Analysis 6 of GEM position resolution

Dean Karlen / February 9, 2001

This document summarizes the analysis of the GEM data taken January 8-10, 2001, in which the 2.5 mm strips were used as the readout structure, instead of the hexagons used in the previous studies. Significant cross talk is present in the data.
 

Index


 

GEM pad layout

The figure linked here shows the GEM strip layout and coordinate system used in the analysis. The strips are numbered from 1 to 8, according to the readout channel. The central strip is read out by both oscilloscopes (channels 4 and 5), to provide a common trigger.

GEM data

The data sets taken on January 8-10 were taken with P10 gas with Vdrift = 3475V, Vgem=3375, using the ALEPH preamplifier, and the xray tube set at 6 kV. The number of events analyzed is quite different for each run. For some runs, a large fraction of the triggers were not coincident between the scopes. The sampling rate was 250 MHz.

The 10 data runs are summarized below. The collimator location is indicated using the coordinate system described above. The first digit of the run number is the day of the month that the data was taken.

As an example, an event from run 903 is shown here. The far away strips have very small induced pulses. The signals are overwhelmed by cross talk and noise. Note that for this data, there was no attempt to reduce the cross talk in the ALEPH preamps, by using alternate channels, for example.

 
run number
x_coll (mm)
events
801
0.00
470
802
-0.25
360
803
-0.50
315
901
-0.75
251
902
-1.00
311
903
-1.25
314
904
-1.50
128
905
-1.75
92
907
-2.25
120
908
-2.50
179

GEM data analysis programs

The results shown below come from the gemanal program (version 1.0) located in the directory /home/karlen/gem. An associated paw kumac file, gems.kumac (note: new filename), is found in the same area.

Separation of direct and induced components of signals

As in the previous analyses, the direct charge component of a signal is deduced from the amplitude measured a fixed time after the peak (referred to as the "late" amplitude). In this analysis the delay is chosen to be 600 ns.

The figure linked here shows the mean ratio of the "late" to the peak amplitudes on strips 3,4, 5 and 6 as a function of the collimator position. The scaling factor for all pads is taken to be 0.71 for this data. (No direct measurements were made to set strip by strip values for this).

Gain variation

The gain of the system shows some variation over these runs, as can be seen in the figure linked here. The plots show the total charge collected by all strips, as deduced by the "late" amplitude and scaled by the factor from the previous section.

Pedestals

The data for each channel is corrected by using a pedestal defined by the average of measurements before the pulse (time bins 10-60).

Position analysis from direct charge sharing

Observed charge fraction in pad 1 - determination of cloud size
The figure linked here shows the observed charge fraction in strip 4/5, as a function of the x-coordinate of the collimator. The curves represent the expected charge fraction for the simple Gaussian model with 550 microns (solid line) and 500 and 600 microns (dashed lines) cloud sizes. Poor agreement is seen, at least partially due to the presence of cross talk. For example, when the collimator is directed at the centre of strip 4/5, the overshoots in the neighbouring channels (for example, in the event shown here) are included in the total charge with opposite sign compared to the charge in the central strip. As a result, the estimated total charge collected in all strips is actually LESS than the charge collected in the central strip, and so the observed charge fractions are greater than 1. No software correction for the cross talk has been implemented.
Determining position from charge fractions
It is evident from the previous section that cross talk will cause biases in the position determination from charge sharing if a simple Gaussian model is used. The inverse mapping of the cumulative 1D Gaussian (representing the charge fraction) to the x coordinate, has not yet been implemented, but is simple compared to the 2D problem that was implemented for the hexagonal pads.

To estimate the resolution that could be achieved (in the absence of cross talk), the standard deviations of the charge fractions are determined for each run, and are shown in the figure linked here. The standard deviations for the charge fraction in the central part of the strip is about 0.026 and for measurements near the edges is 0.043. The difference between these two is easy to understand. When the collimator is positioned on the edge of a strip, the observed charge fraction depends sensitively on the location of the centroid of the cloud and on the width of the cloud. The distributions of cloud centroid positions and widths therefore contribute to the standard deviation of the charge fractions. When the collimator is centred over the strip, the cloud centroid position and width distributions contribute much less to the standard deviation of the charge fractions.

In the region within 0.5 mm of edge of a strip (therefore 1mm for every 2.5 mm wide strip) the charge fraction changes by 0.32 for a 0.5 mm translation of a cloud centroid (for 550 micron width cloud). Inverting this give us:

Resolution in absence of cloud width and position fluctuations: 0.026 x 0.5 mm / 0.32 = 41 microns
Resolution in presence of cloud width and position fluctuations: 0.043 x 0.5 mm / 0.32 = 67 microns

Contribution to resolution from cloud width and position fluctuations: 53 microns (subtract the above two in quadrature)

Simulation studies show that the standard deviation of the distribution of cloud widths would be of order 10% or less.  The sensitivity to cloud width is proportional to the distance from the edge of the strip. Right at the edge of the strip, there is no sensitivity whatsoever. Since the charge fraction resolution figure does not show a strong dependence on the collimator position between x_col = 0 to x_col=-0.5, the variation in charge cloud sizes appears to not play a significant role in the overall resolution.

In summary, if one used charge sharing events within 0.5 mm of the strip edges, the position residual distribution would have a width of about 70 microns, where about 50 microns come from the scatter of cloud centroids and 40 microns come from factors that determine the intrinsic resolution of the system (electronics noise, finite statistics, etc.).

Position analysis from induced pulses

To determine the x-coordinate from induced pulses, the same approach can be used as for the hexagonal pad analysis. Since there is only one coordinate, the procedure is simplified.

The ratio of the peak amplitude of the induced pulse to the total charge of the event as a function of distance to the strip centre is shown in the figure linked here. There is surprisingly little scatter in the points. The gain for strip 2 is increased by 5% and the gain for strip 6 is reduced by 8% to bring the points into better agreement. The curve is the result of a fit to a 4th order polynomial.

The observed response function is likely affected by cross talk. Nevertheless, the position resolution from induced pulses can be estimated. In the case the x-ray collimator is centred over strip 4/5, the standard deviation of induced pulse fractions on pads 3 and 6 is about 0.0085. The slope of the response function around the point x=2.5 mm is 12 mm. The residual for position estimates from a single induced strip would therefore have a standard deviation of about 100 microns. Using both neighbouring strips for this case would give a residual width of about 70 microns. The use of second neighbour strips would only slightly improve the residual width, since the slope of the response function is about 3 times larger at distances of order 5 mm.

Comments on readout geometry (Feb 9, 2001)

It is interesting to note the differences in the induced pulse response function for 2.5 mm pitch strips and 2.5 mm pitch hexagons. For an ionization cloud 2.5 mm away from a strip, the amplitude of the induced pulse is about 14% of total collected pulse. The amplitude of the induced pulse in the hexagon geometry is about 3 times smaller for the same situation. This behaviour is not surprising, but the factor of three is an important consideration given the difficulty of reading out small signals in the design of a real TPC tracker.

More importantly, the slopes of the two induced pulse response functions are quite different for the current setup. For example, at 2.5 mm,  the slope of the response function is 12 mm for the strip geometry, compared to 19 mm for the hexagon geometry. The ratio of (intrinsic resolution in distance from the strip centre) to (resolution in distance to hexagon centre) is about 0.6.

Here is a specific example. With 8 bit linear readout, it will be difficult to achieve resolution of 0.01 on the induced pulse fractions. If that is achieved, the resolution of the position measurement using the induced pulse amplitude from a single neighbouring pad (whose centre is 2.5 mm away) would be 120 microns for a "strip" and 190 microns for a "hexagon".

In the TPC readout of tracks where the azimuthal coordinate is critical, these arguments suggest that short strips may be preferred to hexagons. Simulations are necessary to fully understand the tradeoffs, however.

Conclusion

The data taken in early January, 2001 with the strip geometry has significant cross talk, but indicates that position resolution below 100 microns is achievable for both methods, charge sharing and induced pulses. A complete analysis will be done once a larger data sample is recorded in which the cross talk problems are eliminated.
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