The output of a analog pulse shaper typically shows an offset caused by the detector leakage current, the AC coupling and the non-zero area of the weighting function of the shaper, the pedestal or baseline. Additionally, because of noise pickup or variations in the detector leakage current, the baseline shows fluctuations or drifts as visible in figure 2.9.
In an typical analog spectroscopy amplifier a baseline restorer [52] is used to restore a zero baseline value in between events or to store the actual baseline value on a capacitor and subtract it from the shaper output.
The pedestal of the trapezoidal filter gives rise to an offset of the energy spectrum. In case of a noise trigger12 the output of the filter is non-zero and this event causes a peak at the low end of the energy spectrum, the zero energy or baseline peak. For each normal event the pedestal adds to the filter height. It is obvious that the pedestal has to be subtracted from the filter value for each event.
It is important to note the different meanings of offset and baseline. The actual offset of the signal is defined as the offset before the leading edge of the detector pulse, expressed either in ADC units or mV, which changes for each event especially at high rates when one event is sitting on the exponential decaying signal of the previous event. The baseline or pedestal is the offset the signal will decay to after an infinite amount of
12
time.
Equivalently, the offset of the trapezoidal shaper output is a measure of the signal baseline since the trapezoidal shaper output returns to its baseline value when applied to the exponential decaying signal after the leading edge. Therefore the trapezoidal filter baseline is a measure of the offset the preamplifier signal will finally decay to.
The energy informationE
is the difference between the trapezoidal filter value
T at
the end of the flat top and the baseline valueBin front of the trapezoidalE
=T B and
therefore the variance of the energy information is then not only determined by the vari- ance of the energy filter height but also by the variance of baseline, i.e.
tot q 2 T + 2 B . Clearly, if the variance of the baseline is larger than zero the energy resolution will be worsened [29]. In order to decrease the delta noise contribution to the baseline and re- duce the baseline variance to a tolerable level, another low-pass filter is applied to the baseline samples. For this the output of the trapezoidal filter, already being the result of a low-pass filter operation, is (re)sampled at a lower rate and send to the baseline filter. Ideally, the baseline should be a constant value and therefore the proper filter for base- line averaging should be of the low-pass type. Two types of low-pass filters have been evaluated in soft- and hardware for the determination of the trapezoidal filter baseline: a moving average filter (MA) and an exponential averaging (EA) filter13. Both filters
showed equivalent performance in software and are presented in section A.3.
Remembering that the origin of the pedestal of the trapezoidal filter lies in the detec- tor leakage current (source of step noise), the process of baseline restoration can also be understood as separation of the charge created in the -ray interaction from the leakage
current, whose step noise contribution is subtracted from the total signal, extracting the charge created in the interaction process.
Figure 2.9 demonstrates that the detector leakage current is not constant which sets an lower limit onto the cut-off frequency of the baseline filter. If the baseline would be a constant value plus a delta noise contribution, the optimal baseline filter would simply average all baseline samples. The need to track the changes in the detector leakage current, leads to a windowed operation where only a certain number of the most recent filter baselines is used for the averaging process.
To summarize, in a digital spectroscopy systems the baseline restorer determines the energy filter baseline value in between events and subtracts the baseline value from the filter value on an event-by-event basis, revealing the charge produced in the -ray
interaction process. In order to reduce the contribution from the baseline fluctuation to the line width, the baseline restorer averages multiple measurements of the baseline to determine the actual value of the trapezoidal filter baseline with higher precision.
The radiation-free time span is indicated by the absence of any trigger and the fact that the actual filter sample is below a user-defined threshold value. The trigger signal is generated by a filter with a much shorter shaping time and is therefore stronger influenced by the noise. On the other hand, the baseline cut-off value is applied to the trapezoidal filter output and takes advantage of the longer shaping times of the energy filter. This threshold corresponds directly to the maximal energy contribution to the baseline average, limited only by the fluctuations of the baseline. The combination of both methods is used to ensure that the baseline samples are radiation-free, i.e. are due to the detector leakage current only. This is important because in the case of the EA filter a single bad measurement leads to an infinite response of the EA filter, which in
13
2.5. -ENERGY - MOVING WINDOW DECONVOLUTION 37 10000 30000 50000 70000 90000 1760 1840 1920 2000 2080 2160 2240 2320 Amplitude [a.u.] time [a.u.]
Figure 2.9: Drift of the pedestal level after power-up of a MINIBALL HPGe detector. If the
average value of the pedestal would not be measured and subtracted from the energy filter output, the position of a -ray peak would shift by about two times the FWHM.
The spikes are caused by bad baseline measurements due to undetected events.
turn degrades the accuracy of the baseline average for a certain period. However, if for example the parameter for the EA is<<1, i.e. the EA shows a long impulse response,
the contribution of a single sample to the average is small too and if is close to 1 the
impulse response is very short. Another advantage of the two threshold condition is the possibility to allow for a high fast trigger threshold, with the consequence that low- energy events will not be detected, while at the same time the baseline samples will be acquired only if the energy is (almost) zero.
The frequency of the baseline sampling process is a parameter of the baseline filter module. As mentioned above, the trapezoidal shaper output is the result of a moving average operation applied to the deconvoluted data. From the discussion of the finite duration of the sampling process it is clear that the optimal sampling frequency is the inverse of the length of the moving average window size, i.e L in case of the MWD.
Similarly, the baseline sampler and the moving average operation form a decimation unit (see section A.5) and the properties derived for the decimator apply also to the baseline sampling process. The baseline samples are correlated on the timescale of the peaking timeL.