\section{Layer-pitch control}

 
   The relative position of two adjacent  two tubelayers is determined by
 the precise geometry of stacking blocks in the assembly jig and 
 the positioning of the spacer on these blocks during glueing. 
 This position is monitored by the RasAss towers 
 at each corner of the chamber.
 In addition the sag of the HV and RO cross-plates 
 affects the layer distance inbetween the stacking towers.
 This sag is controlled by the sag compensation system of the assembly jig 
 [ see Assembly.SagComp]
 and monitored by the XP-Rasniks. 
 
   The position and sag of the middle cross-plate
 is inferred from monitor data of the Inplane Rasnik system
 mounted on the spacer, but this only concerns the
 relative position of the tubes, not the wires.
 
   To achieve the desired muon momentum resolution the relative position
 of tube layers should be within 10 \mum rms in z and y at the HV and RO
 crossplates and with 100 \mum in between, compared to a fixed chamber
 geometry used in the reconstruction .

    For each new chamber the Rasnik systems are calibrated by placing 
  the bare spacer on the Assembly jigs in all the 6 positions and orientations
  that correspond to the glueing situation of the six tube layers.
    In addition, in each position, the spacer is moved by 
  approximately +-1 mm in the x- (wire-) direction 
  to check the relative orientation angles of the 
  chamber x-axis and the optical axes of the 4 RasAss towers. 
  These angles are used to correct the registrated RasAss y- and z-values
  to those corresponding to the nominal zero x-position of the cross-plates,
  since, with a total chamber length of 5m, even small temperature effects
  must be taken into account. 
  This procedure results in zero-values for all Rasnik systems 
  in all 6 glueing positions for this particular chamber.
  The monitor program registrates the deviation from these values when preparing
  for and during glueing of the spacer to a tube layer held in the jig.
 
 
   We first discuss the positioning monitoring results 
 at the end crossplates in z and y respectively , 
 and the comparison of these results with
 data for the three chambers which were scanned in the X-ray tomograph.
 
 
\section{  Layer Z-pitch }

 
  In fig[zshav] we plot for chambers BOL0 to BOL8 
 the RasAss deviations from the zero z-position at the end of a
 glue curing period of typically 16 hours.
 
 The points shown are the deviations seen by
 the reference-side RasAss-towers at the HV- and RO-ends respectively.
 Temperature effects can be neglected on the reference-side 
 since the distance from the stacking block fixing the z-position  
 to the mask of the rasnik system on the cross-plate is only 14cm.
 During curing the corresponding Rasnik values are found to be 
 stable within +- 2\mum (see also Fig.~\ref{mooi} ).
 In contrast the z-values at the non-reference side fluctuate
 by typically +-5?\mum as a consequence of small temperature ( +-0.1? deg)
 variations and the 2m length of the cross-plate. When corrected
 for, by using the temperature sensors mounted on the cross-plates,
 the z-positions at the two sides are found to be consistent within ?? \um.
 
 The data are plotted separately for each layer within a 
 multilayer at the HV- and RO- ends. In addition a histogram of 
 all deviations is shown. As can be seen, all positions are 
 well with the desired range, except for the first two chambers.
 For these chambers the 'spacer landing-gear' of the assembly
 jig (see [Assembly.LandingGear] ) was not yet installed, and consequently
 spacer-positioning was not as precise due to resistance of the
 glue in between the tubes.
 
 In Fig.~\ref{ztomras} we compare the z deviations  described above with those
 obtained from the analysis of the X-ray tomograph data for chambers
 BOL0,BOL2 and BOL3. In order to compare different multilayers,
 the Rasnik deviations are shifted such that the average deviation
 is zero for the HV- and RO-side respectively. This corresponds 
 to the combined fit applied to the tomograph data 
 for a scan through  each end of the chamber with the zero position taken at
 the middle between the two multilayers.
  The two sets of data ar nicely correlated with
 an rms of the difference of 6 \mum.
 
\section{  Layer Y-pitch }


  In fig[yshav.ps] we plot for chambers BOL0 to BOL8 
 the deviations from the nominal y-pitch (26.011mm)
 as expected from the Rasnik monitor data and 
 the CNC measurements of the layer-stacking blocks ( deviations ~ +4 \mum ).
 The Rasnik deviations are calculated by 
 taking the average deviation from the calibration values of 
 the East- and West-side RasAss-towers at the HV- and RO-ends respectively
 and adding 2/3 of the cross-plate sag as observed by the XP-Rasniks 
 ( assuming a parabolic sag of the cross-plate).

 The data are plotted separately for the inner(layer12) and outer(layer23)
 layers within each multilayer. Furthermore the data is shown at the start
 of the layer-glueing(Wet) and after the glue has cured (Dry).
 
   As can be seen the layer pitch of the inner layers is 
 of the order of ~20 \mum larger than nominal after the glue has cured,
 while it is much closer to nominal at the start of glueing.
 We attribute this to the shrinkage of the particular glue [XXX]
 that is used to glue the innermost layers to the spacer. 
 For this glue we observed in a simple test 
 a shrinkage of the order of a few permille??.
 This can explain the observed change in layer distance over time, 
 considering that the distance between the cross-plates and the
 tube-layer.

     A typical example of  RasAss and XPAss Y-values  versus time 
 are shown in Fig.~\ref{mooi} for the glueing of the first 4 layers
 of the BOL8 chamber.


  In contrast the layer pitch of the outer layers does not change
 during curing of the [YYY] glue used for these layers. In this
 case the distance between the tubes in the two layers is of the order
 of 70 \mum and no obervable shrinkage effect is expected. 
 For the outermost layers the average pitch deviation is
   +5 \mum  with an rms of 5 \mum.
 
 In fig[tomrasy.ps] we compare the Y-pitch deviations  described above with those
 obtained from the analysis of the X-ray tomograph data for chambers
 BOL0,BOL2 and BOL3. The two sets of data ar nicely correlated with
 an rms of the difference of 7 \mum.
 
 
 
\section{  Relative positioning at the middle cross-plate }

     In fig[hismid.ps] we plot the deviations from the nominal layer pitch
  in z and y, for all the Inplane Rasnik readings ( 4 per chamber and layer ).
  The results show that the relative position of the tubelayers in the
  middle of the chambers is centered  at the nominal value 
  with an rms of less than 10 \mum in both directions.
  This is well within the required precision in order to satisfy
  the criterium that the wires must be whithin 100\mum rms at the centre
  of the tubes, as the mechanical precision of the middle stacking blocks
  is also of order 10\mum ( see [AssJig.par] ).

 

  We conclude that the layer glueing  is controled within +-5 \mum in z and y
 and that  fixed geometry parameters for the BOL chambers  
 as presented in table  [Tomo.sitep]
 can be assumed with a negligible effect on the muon momentum resolution.
 
 




\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(0,0){\mbox{\epsfysize=14cm\epsffile{zshav.ps}}}
\end{picture}
\end{center}
\label{zshav}
\caption{\sl Z shift av }
\end{figure}

\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(0,0){\mbox{\epsfysize=14cm\epsffile{ztomras.ps}}}
\end{picture}
\end{center}
\label{ztomras}
\caption{\sl z tomo and ras }
\end{figure}

\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(0,0){\mbox{\epsfysize=14cm\epsffile{yshav.ps}}}
\end{picture}
\end{center}
\label{yshav}
\caption{\sl y shift av}
\end{figure}

\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(0,0){\mbox{\epsfysize=14cm\epsffile{mooi.ps}}}
\end{picture}
\end{center}
\label{mooi}
\caption{\sl mooi toch}
\end{figure}

\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(0,0){\mbox{\epsfysize=14cm\epsffile{tomrasy.ps}}}
\end{picture}
\end{center}
\label{tomrasy}
\caption{\sl tommie and ras y}
\end{figure}

\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(0,0){\mbox{\epsfysize=14cm\epsffile{hismid.ps}}}
\end{picture}
\end{center}
\label{hismid}
\caption{\sl his mid}
\end{figure}













