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\title{ \begin{center}
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	\\
	{\huge My Summerstudentship at DESY Hamburg}
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\author{Sophie de Rijk \\
Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland }


\date{\normalsize \today}

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\begin{abstract}
\noindent

This document serves as a report for my work as a summerstudent at DESY Hamburg. Firstly, the CMS detector, its tracker and the tracker upgrade are presented. Following this, the main subject of my work which are two measurement setups (optical deformation setup and thermal characterization setup) are presented along with the finite element calculations which they are meant to validate. Then, for each setup my work concerning their design, testing and preparation is detailed.



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\section{Introduction}
\label{intro}

After completing my Bachelor degree in Mechanical Engineering at EPFL (Switzerland), I have spent 8 weeks of the summer of 2011 as a summerstudent with the CMS group at DESY. This report is to account for my work in the group.\\
I have contributed to the experimental validation of thermal and mechanical finite element calculations concerning the module design for the upgrade of the CMS tracker.\\
In this report, the CMS experiment and the upgrade of its inner tracking system will be briefly presented.
After that, the main results of finite element calculations on the tracker modules are presented. These calculations set the base of the validation measurements and my work. Following that, the two measurement setups designed for the validation measurements and their principles are presented. Finally, my contribution and its results on these two projects are shown.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{The CMS experiment}

The CMS experiment (Compact Muon Solenoid) \cite{cms_site}  shown in a 3D blowup in figure \ref{cms_blowup} is a particle detector that is currently taking data at the LHC (Large Hadron Collider) at CERN. In figure \ref{cms_blowup}, one can see the various layers of detection built concentrically around the beam shown by the arrows. 

 \begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{cms_blowup.jpg}
\caption{CMS detector blowup 3D view}
\label{cms_blowup}
\end{center}
\end{figure}

The CMS detector is composed of several detection layers and a superconducting solenoid magnet as shown in the slice representation in figure \ref{slice}. 
  
 \begin{figure}[H]
\begin{center}
\includegraphics[width= 0.9 \textwidth]{CMS_Slice}
\caption{Slice of the CMS detector with various particle behavior on the different sub-detectors}
\label{slice}
\end{center}
\end{figure}

The first layer is a multilayered silicon tracker placed in the magnetic field generated by a superconducting solenoid. This tracker allows to detect the trajectories of the charged particles (e.g. electrons, positrons, charged hadrons, muons) crossing it. The tracking of particles is achieved through the deposition of energy by the particles in the detector. This energy deposition is then converted in an electrical signal which represents one given position. Once a collection of positions are detected, tracks can be reconstructed. The inner layer of the tracker is a pixel detector. The specificity of the pixel detectors is that they give the position of particles in 3D (radial, axial and angular direction) whereas the outer layer of the tracker only give out positions in 2D (radial and angular direction).\\
The solenoid magnet generates a 3.8 Tesla magnetic field which bends the trajectories of charged particles. Thanks to this bending, from the trajectories detected in the tracker, is is possible to determine the charge and momentum of the particles detected in the tracker.\\
The next step is to determine the energy of the particles by means of calorimetry. Particles are stopped by the very dense material of the calorimeter and deposit their energy. The deposited energy is then converted in an electrical signal giving the energy of the particle. Different types of calorimeters are required for different types of particles. The first calorimeter, called the electromagnetic calorimeter (ECAL) is used to measure the energy of electrons and photons. The second calorimeter is the hadronic calorimeter (HCAL) which measures the energy of hadronic particles. Beyond these calorimeters, only muons still subsist, the other particles having been stopped by the inner layers of the detector.\\
The outer structure is composed of alternating layers of steel plates, the return yoke, and of muon chambers. The return yoke's function is to guide the magnetic field lines shown in figure \ref{magfield} and is complementary to the solenoid. The result is a magnetic field following the axial direction inside the solenoid and a parallel magnetic field that has opposite direction outside the solenoid. This change of direction in the magnetic field can be seen by observing the S shaped tracks of muons shown in figure \ref{slice}.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{mag_field}
\caption{Side view of the detector with the magnetic field}
\label{magfield}
\end{center}
\end{figure}

The muon chambers track the trajectories of muons. Since all other particles can not cross the detector beyond the hadron calorimeters, all particles detected in the muon chambers are necessarily muons.\\
The CMS detector is hence equipped to identify particles from their various interaction behavior with the different detection components as shown by the different tracks in figure \ref{slice} and is also capable of determining their momentum.

\subsection{The Tracker and its upgrade}\label{tracker}

The barrel region of the current tracker is composed of five concentric layers as shown in figure \ref{barrel_schem} each equipped with detector modules that overlap in both $\varphi$ and z directions in the coordinate system shown in figure \ref{coord}.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.6 \textwidth]{barrel_schem}
\caption{Transverse view of the silicon barrel detector}
\label{barrel_schem}
\end{center}
\end{figure}



\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.6 \textwidth]{coord_sys}
\caption{Coordinate system of the CMS detector and its tracker}
\label{coord}
\end{center}
\end{figure}

   
In forward direction, the tracker consists of two endcaps each in turn comprised of nine discs equipped with detection modules. The global assembly of the tracker barrel and endcaps is shown in figure \ref{tracker}\cite{tdr_tracker}.

   
\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{tracker3d}
\caption{3D view of the tracker assembly}
\label{tracker}
\end{center}
\end{figure}
   
   

This tracker system is planned for an upgrade following the increase of luminosity of the LHC. For the tracker to still be effective, its detection granularity has to be improved such that it is capable of distinguishing particles from one another with higher particle density in the detector.\\

Figure \ref{tracker_old} is composed of two silicon strip sensors of 10x10 cm size bonded together. Each strip sensor is segmented with a pitch of 50 $\mu$m as shown in figure \ref{strips}. The strips give out an electrical signal if a particle crosses the detector at its position. By bonding two sensors together, 20 cm long detection strips are obtained. These sensors  are supported by a carbon fibre structure surrounding them and read out from one side by readout chips. The tracker modules are kept at 10 \textcelsius{} when in operation.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.55 \textwidth]{tracker_old}
\caption{Standard layout of the current tracker modules}
\label{tracker_old}
\end{center}
\end{figure}

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.55 \textwidth]{strip_pattern}
\caption{Strip pattern on the silicon sensors}
\label{strips}
\end{center}
\end{figure}



With the increase of luminosity, the density of particles in the detector will be significantly greater. For the tracker to still be able to track effectively this higher density of particles, the following changes have to be made on the design of the modules :
\begin{itemize}
\item{Make shorter detection strips to increase the detection granularity of the modules to allow tracking of a higher density of particles}
\item{Cool the sensors to -20 \textcelsius{} to prolong their life time when irradiated and allow for operation after irradiation}
\item{Use better irradiation resistant materials for the sensors}
\end{itemize}

Moreover, to reduce multiple scattering of particles while passing through the tracker, the newer modules will have less passive material.

Figure \ref{tracker_new} shows a preliminary design of such a new module. Its global dimensions are of about 10x10 cm. The length of the strips is of 2.5 cm in this design by adding segmentation along the direction of the strips. The module is cooled by evaporative $\mathrm{CO}_2$ through cooling loops at each extremity of the module. The support of the module is achieved with a construction of a sandwich of materials as shown in the cut figure \ref{modulecut}. The module will be cooled to -20\textcelsius{}. Being composed of various materials and cooled by 40 Kelvin, the new module will sustain sizable stresses due to the various thermal expansion coefficients. These issues will be discussed in chapters \ref{finiteelement} and \ref{experimental}.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{tracker_new}
\caption{Standard layout of the upgraded tracker modules}
\label{tracker_new}
\end{center}
\end{figure}


\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.6 \textwidth]{modulesandwich}
\caption{Upgraded tracker module transversal cut view of the support structure}
\label{modulecut}
\end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{The Finite Element calculations}\label{finiteelement}

The choice to build the new tracker modules with little but various material sandwiches that need to be cooled to -20\textcelsius{} imply that mechanical and thermal issues will be of great importance. In order to check if the new module design is reasonable from the thermal and mechanical point of view, finite element calculations for both temperature and deformation distributions over the module have been made. The advantage of finite element calculations is that is is an easy and unexpensive way to sort out design ideas that are not worth the construction of a prototype which are far more costly. \\

The modules have two symmetry planes as shown in figure \ref{2dmodule}. By taking profit from these symmetries, only 1/4 of the module needs to be considered in the simulations.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.5 \textwidth]{2dmodule}
\caption{2D view of the module and its 2 symmetry planes in red}
\label{2dmodule}
\end{center}
\end{figure}



\subsection{Temperature calculations}
The first issue to address is that the sensor needs to be kept at low temperatures. However, the sensor and the readout chips produce heat  when in use. To cool the modules, a $\mathrm{CO}_2$ cooling circuit runs on both sides of the modules. Calculations shown in figures \ref{temp1} and \ref{temp2} are made to verify that the sensor remains at the desired temperature when it and the readout chips are powered and the module is cooled.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{temp1}
\caption{Overall temperature distribution with CO2 cooling, sensor and chips producing heat}
\label{temp1}
\end{center}
\end{figure}

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{temp2}
\caption{Temperature distribution on just the sensor with CO2 cooling, sensor and chips producing heat}
\label{temp2}
\end{center}
\end{figure}

What we can see off these results is that the temperature difference between the warmest spot which is at about -28\textcelsius{} and the cooling circuit which is at -35\textcelsius{} is of only about 7\textcelsius{} which is a very encouraging result. Secondly, we can see that the temperature difference over the sensor itself is of about 1/2 a degree which is also a very encouraging result.
\subsection{Deformation calculations}

Since the module is in essence a sndwich of very different materials, when cooled, each component will shrink/expand in a different way. The deformation calculation shown in figure \ref{defofem} accounts for these different thermal expansion behaviors.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{defofem}
\caption{Deformation of the module when cooled}
\label{defofem}
\end{center}
\end{figure}

What we can see off the deformation results is that the maximum amplitude of of 100$\mu$m. Moreover, the deformation mode includes a twist of the module. These results indicate that the deformation induced in this design is rather large and of a complex mode. We can suspect that this module might eventually suffer fatigue and breaking when undergoing several loading cycles. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{The measurement setups}\label{experimental}

The aim of the two measurement setups that will be described in this chapter is to validate the thermal and deformation results obtained in the finite element calculations presented in chapter \ref{finiteelement}. To validate those results, two different approaches were adopted.
The first approach is to verify the temperature distribution on the tracker modules. This is measured with the thermal characterization setup.
The second approach is to verify the deformation of the module when undergoing thermal stresses. This is measured with the optical deformation setup.

\subsection {The thermal characterization setup}

The thermal characterization setup aims to measure the thermal properties, i.e the thermal conductivity of novel materials and test composite structures.
The setup shown in figure \ref{therm_setup} will have to provide a stable and controlled environment. To do so, the whole measurement takes place in a vacuum pumped enclosure to eliminate any heat exchange by convection, which could falsify measurements. The structures that will be measured will both need heating and cooling. The cooling is obtained by use of a silicon oil chiller. To heat the components, various heat sources will be connected to a controllable voltage and current source. The temperatures will be measured by thermal resistors.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7 \textwidth]{ThermalSetup1}
\caption{Thermal characterisation setup}
\label{therm_setup}
\end{center}
\end{figure}


After commissioning the setup with known materials,  it will be to used in the first place to determine the thermal conductivity of a carbon based compound, PGS \cite{PGS}. PGS having a high thermal conductivity, it would be used to conduct more efficiently heat from the heat source (readout chips and detectors) to the cooling circuit in the tracker modules. Later on, the setup will be used to measure the tracker module prototypes.\\


\subsection{The deformation measurement setup }
\subsubsection{Basic principle}

This measurement setup's aim is to determine by optical means, hence non-intrusive, the deformation of any reflective surface.
The basic principle of the measurement setup shown in figure \ref{optic_schem}. A grid of dots is illuminated from the back and projected on the reflecting surface of the object we want to measure. A first picture is taken by a camera. The object is then deformed and on reflected image of the dot grid, the dots have shifted relative to each other compared to the initial image. A second picture is taken. Both pictures are taken in a dark environment. By comparing the position of the dots on both images, we can determine the displacement of each dot with respect to the reference first image. To match each dot of the first image to its counterpart in the second image, the dot in the center of the projected grid has a distinctable color (for example red). This red dot serves as a reference for the indexing of the dots. From the displacement of the dots in the image, the vertical displacement of each position of the surface represented by the dots can be calculated. By means of spline fitting, the deformation of the surface can be reconstructed.

 \begin{figure}[H]
\begin{center}
\includegraphics[width= 0.85 \textwidth]{optic_schem}
\caption{Deformation measurement basic setup}
\label{optic_schem}
\end{center}
\end{figure}

A few remarks on this method have to be made. Firstly, this method only reconstructs the vertical (perpendicular to the reflective surface) displacement of the object. Secondly, when both images are compared, both colored dots are superposed. As a result, the reference colored dot will always have no displacement in the reconstruction. Thirdly, as this method compares two situations, it measures the displacement of the body, not its actual shape. A simple depiction of this distinction is shown in figure \ref{defo_schem}. Curve A represents the initial shape of the object. Curve B is the deformed object. Curve C is the difference between the initial and deformed shape (C = B - A) which represents the actual output of the reconstruction.

 \begin{figure}[H]
\begin{center}
\includegraphics[width= 0.6 \textwidth]{defographs}
\caption{Real shape and displacement distinction}
\label{defo_schem}
\end{center}
\end{figure}

\subsubsection{Pattern recognition and reconstruction software}\label{patternreco}


The pattern recognition and reconstruction software is used to translate the two pictures taken from the measurement setup to a reconstruction of the deformation.
The first step in the program is to locate all the dots in both images, to do so it follows a three threshold logic as shown in figure \ref{3step} \cite{jan_defo}. All pixels of the image are scanned row by row and their greyscale ADC values are determined. If a pixel's greyscale value is larger than a first threshold (step1 seed), the program evaluates the greyscale average values over neighboring points. If this average is larger than a second threshold (step2 seed), the center of gravity of the dot is determined whose greyscale level should be larger than a third threshold. Finally, it determines if a dot is considered red (or the color that was chosen for the central dot) with means of a color ratio threshold. 

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.4  \textwidth]{3step_defo}
\caption{Center of mass search of one dot}
\label{3step}
\end{center}
\end{figure}

Once the images have been processed and all dots localized, the dots have to be indexed, this sequence is shown in figure \ref{index}. The indexing starts at the red dot which is the reference point \textless0,0\textgreater. The program then starts looking for the next dot in a circular region located at a certain average spacing of the previous dot. This average spacing is a parameter that has to be set by the user. This locating process continues line by line from one dot to the next. It is possible that certain dots are not localized in the image. This is accountable to the fact that certain points (especially on the borders) are no longer reflected to the camera due to the deformation, or that the reflection is of bad quality because of surface quality or diffraction.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7  \textwidth]{index_dots}
\caption{Indexing of found dots}
\label{index}
\end{center}
\end{figure}

Now that the dots are localized and indexed, the displacement of the dots between the reference and the deformed picture can be determined. This displacement is calculated using a number of parameters  (focal length, distance between object and camera/dot grid) which have to be entered in the program. Systematic studies on these parameters are discussed in section \ref{syststud}.\\

The last step is to fit quadratic splines through the 2D array of vertical displacements shown, the process is shown in figure \ref{splines} \cite{jan_defo}. Since perpendicular splines are dependent on each other, the fitting of splines have to be adjusted on each other. This adjustment is made first based on the splines in one direction, then on the splines in the other direction. Finally, all adjustments are averaged to obtain a smooth surface.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7  \textwidth]{splines}
\caption{Deformation reconstruction with splines}
\label{splines}
\end{center}
\end{figure}

We now have reconstructed the deformation of the surface based on the two images taken from the setup. In essence, we translate two images into a smooth deformation surface reconstruction as shown in figure \ref{twotoone}.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7  \textwidth]{twopicstoone2}
\caption{Translation from two images to one 3D representation of the deformtion}
\label{twotoone}
\end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Work on the thermal characterization setup}

\subsection{Vacuum and natural convection issues}
For the thermal characterization setup, most of its components were already present. However, the vacuum setup still needed commissioning. I have helped with the leak search of the setup and with identifying and solving the leak and degassing issues of the setup. Seeing that reaching high vacuum was less straightforward than expected in the first place, I have started to search for a means to estimate which level of vacuum truly needed to be reached to eliminate sufficiently convection inside of the vessel, which is the reason for performing the measurement in vacuum. \\

\subsubsection{Natural convection at low pressure}

Natural convection is a process that depends on the following parameters:
\begin{itemize}
\item{temperature of the solid body (wall)}
\item{temperature of the convecting gas}
\item{density of the convecting gas}
\item{dynamic viscosity of the convecting gas}
\item{thermal diffusivity of the convecting gas}
\item{gravitation}
\item{size, shape and orientation of the surface of the solid body }
\end{itemize}

However, all parameters of the convecting gas also depend on its pressure. The aim of the vacuum setup is to eliminate natural convection, knowing that the better the vacuum, the less convecting air and the less natural convection is present. The effort necessary to reach a given level of vacuum growing steeply with the level of vacuum, it would be very useful to be able to determine which level of vacuum would truly be necessary for our setup.\\

After some research for specific studies, I have found a graph shown in figure \ref{convection} \cite{patent} correlating the pressure of the air to the heat loss through convection (gas loss). From this graph we see that the heat loss by convection decreases linearly with pressure in log-log scale when the pressure of the air is below $5\cdot10^{-3}$ mbar.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7  \textwidth]{convect_pressure.jpg}
\caption{Correlation between heat loss by convection (gas loss) and pressure of the gas}
\label{convection}
\end{center}
\end{figure}

$5\cdot10^{-3}$  mbar having already been reached by the setup, this graph shows that if we reduce tenfold the pressure in the vessel, the convection will also reduce tenfold. These findings look very encouraging for our setup and show that the effort to obtain lower pressure will  effectively reduce convection.

\subsection{Thermal calculations for inner support plate} 

Inside of the vacuum vessel, all component are supported by a cooled circular plate. This plate needs to be supported in some way inside the vessel, without being heated by the outside by conduction through the vessel and its own support system. The support system devised hence needs to have a high thermal resistivity to isolate the plate thermally as much as possible from the outside. Two solutions shown in figure \ref{2supports} were proposed. The first solution was to use two stainless steel tubes placed concentrically to support the plate and have effectively a long traveling distance that heat from the outside would have to cross. The second solution was to use small cylinders made out of a very low thermal conductivity polymer that is very suited for vacuum applications, PEEK (Polyether Ether Ketone). A choice had to be made between both solutions. \\

\begin{figure}[H]
\begin{center}
\includegraphics[width= 0.7  \textwidth]{therm_inside}
\caption{Representation of both solutions for the support plate}
\label{2supports}
\end{center}
\end{figure}

To determine which solution to choose I have made detailed study calculating the length of the outer stainless steel tube compared to the length of the PEEK foot to achieve the same thermal resistivity. These length ratios are calculated for a range of diameters of the inner stainless tube and PEEK foot. The results show that the stainless steel solution has to be between 100 and 800 times longer than the PEEK feet to obtain the same thermal resistivity for the same position of the support plate for reasonable dimensions of both PEEK foot and steel tubes. Based on these results the PEEK solution was chosen.\\

The next step was to dimension the PEEK feet. The main concern is to avoid the support plate to be heated by the outside through its support. To dimension the PEEK feet, I made finite elements calculations. 

My first attempt shown in figure \ref{20x20temp} was made with 3 PEEK feet, 20 mm in diameter and 20 mm high. The top of the feet are kept at -20\textcelsius{} which simulates the cooled support plate. The feet are placed on a 20mm thick aluminum plate which represents the bottom on the vacuum vessel and is subject to natural convection with ambient air from the bottom.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 1  \textwidth]{20x20therm}
\caption{Finite element calculation with 20 mm diameter, 20mm high peek feet, -20\textcelsius{} on top}
\label{20x20temp}
\end{center}
\end{figure}

What we can observe here is that the aluminum vessel keeps a very homogeneous temperature of 18.6\textcelsius{}. The PEEK feet present a temperature gradient between the -20\textcelsius{} imposed at their top and the 18.6\textcelsius{} of the bottom plate. However, the region at -20\textcelsius{} is rather small, considering that the boundary condition set at the top of the feet is an optimistic representation of the real situation where the plate might still locally be heated up. \\

To be on the safer side, I made a new simulation shown in figure \ref{15x20} where I reduced the PEEK feet diameter to 15 mm to reduce the heat exchange surface. All other setting are kept the same.

\begin{figure}[H]
\begin{center}
\includegraphics[width= 1  \textwidth]{15x20temp}
\caption{Finite element calculation with 15 mm diameter, 20mm high PEEK feet, -20\textcelsius{} on top}
\label{15x20}
\end{center}
\end{figure}

We see here that the temperature of the aluminum bottom plate has increased to 19.3\textcelsius{}. Moreover, the region in the PEEK feet that  remains at  -20\textcelsius{} is slightly bigger. These dimensions are hence a safer choice. For the real application, based on these results I would recommend 15 mm diameter and 20 mm or more height.\\

In the eventuality that the setup would be used at lower temperatures, I have also tested situations were the support plate would be cooled to -30\textcelsius{} (figure \ref{m30}) and -40\textcelsius{} (figure \ref{m40}).

\begin{figure}[H]
\begin{center}
\includegraphics[width= 1  \textwidth]{m30temp}
\caption{Finite element calculation with 15 mm diameter, 20mm high PEEK feet, -30\textcelsius{} on top}
\label{m30}
\end{center}
\end{figure}

\begin{figure}[H]
\begin{center}
\includegraphics[width= 1  \textwidth]{m40temp}
\caption{Finite element calculation with 15 mm diameter, 20mm high PEEK feet, -40\textcelsius{} on top}
\label{m40}
\end{center}
\end{figure}

In both cases we see that the aluminum vessel remains at about 19\textcelsius{}. The temperature gradients remain relatively similar to the case where the temperature is set to -20\textcelsius{}. We can conclude that the behavior will not radically change should we cool the support plate to lower temperatures.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Work on the deformation measurement setup and software}
\subsection{Expected reconstruction precision}

The pattern recognition and surface reconstruction software that already exists and is described in section \ref{patternreco}. Its precision and behavior depending on certain settings needed to be determined. \\
In order to simulate certain scenarios on the not-yet-existing setup, I have used an open source ray tracer program called POVRay \cite{pov} capable of simulating what image the camera would capture. In POVRay it is possible to program known deformations on the reflective surface that will be measured.\\
The first step was to test the behavior and limits of the program. The aim was to determine the influence of the various parameters of the setup on the reconstruction and overall precision of the setup:
\begin{itemize}
\item{the focal length of the camera's lens}
\item{the angle at which the camera and dot grid are placed from the absolute vertical position, see figure \ref{viewangle} }
\item{the distance between the object and the camera/dot grid}
\item{the spacing between the dots on the dot grid }
\end{itemize}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.55 \textwidth]{viewangle}
\caption{Viewing angle of the camera and dot grid}
\label{viewangle}
\end{center}
\end{figure}

In order to compare all the scenarios that are tested, the same deformation is programmed in POVRay  and is of the form:
$y=ax^2+az^2$ shown on figure \ref{defobow}.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.6 \textwidth]{defo_bow2}
\caption{Simulated deformation}
\label{defobow}
\end{center}
\end{figure}



\subsubsection{Optimization of the setup}\label{optim}

\textbf{Camera and dot grid angle}

One determining parameter in the setup is the viewing angle of both the camera and the dot grid shown in figure \ref{viewangle}. Ideally, both should be placed precisely above the measured reflective surface, for practical reasons that is not possible to achieve. Both objects have to be placed with a certain angle from the absolute vertical position.\\

However, by doing so, the reflected pattern and captured image are slightly distorted. This could be a serious source of error in our measurement if not corrected for the reconstruction program. To determine the influence of the viewing angle on the reconstructed deformation, I have simulated different viewing angles and compared the bowing and the location of the minimum of a given slice of the result surface (parabola passing through the center of the surface) relative to the smallest possible angle. The results are shown in figures \ref{anglebow} and \ref{anglecenter}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{anglebowing-1}
\caption{Relative error on bowing in function of the viewing angle}
\label{anglebow}
\end{center}
\end{figure}

We can see by these first results that the dependency between the viewing angle and error on the bowing relative to an angle of 1 degree is not entirely regular. We can mainly observe that past a angle of about 8 degrees, the relative error on the bowing is of the order of a few percent. From these results we see that in the interest of achieving a precision of less that a few percent, the viewing angle should be kept at a bare minimum and/or the viewing angle should be taken and corrected accordingly before processing.\\

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{angle_center}
\caption{Relative error on center of surface in function of the viewing angle}
\label{anglecenter}
\end{center}
\end{figure}

Concerning the position of the center of the surface, the behavior is rather erratic. What is interesting to see here is that the relative error on the position of the center is only of the order of a few \textperthousand. From that aspect, the viewing angle is of little importance.\\

\textbf{Dot spacing}\\

Another parameter that needs determining is the spacing between the dots on the dot grid. Intuitively, if the spacing is small we have more points for the surface reconstruction. However, a large number of points costs more time to process. Moreover, should the surface deform in such a way that the spacing between the dots becomes smaller, the dots should not touch or merge for the image to be processable. 
The first spacing that was considered was of 1 cm. To see the influence of changing the dot spacing we yet again compare the bowing of a slice of the reconstructed surface. The variation in bowing is plotted, relative to the 1 cm reference spacing and is shown in figure \ref{dotspacing}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{dotsbowing}
\caption{Relative difference on bowing as a function of the dot spacing}
\label{dotspacing}
\end{center}
\end{figure}


The changing of the dot spacing, does not have a very predictable effect on the results. Indeed, is is very dependent on the deformation of the surface. It is difficult to draw any solid conclusions from this test except that changing slightly the spacing can result in variations of several \% in the results. 


\subsubsection{Systematic studies}\label{syststud}

As mentioned in section \ref{patternreco}, certain parameters of the setup have to be known and given to the reconstruction program in order to calculate the vertical displacement of the dots. However, these parameters need to be measured, which can only be done with a certain precision. Any error in the parameters will generate errors in the final reconstruction. Systematic studies were performed to determine by how much a given error on the parameters generates an error in the reconstruction. The two parameters tested are the focal length of the camera's lens and the distance between the camera/dot grid and the measured surface.\\

\textbf{Focal length}\label{focus}\\

To determine the influence of the error on the focal length of the lens on the reconstruction, we simulate image captures with a known focal length. Then, these images are processed by the reconstruction program with a given error on the focal length. Finally, the reconstructed surface is fitted and the bowing of a given slice of the surface is compared for various errors on either the focal length.The relative error on the fitted bowing in function of the error as a function of the focal length is shown in figure \ref{focalbow}.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{focal_bowing}
\caption{Relative error on fitted bowing as a function of the error on the focal length of the camera's lens}
\label{focalbow}
\end{center}
\end{figure}

We observe that the dependency between the error on the focal length and the error on the bowing is linear. However, for a not unreasonable error of 1mm, which is the precision on the focal length determination by the camera, the relative error on the bowing is already of the order of 2\%. These results tell us that determining with good precision the focal length of the camera's lens will be of sizable importance.\\
 

\textbf{Distance between measured surface and camera/dot grid}\\

To determine the influence of the error on the distance between the surface and the camera/dot grid, we follow the same method as in section \ref{focus}
The relative error on the fitted bowing in function of the error on the distance is shown in figure \ref{distbow}.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{distance_bowing}
\caption{Relative error on fitted bowing in function of the error on the distance between the camera and the sensor}
\label{distbow}
\end{center}
\end{figure}

What we can observe here is a linear dependency between the error in distance and the relative error on the bowing. However, the relative error on the bowing is of only 0.24\% for a sizable error of 6mm. This tells us that with a reasonable precision on the positioning of both the camera and the dot grid, only very little error is to be expected.\\

\subsection{Test setups}
\subsubsection{Proof of principle setup} 
After having simulated the setup with the ray tracer program, the next step was to make real pictures with a first very simple mockup of our setup. The aim here is to see first hand what kind of practical problems we will encounter and to test the reconstruction program on real pictures of both reflections off a mirror and off a silicon detector. This test is also a means of testing which camera settings (focal length, number of pixels, exposure time, aperture...) will be necessary for the final setup. The camera used here (Canon EOS 550D) is the same as the one that will be used in the final setup, the lens however is not identical.\\

The test setup shown in figure  \ref{tripods} is obtained by hanging an aluminum plate with the pattern of dots drilled in it and illuminated from the back with an office lamp. The colored reference dot in the middle of the grid is created by illuminating the hole in the middle with a small blue LED.  This first part is attached on a first tripod. On a second tripod we place the camera, controlled remotely by a computer. Either the mirror or the silicon detector are placed across from the two tripods at distance of 1.8 m which is very similar to the one in the final setup. 

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.6 \textwidth]{tripods.jpg}
\caption{First simple mockup of the optical setup}
\label{tripods}
\end{center}
\end{figure}

The first pictures taken were reflections off a mirror. One of the pictures taken is shown in figure \ref{mirror}. We can see off this picture the dot grid and the blue dot very distinctly. For this picture the settings of the camera were the following:
\begin{itemize}
\item {focal length : 70 mm}
\item{exposure time : 2.5 s}
\item{aperture : F25}
\end{itemize}


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.65 \textwidth]{mirror.jpg}
\caption{Picture of the reflection off a mirror, taken with the test setup}
\label{mirror}
\end{center}
\end{figure}


We now try to take a picture of the reflection off the current silicon detector modules described in chapter \ref{tracker}. The silicon detector used is shown in figure \ref{silicon_light}. On this picture, the reflection of the dot grid is also visible.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.4 \textwidth]{silicon_light.jpg}
\caption{The silicon detector used in the test setup and the reflected dot grid}
\label{silicon_light}
\end{center}
\end{figure}

In this picture, although the ambient light is still switched on, we can already see a diffraction pattern on the reflected dot grid. The challenge later on will be the dot finding part of the reconstruction program on these less than perfect pictures. The next pictures are taken with the ambient lights off. The picture shown in figure \ref{silicon1} is taken with the same settings as with the mirror but cropped.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.6 \textwidth]{silicon25F25.jpg}
\caption{Reflection off the silicon detector 2.5 s exposure time, F25 aperture, cropped}
\label{silicon1}
\end{center}
\end{figure}

On this image, the diffraction pattern is very visible. Not only has the global color of the dots shifted to purple but several intermediate dots appear. In an attempt to render less visible these phantom dots, we tryed a shorter exposure time. The resulting image is shown in figure \ref{silicon2}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.6 \textwidth]{silicon1F25.jpg}
\caption{Reflection off the silicon detector 1 s exposure time, F25 aperture, cropped}
\label{silicon2}
\end{center}
\end{figure}

With the shorter exposure time, the so called ''phantom'' dots are far less visible while the real dots are still nicely visible. This image will be much easier to process later on for we have less risk of considering diffractive dots as real dots. \\

I have then tried to find the correct settings such that the reconstruction program finds all the points. the settings to determine were the 3 ADC greyscale thresholds, the red/cyan threshold for the central point, the size of the margin around the image with no dots and the estimation of the average spacing necessary for indexing.
The main difficulty was that changing one parameter influenced on the setting of the other parameters. It is mainly an iterative process to reach the appropriate set of settings. For further use, the dot finding and indexing part of the reconstruction program should be rendered more user friendly to determine the appropriate settings. Once the correct settings were found on two copies of the same image I have tried to run the program when scaling one of the images, simulating an actual deformation. The resulting reconstruction is shown in figures \ref{scaling_surf} and \ref{scaling_bow}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{scaling_surf}
\caption{Reconstruction of the deformation simulated by scaling one image }
\label{scaling_surf}
\end{center}
\end{figure}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{scaling_bow}
\caption{Fit of one slice of the deformation surface }
\label{scaling_bow}
\end{center}
\end{figure}

From these two plots we can see that the reconstruction is complete with the exception of a few points on the edges which have been lost and create the local vertical edges. The deformation is a smooth surface which is to be expected since the scaling of the input image is uniform. Apart from the bowing, the reconstruction produces a tilt of the surface. This tilt is accountable by the fact that the scaling of the input image displaces slightly the center dot which is interpreted as a tilt.


\subsubsection{Mock setup and calibration device}

After having tested the principle of the measurement with the rather primitive test setup, it was time to build a more stable and permanent mock setup made out of aluminum profiles. This setup would then be used to test a new component of the final setup to be built, the calibration device.\\

The calibration device will be used as reference deformation measurement in order to account for systematic offsets in later measurements. Its basic principle is that one can impose on an stainless steel sheet of 1.5 mm thickness a given deformation by means of a micrometer screw. The calibration setup is shown on figure \ref{calib}.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{calibration}
\caption{Picture of the calibration device}
\label{calib}
\end{center}
\end{figure}

The optical setup will be used to measure the deformation of the stainless steel sheet imposed by the micrometer screw. The possible discrepancy between the amplitude of the reconstructed deformation and the value set on the micrometer screw screw is taken as a calibration coefficient for later measurements.
The rest of the test setup in aluminum profiles is shown on figure \ref{mocksetup}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.4 \textwidth]{mocksetup}
\caption{Picture of the mock setup}
\label{mocksetup}
\end{center}
\end{figure}

On this mock setup both dot grid and camera are orientable with a 5 degrees and can be slid along the horizontal profile to change the viewing angle.\\

\textbf{First pictures taken}\\

First measurement pictures were taken with the mock setup. A first picture was taken with no displacement on the micrometer screw. The second picture was taken with the micrometer screw set at a displacement of 200 $\mu$m. Both pictures placed next to each other are shown in figure \ref{firstpic}.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.6 \textwidth]{2halves200mu2}
\caption{First measurement pictures compared}
\label{firstpic}
\end{center}
\end{figure}

We can see of figure \ref{firstpic} that there is a clear difference between the reference image and the second image. The deformation amplitude in the second is in fact smaller than the 200 $\mu$m imposed by the micrometer screw because the region covered by the dot grid is much smaller that the supported region of the calibration device. Considering this, these results are very encouraging. These first two pictures were also processed by the reconstruction program which completed its analysis shown in figure \ref{reco200mu}. The setting of the parameters in order to have a complete and satisfactory reconstruction required a small amount of trials, which is also very encouraging.

 \begin{figure}[H]
\begin{center}
\includegraphics[width=0.6 \textwidth]{200msurfacebis}
\caption{Reconstruction of the deformation with 200 $\mu$m on the micrometer screw}
\label{reco200mu}
\end{center}
\end{figure}

In order to calibrate the setup with the calibration device, a bigger dot grid will be needed. In order to have the full displacement of the micrometer screw visible on the images captured, at least one dot of the dot grid should reflect off a part of the surface that has zero displacement.


\subsubsection{Final setup}

The final setup will need to fulfill several requirements to guarantee consistency and precision in the measurements. Firstly, the inside of the setup needs to be entirely dark to ensure that only the reflected dots are visible to the camera. Secondly, the setup has to be absolutely stable. This is necessary because the first picture will be taken with the to be measured object at a reference temperature. The second picture, however, will potentially be taken several hours later because the object has to be cooled or heated. During this cooling/heating time, the setup must not deform in any way or these deformations will be interpreted as a deformation of the object under study. Thirdly, because of the cooling process, the air inside the setup has to be dried to avoid condensation in the case one cools below the dew point. And finally, the setup has to be compatible for either the smaller modules for CMS which are of the order of $10 \times 10 \;\mathrm{cm}^2$ of and the larger structures for ATLAS that are of the order of  $40 \times 65 \;\mathrm{cm}^2$. To guarantee this compatibility, the dot grid has to be made large enough to cover the ATLAS modules, the colored center dot has to be movable (see section \ref{optim}, the camera has also to be movable to match the position of the colored dot and both camera and dot grid have to be orientable so that they both point to the center of the measured module.\\

To respect those criteria, the final setup shown without its side walls in figure \ref{final1} will be composed of a massive granite table on which the object under study will be placed. Around this granite table, a completely closable aluminum profile enclosure will be built. On the top of the enclosure, the camera and dot grid will be attached on orientable profiles such that their angle from the horizontal position will be adjustable along with their distance from the projected center of the measured module.

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7 \textwidth]{Messstand1}
\caption{3D open view of the final setup}
\label{final1}
\end{center}
\end{figure}


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\section{Acknowledgments}

I would first like to thank my supervisor Andreas Mussgiller for giving me the opportunity to work with the CMS group. I would also like to thank him for all the time he spent explaining to me all I needed to know about CMS and the tracker upgrade, for his patience and for being of excellent company in general. Thanks also for helping me in the writing of this report. I have learned a lot and have enjoyed my work. \\

I would also like to thank Carsten Muhl for helping me with my projects, for introducing me to the design and simulation program I-DEAS and for being a great fellow engineer in this crowd of physicists. Thanks to Jan Olzem for his much needed help with the reconstruction program he made and I used. I would also like to thank Holger Maser and Adam Zuber for building the setup so efficiently and being very forgiving for my drawing mistakes.\\

Thanks a lot to Olaf Behnke, Doris Eckstein and Andrea Schrader for organizing the Summer Student Program and giving me the opportunity to spend these awesome two months in DESY and Hamburg.\\

To all the members of the CMS group I have met, thanks for their friendly company and giving me an insight into the DESY CMS group.\\

Finally, I would like to thank specially Constanze, Phill, Thomas, Louis, Christian, Oskar, Nastya, Macha, Katya, Benni, Sarah, Artur, Matthias and Yunfan for making these two months such a great experience. Thanks to you all, I have had lots of fun with no interruption. We have explored Hamburg, the North and Baltic seas coasts and have spent very cool cooking, movie, poker, skat and YouTube evenings together.

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\bibitem{cms_site}CMS internet site : http://cms.web.cern.ch/cms/Detector/index.html

\bibitem{Pitzl_talk} {\em D.Pitzl}, Detectors for Particle Physics, DESY summerstudents lecture, DESY, Hamburg, 1.8.2011


\bibitem{upgrade_andreas}{\em Andreas Mussgiller}, Hardware and Upgrade activities of the DESY CMS Group,Presentation for summerstudents, DESY, Hamburg,  24.9.2011

\bibitem{tdr_tracker} CMS, The Tracker Project, Technical Design Report, CERN, Geneva, 15.4.1998

\bibitem{PGS} Panasonic site for PGS material : http://www.panasonic.com/industrial/electronic-components/protection/heat-sinking-material.aspx

\bibitem{jan_defo} {\em Jan Olzem}, Optical deformation measurements, setup plans and software, Presentation, DESY, Hamburg  

\bibitem{pov} Persistance Of Vision ray tracer : http://www.povray.org/

\bibitem{patent} {\em D.Bills, M.Dale}, Methods of pressure measurement, US patent no: US 6,227,056 B1, 8.5.2001



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