Time of Flight (ToF): basics
Start counter Stop counter
• TOF – General consideration - early developments combining particle identifiers with TOF• TOF for Beam Detectors or mass identification - TOF Constituents - based on the use of SEE effect: - Thin Foils (SE generation) - SE transport -------------------------------------------------------------------------------------------------------------------------------------------------------------
- SE detection ( mainly MCP – some basic set-up )• Fast electronics - Fast preamplifiers and discriminators LE; CFD; ARC-CFD - Time walk and jitter –basic consideration
2. part
Timing measurements
• Pulse height measurements discussed up to now emphasize accurate measurement of signal charge
• Timing measurements optimize determination of time of occurrence timing output signal ( “time stamp” )
• For timing, the figure of merit is not the Signal / Noise ratio but the Slope / Noise ratio
Fast Timinga) Timing measurements Detectors for Timing and their FEE - Scintillator & Photomultiplier assembly - MCPs & Fast Preamplifiers - Semiconductor detectors & Preamplifiers ( CSP vs. Current )
b) Ultra-fast Timing Circuits and Signal - Time - stamp - Time - walk and Time - jitter
239Pu 241Am 244Cm
Counts
5.155 5.486 5.804 [MeV]
Cou
nts
IKP - TOF & BPM Preliminary results
- 250 +/- 50 ps - coincidence with energy measurements (SC + DGF-4C-rev.F) - transparent beam detector and tracking with 32x SC matrix as Stop detector (real beam test is requested!)
244 C
m
241 A
m
239 P
u
( ~200 keV energy loss )
Tim
e of
Flig
ht
[ns
]
3rd layer 1st layer
2nd layer
~300
ps
~
250
ps
~3
50 p
s
a) Timing measurements Detectors for Timing and their FEE
- Scintillator & Photomultiplier assembly - MCPs & MCP-PMT and Fast Preamplifiers and very briefly about other ultra-fast detectors - Semiconductor detectors (Si, Diamond) & their Preamplifiers ( CSP vs. Current )
Scintillators & Photomultiplier tubes (PMT)
Gain ~ 106 sec. secondary electrons / photo-electron
Circular-cage type PMT
Detector
Photomultiplier tube - (PMT)
Different geometries of PMT
Box-and-grid type PMT
Linear-focused type PMT
and the typical electron trajectories
Pho
toca
thod
e R
adia
nt s
ensi
tivity
(mA
/W)
Wavelength (nm)
Tran
smitt
ance
(%
) The transparent window material commonly used in PMT:
- MgF2 crystal ; - Sapphire ; - Synthetic silica; - UV glass; - Borosilicate glass
Basic Photocathode commonly used in PMT:- Cs-I 100 M - Cs-Te 200 S;M- Bialkali (Sb-Rb-Cs, Sb-K-Cs) 400 U;S;K- Multialkali (Sb-Na-K-Cs 500 K;U;S- Ag-O-Cs 700K;S-1- GaAsP(Cs)
Wavelength (nm)
Detector WLS
Wavelength shifter
Photons• transport• WLS
BriLanCe Crystals - Properties (1)
BriLanCe Crystals - Properties (3)
s/n!
BriLanCe Crystals - Properties (2)
Countermeasures for very fast response circuits (the “miraculous” (small) series resistor and not parallel capacitor)
The effect of damping resistor on ringing
( remember the influence of resistor in the quality factor of an oscillator or larger capacitor value in a low-pass frequency filter :)C - filter-change the frequency !Rs –oscillation damper !
Signal output problem and the solution
The importance of Poles and Zeros
Pole-zero diagram
Step 1 Step 3Step 2
Ideal oscillator
real oscillator - R series
e.g. 10 pF * 10 nH 500 MHz
Going from PMT ( Photomultiplier Tube) to MCP (Microchannel Plate)
• from a discrete dynode structure to a continuous distributed dynode structure but also• more than 8 orders of magnitude scaled down design in volume ( 102 in length and > 103 in diameter )
Multi-channel Plate Detectors
Channels
Electroding(on both face)
- e initial velocity ( ~1eV)
- channel length/diameter ratio
Kc - constant
MCP assembly in chevron configuration
Metallized ++ Metallized+
• Much stable operation vs. external high magnetic fields in comparison with PMT • lower gain but in chevron configuration the gain ~106
• lower power consumption (gain vs. HV)
MCPs in Single, vs. Chevron and Z-stack configurations
Gain:
103-104
106
108
Comparison of gain characteristics of various single and multi stage MCPs
Comparison of gain characteristics of three different types of 2-stage MCPs
MCP gain dependence vs. - parameter and stage configuration
MCP gain dependence vs. channel diameter and technology
Comparison of timing characteristics of chevron 2-stage MCP-PMT, one with6 µm and another with 12 µm pore diameter
Parameter6 µmChannel
12 µmChannel
Rise time [ ps] 167 245Fall time [ps] 721 716Transit time [ps] 406 650Transit time spread [ps] 67 81
Time x10 -8 s
Mesh form anode ( e.g. X,Y delay lines signal pulse amplitude only 15-20% comparedto the solid anode standard version)
?
HV ~ 3 kVRise time ~150psFall time ~350 psFWHM ~ 300 ps
HamamatsuR-3809 U-50
• Photocathodediam. ~10mm• Price - !
Standard operating circuit for an MCP-PMT
Incoming Particle Trajectory
Would like to have return path be short, and located right next to signal current crossing MCP-OUT to Anode Gap
Signal
Signal & Return
Anode Return Path Problem
Current out of MCP is inherently fast- but return path depends on where in the tube the signal is, and it can be long and so rise-time is variable
The Signalis a currentand not a potential
Load
10cm wire; 0.2mm diam 150 nH Impedance @ 1Ghz ~ 1 kOhm
10 pF ~ impedance@ 1GHz ~ 1.5 kOhm
Detector Signal Collection
Circuit development
• Low Z output voltage source circuit can drive any load
• Output signal shape adapted to subsequent stage (ADC)
• Signal shaping is used to reduce noise (unwanted fluctuations) vs. signal
ZoZ+
-
High Z
Low Z
Low Z
T
Voltage source • Impedance adaptation• Amplitude resolution• Time resolution• Noise cut
Rp
Quo vadis ?
Z+
-
Detector
Rp
FEE (Input stage)
if Z is highcharge is kept on capacitor nodes and voltage
builds up (until capacitor is discharged)• Advantages: - excellent E resolution - friendly pulse shape analysis• Disadvantages: - channel-to-channel crosstalk - pile up above 40 k c.p.s. - sensitivity to e.m.c.
Detector as fast signal generator electron-hole pairs collection only electrons (or particles)
Front-end electronics – overview
~ Ci
Detector as fast signal generator electron-hole pairs collection only electrons (or particles)
Z ~ Ri+
-
Detector
Rp
FEE (Input stage)
if Z is lowcharge flows as a current through the
impedance in a short time.• Advantages: - limited signal pile up - limited channel-to-channel crosstalk - low sensitivity to parasitic signals - good timing resolution• Disadvantages: - pour signal/noise ratio - sensitive on return GND loop !
Front-end electronics – overview
Current from MCP-OUTReturn Current from anode
Capacitive Return Path Solution
~25mm
Ultra-fast detectors, extremely user-friendly solutions, the only disadvantages: - small area of photocathode and extremely expensive
?
CERN - LHC experiment
ChemicalVapourDepositiontechniques
CVD-Diamond
E. Berdermann et al, CVD-Diamond Detectors… Nucl. Phys. B 78 (1999), 533
E. Berdermann et al, The use of CVD-Diamond for heavy ions… Diamond and Related Materials 10(2010),1770
Two “optical grade” CVD and ~ 100µm thickness
The largest diamond detector of 60 x 40 mm2
and ~200µm thickness <0> in the focal planedetector of a magnetic spectrometer
• a 30 x 30 mm2 detector with 9 stripswith a pitch of 3.1 mm and• a 20 x 20 mm2 pixel detector with apixel size of 4.5 x 4.5mm2
the first large-area CVD diamond detectorsInstalled at SIS
the CVD - Diamond Detectors
• very fast active integrator
• tr < 1ns (sub-nanosecond CSP)
• A0 ~ 1,000-10,000
• Transconductance amplifier
• ASIC integrated structure
Charge Sensitive Preamplifier
Active Integrator (“Charge Sensitive Pre-Amplifier”)• Input impedance very high ( i.e. NO signal current flows into amplifier)• Cf (Rf ) feedback capacitor (resistor) between output and input• very large equivalent dynamic capacitance• sensitivity A(∆qi) ~ q / Cf• large open loop gain Ao ~ 10,000 - 150,000
Ci
∆Qi
E. Berdermann et al, The use of CVD-Diamond for heavy ions… Diamond and Related Materials 10(2010),1770
Ultra-fast branch of a CSP
Simulation results of the amplifiers with THS 3201 ultra-fast current feedback amplifier
tr ~ 1.2 ns
(10 to 90%)
G1 G2
G1 > G2 to minimize S/N ratio
Standard current amplifier solution
HSMP 3862 series
Imax (1µs)~ 1APeak Inverse Voltage ~50VTj –Max. Junction Temperature ~ 150°C (OK to be used in vacuum)
Signal Output A1. A2. A3 . e
Noise Output A1.A2.A3. e1 + A2.A3. e2 + A3.e3
the gain of the first block of amplification must be kept as highas possible, in order to reduce the importance of the noise contributions coming from the following blocks i.e. the preamplifier gain has to be as large as possible ! Ao >>10 4
b) Ultra-fast Timing Circuits and Signal -Time-stamp - Time-walk & Time-jitter as perturbation effects
* Timing – time stamp but actually timing means measurement of time intervals (from fs to ms)
Walk effect - variation of time stamp (timing) caused by signal variation in amplitude and/or rise time
Jitter effect - timing fluctuations caused by noise and/or statistical fluctuations in the detector (intrinsic noise) two identical signal will not always trigger at the same point (time stamp) time variation dependent on the amplitude of fluctuation – slope/noise ratio
Fast Pulse Shaping
The noise bandwidthapproaches thesignal bandwidth
the timing jitter
tra ~ tc
“MVP “in fast time domain
New fast amplifiers:
- Ortec 9327 (1 GHz Amplifier and Timing Discriminator) - Ortec 9309-4 ( Quad Ultra-Fast Amplifier) - Ortec 9306 (1-GHz Preamplifier)
- the Ortec 579 – to slow for fast timing
• this is the reason while only 1-2 amplifier stages *
* this can be implemented only if the product [gain x bandwidth] of the amplifier is large enough !
10 cm wire; 0.2 mm diam 150 nH Impedance @ 1Ghz ~ 1 kOhm
Simulation results of the amplifiers with THS 3201 ultra-fast current feedback amplifier
1 pF ~ impedance@ 1GHz ~ 150 Ohm
Simulation results of the amplifiers with THS 3201 ultra-fast current feedback amplifier
Current Feedback Amplifier THS-3201 Main features:
- 1.8 GHz; - 6700 V/µs @ G= 2V/V; RL =100 Ohm - 18mA @ +/- 3.3V (120mW vacuum)
Gain ~10(th. 20)
Gain ~7(th. 10)
tr ~ 1.2 ns
(10 to 90%)
Wire impedance skin effect (i.e. skin depth calculator)
R0 = 1 /πro2 σ (DC & low frequencies)
- σ bulk conductivity - r0 wire radius
L0 = μ / 8π
- μ permeability (μ0 = 4π.10-7 Henry/Meter)
Rs = 1/ (σδ); q = √2 r0 / δ
δ is the “skin depth” (πfμσ)-1/2
* - this “calculator” only cover the range q < 8Which roughly correspond to r0/δ < 5 … above this value the Bessel functions become hard to evaluate…
* to remember about skin effect:- Material dependence (e.g. Ni vs. Cu ~ skin effect depth one order of magnitude)- Frequency dependence
Time walk
Accuracy of timing measurement is limited by two factors:- time jitter ( ~ to the slope/noise)
- time walk *) (due to dependency on signal amplitude and rise time variations) *) - if the rise time is known and constant, the “time walk” can be compensated in software event-by-event by measuring the pulse height and correcting the timing - if rise time vary (e.g. HP-Ge Det.) this technique fails! PSA required
Hardware: - threshold lowest practical level (i.e. > noise) or compensation technique (e.g. CFD)
Time walk for a fixed trigger level time stamp (time of threshold crossing) depends on pulse amplitude
Time jitter in LE discriminator due to: - noise on the Input Signal - pulse high variation
Time Walk in LE discriminator due to: - amplitude and rise time variations - charge sensitivity
LE – method • timing occurrence function of: - amplitude - rise time - noise
going from LE to CFD
Constant Fraction Timing
Idealcomparator
+
--
• Implementing an “active threshold”, namely the threshold is derived from the signal passing it through an attenuator Vt = f Vs ; (f < 1)• The signal applied to the comparator input the transition occurs after the threshold signal reachedIts maximum value: VT = f V0
tr
delayed input signal
attenuated input signal
Timing occurrence at the output
The circuit compensates for amplitudes and rise time if pulses have a sufficiently large range that extrapolates to the same origin
• The condition for the delay must be met for the minimum rise time
and in this mode the fractionalthreshold VT / V0 varies with rise time
For all amplitudes and rise times the compensation range the comparator fires at the time time stamp
t
Op.Amp
+/- 1.
Another view of CFD, namely the CFD can be analyzed as a special pulse shaper
Pulse Shaper, comprising the - delay (td) - attenuator (f) - subtraction followed by a zero cross trigger
The new timing jitter depends on: - the slope at the zero- crossing (depends on choice of f and td) - the noise at the output of the shaper (which increases the noise bandwidth)
Signal formation in a CFD & ARC-CFD
Ortec AN 42 – Principles and Applications of Timing Spectroscopy
T.J. Paulus - Timing Electronics and Fast Timing Methods with scintillation detectors; IEEE Trans. NS NS-32, (1985), 1242
Constant-Fraction Discrimination for TFC Bipolar Signals
vs.
Constant-Fraction Discrimination for or ARC Timing
T.J. Paulus, Timing Electronics and Fast Timing Methods with Scintillation Detectors, EG&G Ortec, IEEE Trans. on NS, Vol.NS-32; No-3 (1985), 1242
r.m.s. value of the input noise
CFD attenuation factor
mean-square value of the input noise
autocorrelation function of the input noise
CFD shaping delay
-for uncorrelated noise / signals:
Timing uncertainty due to noise- induced jitter for TFF timing signal noise
For ARC timing with linear inputsignal the slope of the CFD signalat zero crossing is
Combining former equations, we getthe expressions for noise-induced jitterwith linear input signals:
- for TCF timing
- for ARC timing
CFD a realistic approximation In the case of MCP real signals i.e. non-linear rise times
The development of MSCD method for picosecond lifetime measurement.
J.-M. Regis- PhD work 2010
• the prompt curve determination energy dependent walk in CFD• the prompt curve has to be calibrated for each branch but the timing asymmetry in the branch timing characteristic is canceled when a new physical quantity is defined, namely the Centroid Difference:
Mirror Sensitive Centroid Method
M.A. El-Wahab et al, CFT with scintillation detectors, IEEE Trans. On NS, Vol.36, No.1,(1989) 401-406
(a) CFPHT
(b) ARC-Timing
• Variation of resolving time (W*1/2) withthe attenuation factor for three cases of CFD timing: (1) - CFPHT, ~equivalent to LE timing (2) - ARC timing where ts =tr td and tm from numerical solution (3) – ARC timing where F(tm) =A; F(tm-td)=A² and ts calculated from Eq.10
• Variation of resolving time (W*1/2) with attenuation factor for different delay times
Attenuation factor A
Attenuation factor A
M.A. El-Wahab et al, CFT with scintillation detectors, IEEE Trans. On NS, Vol.36, No.1,(1989) 401-406
CFD
ARC- CFD (a)
ARC- CFD (b)
LE
CFD
LE
Walk
CFD
Ortec 583B , Ortec 584, Ortec 935, ESN-4000
Different design for walk adjustment, i.e. “monitor-inspect out.”
Ortec 572Filter Amplifier
Ortec 572Filter Amplifier
T1 T2
E2E1
Typical Fast / Slow Timing system for gamma-gamma coincidence measurements with scintillators and photomultiplier tubes
Dynode Dynode
AnodeAnode
Ortec 113Preamplifier
Ortec 113Preamplifier
• Anode vs Dynode as timing signal is still an open dispute ?!
Timing MCA
a) Classical approach TPHC (TAC) – ADC
b) TDC - direct Time-Digitizer (TDC) - Time - Expansion (Time-to-Charge) - direct Digital Interpolation TDC
Principle of TPHC (TAC)
ADC (13-14 bit) Dead Time 1-4 µs CC interface
Principle of Direct Time Digitizer
Time expanding (multihit) TDC
Principle of Interpolating in Direct Time Digitizers
Waveform diagram “vernier like scale”- TDC
Measurement of:
5.0 mm
5.1 mm
5.5 mm
An interpolating Time-to-Digital converter implemented on an FPGA structure