time of flight ( tof ) : basics

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)


s/n!

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


1 pF ~ impedance@ 1GHz ~ 150 Ohm


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

time of flight ( tof ) : basics

Documents