Offline alignment

Tools

The positions and orientations of the silicon detectors in the modules were measured using an optical alignment machine (Wenzel LH1210). The modules were mounted on a teststand (see figure) which presents the same interface to the module as the wheel infrastructure in the HERMES experiment does. The small, square, green faces in this figure are machined with precision to be in one plane, on which the modules are mounted using screws and precision dowels (large green arrows). The coordinate system of the measurement machine has its xy-plane coincide with the plane through these squares. The x-axis is parallel to the front of the teststand, the y-axis in the plane through the contact faces, pointing in what will be the direction of the beam. The z-axis is perpendicular to this plane, pointing upwards. (Note: in the drawing the negative z-axis is indicated. The origin of the coordinate system is in the symmetry plane of the teststand. The silicon detectors are in the empty centre of the testframe. The flat face of the detector and both vertical edges can be viewed by the alignment machine from the outside. The uncertainties in the measurements taken with this machine are about 5 µm

Alignment markers

The silicon detectors (see figure) have two markers (crosses A and B) near the base of the trapezium. Near the narrower tip two very small, square probepoints are used for the alignment. The line CD is the centre line of the silicon, determined using the measured points and the drawings of the silicon masks, obtained from the supplier. These features are indicated in the figure (not to scale). The position of the detector is determined by the position of point C, halfway between the markers A and B. The orientation of the detector is described by three angles α, β and γ. The angle α is the angle between the projection of the vector AB on the xz-plane and the x-axis. The angle β is the angle between the projection of the vector AB on the xy-plane and the x-axis. The angle γ, finally, is the angle between the projection of the vector CD on the yz-plane and the z-axis.

The tables show that the uncertainties in the positions are about 0.05 mm, somewhat smaller for the detector at z = 45 cm, slightly larger for that at z = 50 cm. This difference is caused by the construction of the module which is produced as two halves, aligned in the same way, which are assembled to one module. The position of the module is, however, determined by the front half (indicated by the green arrows in the figure above). The error in the assembly is therefore present only in the second half (and is very small).

The uncertainty in the angle α is again determined by a mechanical alignment procedure, with a similar result: 0.05 mm on a 85 mm base is about 0.5 mrad. The angle β is determined by the mechanical alignment plus the variation in the thickness of insulation disks and two layers of glue. The result is therefore slightly worse (2.5 mrad). The angle γ, finally, is not very well defined. Two points only fix the position of the detector. They are on the edges .. mm below the crosses. The kapton which carries the connections of the strips to the electonics, pushes the base towards negative (the detector at z = 45 cm) or positive (the detector at z = 50 cm) y thereby causing a small negative (positive) offset, respectively.