Charge Measurement 

Using TWR system

Introduction

The Transient Waveform Recorder (TWR) is designed to improve the energy resolution for high energy phenomena such as Extreme High Energy Neutrino, High Energy Cascade and Gama Ray Burst.
During the last pole summer season (Dec 2001 - Feb 2002) the prototypes of 48 channels are installed (green in the figure). All remaining channels will be installed  in this summer season (Dec 2002 - Feb 2003). In this note we will describe an analysis for charge measurement using the TWR data. More information about TWR system can be found in TWR home page.

Sample & Event Selection

For this analysis we use the N2 Laser data that have been taken for the calibration purpose. The source of N2 laser is located close to OM 35 on string 5 (blinking in the figure). The intensity of laser light can be adjusted by changing the attenuation factor.  The following summarizes  the information of the data set used  and detailed information  can be found in Andrea's note.

The data recorded by the TWR DAQ is merged into the standard AMANDA DAQ data by matching the event times of these two DAQ systems (wavemerger). To eliminate the atmosphere muon events from N2 laser data we require that event should have reasonable number of waveforms, which is similar to the Nch variable in normal data analysis. Figure 1 shows the distribution of number of waveform (N_wf) for R5337. The bump in the lower N_wf region is corresponding to non-N2 laser event like the atmosphear muon event. So we require N_wf >  25.

Figure 1 : Number of waveform distribution.

Example waveforms

Figure 2 shows an example of waveform for OM 360. Due to the long distance between laser source and OM only few number of photons can reach the PMT. There are clear two signal pulses in the figure. Each pulse corresponds to the single photoelecton signals. In the current TWR system  one channel records 1024 bins for an event, where one bin is corresponding to 10 ns time.  The figure 2 is just a part of the full waveform after removing no signal parts.  Small size of overshoots are observed in the tail parts of pulses.

Figure 2 : Waveform of OM 360

   
Figure 3 shows another example waveform of OM 662 which is located in more bright position (distance from laser source is d=176 m).

Figure 3 : Waveform of OM662.

Here we can still distinguish individual pulses for each photoelectons. Larger size of overshoot than OM 360 is seen. Each signals are close so that the baseline of later signal can be shifted by the overshoot of earlier pulse.   
Figure 4 shows very bright example of OM 621 (d=145m). Due to the short flight distance of the incoming photons, there is large number of photoelectrons signals with the narrow time spread. Now it is almost impossible to count each photoelectron.   

Figure 4 : Waveform of OM 621

Here the baseline shift caused by overshoot is significantly larger than OM 662. An after pulse is also observed around 4 micro second after the primary pulse.
An extremely bright example is shown in Figure 5.  This is the waveform of OM 500 which is located at a distance d=54 m from the light source.

Figure 5 : Waveform of OM 500.

Even though we expect huge and clean signal in this bright OM, only a part of the signal is shown in this wave form. The waveform is saturated by the maximum voltage limitation of the ORB prompt output. A very broad pulse appears about after 2 micro second after the primary peak. This peak is not contributed by real photoelectron, but is caused by the discharge procedure of the capacitor. Also here the after pulses are clearly shown at about 4-5 micro second after the primary pulse.

How to measure the charge

1. Fixed Baseline  and Moving Baseline Method

Figure 6 : Fixed baseline and moving baseline method

One of the simple way to measure the charge from the waveform is the fixed threshold method. The charge is easily obtained by integrating the waveform under the fixed threshold. This method is similar to that for obtaining  the peak ADC in the muon DAQ. We can have the stable and quick software using only a few lines of code. However this method has the problem of a wrong charge reconstruction due to the baseline shift caused by the overshoot and the fake peak of the discharging process. The moving baseline  method can solve this problem. If we can trace the correct baseline under the signal pulses, the moving threshold can be obtained by taking an offset from this baseline. Then charge is calculated by integration the waveform over the threshold. However this is more complicated than the fixed threshold method.

2. Algorithm of Moving Baseline method

The most important feature of the baseline method is how to find the correct baseline.  The basic idea of the baseline finder is based on a cleaning procedure. We remove all peaked data points in the waveform, then the baseline is obtained by connecting the remaining points.  Figure 7 briefly explains how to get the baseline.
First, we remove the points with large deviation. The deviation of the given point is determined by the voltage difference from its neighboring points. If these deviations are larger than 30 mV the point is removed. Basically most of peaked points are well cleaned by this procedure (See Figure 7b).
Second, we remove the "clusters" with large deviation. As it can be seen from Figure 7b, there are still remaining points after the first cleaning procedure, which are usually appeared in the plateau region of signal peaks. To remove these plateau points, we construct the clusters by connecting the remaining continuous data points. Then we remove the cluster if the average voltage of cluster is largely deviated from those neighboring clusters.
Third, we remove the tail part of signal peak. The remaining data points in the tail part of the signal causes the unstable fluctuation of the baseline. More smooth baseline can be obtained by removing this tail components  (See Figure 7c). Because of the long falling time of PMT signal, the data points in this part usually do not have large voltage deviations so that the previous cuts are not so effective to remove it. We developed a simple pattern recognition technique to  find tail structure. We 1) take the four continuous points; 2) compare those deviations (slopes); 3) if the first deviation is larger than 10mV and the slopes are decreasing as the time increase, the four points are removed from the baseline calculation (Figure 7d).
Fourth, the baseline is obtained by connecting all remaining points. In order to reduce the statistical fluctuation, we calculate the average voltage for each 80 ns bins and then make a average line connecting those bins.  
Finally, charge is simply calculated by integrating the waveform under the baseline.

Figure 7a : Example waveform which has two signal peaks.

Figure 7b : Waveform after removing the points with large deviation.
A few points in peak can be remained (in the red circle)


Figure 7c : Waveform after removing the cluster with large deviation
The tail components of each signal peaks are still remained.


Figure 7d : Waveform after cleaning tail component.
Now base line can be obtained by connecting all remaining points
 

Figure 7e : Waveform and obtained baseline.
Charge is calculated by integrating the waveform under the baseline.

Results

1. Example waveform

As some examples are shown in Figure 8 the baseline finder looks well running.  Baselines are reasonably obtained not only for the simple waveforms which contain one or two signal peaks, but also for complicated waveforms consisted number of photoelectrons . The baseline shift due to  the overshoot, and even oscillated baseline, are also well corrected.  The fake signal from the intermediate discharge procedure is well traced by our program.

Figure 8 : Waveforms are obtained baseline
Time scales are different.
Where blue line and circle is original waveform, red line is the obtained baseline
and color filled circles indicate signal peak over the threshold (20mV) ;
green circle is leading edge, yellow is trailing edge and red is for others.

2. Monte Carlo Test

To verify our method, we test the program with Monte Carlo. MC laser samples are generated by the AMASIM with the PHOTONICS. The number of photons is found to be 1.3*10^11 for the ND=0.0 laser source. This value is determined by comparing the N_wf distribution between MC and Data.
Figure 9 shows the measured Q distribution as a function of the arrival number of photoelectron (Npe) which contribute to make signal pulse in PMT.  Where Q is the integrated charged for given waveform which is obtained by the moving baseline method. And Npe is by MC generator information.  A Good linearity between the Npe and the measured Q is shown (around the red line in the figure) upto about 2000 Npe.  The OMs with different slopes in the figure are due to the different gains of OMs.  Also two OMs with huge Npe show clear saturation.

Figure 9 : Measured Q distribution vs. as Npe.
The Qs are measured by the moving threshold method.

Figure 10 shows the peak ADC distribution as a function of Npe, here the peak ADC is the pulse height recorded in HIT information (with muon DAQ).  The saturations are started from OM with Npe=50~100.  It indicates that TWR system can improve the dynamic range by more than factor few tens.

Figure 10 : Peak ADC vs. Npe.  
Scale of x-axis is just 1/10 of Figure 9

Figure 11 compares two methods of the fixed threshold method and the moving threshold method.  Except some OMs having large overshoot characteristic, basically there are good linearity between results of two methods. Because the MC baselines are much stable than real data, two methods should give us similar results in MC.

Figure 11 : Q Moving Threshold vs. Q Fixed Threshold.

3. Laser Data Result.

Figure 12 shows an example of measured Q distributions obtained in the N2 laser Data.  Where the laser intensity is ND=0.0 and OM  number is 662.  For the peak ADC distribution from Mu DAQ system, the saturation is clearly visible at about 2000 mV.  Instead of this  there are no saturation in the TWR measurements.  Furthermore the distributions of TWR measurement are reasonably symmetric. Since the overshoot of this OM is not so serious, the results from both methods are comparable.  The moving threshold method reduces the tail of the lower Q region in the fixed threshold method. While it  makes the a little longer tail the upper Q side. The relative spreads (rms/mean) of two methods are almost same. 

Figure 12  : Measured Q distributions of OM 662 with N2 laser Data.

How TWR system increases the dynamic range is well shown in Figure 13. It is a scatter plot of the measured Q with TWR vs. peak ADC with muon DAQ. The moving threshold method is used for TWR measurement. The good linearity in lower Q region is broken at ADC~2000mV or 3500mV. These saturation voltages are channel dependent. However we should note it does not mean that the Q using TWR is correct.  

Figure 13 : Q from TWR(moving threshold) vs. Peak ADC from Mu DAQ

In the real data it's difficult to verify our method since the true Npe is not available. However we still have some indirect method. Since the optical property of south pole ice is well measured, we can expect the number of arrival photons using the attenuation relation,

N^ph=N₀  1/r  e^-r/lambda,

where,  N_ph is number of arrived photons, N₀ is number of emitted photons at laser source, r is the distance between laser source and OM, and lambda is effective attenuation length.  Assuming the Q is proportional to the number of arrival photons, if we take the Q x r distribution as a function of r, the distribution is expected to be linear in the logarithm scale.  The fluctuation is caused by the limited statistics, gain variations of PMTs and the depth dependence of ice properties. Because the AMASIM simulates the depth dependence of ice properties and gain variations of PMTs,  it is valuable  to compare it with MC.  The results are shown in Figure 15.  Where, the moving threshold method is used and the Npe expectation of MC is obtained from the true Npe in order to see only ice property effect eliminating the gain variation of PMT (Scaled for the comparison). There is good agreement between Data and MC in the low Q region (r > 100~150m).  Also the flat distribution due to saturation is observed below r=125~150 m.

Figure 14 : Q x r  vs. r.

4. Saturation and After Pulse Method

As you see in the Figure 14.  The saturation in the real Data is more serious than MC simulation.  The measured Q value for the brightest OMs is roughly  ~10 times smaller than MC. It may indicate the weak point of our simulation for the saturation effect. In other words, our expectation on the dynamic range in the previous chapter (Figure 9) should be ~10 times  overestimated.
We are trying to develop this restricted dynamic range using the after pulse information.  We can extract the after pulse component in the given waveform using the time difference between primary pulse and secondaries. Since after pulse probability is well known, the original primary charge information can be estimated from the measured charge of the after pulse and its probability (See Figure 15).

Figure 15 : Estimation of original primary charge using after pulse.

We integrated the charge of the secondary pulses which have  the time interval  4 to T_max   (micro seconds) after the primary leading edge,  where T_max is the maximum time interval up to the available maximum time bin for given waveform. The T_max  is determined by the time difference between the leading edge of the primary pulse and the last time bin (10240 ns) of TWR. The after pulse probabilities in this time range are obtained  for each OMs in the waveform-by-waveform basis.  Figure 16 shows the results. We see a big improvement in Q measurement.  No saturations is seen using after pulse method. Also there is very good agreement between MC expectation and the after pulse result.

Figure 16 : Measured Q using After Pulse.

However we should note that the Q in Figure 16 is just taken in average. Because of its small probability, the normal OMs have no after pulse in the most of all events. The only very bright OM or very big primary pulse can make enough number of after pulses so that we can get the reasonable size of error. Figure 17 shows the Q distribution of OM 500 measured by the after pulse method. The OM 500 is the brightest OM and about 25% of error is achieved.
 

Figure 17 : Q distribution of OM 500 measured by the after pulse method

5. Results with 2003 Data

Since the 2002-2003 Summer season, TWR system has been available for most of all OMs.  Figure 18 shows Npe x r distributions for N2 laser data with all TWR available OMs.  Top figure is for electrical channels and the bottom is optical channels. The dynamic range with TWR After pulse measurement for electric channel is about two order of magnitude higher than Muon Daq while the Npe with TWR primary pulse measurement is limited by a saturation due to a limited voltage window of  TWR digitization. For electrical channels, the dynamic range with TWR After pulse is extendeds upto more than 2000 Npes which is about three order of magnitude higher than Muon Daq while  primary pulse for optical channels is about an order of magnitude higher than Muon Daq.
 

Summary & Discussions

Base on the prototype TWR system we developed the charge reconstruction method for AMANDA experiment. Several methods such as the fixed baseline method, the moving baseline method and after pulse method, have been tested. For the normal channels and events with the stable baseline, both results of the fixed and moving baseline method shows good agreement. But in the channels with large overshoot, the difference between two method become large. For the very bright OM with huge Npe, the saturation limitation of ORB is the most important factor in the Q measurement rather than which method is chosen. Even TWR system is helpful to increase the dynamic rage, the saturation effect in the real data is more serious than MC expectation. The after pulse method provides an improvement to overcome the saturation effect. For very bright OMs no saturation is observed using this method. The moving threshold method is accompanied by after pulse method. Since the baselines is usually distorted by large signal, more accurate measurement is available when the moving baseline method is used to correct it.   For the after pulse measurement the counting method should be tried in the future. Because the small population of after pulse, the individual waveforms are well separated each other. As a homework in the moving threshold method the stability and fast process is required.  This study should extend to the electrical channels after all channels are equipped with TWR system.