%
   \em The resolution is plotted for plane 3, with different definitions
   of the resolution, depending on the fit to the residual distribution.}
 \label{fig:res}
\end{figure}

\clearpage
%---------------------------------
\subsection{Resolution vs distance to wire}
%---------------------------------
\label{app:dist}
The drift time $t(r)$ and time resolution $\sigma_t(r)$ as a functions of
distance between track and wire are shown in Fig.\ref{fig:trrel1600}{\it a} and
{\it b}, respectively.  Fig.~\ref{fig:trrel1600}{\it c} shows the coordinate
resolution as a function of drift distance estimated using the error propagation
formula,
$$\sigma_r(r)=\frac{\sigma_t(r)}{dt(r)/dr}.$$ One can see that the drift time
resolution at this high voltage is almost independent on drift distance; the
significant non-uniformity of coordinate resolution appears because of the
non-linearity of the $tr$-relation (drift velocity is not saturated).
%
\begin{figure}[!b]
  \begin{center}
    \begin{picture}(420,220)(0,0)
%       \PText(120,80)(0)[c]{d)}  
      \put(30,100){\includegraphics[bb=-100 230 800 540,scale=0.4]{plots/trrel1600.eps}}
      \put(70,-15){\includegraphics[bb=1 1 520 380,clip=,width=8cm,height=4cm]{Tanja/cell_res2.eps}}
    \end{picture}
  \end{center}
 \caption[Resolution vs distance to wire]{\em %
   The $tr$-relation ({\it a}) and time resolution ({\it b}) 
   as a function of distance to the wire 
   for HV=1600 V, thr=800 mV at beam position of 45 cm; 
   the coordinate resolution estimated in the linear approximation
   ({\it c}). The lower plot shows the measured resolution at HV=1550 V, $U_{thr}=700$~mV,
  with the residuals fitted at the core of $\pm 2\sigma$.}
 \label{fig:trrel1600}
\end{figure}
%
\begin{table}[t]
\begin{center}
\footnotesize
\begin{tabular}{|l|l|l|}
  \hline 
  $r$, mm & $t$, ns & $\sigma_t$, ns \\
  \hline
  0       & 0     & 2.929 \\
  0.5     & 4.851 & 2.828 \\
  1.0     & 10.68 & 2.676 \\
  1.5     & 17.78 & 2.579 \\
  2.0     & 26.37 & 2.525 \\
  2.5     & 36.23 & 2.493 \\
  \hline 
\end{tabular}
\normalsize
\end{center}
\caption{Values of $t(r)$ and $\sigma_t(r)$ for $Ar/CO_2$=70/30, 
HV=1600 V and $U_{thr}$=800 mV.}
\label{table:trrel}
\end{table}

%As the gas composition $Ar/CO_2$=70/30 and a high voltage around HV=1600 V are
%likely be used in the LHCb data taking, the $t(r)$ and $\sigma_t(r)$ functions
%shown in Fig.\ref{fig:trrel1600} could be used in the event simulation programs.
In the analysis procedure, the $t(r)$ and $\sigma_t(r)$ functions were
represented by their values in several fixed points on $r$; the values in the
intermediate points were obtained using the interpolation with 3$^{rd}$ degree
B-splines (CERNLIB E210).  For future reference, the functions' values in these
fixed points are given in Table~\ref{table:trrel}, for HV=1600~V, $U_{thr}=800$~mV
and $Ar/CO_2$=70/30.


%====================
\begin{thebibliography}{99}
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\end{document}