Lower Threshold Study:
How to include threshold effects into DRM?

I) Purpose

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Derek Hullinger writes:

Hi guys,

Craig reminded me that the housekeeping file that tells us the threshold
voltage setting actually gives us 256 values: one for each sandwich!  I
think it's very possible that they may be set to different values.  If
that's the case, it seems to me that we need to give batdrmgen the
capability of using 256 different numbers.

I have two suggestions for doing this.  Which one we end up implementing
would depend on how different the sandwiches are from each other:

Method #1) If the "number of detectors that are above threshold vs. energy" curves
are very different from one sandwich to another, then we would need 256
such curves: one for each sandwich.  Each curve could be parameterized in
some way and be a function of threshold voltage.

We would take each curve and weight it according to the number of
detectors that are enabled in that sandwich (the housekeeping file also
gives us that information--it's just a wealth of information!), and then
add them together.  Then we would convolve the result with the response.

Method #2) If all of the sandwich "number of detectors that are above threshold
vs. energy" curves are very similar, then we only need one curve for the
entire array.  We would duplicate it 256 times and modify each one
according to the threshold setting for a particular sandwich, weight it
according to the number of enabled detectors in that sandwich, and then
add them together.  Then we would convolve the result with the response.

Does this sound like a good approach to you?

If it does, then we need to find out whether the different sandwiches have
very different threshold dependences, and if they do, we need 256 curves,
each a function of threshold voltage.  Otherwise, we just need 1 curve.

Another much more detail-intensive approach would be to do something
detector-by-detector, but I don't think we need to do that.

Derek

I) How different are the threshold distribution between different sandwiches?

For each Sandwich:

1. made a histogram of measured threshold for 128 detectors.
2. fitted with a Gaussian function.

Note: Because of little statistics (only 128 data for each sandwich), sometimes the histograms are poorly fitted with Gaussian functions.

Results:

1. The results of Gaussian fitting for 256 Sandwiches

The error bar represents the FWHM of the fitted Gaussian functions.

Array 0 and 14 were operated with a setup value of 20 mV, while the others were with 12 mV.

2. The distribution of the mean parameter for the fitted Gaussian functions.

Because Array 0 and 15 were operated with different setup value (20 mV),
the fitted results for these two arrays are excluded in the parameter distributions below.

3. The distribution of the FWHM for the fitted Gaussian functions.

Conclusions:

Even with the same setup values (12 mV for 14 arrays), the threshold distribuions are somewhat different. The mean values of fitted Gaussans ranges from 7 keV to 12 keV. This variation is comparable to the shift of ~5 keV for the change of setup value from 12 mV to 20 mV.

II) Reconstruction of the total threshold distribution over the entire CZT array

Conclusions: