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% ATLAS Muon Note: Serial Test of MPA Sensors
% Author: H. Kroha
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\begin{titlepage}

\begin{large}
\hspace*{10.5cm}
\parbox[t]{70mm}{
ATLAS Internal Note\\
MUON-NO-169\\
April 1998\\
}
\end{large}
\vspace{2cm}


\begin{center}
{\LARGE\bf
Serial Test 

of Transparent Silicon Strip Sensors

for the Alignment System
\vspace{2mm}

of the ATLAS Muon Spectrometer}
\vspace{1.0cm}

{\Large V.~Bartheld, H.~Kroha and S.~Schael}
\vspace{0.5cm}

{\Large Max-Planck-Institut f\"ur Physik,}

{\Large F\"ohringer Ring 6, D-80805 Munich}
\end{center}


\vspace{3.5cm}
\begin{abstract}
On the order of 1500 transparent MPA-ALMY silicon strip sensors
will be used for the optical alignment systems of the ATLAS muon
spectrometer. A first series of 150 sensor modules with prototype
readout electronics and precision mounting plates
has been produced and passed through a detailed test program.
Most of the prototype sensor modules are in use
in several high energy physics experiments, in detector assembly
setups and in the DATCHA test stand at Saclay.
\end{abstract}

\newpage
\newpage

\tableofcontents
\newpage

\end{titlepage}



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\section{Transparent Silicon Strip Sensors (MPA-ALMY)}
%
The {\bf m}ulti-{\bf p}oint {\bf a}lignment system with collimated laser beams
and transparent silicon strip sensors (MPA-ALMY) developed at MPI Munich for
the optical {\bf al}ignment of the ATLAS {\bf my}on spectrometer
has been described previously \cite{sensors},\cite{sensors1}.
The principle layout and structure of the amorphous silicon (a-Si:H) strip
sensors is shown in Figure~\ref{fig:sensor}.

In this note systematic tests of 150 MPA-ALMY sensors with
custom designed prototype readout electronics are discussed.
Two versions of transparent sensors of $20\times 20$~mm${}^2$ active area
have been manufactured and tested. Each type is
optimised with respect to the light transmission rate
for use in different optical multi-point monitors
in the ATLAS muon spectrometer. The two sensor types are distinguished by the
thickness of the amorphous silicon film but are
otherwise identical. The thickness of the ITO electrode layers has 
also been optimised in each case for minimum refelctivity.
The properties of both types of sensors are
summarised in Table~\ref{tab:sensors}.

At a laser wavelength of 690~nm (GaAlP laser diodes),
the highest light transmission rate of
$T=80~\%$ has been achieved with sensors of type~I
which have a $0.5~\mu$m thick a-Si layer. The spectral sensitivity of 0.1~A/W
of the a-Si:H sensors at this wavelength allows to use
laser beams with rather low power of 200--400~$\mu$W (for $\pm 2\sigma$
gaussian beam diameters of 2--4~mm over 2--20~m and a maximum strip
current of $5~\mu$A limited due to the strip serial resistance; see
\cite{DiplomV}).
For the present maximum output power of 15~mW of
laser diodes coupled to single-mode fibers,
beam and fiber splitting can therefore
be used for light distribution at 690~nm.

With a-Si sensors of type~II even higher transmittances of $\ge 90~\%$
can be reached at a wavelength of 780~nm (GaAlAs laser diodes) where
the spectral sensitivity is already rather low (see Table~\ref{tab:sensors}).
Therefore laser beam intensities of 2--4~mW have to be used which limits
the possiblilties of beam splitting. With a dynamic range of the sensors
and their readout electronics (see below and \cite{DiplomV}) of about 10
without significant loss in position resolution,
a very high transmission rate of $90~\%$ is desirable for applications
with more than 10 sensors along a laser beam.
%
\begin{table}[tb]
\caption{Characteristics of amorphous silicon strip sensors for the
alignment system of the ATLAS muon spectrometer \label{tab:sensors}}

\begin{center}
\begin{tabular*}{10.7cm}{p{6.0cm}cc}
%
%
\hline   
Sensor type                & Type~I   & Type~II  \\
\hline   
a-Si thickness & $0.5~\mu$m & $1~\mu$m \\
%
Transmittance at $\lambda =690$~nm  & $80~\%$ & $60~\%$ \\
Transmittance at $\lambda =780$~nm  & $70~\%$ & $90~\%$ \\
%
Sensitivity at $\lambda = 690$~nm   & 0.1~A/W  & 0.1~A/W \\
Sensitivity at $\lambda = 780$~nm   & 0.01~A/W  & 0.01~A/W \\
%
Recommended bias voltage   & 1~V      & 3~V      \\
\hline
Size        & \multicolumn{2}{c}{$25\times 25$~mm${}^2$} \\
%
Active area & \multicolumn{2}{c}{$20\times 20$~mm${}^2$} \\
%
$\#$~Strips & \multicolumn{2}{c}{$2\times 64$} \\
%
Strip pitch & \multicolumn{2}{c}{$312~\mu$m} \\
%
Strip gap   & \multicolumn{2}{c}{$\hphantom{3}10~\mu$m} \\
%
Strip width & \multicolumn{2}{c}{$300~\mu$m} \\
%
ITO strip thickness & \multicolumn{2}{c}{50--100~nm} \\
%
Glass substrate thickness & \multicolumn{2}{c}{0.5~mm} \\
%
\hline
%
Hall mobility & & \\ 
%
\hspace{4mm}$\mu_p^H$~[cm${}^2$/Vs] &
\multicolumn{2}{c}{$10^{-4}$} \\
%
\hspace{4mm}$\mu_n^H$~[cm${}^2$/Vs] &
\multicolumn{2}{c}{$10^{-2}-10^{-3}$} \\
\hline   
%                       
\end{tabular*}
\end{center}
\end{table}


%Die 3D-explodierten Bilder des a-Si:H-Sensors
%findest Du unter /mnt/home/afmp04/bartheld/almy/kroha,
%die Dateinamen sind asi_psd2(3)(e).eps, wobei
%(3) die bemasste Variante und (e) die jeweils
%englischen Pendants sind.
%Vorsicht: Um sie mit Ghosview anzuschauen, musst
%Du 'EPS-Clip' aktivieren oder das Bild in ein
%Dokument (*.PS) einbinden.

\section{Readout Electronics}
%
The lasers are operated in continuous mode and the sensors are read out
continuously with the internal clock frequency of their electronics.
The position of the gaussian laser beam on the sensor is determined
as the centroid of the photocurrent distribution on the top and
bottom strips. The readout electronics of the strip sensors
is designed such that a position resolution of order $1~\mu$m is achieved
without channel-to-channel calibration.
The photocurrents on the strips are multiplexed,
amplified by a common current voltage transformer, digitised by an
at least 10-bit ADC and stored in a local memory
which can be addressed via a custom designed VME interface board.
The readout principle is illustrated in Figure~\ref{fig:readout}.

For cost and space reasons, integrated readout electronics is foreseen
for the sensor modules for the ATLAS muon spectrometer alignment system
where the top and bottom strips are independently read out by an ASIC chip
which contains the above functions (see Figure~\ref{fig:ASICel}).
A 64-channel analog-digital CMOS chip
has already been developed, produced and tested and is described in more detail
in \cite{ASIC}. It comprises a $1\times 64$ analog multiplexer,
a 10-bit ADC and the local RAM and will be used for the
next series of sensor modules for the DATCHA test stands~\cite{modules}.
The final version of the sensor readout electronics
will contain a controller and interface chip for serial
long-distance transmission of digital data from the sensor to a VME board.

For the test of a first series of 150 sensor modules for use
in DATCHA teststands in 1996/97 and other applications, a
prototype version of the readout electronics
consisting of an analog and a digital board with discrete components
has been used. The top and bottom strip currents are digitised
by a common 11-bit ADC and transferred to the VME data acquisition system
via a parallel interface
The conceptual layout of the prototype electronics is shown in
Figure~\ref{fig:protoel}. Details of the electronics design and of the
VME interface board are described in the user manual \cite{electronics}. 

\section{Prototype Modules}
%


\section{Data Acquisition System}

The VME-based data aquisition system designed for the readout of large
numbers of sensors and the analysis software are 
described in~\cite{DiplomV}. 

\section{Serial Tests}
%
%  types of tests
%
Extensive tests of 150 $20\times 20$~mm${}^2$ sensors equiped with prototype
readout electronics~\cite{electronics}
and precision mounting frames have been performed~\cite{DiplomV}.
About half of the sensors was of type~I, the other half of type~II (see Table~1).



The 150 prototype sensor readout boards have been tested with a
constant-current source. The
rms values of the distributions of currents measured in the channels
for top and bottom strips of each sensor readout board are given in
Figure~\ref{fig:stability}. A very good channel-to-channel stability
of better than $0.05~\%$ has been achieved which enables local
position resolutions on the sensors below $1~\mu$m (see Figure~\ref{fig:localres}).

Furthermore, all sensors have been tested with one reference electronics
board in order to compare the dark current levels and to identify 
bad strips with either zero or too high current. The bad strips were
due to faults in the connection between the sensor and the
analog electronics board. The sensors themselves were delivered
fully tested on an automatic probe station
by the manufacturer (EG\& G Heimann Optoelectronics) according to
specifications.

The typical dark current and noise level of the sensors, including the reference
electronics, is $0.1~\%$ of the maximum signal on a strip of
$5~\mu$A (see Figure~\ref{fig:dark}).

Photocurrents on individual strips must not be larger than $5~\mu$A
because otherwise the voltage drop along the ITO strips
significantly reduces the effective bias voltage across the detector
leading to a corresponding drop in sensitivity due
to incomplete charge collection (see \cite{DiplomV}).
At maximum amplification of $10^6$, $5~\mu$A current
corresponds to the ADC saturation voltage of 5~V.





Due to the low noise level, the local position resolution of the sensors
is a fraction of a micron. The photocurrent measurements are averaged
over 20 readout cycles. The photocurrent distributions on the top and
bottom strips are fitted with a Gaussian.

For applications which require a large measurement range,
the linearity of the position measurement over the
active area of the sensors is important.
This has been studied by scanning the surface of the sensors with a
laser beam of 690~nm wavelength and $2-4$~mm diameter
in steps of $300~\mu$m using a computer controlled stepping motor.
The residuals $\Delta x$ and $\Delta y$
between the position of the laser beam spot measured on the sensor and
the true position defined by the stepping motor to $<1~\mu$m
were recorded for the top ($y$) and bottom ($x$) strips.
Simultaneously, the deflection angles $\delta_x$ and $\delta_y$ of the
laser beam were measured at each scan point with a second sensor
behind the one tested.

The systematic uncertainty in the position measurement due to
sensitivity variations across the $20\times 20$~mm${}^2$ sensor surface 
i.e.\ the rms value of the $\Delta x$ and the $\Delta y$ distribution,
is below $5~\mu$m for $83~\%$ of the tested sensors of type~II
and for $65~\%$ of the type~I sensors (see Figure~\ref{fig:resol}).
The average value of the global position resolution is $3.5~\mu$m and $4.8~\mu$, 
respectively, for the first and the second type of sensor.
All sensors showed a global resolution of better than $10~\mu$m.
Using the scan data, the position measurements can be corrected to give global
position resolutions for all sensors below $2~\mu$m (see Figure~\ref{fig:resolcor}).

The sensitivity variations can be explained by variations of the thickness of the
amorphous silicon since for the laser wavelengths used for
the transparent-sensor application only a fraction of the light is absorbed.
This interpretation is supported by the observation of clear
correlations between variations in the sensitivity and 
in the transmission rate~\cite{DiplomV}.

The a-Si thickness variations are quite regular across the sensor surface,
with periods between 2 and 20~mm and varying amplitudes.
They can be caused by standing waves in plasma of the CVD cavity.
Improvements of the apparatus are under investigation in order to increase the
yield of large sensors with position resolution below $5~\mu$m.
For shorter wavelengths and therefore higher absorption
the sensitivity variations are expected to be smaller for both sensor types.
The effect of the sensitivity variations on the position resolution
is negligible for measurement ranges below 1~mm for all sensors.

The measured beam deflection uncertainty over the $20\times 20$~mm${}^2$ sensor 
surface is on average $9~\mu$rad (rms) for sensors of type ~II and $13~\mu$rad (rms)
for type~I where $90~\%$ of all sensors are below $20~\mu$rad (see Figure~\ref{fig:defl}).
Similar values were obtained for the glass substrates alone.
The thickness variations in the amorphous silicon film therefore
cause little additional beam deflection uncertainty.

The sensor scans with $300~\mu$m step size were used to correct for the beam deflections
by interpolating between the scan points across the sensor surface 
(see~\cite{sensors},\cite{sensors1},\cite{DiplomP}).
After the corrections, the uncertainty in the beam deflection angles
ranges between $1.5$ and $6~\mu$rad for all sensors with an average value of $3~\mu$rad
(see Figure~\ref{fig:deflcor}). This is sufficient for the alignment systems of the
ATLAS muon spectrometer~\cite{MPA},\cite{MPAnew}.



\section{Applications of Prototype Sensors}

A large part of the tested sensors
and the DAQ system are now in use at the ATLAS alignment test stand DATCHA~0
at Saclay and in the HERA-B silicon-vertex and tracking detectors where
long-term stability tests are performed~\cite{DiplomT}.

\clearpage

\begin{thebibliography}{99}
%
\bibitem{sensors}
W. Blum, H. Kroha, P. Widmann, Development of an Optical
Alignment Monitoring for the ATLAS Muon Spectrometer,
ATLAS Internal Note, MUON-NO-047, July 1994 and
MPI Report, MPI-PhE/ 94-22, October 1994;
A Novel Laser-Alignment System for Tracking Detectors Using 
Transparent Silicon Strip Sensors,
Nucl.\ Instrum. and Methods A 367 (1995) 413;
Transparent Silicon Strip Sensors for the Optical Alignment of
Particle Detector Systems,
Nucl.\ Instrum. and Methods A 377 (1996) 404;
A Novel Laser-Alignment System for Particle Tracking Detectors Using
Transparent Silicon Strip Sensors,
IEEE Trans. Nuclear Science, Vol. 43, No. 3 (1996) 1194.
%
\bibitem{sensors1}
H. Kroha, Laser-Alignment System with Transparent Silicon Strip Sensors and
its Applications, MPI Report, MPI-PhE/ 96-20, August 1996,
Nucl.~Phys.~B (Proc.~Suppl.) {\bf 54B} (1997) 80.
%
\bibitem{DiplomV} V.~Bartheld, Diploma Thesis, Technical University
Munich, February 1997, MPI report, MPI-PhE/~97-04, February 1997.
%
\bibitem{ASIC}
B.~Dulny, J.~Fent and H.~Kroha,
ASIC Chip for Alignment Strip-Sensor Readout,
MPI report, MPI-PhE/~96-14, July 1996.
%
\bibitem{electronics}
B.~Dulny, J.~Fent and H.~Kroha,
Manual for MPI Transparent Alignment Sensor Electronics,
MPI report, MPI-PhE/~96-08, April 1996.                                                  /
%
\bibitem{DiplomP} P.~Widmann, Diploma Thesis, Ludwig-Maximilian University
Munich, August 1994, MPI report, MPI-PhE/~94-21, September 1994.
%
\bibitem{MPA} H.~Kroha and A.~Ostapchuk,
{\sl A New Alignment System for the ATLAS Muon Spectrometer},
ATLAS Internal Note, MUON-NO-070, February 1995;
The ATLAS Muon Group,
{\sl The Alignment of the ATLAS Muon Spectrometer},
ATLAS Internal Note, MUON-NO-113, March 1996.
%
\bibitem{MPAnew} J.~Bensinger, H.~Kroha and A.~Ostapchuk,
{\sl The Alignment System
for the ATLAS Forward Muon Spectrometer},
ATLAS Internal Note, MUON-NO-168, June 1997.
%
\bibitem{monitor} H.~Kroha and S.~Schael,
Optical Monitoring System for the MDT Assembly Stations,
ATLAS Internal Note, MUON-NO-156, April 1997.
%
\bibitem{DiplomT} T.~Perschke, Diploma Thesis,
Ruprecht-Karl University Heidelberg, October 1996.
%
\end{thebibliography}

\clearpage

% Figures
%
% 1
\begin{figure}[t]
\begin{center}
\begin{tabular}{c}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/asipsd.eps,height=8.5cm}} \\
\\[20mm]
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/asi_sd3e.eps,height=8.5cm}} \\
\end{tabular}
\end{center}
\caption{
  Cross section (top)
  and three-dimensional exploded view (bottom)
  of an amorphous silicon strip sensor.
  The two ITO electrode layers are segmented into orthogonal strip rows (in the
  cross section shown parallel for simplicity). 
\label{fig:sensor}}
\end{figure}
%
\clearpage
%
% 2
\begin{figure}[t]
\begin{center}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/analog_e.eps,height=8.0cm}}
\end{center}
\caption{Principle of the readout electronics for silicon strip photodiodes.
\label{fig:readout}}
\end{figure}
% 3
\begin{figure}[hb]
\begin{center}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/mpa_as_e.eps,width=0.8\textwidth}}
\end{center}
\caption{Layout of the silicon strip sensor readout electronics with the ALM1
ASIC chip designed for DATCHA tests in 1997.
\label{fig:ASICel}}
\end{figure}
%
\clearpage
% 4
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/mpa_al_e.eps,width=0.8\textwidth}}
\end{center}
\caption{Layout of the prototype version of the silicon strip 
sensor readout electronics for the serial tests.
\label{fig:protoel}}
\end{figure}
%
\clearpage
% 5
  \begin{sidewaysfigure}[t]                                %Die \caption und die \label
                                                   %Anweisung benoetigt die Figure-
                                                   %Umgebung. Positionierung [h]ere
    \begin{center}                                 %Bild zentrieren, Breite=170mm
%     \begin{minipage}[hb]{170mm}                  % Minipage ist 170mm breit
                                             %\epsfxsize=170mm bestimmt die
                                             %Breite der Skalierung
%\mbox{\epsfxsize=170mm
%\epsffile{/home/afmp04/bartheld/tex/diplom/mpi/MPA2.EPS}}
\mbox{\epsfig{figure=/aleph/scratch/kroha/mpa2.eps,width=20.0cm}}
%
%\begin{picture}(136,80)                     %Bild ist 170 mm breit, 100 mm hoch
%    \put(20,140){\special{em:graph mpa}}    %Bild 0 mm nach rechts,
%\end{picture}                               %100 mm nach oben verschieben

\vspace{1cm}
\caption[MPA Sensormodule]{MPA-ALMY sensor module (A) with
prototype readout electronics and precision
mounting plate. The individual components are as labeled:
(1) digital readout board with RAM, parallel interface to VME 
and signal and power connectors (8),
(2) analog readout board with analog multiplexers (7), 
current-voltage amplifiers and ADC,
(3) interface board between sensor (via wire bonds (6)) and analog board
(via kapton cable) fixed, together with the sensor, on the aluminum 
precision mounting plate (4) and (P),
(5) detached aluminum electronics housing.}
        \label{fig:module}                           %Label fuer Querverweise \ref{}
%     \end{minipage}
    \end{center}
  \end{sidewaysfigure}
%
% 6
%\begin{sidewaysfigure}[p]
%\begin{center}
%\mbox{\epsfig{figure=almy_proto.eps,width=16.0cm}}
%\end{center}
%\caption{Drawing of a MPA-ALMY prototype sensor module.
%\label{fig:modulesketch}}
%\end{sidewaysfigure}
%
%
\clearpage
% 7
\begin{sidewaysfigure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/newplate.eps,width=\textwidth}}
\end{center}
\caption{Drawing of the precision mounting frame
of the MPA-ALMY prototype sensor modules.
\label{fig:moduledraw}}
\end{sidewaysfigure}
%
%
%
%\begin{figure}[hb]
%\begin{center}
%\mbox{\epsfig{figure=etest_e.eps,width=1.05\textwidth}}
%\end{center}
%\caption{Test with constant current source.
%\label{fig:current}}
%\end{figure}
%
% 8
\begin{figure}[t]
\begin{center}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/elekref_engl_1.eps,width=1.10\textwidth}}
\end{center}
\caption{Test of the channel-to channel stability
of the prototype MPA-ALMY readout electronics with a constant current source
which was independently connected to the even (E) and odd (O) numbered strips.
The standard deviations of the distributions of the currents $I_{x,y}$ on the
$x$ and $y$ strips are shown in ADC counts
for 150 sensor readout boards tested (the hatched
histograms show the boards which needed repair before the final test was done).
Typical test input currents were at $1800\pm 80$ ADC counts (2048 counts maximum) 
where the error indicates the variation between the different tests.
\label{fig:stability}}
\end{figure}
%
\clearpage
%
% 9x
\begin{figure}[t]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/almy/stabil2/dx1.eps,width=1.00\textwidth}}
\end{center}
\caption{
\label{fig:localres}}
\end{figure}
%
% 9
\begin{figure}[hb]
\begin{center}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/sens_ref_engl.eps,width=1.10\textwidth}}
\end{center}
\caption{Distributions of the
mean and the standard deviation of the dark currents on the strips
in ADC counts measured for 118 sensors with common
reference electronics. The saturation current corresponds to 2048 counts.
\label{fig:dark}}
\end{figure}
%
\clearpage
%
% \begin{figure}[t]                                %Die \caption und die \label
%                                                  %Anweisung benoetigt die Figure-
%                                                  %Umgebung. Positionierung [h]ere
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%                                                  %\epsfxsize=150mm bestimmt die
%                                                   %Breite der Skalierung
%\mbox{\epsfxsize=150mm
%\epsffile{/home/afmp04/bartheld/tex/diplom/mpi/laser.eps}}
%     \end{minipage}
%     \parbox{160mm}{
%       \caption[Me"saufbau f"ur systematische Messungen]{Darstellung des Me"saufbaus f"ur
%         systematische Messungen an Streifensensoren.}
%                                             %Bildueberschrift [kurz] {lang}
%       \label{fig:setupside}}                    %Label fuer Querverweise \ref{}
%   \end{center}
% \end{figure}
%
% 10
%
  \begin{figure}[p]                                %Die \caption und die \label
                                                   %Anweisung benoetigt die Figure-
                                                   %Umgebung. Positionierung [h]ere
    \begin{center}                                 %Bild zentrieren, Breite=170mm
%     \begin{minipage}[t]{170mm}                   % Minipage ist 170mm breit
                                                   %\epsfxsize=170mm bestimmt die
                                                   %Breite der Skalierung
%\mbox{\epsfxsize=170mm
%\epsffile{/home/afmp04/bartheld/tex/diplom/mpi/MESSAUFB.EPS}}
\mbox{\epsfig{figure=/alpeh/scratch/kroha/messaufb.eps,width=13.0cm}}
%%\epsffile{/home/afmp04/bartheld/tex/diplom/mpi/messaq.eps}}
%
%\begin{picture}(170,100)                     %Bild ist 170 mm breit, 100 mm hoch
%    \put(20,160){\special{em:graph messaufb}} %Bild 0 mm nach rechts,
%\end{picture}                                %100 mm nach oben verschieben

\vspace{2cm}
\caption[Messaufbau f"ur 2-D-Scans]{Setup for 2-dimensional
sensor scans: (1) Single-mode optical fiber connecting the diode laser with
an (adjustable) collimator (2) from which a diffraction limited gaussian laser
beam is emitted (see text). The laser ray (dashed line)
traverses the transparent sensors of two MPA-ALMY detector prototype 
modules (4) and (6). A fluorescent plate (5) is used for the initial adjustment
of the laser beam. The first sensor is moved in the $x$ and $y$ coordinates
transverse to the laser beam (as indicated) with a precise stepping motor (3)
to scan the surface.

}
                                              %Bildueberschrift [kurz] {lang}
        \label{fig:setup}                %Label fuer Querverweise \ref{}
%     \end{minipage}
    \end{center}
  \end{figure}
%
\clearpage
% 11
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS17_2.EPS,width=1.05\textwidth}}
\end{center}
\caption{Maximum $x$ and $y$ strip currents $I_{x,y}^{\mathrm M}$
on the first and the second sensor and the ratio of the signals on both
sensors in contour plots
as functions of the true $x$ and $y$ position of the laser
beam on the surface of the first sensor
(``vs~17'') which was moved with respect to the beam
by a precise stepping motor (see text).
\label{fig:scan17a}}
\end{figure}
%
\clearpage
% 12
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS17_4.EPS,width=1.05\textwidth}}
\end{center}
\caption{Residuals $\Delta x$ and $\Delta y$ of the laser-beam
position measurements on the $x$ and $y$ strips of sensor ``vs~17''
relative to the true
position defined by the stepping motor during the scan of the
sensor surface (compare Figure~11).
$\Delta x$ and $\Delta y$
are given as functions of the true $x$ and $y$ position 
of the beam in the
form of histograms, contour plots and distributions.
\label{fig:scan17b}}
\end{figure}
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\clearpage
% 13
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS17_5.EPS,width=1.05\textwidth}}
\end{center}
\caption{Deflection angles $\delta x$ and $\delta y$ of the laser-beam
caused by sensor ``vs~17'' during the scan of the
sensor surface and measured with the second (reference) sensor
relative to the undistorted beam direction (compare Figure~11).
$\delta x$ and $\delta y$
are given as functions of the true $x$ and $y$ position of the beam
in the form of histograms, contour plots and distributions.
\label{fig:scan17c}}
\end{figure}
%
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS85_2.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~11 for sensor ``vs~85''.
\label{fig:scan85a}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS85_4.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~12 for sensor ``vs~85''.
\label{fig:scan85b}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS85_5.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~13 for sensor ``vs~85''.
\label{fig:scan85c}}
\end{figure}
%
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS55_2.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~11 for sensor ``vs~55''.
\label{fig:scan55a}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS55_4.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~12 for sensor ``vs~55''.
\label{fig:scan55b}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS55_5.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~13 for sensor ``vs~55''.
\label{fig:scan55c}}
\end{figure}
%
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS20_2.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~11 for sensor ``vs~20''.
\label{fig:scan20a}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS20_4.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~12 for sensor ``vs~20''.
\label{fig:scan20b}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\mbox{\epsfig{figure=/home/afmp04/bartheld/tex/diplom/mpi/VS20_5.EPS,width=1.05\textwidth}}
\end{center}
\caption{As Figure~13 for sensor ``vs~20''.
\label{fig:scan20c}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\begin{tabular}{cc}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xresI.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xresII.eps,height=8.5cm}} \\
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/yresI.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/yresII.eps,height=8.5cm}} \\
\end{tabular}
\end{center}
\caption{
  Position resolutions $\sigma (\Delta x )$ and $\sigma (\Delta y )$
  from laser-scans of the sensor surface (see text; compare Figure~12)
  without corrections, shown separately
  for sensors of type~I and II.
\label{fig:resol}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\begin{tabular}{cc}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xres_all.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/yres_all.eps,height=8.5cm}} \\
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xres_cor.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/yres_cor.eps,height=8.5cm}} \\
\end{tabular}
\end{center}
\caption{
  Position resolutions $\sigma (\Delta x )$ and $\sigma (\Delta y )$
  for sensors of type~I and II combined
  before and after corrections
  from the surface scan (see text).
\label{fig:resolcor}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\begin{tabular}{cc}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xdefI.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xdefII.eps,height=8.5cm}} \\
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/ydefI.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/ydefII.eps,height=8.5cm}} \\
\end{tabular}
\end{center}
\caption{
  Uncertainties $\sigma (\delta_x )$ and $\sigma (\delta y )$
  in the laser beam refraction angle
  from laser-scans of the sensor surface (see text; compare Figure~13)
  without corrections,
  shown separately for sensors of type~I and II.
\label{fig:defl}}
\end{figure}
%
\clearpage
%
\begin{figure}[p]
\begin{center}
\begin{tabular}{cc}
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xdef_all.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/ydef_all.eps,height=8.5cm}} \\
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/xdef_cor.eps,height=8.5cm }} &
\mbox{\epsfig{figure=/home/iws109a2/kroha/tex/atlas/ydef_cor.eps,height=8.5cm}} \\
\end{tabular}
\end{center}
\caption{
  Uncertainties $\sigma (\delta_x )$ and $\sigma (\delta y )$
  in the laser beam refraction angle
  for sensors of type~I and II combined
  before and after corrections
  from the surface scan (see text).
\label{fig:deflcor}}
\end{figure}
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\clearpage
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\end{document}
