Pre-Alignment: Beam spot correction and hit correlations

Large initial errors of sensor positions degrade the efficiency of track finding and lead to large biases in estimated track parameters. As discussed in the last section, especially the position of a tilted device under test is poorly known and poses two problems:

• To align the device under test with tracks, we need to have enough tracks with hits on the device under test. However, the track finder is hampered by the badly known position of the device under test.

• A device under test may be small and noisy compared to the Mimosa26 reference sensors. In order to add the right hit on the device under test in the track finder, we need to know its position well.

The solution to these problems is a robust pre-alignment of thexandyposition of sensors relative to the beam direction. At first, we compute the correction of thexandyposition of the first sensor based on the position of the beam spot on its sensitive area. In a second step, thexandypositions of all other sensors are corrected using hit correlations between sensors.

The beam spot correction

For a telescope that is well positioned in the beam, the center of the beam spot is visible as a maximum in the density of hits on the localu−vplane of the sensor. In Fig. 4.10, we show a map of the hit density of

a Mimosa26 plane in a test beam at DESY computed from100k events in a run with3.75GeV electrons.

Around the center of the beam spot, the hit density in theu−vplane can be modeled by a2DGaussian probability density. Here, the variablesu_b,v_b are the local intersection coordinates of the beam axis on the sensor plane andσ_b,u andσ_b,v are the sizes of the beam spot andN is a normalization factor. The fitted size of the beam spot is7±1mm inu and10±1mm in thev direction. The central area of the beam spot is 7×10mm²while the active area of the Mimosa26 sensor is10×20mm². The positioning of the beam spot on the active sensor area is challenging but feasible by a careful positioning of the telescope support table relative to the particle beam.

We can use the fitted values forub andvb to correct the initialxandypositions of the sensor relative to the beam axis. In the initial geometry, the estimated beam axis intersection is at

~

while the global coordinates of this intersection point are

~r_b =

Here~r0 andR0 denote the initial sensor shift and rotation matrix. In other words, the real position of the sensor center is shifted from the beam axis by a distance ofxb andyb in global coordinates. In order to align the beam axis with the telescopezaxis, we have to shift the sensor center by ∆x =x_b and∆y =y_baway from the telescopezaxis. The precision of the sensor shifts∆xand∆yis typically in the order of∼100µm. The correction of the sensor position relative to the beam axis is an important first step to suppress shearing in the initial telescope geometry.

Alignment with beam constrained tracks

After the beam spot correction, we can assume that thexandyposition of the first sensor in the telescope is well controlled and will be fixed to provide a reference point in the remaining alignment steps. In order to correct thexandypositions of the other sensors in the telescope, we will present an extension of the hit correlation method presented in Behr [41]. The new method can be viewed as an alignment with beam constrained tracks which allows to correctly handle correlations between reference sensors with tilted devices under test.

A beam constrained track is a3D straight line passing through a hit at a reference sensor, typically the first sensor in the telescope, whose direction is given by the beam axis. The explicit introduction of beam constrained tracks allows to compute the intersections with all other sensors using the current telescope geometry data base. From these predicted intersections, the residuals in theuandvdirection

u in mm

Figure 4.10.: The number of hits on the first Mimosa26 sensor in the telescope. A2D Gaussian model is fitted to the local hit distribution to measure the offsetsu_b andv_bbetween the center of the active sensor area and the beam axis.

with all other hits in the same event are computed. A typical set of residual histograms between the first and the last Mimosa26 sensor is shown in Fig. 4.11. The residual histograms contain a flat side band from wrong hit-to-track pairings and a signal peak containing correct pairings. Without telescope misalignment, the residual peaks would be centered around zero for all sensors. This constraint is employed to compute alignment corrections for the sensor shifts∆xand∆yto center the peaks around zero. A robust truncated average is used to compute the center of residual peaksu0andv0. Bins in the side bands with a height below a user defined threshold are discarded in the truncated average. A typical threshold is>0.5times the height of the signal peak. Then, sensor alignment shifts∆xand∆ycan be computed in the same way as for the beam spot correction.

The alignment with beam constrained tracks has the advantage that it does not require the sensor to be large enough to contain the whole beam spot. This is very useful for sensors with a small active

residual u in mm

Figure 4.11.: Residuals in the localuandvdirection between beam constrained tracks defined at the first sensor in the telescope and hits at the last sensor in the telescope. The full width at half maximum of the residual peak is in the order of0.6mm. The position of the signal peaks can be centered around zero by shifting the center of the last sensor inx andy direction relative to the beam axis.

area as for example for test beams with DEPFET prototype sensors. Furthermore, the alignment with beam constrained tracks offers a way to test the synchronization between the Mimosa26 sensors and the devices under test. If there is no residual peak visible at the devices under test, the run is lost for studies with telescope tracks. That is why it is so important to compute the correlation plots as described here.

The above described methods for telescope pre-alignment are implemented in the DEPFETCorrelator processor. The required inputs are an LCIO run file with hits on all layers, a gear file and the file name of a geometry data base. The processor outputs a new or updated geometry data base with the given file name. After pre-alignment, thexandyshifts of all sensors relative to the beam axis should be known to an accuracy of∼100µm. This method suppresses telescope shearing and gives a good starting point for efficient track finding.