Time over threshold in the presence of noise
TTime over threshold in the presence of noise
F. Gonnella , V. Kozhuharov , , M. Raggi INFN Laboratori Nazionali di Frascati, 00044 Frascati (Rome), Italy University of Sofia “St. Kl. Ohridski”, 1164 Sofia, Bulgaria
Abstract
The time over threshold is a widely used quantity to describe signals from various detectors inparticle physics. Its electronics implementation is straightforward and in this paper we presentthe studies of its behavior in the presence of noise. A unique comb-like structure was identifiedin the data for a first time and was explained and modeled successfully. The effects of thatstructure on the efficiency and resolution are also discussed.
Keywords: time over threshold, noise, scintillator/cerenkov detector, PMT signal modeling.
A common setup in particle physics is to couple a particle-sensitive material (e.g. Scintillator,Cerenkov) to a photosensitive device (photomultiplier, multipixel photon counter) and measure theenergy deposited in the material by reconstructing a given property of the output pulse - the totalcharge collected, the pulse amplitude, etc. The measurement of the time over threshold (ToT), asshown in Fig. 1, is composed of two measurements of time for the signal going above (leading) andreturning below (trailing) a given threshold. This provides information about energy deposited bythe interacting particle through the reconstruction of the difference between leading and trailingtime Θ = t trail − t lead . In addition the impact time could also be obtained from the leading timewith a possible energy dependent correction. The dependence of the deposited energy on ToT (seeFig. 2) has an exponential form and could be parametrized by E (Θ) = α Q (Θ) = α β A (Θ) = k ∗ ( a.e b ∗ Θ + const ) , (1)due to the linear relation between energy, charge and signal amplitude ( α , β , and k are constants).The advantage of using the time over threshold instead of charge or amplitude measurement isthe wider dynamic range accessible due to the logarithmic dependence on the energy. In additionthe measurement of the time is performed using time to digital converters (TDCs) which provideless expensive solution per channel than the analog to digital converters, especially where highsignal rate and short signals are expected.While the charge or amplitude measurements is a well established and mature technique theToT measurement is just becoming attractive nowadays due to the development of high precisiontime measurement devices - tens of picoseconds.In the present article we describe the observation of a peculiar structure in the reconstructeddistribution of the ToT which we could only explain by the superposition of a small amplitudesinusoidal noise on top of the PMT signal.The charge measurement done by the QDC is completely immune to this effect as the integralof a sinusoidal function is zero. 1 a r X i v : . [ phy s i c s . i n s - d e t ] D ec igure 1: Time over threshold a 0.0013 – – Time over threshold [ns]0 10 20 30 40 50 60 70 80 S i gna l a m p li t u t e A [ m V ] a 0.0013 – – Signal amplitude as a function of the ToT + const; [t] = ns, [A] = mV b*t
A(t) = a.e
Figure 2:
Relation between the time over thresholdand signal amplitude. The relation between the signalamplitude and the deposited energy is linear.
The present study was done at LNF-INFN as part of the development of the readout system of theLarge Angle Photon vetoes for the NA62 experiment at CERN SPS [1].The NA62 experiment aims to perform a 10% measurement of the branching fraction of theextremely rare decay K + → π + ¯ νν and subsequently to measure the V td CKM matrix element. Thetheoretical prediction for that value is Br ( K + → π + ¯ νν ) = (7 . ± . ∗ − . The very low raterequires an efficient veto of all the other charged kaon decay modes most of which contain photonsin the final state. The usage of a 75 GeV kaon beam increases the minimal photon energy at whichhigh rejection factor is necessary but still an inefficiency less that 10 − is required for photons withenergy of 100 MeV.
012 345 678 9101112 13 14 15
TriggerTrigger
12 13 14 15
LAV FEE TDCCAENV1190B VMEBridgeV1718
32 ch32 ch VME
LINUX PC
USB
Figure 3: Schematics of the experimental setup for the measurement of the ToT distribution forcosmic rays with Lead-glass block.The Large Angle Photon vetoes [2] consist of lead glass blocks made of Schott SF57 lead glassand are coupled to a R2238 photomultiplier. The blocks are arranged in the form of rings. Atotal of 12 Large Angle Photon vetoes were produced, with 5 or 4 rings for a total of about 2500analog channels. The signal from a 100 MeV photon in the lead glass after propagation throughthe cables to the front end electronics could have an average amplitude as low as 10 mV and isalmost equivalent to the response to the energy deposited by a minimally ionizing particle passing(MIP) through the crystal.The front end electronics of the lead glass blocks was developed at the LNF [3]. It is basedon a 9U VME mother board receiving 32 analog inputs. Each signal is clamped, amplified and2plit into two before being transferred to a high speed comparator with an LVDS output driver.The comparator threshold could be set through a board controller mezzanine, which provides aserial USB and a CAN-Open communication. The minimal effective threshold for all the channelswas found to be less than 5 mV. An additional negative feedback circuit was implemented todynamically decrease the absolute value of the threshold just after the leading edge of the signal.Such a mechanism, referred to as hysteresis, provides a safety margin against fast changing signalswhich would cause the digital LVDS output to oscillate.The experimental setup used during these studies is shown in Fig. 3. The signals coming fromthe lead-glass blocks, after the discrimination, were readout by a V1190B TDC module which isbased on the CERN HPTDC chip [5] and incorporates 2 times 32 input channels. The data istransferred to a PC for further analysis through a V1718 VME controller via a USB connection.The recorded data showed a peculiar shape of the ToT distribution. An explanation basedon the addition of a sinusoidal noise was employed and verified by means of a numerical signalsimulation.
The general function describing the output signal would be A ( t ) = (cid:90) t I ( t − θ ) ∗ f ( θ ) dθ, (2)where I ( t ) is the intensity of the light produced in the active material and f ( t ) is the photodetectorresponse function to single electron. The form of the light intensity was chosen as an exponentialdecay with decay time τ , I ( t ) = N τ e − t/τ , (3)assuming that the energy inside the active media is released instantly (true for small sized detec-tors) and the only contribution comes from light propagation or scintillating centers decay. Thenormalization N is the number of the total photons emitted.The PMT single electron response was approximated with the function f ( θ ) = sin ( aθ ) × e − θ/b , (4)where a and b were taken as free parameters. The use of such a function could be justified with aninitial increase of the signal amplitude due to arrival of first electrons and further a decrease of theamplitude due to full charge collection at the anode of the PMT.An advantage of using functions 3 and 4 is the simple and analytic form of the final signal. Theresulting output signal amplitude at the anode of the PMT would then be described as A ( t ) = − N a + c × e − t/τ τ × (cid:104) e ct ( c sin ( at ) − a cos ( at )) + a (cid:105) , (5)where c = 1 /τ − /b . The width of the signal ∆ T is described by the parameters a - ∆ T = π/a .This signal model had been previously applied to describe the Eljen 212 scintillator coupledto Hamamatsu R6427 photomultiplier. The scintillator decay time constant, the PMT rise timeand fall time were found to be consistent with the specification. Their behavior with the differentPMT voltages were as expected. This check lead to the confidence of applying the chosen signaldescription to model the time over threshold behavior in various conditions.3 ime [ns]0 1 2 3 4 5 6 7 8 9 10 P M T r e s pon s e f un c t i on [ a r b i t r a r y un i t s ] -0.3-0.2-0.10 Figure 4:
Single electron re-sponse function of the PMT
Time [ns]
120 130 140 150 160 170 180 190 200 A m p li t ude [ m V ] -10-8-6-4-20 Time [ns]
120 130 140 150 160 170 180 190 200 A m p li t ude [ m V ] -10-8-6-4-20 Figure 5:
Shape of the output signal of the system Lead-Glassblock - PMT without and with the addition of 300 µ V noise.
The noise was simulated by adding a parasitic signal A tot ( t ) = A ( t ) + A noise ( t ) = A ( t ) + A sin (2 πf t + φ ) , (6)where A is the noise amplitude, f is the noise frequency and φ is a random chosen phase. The noisecould either be picked-up from external sources or generated internally in the front end electronicsby parasitic positive feedback. For the present studies the real origin of the noise is not important.Thus the basic parameters used to describe the characteristics of the output signal were: • Average signal amplitude.
The signal amplitude was simulated as a Landau distributionwith most probable value of 10 mV and a gaussian sigma of ≈ • Threshold.
The threshold was kept fixed during the simulation in order to see what wasthe additional effect of the hysteresis and the noise on top of the PMT signal. Two valueswere studied as examples - 5 mV and 7 mV. • Hysteresis.
The hysteresis is an important ingredient of the time over threshold circuit andit prevents short and oscillating output when the input signal is very close to the threshold.The hysteresis was varied from 0 mV to 3 mV in steps of 300 µ V. • Noise amplitude.
The noise amplitude was varied from 0 mV to 3 mV in steps of 300 µ V. • Noise frequency.
The noise frequency was kept fixed to 300 MHz as was independentlyobserved with a digital oscilloscope.The output quantity is the time over a certain threshold. A signal is considered to be detectedif the time over threshold is longer than a fixed minimal time Θ . In the present studies Θ = 5 nswas used, since it was compatible with the dead time of the HPTDC. With the described experimental setup the obtained time over threshold distribution is shown inFig. 6. It possesses a bizarre feature of multiple peaks - a comb-like structure - which was initially4uzzling and stimulated the presented study. Few explanations were considered ranging from effectsdue to energy deposit and photoelectron emission to TDC miss-functioning effects (stuck bit forexample). Finally the data was reproduced exploiting the signal modeling described in section 3with 300 MHz sinusoidal external (pick-up) noise on the input analog signals.Figure 6:
Measured time over a 10 mVthreshold distribution for cosmic raysfrom a Lead-Glass block.
Time over threshold [ns]0 5 10 15 20 25 30 35 40 45 50
Time over threshold
No noise, 1.5 mV hysteresis
V noise, 1.5 mV hysteresis m Figure 7:
Simulated time over 5 mV threshold distribu-tion for cosmic rays with external noise with amplitudeof 300 µ V The effect on the inclusion of the extra noise is shown in Fig. 7. The blue line is the expectedtime over threshold distribution for a signal from the Lead-Glass block without noise and the redhistogram is the result with the 300 µ V noise. The sinusoidal noise induces a random shift on themeasured leading edge or trailing edge alone but correlates them between each other - if the leadingedge is crossed predominantly when the phase of the noise is π/ π/ const . ∆Θ can be assumed to be half of thedistance between two consecutive clusterisation peaks, as seen in Fig. 7. Then the physics quantity,the energy ( E ∼ A ), will acquire an additional constant term in the resolution dependence as a5 .40 0.96 8.04 22.96 40.20 57.16 71.16 81.24 88.10 91.96 94.520.36 0.38 2.14 13.14 30.08 47.82 63.94 76.70 85.20 90.06 93.320.36 0.32 0.58 5.34 20.26 38.52 55.66 70.56 81.52 87.68 91.940.36 0.18 0.24 1.52 11.12 28.50 46.74 63.04 76.62 85.14 90.360.36 0.18 0.14 0.34 4.32 18.82 37.10 54.70 70.18 81.38 88.620.36 0.18 0.12 0.14 1.04 10.14 27.38 45.88 62.70 76.10 86.000.36 0.18 0.10 0.08 0.20 3.76 17.68 36.32 54.82 69.66 82.000.36 0.18 0.10 0.08 0.08 0.72 9.14 26.68 45.80 62.70 76.960.36 0.18 0.10 0.08 0.06 0.18 2.90 17.52 36.56 54.38 71.460.36 0.18 0.10 0.08 0.04 0.06 0.48 8.48 27.34 45.72 64.260.36 0.18 0.10 0.08 0.04 0.04 0.08 2.66 17.38 36.50 56.18 Noise amplitude [mV]0 0.5 1 1.5 2 2.5 3 H ys t e r e s i s [ m V ] -1 Detection inefficiency in %
Figure 8: Dependence of the inefficiency on the value of the hysteresis as function of the amplitudeof the input noise. An efficient hit is defined if the first leading and trailing edge form time overthreshold longer than 5 ns.function of energy ∆ EE ( E ) T oT = ∆ AA ( E ) T oT = b ∗ ∆Θ = const. (7)This term could be as high as tens of percent ( b ∼ . − and ∆Θ ∼ . A comb-like structure was identified in the time over threshold distribution in cosmic ray data fora first time, was explained to be caused by the pick up of high frequency low amplitude noise, andwas modeled successfully. The effect should be taken into account by every detector readout systemaiming to use ToT as a measurable quantity to describe the data from the detector. In the case ofthe Large Angle Vetoes readout system additional precautions were taken (better cable shielding,extra noise filtering in the crate power supply) to decrease the level of the noise to an acceptablelevel, which does not degrade the efficiency of the system.
Acknowledgments
The present work was performed at the Laboratori Nazionali di Frascati, INFN. The authors areindebted to Antonella Antonelli, Matthew Moulson and Tommaso Spadaro for the pleasure of thejoint work and the valuable discussions on the data and its interpretation. The time over thresholdboard was developed by Gianni Corradi and the authors would like to thank him for the usefuldiscussions. 6 eferences [1] F. Hahn et al. [NA62 Collaboration], http://cds.cern.ch/record/1404985.[2] P. Massarotti et al. , PoS ICHEP , 504 (2013).[3] A. Antonelli et al. , JINST (2013) C01020.[4] F. Gonnella et al. , PoS TIPP2014