Challenges of arbitrary waveform signal detection by
SiPM in beam loss monitoring systems with
Cherenkov fibre readout
Sergey Vinogradov1,2,3, Lee Devlin1,2, Eduardo Nebot del Busto1,4,
Maria Kastriotou1,4, and Carsten P. Welsch1,2
1
- Department of Physics, University of Liverpool, UK
2 - Cockcroft Institute of Accelerator Science and Technology, Daresbury, UK
3 - P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia
4 - CERN, Geneva, Switzerland
Grant 329100
‘SiPM in-depth’
Introduction
Silicon Photomultipliers (SiPMs) are well recognized due to exceptional photon
number and timing resolution. However, due to specific SiPM drawbacks such as high
dark and correlated noises (crosstalk, afterpulsing), and nonlinearity (limited number of
pixels, relatively slow pixel recovery time) their applications are mostly associated with
detection of weak light pulses of nanosecond time scale [1, 2].
In contrast with the typical scintillation and Cherenkov detection - photon number and
time resolving applications - accelerator Beam Loss Monitoring (BLM) systems with
Cherenkov fibre readout have to precisely reconstruct the temporal profile of the light
pulse. This is a rather challenging task for any photon detector because of the high
dynamic range (~106) from a few photons to a few percent of destructive losses and
presumably an arbitrary signal waveforms i.e. localisation of losses (Fig. 1) [3, 4].
Renewal process is considered as a Poisson process of photon arrivals with
exponential distribution of inter-arrival times and Bernoulli detection process with
exponential recovering of probability to detect the next photon (Fig. 3 a).
Reward process is considered as a process of multiplication with a random gain when
the gain depends on time lapsed from the previous firing of the same pixel t with respect
to recovery time τrec (Fig. 3 a).
t

 ph (t )   (t )  exp    (t )dt  
 0

 spdr (t )  PDE (t )   sptr (t )
photon inter - arrival time PDF
single photon detection PDF
PDE (t ) ~ Gain (t )  Gain ( )  1  exp t  rec 
 det (t )   ph (t )   spdr (t )
t
Pdet(t)   ρdet(t )dt 
0
exponential pixel recovery
detected event PDF & CDF
Renewal equation and mean reward rate are evaluated accordingly known rewardrenewal theory and its applications, and the analytical results are shown on Fig. 3 b.:
Renewal equation and mean reward rate (SiPM response) :

E [ N det (t )]  Pdet (t )   E [ N det (t   t )] ρdet (t )dt 
0
~
L Pdet (t )( s )
~
L E [ N det (t )]( s ) 
~
1  L Pdet (t )( s )

E [ N det (t )] - mean number of detected events
solution of renewal equation (Laplace transform)

dE [ N det (t )]
E [ I SiPM (t )]  E renewal rate  E reward  
 E [Gain (t )]
dt
0.01
110
10
3
110
100
4
110
5
110
6
110
7
110
Number of phot ons
0
50
100
Number of photons, Nph
4.0E-06
5
1
0.5
0.1
Pixel load λτ → 0
PDF(Gain) → delta-function)
3.0E-06
ENF  1 
2
 Gain
Gain
2.0E-06
2
1.0E-06
RC recovery model
Binomial pixel saturat ion model
Dead time sat uration model
Min binomial P NR model
Min dead t ime PNR model
0
Probability Density Function
5.0E-06
0.1
3
SSPM signal
distribution
Pixel load λτ =
Pixel load λτ =
Pixel load λτ =
Pixel load λτ =
0.0E+00
0.0E+00
2.0E+05
4.0E+05
6.0E+05
8.0E+05
1.0E+06
Gain
Fig. 2. Degradation of SiPM response and performance due to nonlinearity [2, 6]
a) General schematic outline: nonlinearity of calibration curve (output vs input) affects resolution;
b) Photon number resolution models: binomial distribution, fixed dead time, exponential recovery.
c) Probability density function of SiPM Gain: degradation from ~ delta-function due to incomplete
recovering of pixels at high photon arrival rates.
Mean SiPM response, arb. un.
Reward-renewal model of transient SiPM response
Photon signal
distribution
SSPM equivalent
photon distribution
Calibration
Photon Number Resolution
Nonlinearity of a photodetector response inevitably degrades its resolution (Fig. 2 a).
SiPM nonlinearities are associated with losses of photons due to limited number of pixels
and non-instant pixel recovery (dead time) [2] (Fig. 2 b). Moreover, incomplete recovering
of pixels during detection of long light pulses results in a distortion of the probability
distribution of Gain to lower mean values of Gain and to higher excess noise (Fig. 2 c).
6.0E-06
1
1
 Nph   Ns
d  Ns 
d  Nph 
Renewal model responses, arb. un.
Challenges of intense light signal detection due to SiPM nonlinearity
50
SSPM signal, fired pixels Ns
This study, in advance of an initial approach [5], is focused on the consideration of a
transient SiPM response as a reward-renewal Markov process formed by nonhomogeneous Poisson process of photon arrivals and exponential pixel recovery process
conditional on previous firing of the pixel.
Fig. 1. a) Beam Loss Monitoring (BLM): 150 MeV electrons in a beam line; an optical fibre for
loss electrons to Cherenkov light conversion; SiPM (MPPC) as an upstream photon detector.
b) SiPM (MPPC) readout of typical BLM signal: raw output (red, left scale) and a result of
deconvolution (black, right scale) with single electron pulse response function (red, inset) [3].
PDF of potential inter-arrival times
Pixel recovery process of PDE(t)
PDF of detected inter-arrival times
Evolution function of detected events
0
2
4
6
8
10
Intensity 3 phe/pix/rec
Intensity 1 phe/pix/rec
Intensity 0.3 phe/pix/rec
Intensity 0.1 phe/pix/rec
0
2
4
6
8
10
Time, relative to pixel recovery time
Time, relative to pixel recovery time
Fig. 3. Reward-renewal Markov process model of SiPM response to high-intensity stepfunction light pulse:
a) Response components & contributions: probability density function (PDF) of inter-arrival times
of potential events, transient pixel recovery process recovering its PDE during “dead time”, PDF
of actual detected event times; evolution function (mean detection rate) of events after the first
detection (plots are given for intensity of 3 phe/pixel/recovery).
b) Mean SiPM response as a result of renewal process with a mean detection rate and reward
process with a mean gain affected by incomplete recovering of pixels.
E [ I SiPM (t )]  SiPM response
Intensity ~ 0.24 phe/cell/recovery
Intensity ~ 0.44 phe/cell/recovery
Intensity ~ 1.1 phe/cell/recovery
Intensity ~ 4.3 phe/cell/recovery
Experimental studies of transient SiPM response
Experiments have been carried out with rectangular pulses (8 ns rise & fall times)
of a 440 nm LED with variable intensity, repetition rate, and pulse width (Fig. 4). SiPM
response has been read out without a preamplifier at a 50 Ohm input to avoid any
possible saturation at high output signal level in analog bandwidth from DC to 1 GHz.
Single electron response was measured with a 20 dB, 4 GHz external amplifier MiniCircuits ZX60-4016E+. Hamamatsu MPPC S10362-33-050C of 50 μm cell size 3x3 mm2
area was used as a well known and very popular SiPM representative.
Conclusion
The transient SiPM response reveals a rather complex dynamic behavior with a strong
dependence on the mean number of detected photons per pixel per recovery time.
Reward-renewal Markov process model has been applied to SiPM response
analysis for the first time and promising analytical results have been obtained. In
the case of a rectangular light pulse detection the model allows to get an analytical
expression for the mean SiPM response as a result of renewal process with a mean
detection rate and reward process with a mean gain affected by incomplete recovering of
pixels, which are in agreement with analytical and experimental results [5].
Acknowledgments
This work has been supported in part by the EC under Grant Agreement 329100 “SiPM in-depth”
and the STFC Cockcroft Institute Core Grant No ST/G008248/1.
References
[1] P. Buzhan et al., Silicon photomultiplier and its possible applications, NIMA 504, 48–52, 2003.
[2] S. Vinogradov et al., “Efficiency of Solid State Photomultipliers in Photon Number Resolution,” IEEE TNS 58, 9–16, 2011.
[3] D. Di Giovenale, L. Catani, and L. Frohlich, “A read-out system for online monitoring of intensity and position of beam
losses in electron linacs,” NIMA 665, 33–39, 2011.
[4] L.J. Devlin, C.P. Welsch, E.N. delBusto, 'Update on Beam Loss Monitoring at CTF3 for CLIC', IBIC 2013, Oxford, UK, 2013.
[5] S. Vinogradov, A. Arodzero, R.C. Lanza, and C.P. Welsch., 'SiPM response to long and intense light pulses', NIMA 787,
148-152, 2015.
[6] S. Vinogradov, “Probabilistic analysis of Solid State Photomultiplier performance”, Proc. SPIE 8375, 83750S, 2012.
Fig. 4. Comparative responses of Hamamatsu MPPC S10362-33-050C of 50 μm cell size 3x3
mm2 area to rectangular light pulse of uniform illumination over active area; green trace is a LED
pulse profile; blue trace is a MPPC response. Horizontal scale is 20 μs/div, vertical scales are 2,
10, 50, and 200 mV/div correspondingly. Direct readout of MPPC output signal to 50 Ohm
oscilloscope input: DC – 1 GHz analogue bandwidth.
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