Our original analysis (c. 1998) of the XRCF Carbon-continuum SSD measurements only included the Phase E measurements (1000 s on each shell), and used approximate corrections for pileup, since accurate modeling was beyond our mental and computer-power capabilities of the time. The new analyses use two approaches: probabilistic and Monte Carlo (by Diab). The former method has been applied to the 4 phase-E measurements, plus 1 phase-C all-shell measurement (aperture position was about 1 mm off, so not useful), 4 phase-D measurements (results similar to phase E but with only about 1/4 the counts), and phase-D measurements for shells 1 and 3 using 500-um apertures instead of the standard 2-mm apertures. (There was a data collection failure for ssd_x with Shell 4.) There are additional sets of phase-D measurements using even smaller apertures, but these were not deemed to be worth the effort.
The probabilistic method is much faster than the Monte Carlo method for modeling 2-event pileup and deadtime (~10 seconds to run) but takes over an hour for 3-event pileup. I therefore iterated the 2-event modeling several times to get a nearly final result and then ran once or twice with 3-event modeling to obtain the final answer. The MC method takes less than 1 hour (?) to run and treats all orders of pileup at once. It does not, however, include iteration/convergence capabilities so we used the probablistic method to `de-pile' the SSD spectra and then confirmed those results with the MC method.
The final results are not very different from what we got in 1998--a percent or two here and there, somewhat more at very high energies where pileup is more significant. Ping Zhao will present a comparison of HRMA EA's derived from the new and old analysis results.
Diab has already outlined the modeling methodology (see pdf above).
The (slow) shaping
amplifier output pulse profile for a 2-us shaping time was previously
obtained from an oscilloscope trace with 0.1-us time intervals.
Note that the trace must be carefully smoothed to avoid problems
with spurious peak-finding.
|Twide||Slow amp pulse width = PUR inspection time interval||Number of modeled output pulser counts must match obs'd||19.5±0.5 us for ssd_x|
|Tfast||Fast discriminator output pulse width||Make model pulser/X-ray pileup match obs (espec. true pileup)||1.0±0.1 us|
|Tpeak||Time for shaping amp output pulse to reach maximum||Read from oscilloscope trace||4.0±0.1 us|
|PURlim||PUR (fast discriminator) threshold||Make model pulser/X-ray pileup match obs (espec. tail pileup)||Channel 256±4 (1280±20 eV) for ssd_x|
|MCB LLD||ADC lower level discrimanator||Lowest channel in acq*.pha file||Variable, usually around channel 58|
|MCB Tdead||ADC processing deadtime (after pulse max is found)||Ortec manual||1.5 us|
Parameters for ssd_x were determined from modeling the phase E data,
which had by far the best statistics. The parameters also did a good
job for the phase C and D ssd_x data (see plots). It was difficult
to determine the best parameters for ssd_5 data. In some cases
it appears that the shaping time was not the recorded value, but
the ssd_5 rates were so low that pileup was negligible and all
that matters is that the deadtime make the model match observation.
In fact, the standard pulser_out/pulser_in deadtime correction
method is completely adequate.
Same plots (+ssd5 from below) but including the rejected 2- and 3-event counts:
In the figure below, the top panel shows model output divided by input. If there were no pileup this would be a flat line equal to the the detector livetime. The bottom panel shows the same curves normalized to the pulser peak livetime, revealing the net pileup correction factors. The old (1998) correction factor for shell 1 is also shown; the other old correction curves are not shown to avoid clutter.
The old corrections were obtained using the pulser/X-ray pileup counts
to make a rate-dependent event redistribution function. As you can
see, it wasn't bad. (Also keep in mind that computers are ~100 times
faster now so the more accurate analysis done here would not
have been feasible in 1998, especially since many
runs were necessary to test and debug the code.)
The large differences between old and new below around
channel 300 (1500 eV) are because the old analysis could not account
for the PUR threshold, but this doesn't matter because results
below that energy aren't useful anyway because of uncertainties in
detector icing (i.e., QE).