A third analysis of 2D GEM position resolution

Dean Karlen / October 12, 2000

This document describes in detail the analysis of the GEM data taken from October 10 2000. The analysis follows the general approaches described in the second analysis. The goal of this analysis is to further understand the point resolution properties of the GEM setup with hexagonal pads. Three major differences compared to the previous data set are that the gas was changed from Ar-C02 to P10, the preamps were changed from HQV810 to ALEPH, and the HV settings were reduced. The P10 gas is slower and has larger diffusion. The ALEPH preamps are slower than the HQV810. As a result, the scope time scale was increased by a factor of 4. The data recorded here therefore correspond to 125 MHz sampling.
 

Index


 
 

GEM pad layout

The figure linked here shows the assumed GEM layout and coordinate system. Dimensions are in mm. The pads are numbered from 1 to 8, according to the readout channel. The central pad is read out by both oscilloscopes (channels 1 and 5), to provide a common trigger. The coordinates of a few points are shown in colour.

GEM data

The data sets taken on October 10 were taken with P10 gas with Vdrift = 3475V, Vgem=3375, using the ALEPH preamplifier, and the xray tube set at 6 kV. About 1000 events are taken for each run, except for the final two runs where only 500 events were recorded.

The data runs are summarized below. The collimator location is indicated using the coordinate system described above.
 
 
run number  x_coll (mm)  y_coll (mm) 
1001  0.  1.443 
1002  0.  1.543 
1003  0.  1.243 
1004  0.  1.043 
1005  0.  0.843 
1006  0.  0.643 
1007  0.  0.443 
1008  0.  0.043 

GEM data analysis programs

The results shown below come from the gemanal program (version 0.8) located in the directory /home/karlen/gem. An associated paw kumac file, gemanal.kumac, is found in the same area.

Gain variation

The gain of the system is constant over these runs only to within about 20%, as can be seen in the figure linked here. It appears that the GEM needs to be left at operating voltage for several hours before the gain stabilizes. The GEM will be left near operating voltages overnight in the future.

If the gain variation was due to changes in gas composition, then there might be a visible change in the drift velocity. This would, in turn, change the width of the induced pulses, since the full width of these pulses is just the drift time across the GEM induction gap. The FWHM of induced signals in pads 3,4,6, and 7 do show variations in the pulse width, but the variations are not consistent from one pad to another and therefore cannot be attributed to changes in drift velocity. Just as in the 2nd analysis, the variations are largest in pad 4.  This may indicate a problem in the electronics for channel 4 downstream of the preamps.

The GEM position analysis uses ratios of peak voltages, so the run-to-run gain variation should have a small effect, provided that pedestals are properly accounted for. However, if the pads do not have equal gains, then this could cause difficulties. A future data set should include calibration runs where the x-ray collimator is on runs where the x-ray collimator is placed roughly over the centre of each of the 7 pads under study.

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). There are, however, baseline shifts that remain after this correction.

The figure linked here shows data from a typical event, after pedestal correction, when the x-ray collimator was positioned over the coordinate (0.,1.243) (mm). Note that the baselines for the induced pulses in pads 4 and 6 are not zero, after the induced pulses. These baseline shifts unfortunately are not constant from one run to the next. The size of these shifts (of order 1 mV) correspond to the scale of changes in the induced signals that result when the x-ray pulse is moved 100 microns, so this effect is important to understand (and to reduce as much as possible in future data taking).

Some plots have been produced to characterize the baseline changes: The pulse shape is fit to a quadratic 600ns - 1800 ns after the induced pulse. The value of the fit at the point 1200 ns after the pulse defines the "baseline". The value of the baseline for the different runs are shown in the figure linked here. The baseline in pads 4 and 6 are roughly constant for ycol > 0.4 mm but reduces for ycol = 0.043. The baseline in pads 3 and 7 reduce smoothly as the collimator moves closer to the centre of pad 1. Unlike the 2nd analysis, the variation is consistent with a small amount of charge sharing: pads 4 and 7 behave similarly as do pads 3 and 6. There appears to be a constant positive offset of about 3 mV (overshoot from electronics?) that is canceled by varying degrees by some small direct charge component. As the x-ray collimator moves closer to the pad, more charge is deposited on the pad and the cancellation becomes larger.

The hypothesis that the baseline variation is due to charge sharing is confirmed by looking at how the baseline is related to the x coordinate of the individual events (determined through the charge sharing from pads 1,2, and 8). The figure linked here, shows the scatter plot of the baselines vs. x coordinate of the x-ray absorption, for pads 3 and 7 for run 1006. Events with x-rays closer to pad 3 have more negative baselines for that pad, and a less negative baselines for pad 7.

Unlike the previous analysis there is no evidence for crosstalk between channels. Whereas in the previous analysis, the baseline in pad 4 was strongly correlated to the amplitude of the pulse in pad 2, this data sample has the the baseline in pad 4 roughly constant for a wide range of y-collimator positions (and therefore a wide range of pulse amplitudes in pad 2). The most likely explanation is that the cross talk originated in the HQV810 preamplifier cards.

Note that because there are multiple changes compared to the previous data set, one cannot be certain that the cross talk seen in the 2nd analysis is not present here. Because of the change in the scope time division, the baseline measurement is taking place much later (1200 ns after the pulse) than in the 2nd analysis (300 ns after the pulse).

Separation of direct and induced components of signals

As in the 2nd analysis, the direct charge component of a signal is deduced from the amplitude measured a fixed time after the peak. In this analysis, the delay is chosen to be 1200 ns (compared with 300 ns in the 2nd analysis).

The figure linked here shows the mean ratio of the "late" to the peak amplitudes on pads 1,2, and 8 for different collimator positions. The error bars indicate the standard deviations of the ratio. (The mean and standard deviations are found by fitting each ratio distribution to a Gaussian). Since the standard deviation is less than 1%, the late amplitude is used instead of the peak amplitude for the charge fraction determination of both direct and mixed signals. The ratios differ for pads 1, 2, and 8, by only about 2%. In the 2nd analysis, the ratios differed by 6%, presumably due to slightly different time constants in the readout electronics.

Position analysis from direct charge sharing

Determination of charge
The data from t The data from these runs were used to map out the pad response function for direct charge collection. The charge collected by a pad is assumed to be proportional to the peak amplitude of the pulse for signals dominated by direct charge collection. Rather than use the peak amplitude (VP) directly, the "late" amplitude (AF) is used, and scaled to a new value (AN) corresponding to the peak amplitude,  as follows:
AN_pad = AF_pad / R_pad
where R_pad is the mean ratio of late to peak amplitudes, from the previous section. R_1 = 0.518, R_2 = 0.522, and R_8 = 0.527.
Observed charge fraction in pad 1 - determination of cloud size
The figure linked here shows the observed charge fraction in pad 1, as a function of the y-coordinate of the collimator. The solid curve shows the prediction of the model when sigma_x=0.53 mm. The dashed curves show the predictions for sigma_x = 0.50 and 0.56 mm. As expected, the cloud is broader than was observed in Ar-CO2, because the diffusion is larger.
Determining position from charge fractions
The figure linked here shows histograms of the x and y coordinate estimates, with respect to the x and y collimator position, for run 1001. Fitting the distributions to Gaussians, gives central values of (0.007 mm,-0.003 mm) and standard deviations of 52 and 57 microns in x and y, respectively. Just as seen in the 2nd analysis, the spread in measurements is about 50-60 microns, even though the diffusion is much larger in this gas. This indicates that diffusion does not contribute a significant amount to the spread in observed measurements.

A summary for the x and y measurements for the runs is shown in the figure linked here. The left plot shows the mean and standard deviation of the x estimates, and the right plot shows the mean and standard deviation of the y estimates (with respect to the y collimator position). The right plot shows two new effects. There is a small bias in the measurement that grows as the collimator moves away from the 3 pad vertex. The second effect is that the standard deviation of estimates grows as the collimator moves away from the 3 pad vertex.

The first effect is easily corrected by increasing the size of the cloud in the model, from 0.53 mm (as determined above) to 0.56 mm. It is not clear why the determination above does not result in a bias free y coordinate measurement. The summary of the x and y measurements with this new cloud size is shown in the figure linked here.

Contribution to measurement spread from cloud size variation
The growth in the standard deviation of y estimates remain after this correction. The additional contribution to the spread in the y coordinate measurements can be explained by coming from the variation in cloud sizes that arrive at the GEM pads. For x-rays absorbed on the line x=0, the size of the cloud does not affect the x coordinate determination. This is also the case for the y coordinate for x-ray absorbed directly over the 3-pad vertex. However, for the other locations, the estimated displacement from the 3-pad vertex in the y direction depends linearly on the input cloud size. X-rays that convert in different regions of the drift gap will have different cloud sizes, and thus the spread in the y coordinate estimates increase.

The observed increase in the spread is also consistent with this explanation. The variance of the measurements should be the sum of the variance due to non-diffusion effects and the variance due to the cloud size variation. The latter term scales as,

var(cloud size) = (fraction * displacement from vertex)**2

where "fraction" is the 1 standard deviation of the cloud widths divided by the mean cloud width. The variance of the y measurements is shown versus the square of the displacements from the vertex in the figure linked here, and is fit to a line. The fit result for "fraction" is sqrt(0.0070) = 0.084. In other words this model ascribes the additional spread due to cloud size variation, with the cloud size distribution having a mean of 560 microns and a standard deviation of about 50 microns.

Now to compare this to expectations: Since x-rays can be absorbed anywhere in the drift volume, the total drift length is between 8 and 12 mm. The cloud size scales like the square root of the total drift length. So cloud sizes would vary between 610 and 500, due to the different conversion points in the z direction. This is very similar to the standard deviation derived from the data above.

Summary of charge sharing results
The charge sharing method determination of coordinates works well for the data with slower and more diffuse gas. Unlike in the 2nd analysis, the spread in measurements has a contribution from the variation in the cloud sizes. This is more visible in this data because the charge sharing analysis is effective at larger distances from the vertex. Still, it is not understood why it was not seen whatsoever in the 2nd analysis.

Position analysis from induced pulses

To determine the coordinate from induced pulses, the same approach is used as in the 2nd analysis. The amplitude of the induced pulse is assumed to be proportional to the total charge of the event and a function of the distance from the cloud centroid to the pad centre. An algorithm combines the radial information from all pads that have an induced pulse to determine the x-ray location.

The data taken along the line (x=0) is used to characterize the induced response function. The ratio of the peak amplitude of the induced pulse to the total charge of the event is shown as a function of distance to the pad centre is shown in the figure linked here. The response function from the various pads do not perfectly line up. This is assumed to be due to unequal gains of the preamps, and so scaling factors (of order 5%) are applied to the observed pulse amplitudes (one for each each pad). This improves the agreement, as shown in the figure linked here, so that a universal pad response function can be used. This function defined by a 2nd order polynomial fit to the data, shown in the previous figure.

The summary of the x and y measurements are shown in the figure linked here. In the left plot, the vertical axis is the difference between the measured x location and the x location of the collimator (for this data xcol=0). The vertical bars represent the standard deviation as determined from fits of the data to Gaussians. The right figure is the same for the y coordinate measurement. There are some systematic biases in the y coordinate measurement of order 50 microns, which is not present for the x estimate. The 1 standard deviation spread in x measurements varies from 50 to 80 microns; for y measurements it is 90-100 microns. Unlike the charge sharing measurement, the spread in the y measurements does not depend strongly on the y collimator position.

Combination of charge sharing and induced measurements

The two position estimates are highly correlated, just as in the 2nd analysis. This can be understood to arise from the fact that the intrinsic resolution of the methods is similar in scale to the variation of cloud centroids due to factors such as spot size and diffusion.

Conclusion

The comparison of this analysis and the 2nd analysis shows that diffusion (and therefore primary electron statistics) does not limit the position resolution from the charge sharing measurements. The spread in the estimates is likely due to the x-ray spot size and perhaps the non-symmetric x-ray ionization pattern. The variation of the cloud sizes do contribute to the resolution of the charge sharing when the cloud centroid is sufficiently far from the 3-pad vertex.

The intrinsic position resolution of the GEM devices therefore is even better than the 50-60 microns quoted by the 2nd analysis.
 
 
 
 

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