Appendix A: The RASNIK Alignment System

The Red Alignment System NIKhef (RASNIK) consists of a coded mask, a lens
and a video image sensor[RasnikPaper]. The mask, illuminated with (infra-red)
LEDs from behind,
is projected by the lens onto the image sensor. A daylight-blocking filter
is placed before the
image sensor.
If the lens is displaced in the direction perpendicular to the optical axis,
then the image on the sensor will be displaced in the same direction,
magnified with a factor (v+b)/v,
where v is the object distance and b the image distance.
If the lens is displaced along the axis, the image scale S will change following S = b/v.
Finally, if the mask rotates around the optical axis with respect to the sensor,
the image rotates accordingly. From the analysis of a RASNIK image, four parameters
can be deduced: two tranversal displacements, one displacement along
the optical axis, and the relative rotation between the mask and sensor
around the optical axis. The changes are relative: a common shift of three
components does not change the readout values. The changes can be expressed,
for instance, in terms of a mask displacent or a lens displacement.

A typical RASNIK image is shown in fig. ?, clearly displaying the chessboard pattern,
in which each 9th row and 9th column is carrying a digital code.
This code has the values (0,0) in the bottom left of the masks,
and increases linearely with the coded column and
row numbers into the direction of the top-right corner in the mask.
In this way the coarse position of the image, showing only a small part of a large mask,
can be identified.

The video signal of the sensor is digitised by means of a frame grabber in a pc.
After differentiating the image data, the contours of the chess fields appear as
an orthonormal grid pattern. From this, the 'fine' image position, image scale
and image rotation are obtained.
After detecting and decoding the 9th row and columns, the coarse image position
is obtained.

Due to the large summed length of chess field contour on an image (~ 100 mm,
in both directions),
a precision of 50 nm (RMS) is obtained in the two transversal directions in terms
of image position on the sensor, per image. The image scale is measured
with a resolution better than 5 x 10^^(-5) (RMS), and the resolution of the
image rotation is 20 micro-rad (RMS). When placed in air, the RASNIK performance is
limited by the gradients and fluctuations in the gradient of the air temperature.
The linearity of the system is exclusively determined by the precision of the mask.
For ATLAS, we applied low- cost 'contact copies' of mother-masks made in VRSI industry,
and their precision was guarantied to be better than 0.1 micro-m.
The range of a RASNIK system is determined only by the mask size, and can be
as large as 125 x 125 mm2. For the InPlane systems we applied mask segments of 20 x 20 mm2,
and for the projective systems masks of 50 x 50 mm2 were used.

A RASNIK system can be calibrated by placing the three components in a well known
relative position, while recording the readout values. After that, the deviation from
the initial alignment can be obtained from the difference between the actual readout
values and the calibration values.

Fig. ?  Typical RASNIK image with the chess sboard pattern and the coded row
        and columns. The light intensity of the pixels under the indicated line
        is plotted, together with its derivative.  The Gaussian peaks
        (positive and negative) determine the fine position of the image, as well as
        the image scale.


[RasnikPaper] The RASNIK alignment system. To be published in Nucl. Instr. & Meth.