
 Possible rotation of the MASK or CCD over the optical axis leads to
 misinterpretation of the RASNIK readings.
To calibrate the RASAS system we constructed a calibration tower with similar dimensions as the RASAS towers, but equipped with a mask.
As we will see in Sec.~\ref{rasas} we need to know the orientation of the mask with an accuracy of about 200~\urad.
To determine the rotation of the MASK in the calibration tower we use a 3D measuring device with additional RASNIK tooling. This setup also allows to compare RASNIK and the 3D measurement device over a large range to the micron level. These results are also presented in this section.

The 3D measuring device is equipped with a platform holding a CCD en  lense, which together with the MASK in the calibration tower form a complete RASNIK system. The calibration tower is positioned on a granite table. The RASNIK response corresponding with a well controlled and known movement in Y of the 3D device allow to extract the MASK rotation. In fact, the (small) rotation follows directly from the ratio of horizontal and vertical changes of the RASNIK readings, dX/dY.
\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,10)
\put(-1,0){\mbox{\epsfysize=10cm\epsffile{rotcali.ps}}}
\end{picture}
\end{center}
\label{rotcali}
\caption{\sl Schematic view of the platform holding a CCD and lense. The platform can be mounted o n the 3D measuring device to calibrate the mask in calibration tower.}
\end{figure}
 
Both the 3D measuring device and RASNIK have measuring errors less than a micron. Thus, a measurement of the MASK rotation is intrinsically accurate to about  1um/52mm=20urad. However, the dominant error source is expected to originate from the flatness of the granite table and has to be investigated carefully.

\subsection{Results of the calibration}
The first measurements  are used to reposition the mask in the calibration tower, attempting to eliminate as good as possible all rotations of the mask. The mask is then fixed, actually glued, in the calibration tower. Here we present the results for the final setup.

Comparision RASNIK and 3D device. 
The 3D device is moved  vertical (Y) over a distance of almost 60mm. We observe that the change in the Z-reading of RASNIK, which represents the distance between MASK and CCD is constant within 10um, which implies that the angle between mask and an imiginary optical axis can be ignored. The small change in the X reading of RASNIK are  related to the rotation of the mask over the optical axis as discussed in the next paragraph. First we compare the Y reading of RASNIK to the Y reading of the 3D device, see Fig.  
The response of RASNIK and the 3D device are consistent  over the full range of Y.

Similar checks were performed for small ranges in Y. The results for steps of 5um, 10um and 20um are shown in Fig a b c respectively.  We conclude that RASNIK and the 3D device agree within the errors. 
The rotation of the MASK in the calibration tower
In the previous section we have shown that RASNIK and the 3D device can be trusted to below the micron level over small (5um) and large (50mm) range. The MASK rotation is now simply extracted from the ratio of the changes in RASNIK X and Y reading for a vertical movement of the 3D device. Figure ? shows the X reading versus the Y position. The only small change in X of a few microns represent a small rotation of the mask. From a line-fit we obtain a rotation of 45urad +- 8urad.  The measurement was repeated along several X positions, leading to consistent results.
The flatness of the granite table is expected to be the dominant error contribution. To study we repeat the measurements for different positions of the calibration tower on the table and find an error contribution of 20urad. Finally, we note that we are aware of the fact that the flatness of the table in the NIKHEF BOLROOM leads to additional uncertainties when the calibration tower is actually used in situ. However, the uncertainties are still comfortably small. 
Conclusions
We have determined the rotation of a calibration tower for the rass-ass system and in-plane system using a 3D device equipped with additional RASNIK tooling. The measurments allowed a comparison between RASNIK and the 3D device below the micron level. Consistent results were obtained over the full range from 5um to about 50mm.
For the MASK rotation in the calibration tower we find:





