NESTOR Analysis Tools: Signal Processing. A. Leisos, S. E. Tzamarias and A. Tsirigotis. Particle and Astroparticle Physics Group. School of Science and ...
NESTOR Analysis Tools: Signal Processing A. Leisos, S. E. Tzamarias and A. Tsirigotis Particle and Astroparticle Physics Group School of Science and Technology Hellenic Open University
Abstract The Data Acquisition system of the NESTOR detector stores the accumulated data packets in data files containing the digitized pulses and the operational and environmental parameters of the detector. The signal processing algorithms decode these data files and restore the original form of the pulses taking into account the response function of the system and the calibration data. In this note we describe the functions of the signal processing procedures, which were used during the 2003 Run of the NESTOR prototype deployed in March of 2003.
1. Introduction In March of 2003 a prototype of the NESTOR detector [1,2] was deployed at a depth of about 4000 meters. The detector constituted of a fully equipped NESTOR floor along with many environmental systems attached to the sea bottom station (Figure 1).
Figure 1 The NESTOR floor (left) and the Bottom station Pyramid (right) deployed in March 2003.
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At the tip of each arm of the hexagonal titanium floor there is a pair of two 15 inch photomultiplier tubes (PMTs) inside benthos glass housings [3], one looking upward and the other down wards. The electronics, which are responsible for signal sensing, triggering, digitisation and data transmission to the shore are housed inside a large titanium sphere (1m in diameter) located at the center of the hexagonal floor. The electrical pulses of the PMTs, are digitized by the Analog Transient Waveform Digitizers (ATWDs) of the floor electronics board (Floor board). The digitized waveforms are transmitted to shore, along with any other environmental and operational parameters [4]. The main electronic board of the Data Acquisition system at the shore (Shore Board) receives the data and stores them in data files [5]. The accumulated data files contain all the available information (environmental, operational parameters and digitized waveforms) of 2613 events [5] formatted according to the raw data protocol. The program that performs the signal processing decodes the raw data and reconstructs the PMT waveforms taking into account the calibration data [6] and the response function of the electronic circuits. After the processing the results are stored in a database of RZ-files. These files are read from the Data Quality Monitor [7], in order to examine the status of the detector during running periods. On the other hand the physics analysis programs use this database to estimate the track parameters. The signal processing procedures include the following functions: 1. Raw data decoding and extraction of the operational parameters. 2. Quality checks of the digitized data. 3. Transformation of the digitized data to PMT pulses. 4. Subtraction of the electronic noise. 5. Treatment of overflow pulses. 6. Pulse corrections. 7. Treatment of overlapping pulses. 8. Estimation of hits. 9. Update of the database. Each of the above steps is described in detail in the next sections of the document.
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2. Raw Data Decoding and Extraction of the Operational parameters. Each event packet trnasmitted from the Floor board, is received from the Shore board which formats the event according to the raw data protocol. The packet constitutes of 2560 16-bit words (D[15..0]) where the 2 less significant bits (D[1]D[0]) indicate if the event is corrupted or not (flag bits). The event packet contains the following operational parameters of the detector : The trigger time window (W). The majority trigger logic (M). The threshold values of the ATWDs. The High Voltage of the PMTs. The acquisition mode (Calibration or Normal). The software event counter of the Data Acquisition program at the shore. A trigger is formed when M pulses, from different PMTs, have height above the threshold value of the corresponding ATWD and lie inside the time window W. Each trigger defines an event and all the available information from the detector units is transmitted to shore. The Data Acquisition program at the shore laboratory counts the received events (software counter) and stores them in data files. The environmental parameters are coded to the sixth bit D[5] along with some extra parameters essential to the signal processing : The timestamp of the event (number of clock periods 1 from the start of the acquisition until the occurence of the trigger) The pulse counts of each PMT between two triggers. The hardware event counter (number of events transmitted from the Floor board). The comparison of the software with the hardware event counter indicates if some data are lost. This occurs when the trigger rate of the Floorboard becomes larger than the maximum acquisition rate of the Shore board (about 30 Hz). This can happen during bioluminescence activity [8] as it is demonstrated in Figure 2.
1
The clock period is 25 ns.
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Figure 2 a) The number of lost events during a period of bioluminescence activity (black points) and the rate of event accumulattion at the shore (red line). 75 and 320 seconds after the beginning of the run, the rate is enhanced beyond the maximum accumulation rate of 30 Hz resulting in the loss of 450 and 300 events respectively. b)
At the same time the trigger rate of the Floor board increases rapidly to a few kHz.
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3. The Quality Checks of the Digitized Data. Each event packet contains the pulses of 12 PMTs (3 channels per ATWD), the clock waveform (1 channel per ATWD) and the corresponding trigger signal. Although the flag bits account for the correct transmission of the data to shore, there are cases where the data are corrupted even if the transmission is successful. The effect was discovered during the lab tests of the Data Acquisition system, when we realized that occasionally the clock signal is partially digitized and the PMT pulses are deformed. These events (rotated events) can be detected by checking the number of clock periods that are digitized to the corresponding ATWD channel. If this number is less than 16 then the events is marked as a corrupted event (the expected number of periods of the digitized clock signal is 18.6 2 ).
4. Transformation of the Digitized Data to PMT Pulses. Each ATWD [9] channel contains 128 Wilkinson ADCs each one having its own pedestal. The pedestal must be subtracted from the digitized pulses in order to adjust the baseline to zero. The pedestals were measured at the lab and their stability was continuously checked during the 2003 Run. The deviations were less than 1% in agreement with the statistical error. In Figure 3 is shown a digitized pulse before any processing and after the pedestal subtraction.
Figure 3 A digitized pulse before any processing (a) and after the pedestal subtraction (b).
2
The time scale of an ATWD channel is 465 ns and the clock period is 25 ns.
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To transform the ADC counts (0-1023) to voltage we need the gain of each ATWD channel. The gain was measured at the lab and during the calibration runs at the deep sea. It was found to be extremely stable. The transformation of the sample number (0-127) into time is performed by measuring the sampling interval of each ATWD channel. The sampling interval can be estimated from the digitized clock signal, which has known frequency (f). If we assume that δn is the number of samples that cover N periods of the clock signal then the estimation of the sampling interval is t s =
N . For demonstration in Figure 4 is δn ⋅ f
shown the clock signal after the quadratic extrapolation in order to find the interval δn with big accuracy.
Figure 4 The digitized clock signal is used to measure the sampling interval of the ATWDs. Δn=n2-n1 is the number of samples that contain 17 periods of the signal. The estimated sampling interval is about 3.48 ns.
In Figure 5a is shown the waveform of Figure 3 after the use of the gain and the sampling interval value. Then more samples can be estimated by using a quadratic extrapolation of the 128 samples (Figure 5b).
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a)
b)
Figure 5 (a) The digitized pulse of Figure 3 after the use of the gain and the sampling interval of the corresponding ATWD. (b) The waveform after the quadratic extrapolation in order to increase the sampling points.
5. Subtraction of the Electronic Noise. The resulting pulse of Figure (5b) indicates that there is a small interference between the PMT and clock channels. This interference appears as a periodic waveform with frequency 40 or 80 MHz (depending on the channel) and with an amplitude between 10 and 15 mV. These noise characteristics were measured in the lab for each individual channel and they were used in order to correct (subtract background noise) the PMT waveforms. Specifically, we found that this interference noise appears always in phase with the digitized clock waveform. This observation was used in order to estimate the mean noise waveform for each individual channel. In order to estimate the mean noise in each channel we terminated the input of the specific channel to 50 Ω (empty channel) and several events were collected. The digitized clock waveform was used to shift in time the digitized waveforms of the empty channel in each event in order all the events to coincide in phase. Finally the mean noise waveform was defined as the averaged shifted waveforms of the empty channel. For a demonstration in Figure 6 it is shown the waveform of a PMT before and after the noise subtraction.
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a)
b) Figure 6 The PMT waveform before (a) and after (b) the noise subtraction.
6. Treatments of Overflow Pulses. The range of the ADCs of the ATWD channels is 1.8 V. Consequently pulses above this value (overflow pulses) appear cut. These pulses are fitted with the standard pulse shape established at the lab in order to reconstruct the original waveform. The standard shape used is formed by two one tailed Gauss functions with common height and different variances. Figure 7 shows an overflowed PMT pulse before and after this correction.
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Figure 7 An overflow pulse before (red line) and after the correction (black line).
7. Pulse Reshaping. The PMT signals propagate in the Floor Board through the transmission and delay lines. Any passive or active electronic circuit deforms the original shape of the waveforms be stretching them and attenuating them. The deformation of the PMT signal has been studied at the lab by measuring the response function of the propagation lines (Figure 8). Specifically standard pulses produced by a pulse generator have been guided in the input of the Read Out system and have been digitized following the normal procedure. The input and the digitized pulse have been analyzed by Fourier expansion and the phase and the amplitude of the Fourier coefficients were compared, The response functions of each channel were defined as the ratio of the corresponding input and output coefficients as a function of the frequency.
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Figure 8 The response function H(f) of a propagation line. a) the amplitude and b) the phase.
Assuming that the PMT signal is digitized in a time window T in N samples then the original waveform can be obtained by applying the inverse discrete Fourier transformation: x(t n ) =
1 N-1 i2πf t Y(f j ) H (f j )e j n , n=0,...,N ∑ N j=0
where N-1
Y(f j ) = ∑ y(t n )e
-i2πf j t n
is the discrete Fourier transformation of the measured
n=0
digitized signal y(tn), tn = n ⋅ Δt ,
f j = j ⋅ Δf , T = N ⋅ Δt , and
Δf =
1 N ⋅ Δt
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For a demonstration in Figure 9 is shown the result of the above correction to a PMT pulse. A known pulse (red line) is digitized by an ATWD channel. The digitized pulse (blue line) is restored by the procedure described above (black line) and compared to the original pulse.
Figure 9 The demonstration of the signal processing. An electrical pulse (red line) is applied to the system. The digitized waveform is deformed during its propagation (blue line) but is restored by the processing procedure (black line).
8. Treatment of Overlapping Pulses. The stretching of the pulses due to the propagation effects results in the overlapping of close in time pulses. In the most cases the correction of the attenuation, as described in the previous Section, separates the individual pulses, as it is demontrated in Figure 10.
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Figure 10 Overlapping pulses can be discriminated after the correction for the attenuation.
However there are cases where overlapping pulses are not resolved after the correction. Such cases are treated in the following way: If there are more than one maxima between the threshold crossing times then the waveform is fitted with the standard shape of the PMT pulse. For example in Figure 11 it is shown the result of such a fit which disentangles the two overlapping pulses.
Figure 11 Two overlapping pulses (black points) can be seperated by applying a χ2 fit with two standard shapes.
In case when there is only one maximum but more than two inflection points 3 the waveform can be fitted again using two standard shapes. For example in Figure 12 it
3
A single pulse has two inflection points: one at the rising and one at the falling edge of the pulse.
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is shown that the above procedure can seperate two overlapping pulses and estimate the arrival timing and the amplitude of each pulse.
Figure 12 The black line represents the digitized waveform. The inflection points are four (arrows) indicating that there is an overlap between two pulses. The signal processing procedure seperates the two pulses and estimates their timing and amplitude.
9. Definition of Hits. The arrival time of a pulse is defined as the intersection point of the time-axis with the tangent of the pulse shape at the inflection point of the rising edge. The pulse arrival time together with the pulse amplitude are the main characteristic of the PMT pulse. At this point the calibration data are used [6] to correct the arrival time of the pulse due to slewing (dependence of the definition of the arrival time on the pulse amplitude). In addition the statistical error of the arrival time definition is estimated from the calibration data [6]. The analysis software estimates the time of occurance of the trigger using an algorithm, which describes the functionality of the hardware [10] and the experimental run parameters (majority logic M and the trigger window W). Specifically if tik (k=1,…,Ni) is the arrival time of the kth pulse of the ith PMT then the window W that includes M pulses from different PMTs is calculated. The arrival time of the Mth pulse corresponds to the trigger time tM. Every pulse inside this window is called a hit and it is characterized from the arrival time and its amplitude. The HOU-NS-TR-2004-08-EN 13
amplitude is measured in units of the mean value of the pulse amplitudes corresponding to one photoelectron [6]. In parallel the analysis software estimates the trigger formation time TMthres using instead of the arrival time of the pulses defined above the earlier time that a specific pulse crosses a threshold value. This is called arrival time of the “software trigger” and it is compared in each event to the arrival time of the electronic trigger which has been measured from the digitised trigger signal. The conmparison indicates a perfect agreement which is demonstrated in Figure 13. Notice that the electronic trigger is digitized with a sampling interval of 3 ns. Consequently a sigma of 0.8 ns in the distribution of the difference between the arrival times shown in Figure 13 is in agreement with the digitization accuracy. In the same Figure it is shown the same comparison but in the case where the digitized PMT pulses have not been corrected for the effects caused by the propagation lines.
Figure 13 The distribution of the difference between the electronic and the software trigger before (open circles) and after (solid points) the signal processing. The solid line represents the fit of the distribution with a gaussian with sigma equalk to 0.8 ns.
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10. Update of the Database. The results of the signal processing for each event are stored in a database in a form of a RZ-file. Specifically the following parameteres are stored:
•
The envorimental and electrical parameters of the detector.
•
The operational parametrs as the time window, the majority logic and the PMT thresholds.
•
The generation information in the case that the events come from Monte Carlo simulation.
•
The parameters from the calibration data.
•
The timestamp of the event trigger.
•
The PMT counting rates when the event has been recorded.
•
The sampling intervals of the ATWDs.
•
The arrival times and the amplitude of the PMT pulses.
•
The trigger window as detrmined from the software trigger.
•
The hits inside the software trigger.
•
The time of the software and the electonic trigger.
•
The coincidence level of the event.
•
The characterization of the event (corrupted or not, bioluminescence activity or not etc)
•
The PMT waveforms after each step of the processing.
The above information is used from the Data Quality Monitor in order to inspect the detector operation, while the information concerning the hits are used as the main input to the track reconstruction software [11].
11. Conclusions In this note we described the signal processing procedures we have developed in order to transform the raw data recorded with the NESTOR test detector to essential information that are used in the next stages of data analysis. The algorithms check the quality of the raw data, reconstruct the PMT pulses taking into account the PMT characteristics and the electronic noise and apply all the necessary corrections in order to eliminate the effect of the propagation lines to the recorded waveforms. It was HOU-NS-TR-2004-08-EN 15
demonstrated that the signal processing algorithms could separate overlapping pulses and estimate the form of overflow pulses using standard shapes. Finally it was presented the definition of hits inside the trigger time window and the database, which contains the results of the signal processing procedure as well as the environmental and operational parameters of the detector.
Acknowledgments The authors of this note wish to thank the members of the NESTOR collaboration, the stuffs of the NESTOR Institute as well as the academic and technical personnel of the School of Science and Technology of the Hellenic Open University for their help, scientific, technical and financial support.
References [1] NESTOR: Proceedings of the 2nd NESTOR International Workshop, L. K. Resvanis editor (1992); Proceedings of the 3nd NESTOR International Workshop, L. K. Resvanis editor (1993); website http://www.nestor.org.gr. [2] L. K. Resvanis et al. High Energy Neutrino Astrophysics (1992), V. J. Stenger, J. G. Learned, S. Pakvasa and X. Tata editor. [3] E. G. Anassontzis, et al, Nuclear Instruments and Methods A479, pp 439-455 ( 2002). [4] S.E. Tzamarias, ``NESTOR first results. Electronics-DAQ-Data Analysis'', Published in Amsterdam 2003, Technical aspects of a very large volume neutrino telescope in the Mediterranean Sea. [5] The architecture of the Data Acquisition System at the shore Laboratory of the NESTOR Experiment, HOU-NS-TR-2004-05-EN. [6] Performance of the NESTOR Calibration System, HOU-NS-TR-2004-02-EN. [7] The Data Quality System of the NESTOR experiment, HOU-NS-TR-2004-06-EN. [8] NESTOR Data Analysis: Background Sources and Rejection Techniques, HOU -NS-TR-2004-04-EN. [9] Stuart Kleinfelder, “Analog Trasient Waveform Digitizer”, LBNL 1998. [10] Joshua Sopher, “NESTOR FLOOR BOARD”, Technical Report, Internal NESTOR publication 2002. HOU-NS-TR-2004-08-EN 16
[11] NESTOR Analysis Tools : Track fitting, HOU-NS-TR-2004-09-EN
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