\section{Assembly Monitoring}
\label{monitoring}
\subsection{RASAS system}
The precise positioning at the level of 10~\um of the spacer (with tube-layers already on it) on the
sphere holders is of crucial importance. Mis-positioning leads to layer-wise
difference in the Y-pitch and Z-pitch. 

To monitors the spacer position during the gluing procedure we developed the 
RASAS system. The RASAS towers are fixed to the granite table and accomodate 
a CCD en lense. Together with a mask embedded in the 'ears' on the spacer this
forms a (standard) RASNIK system.

To translate the RASNIK coordinates into our Global Coordinate System we have
to know the relative tranlation and rotation of the coordinate frames.
The quantities directly measures by RASNIK are the position ($X_R$, $Y_R$, $Z_R$) and angle ($A_R$) of the
mask with respect to the CCD-lens system.
% The RASAS towers accomodate the camera and lense, while the mask is housed in the ears of the outer xross plates. 

The optical axis points roughly into the
global X direction, RASNIK X and RASNIK Y point roughly in the global Z and Y direction respectively.
The rotation around the optical axis of the mask, $A_M$, has to be known with an accuracy such that $\sigma_{angle} arm = \sigma_{position}$. When we aim for a calibration error of 5~\um, with  the $arm$ to be the largest step size of 26mm, we obtain $\sigma_{angle} arm =5\mu m/26mm=200$ \urad.
Other rotations of the mask can be ignored; these effect the results only at the second order level. The construction of the RASAS towers and ears, guarantee that these rotations are comfortably small ($<$25mrad).
The precision on angle of the optical axis (CCD-lense) with respect to the global X axis in the global X-Y plane, $A_{XY}$, and X-Z plane, $A_{XZ}$, is set by
 possible movement in $X$ of the spacer of about 10~mm.
This leads to an accuracy of  $\sigma_{angle}$ = 5\um/10mm=0.5mrad for $A_{XY}$
and $A_{XZ}$.

The coordinate transformation can now be expressed in measurable quantities:
\begin{eqnarray}
 Z_G= X_R + Z_R A_{XY} +  Y_R A_M - X_offset \\
 Y_G= Y_R + Z_R A_{XZ} -  X_R A_M - Y_offset
\end{eqnarray}
where the suffix R and G represent the coordinate systems RASNIK and Global respectively.
Note that the CCD is treated as a point when the RASNIK coordinates are extracted. Therefore the CCD rotation ($A_{CCD}=A_R + A_M$) has not entered these equations. 

\subsubsection{Calibration Constants}
\paragraph{Pre-calibration CCD rotation}
The rotation of the RASAS CCDs $A_{CCD}$ with respect to a granite table are measured using the special precalibration tower. The RASAS precalibration tower is equipped with a mask of known rotation.
The RASAS- and precalibration tower is are put on the granite table such that the mask image is properly projected on the CCD. The angle is measured by RASNIK to a high statistical accuracy. However, we observed that small  movements of the towers lead to large fluctuations of the measured angle. These systematic effects are not completely understood and therefore we assign an uncertainty to the precalibration of 200~\urad corresponding to the size of these fluctuations.

\paragraph{The calibration of rotations}
The spacer is positioned in the central stacking position and the RASAS system is read out. It provides the RASNIK coordinates $X_R$, $Y_R$, $Z_R$ and rotation of the mask $A_R$, relative to the CCD en lense system.  Note that the rotation of the masks $A_M=A_{CCD} - A_R$ is already known to about 200~\urad, when we ignore the positioning error of the RASAS towers on the granite table.

The direction of the optical axis, represented by the angles $A_{XY}$ and $A_{XZ}$, are determined by moving the spacer (and thus the masks) in the RASNIK Z (Global X) direction.
The angles follow from the change in RASNIK readings as function of the movement in $X$ using:
\begin{eqnarray}
 X_R = A_{XZ} X \\
 Y_R = A_{XY} X 
\end{eqnarray}
 The uncertainty on $A_{XY}$ and $A_{XZ}$ is dominated by the uncertainty in the sphere tower orientation of about 0.5~mrad.

\paragraph{The calibration of off-sets} 
There is no direct way to calibrate the absolute off-sets of the RASNIK system.
For the assembly in general it is sufficient to check that all steps in $Y$ and $Z$ for the three stacking positions are reproduced within 5~\um. In this
 case the RASNIK readings in the central stacking position are used as off-set.

\paragraph{Consistency check}
We can position the spacer in all orientations, such that all four RASAS-masks are viewed once by the four RASAS towers. This provides information on the intercalibration of the mask angles.
In addition,  data obtained in all the stacking positions of the spacer contains information on the possible stacking block deviations  and provides information on the absolute calibration of the mask angles. 
We attempt to extract this information in a fit procedure using the RASAS readings.

In the free parameters in the fit procedure are:
\begin{itemize}
\item the mask angles (4 param.),
\item the $Y$ deviations of the layer one and three stacking blocks ( 8 param.)
\item the $Z$ deviations of these blocks at the reference side (4 param.)
\end{itemize}

The residuals, see Table~\ref{gfit}, amount only a few microns, 
consistent with the expected stacking reproduction errors. 
\begin{table}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,10)
\put(0,0){\mbox{\epsfysize=10cm\epsffile{gfit.ps}}}
\end{picture}
\end{center}
\label{gfit}
\caption{\sl Results of the Grand Fit}
\end{table}

\begin{table}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,10)
\put(0,0){\mbox{\epsfysize=10cm\epsffile{amask.ps}}}
\end{picture}
\end{center}
\label{amask}
\caption{\sl Results of the Grand Fit}
\end{table}

\begin{table}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,10)
\put(0,0){\mbox{\epsfysize=10cm\epsffile{block.ps}}}
\end{picture}
\end{center}
\label{block}
\caption{\sl Results of the Grand Fit}
\end{table}

 





The resulting mask angles are listed in Table~\ref{amask}. The mask angles, determined in the fitting procedure, are compared to the initial angles determined from the
relative CCD-MASK angles provided by the RASAS systems and the precalibration of
the CCD angles.
We observe deviations, consistent with the systematic uncertainties of 200~\urad.

The block deviations are displayed in Table~\ref{block}. These deviations are below 10~\um as expected from the CNC measurements desribed in Section ??.

\subsection{RASNIK systems on the spacer}
In this Section we decribe the system with all the components on the spacer, contarily to the RASAS system which has its basis on the grnaite table.

\subsubsection{In-Plane and Cross-Plate system}
The In-Plane system consists of four RASNIK systems and is described elsewhere~\cite{tdr}. This system will be used in the experiment, but it constitutes a usefull monitoring system during the assemly of the chambers as well.

The Cross-Plate system consists a RASNIK system running parallel with the cross-plate. For the production the outer cross-plates are equipped with these systems to monitor the gravitational sags.

After the assembly of the bare spacer these systems are calibrated by taking the average readings in the 'up' and 'down' orientation in the central stacking position.

\subsection{End-Plug Laser System}

\subsection{ Automated assembly manager}
To prevent mistakes and to automate the monitoring of the assembly procedure
we use an 'assembly manager' embedded in a computer-programme. 

The assembly manager presents the assembly step to be performed by the crew
in text and pictures. 
Before each step it checks whether it is allowed to perform the 
step based on
\begin{itemize}
\item temperature measurement of the environment, table and spacer,
\item vacuum of the tube-suckers,
\item pressure readings from the sagcompensation system. 
\end{itemize}
After each check
it checks te result of the relevant system, such as: 
\begin{itemize}
\item RASAS, In-Plane and Cross-Plate RASNIK readings,
\item Guido-Laser system
\end{itemize}
 During glue-curing it monitores the environment continuoully and generated warnings (emails) in case of attention is needed.
 
It also generates output for to evaluate the
 quality of chamber under construction.













