
To calibrate the CCD rotation RASAS system we constructed a calibration
 tower with similar dimensions as the RASAS towers, but equipped with a mask. 
The idea is to fix and/or determine the rotation of this mask once, after which
the tower can be used to calibrate the towers of the RASAS system.
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.

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.eps}}}
\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  1\um/52mm=20\urad. 

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 10 \um, which implies that the angle between mask and an imaginary optical axis can be ignored. 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. The Y readings of the 3D device and RASNIK are consistent over the full range as shown in Fig.~ref{rasnik3d}. 
\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(4,0){\mbox{\epsfysize=12cm\epsffile{rasnik3dlarge1.ps}}}
\end{picture}
\end{center}
\label{rasnik3d}
\caption{\sl top) Y-RASNIK versus Y-3D measurment device. bottom) The difference of RASNIK and the 3D device as function Y-3D.}
\end{figure}

Now, we can study the residual variation of the X reading of RASNIK, which are  related to the (small) rotation of the mask over the optical axis.
The variation of X amounts only a few micron over the full range of Y as  shown in Fig~\ref{towercal}.
\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,10)
\put(5,0){\mbox{\epsfysize=10cm\epsffile{towercal2.ps}}}
\end{picture}
\end{center}
\label{towercal}
\caption{\sl The variation in RASNIK X as function Y of the 3D device.
 The fitted line is used to determine the rotation of the mask. }
\end{figure}
Finally, from a line-fit we obtain a rotation of 45\urad +- 8\urad.  The measurement was repeated at 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 20\urad.   Additionally, when the calibration tower is used in situ, the flatness of the corresponding granite table adds to the uncertainties. 

