F9180: Diagnostické metody 2 Time-Correlated Single Photon Counting Methods Tomáš Hoder Doporučená literatura: [1] D.V.O'Connor and D.Phillips - Time-correlated Single Photon Counting, 1984 [2] W.Demtroeder - Atoms, Molecules and Photons, 2006 [3] W.R.Ware - Techniques of pulse fluorometry Time-Resolved Fluorescence Spectroscopy in Biochemistry and Biology (NATO ASI Series A: Life Sciences) vol 69, ed R.B.Cundall and R.E.Dale (New York: Plenum), 1983 [4] K.V.Kozlov et al. 2001 Spatio-temporally resolved spectroscopic diagnostics of the barrier discharge in air at atmospheric pressure, J.Phys.D:Appl.Phys. 34 3164 [5] W.Becker 2007 Advanced Time-correlated Single Photon Counting Techniques [6] W.Becker 2014 TCSPC Handbook Overview • TC-SPC technique/idea • Time scales, where we can use it, where not • Light emission, fluorescence, quenching • Sensitivity, StNR, time resolution, PMT transit • Use in plasma-physics and synchronization • Selected examples for gas discharge quantitative spectroscopy TC-SPC technique MAIN-Signal: • random single photons • spatially resolved • spectrally resolved micro-discharge SYNC-Signal: • represents shape of the full light pulse • giving a time reference STOP n_n_nJ Delay relative ■ time information L single photon accumulation first counted photon triggering possible on stochastically appearing events in time as the time reference is set on the discharge itself »> cross-correlation spectroscopy time TC-SPC basics Detector Signal: Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period N Result after many Photons Original Waveform (Distribution of photon probability) Time Instead of having problems with slow analogue PMT signal... TC-SPC obtains light intensity by counting pulses as a digital units in subsequent time channels: ■ free of gain noise of PMT ■ free of electronic noise of accidental signals to PMT ■ high signal-to-noise ratio (to PMT background counting rate) ■ higher time-resolution (Transit Time Spread « Single Photoelectron Response/Transit time) Becker 2006 Advanced TCSPC techniques Basics 0 ^.:..................T......................T...................... ......................] WJffl w Vf111 Wl .......... \ 4- Fig. 102: Single-photon pulses delivered by a R5900 PMT (left, 1 ns / div) and output signal of the PMT at a 1 -1 photon detection rate of 10 s" (right, 100 ns / div). Operating voltage -900V, signal line terminated with 50 Q. Excitation pulse sequence, repetition rate 80 MHz 100ns Fluorescence signal (expected) Detector signal, oscillocope trace I I I j I.......[ , \, t I, L, i\i Fig. 103: Detector signal for fluorescence detection at a pulse repetition rate of 80 MHz TC-SPC solves • Problems of triggering/synchro - recording of irregular emission events • Problems of time resolution - no limitation by transit times or SER of detectors • Problems of sensitivity - statistical principles behind the accumulative recordings Convolution -> cross-correlation 1. Express each function in terms of a dummy variable r. 2. Reflect one of the functions: g(T)-*g( — 7"). 3. Add a time-offset, t, which allows g{t — r) to slide along the T-axis. 4. Start f at -°° and slide it all the way to +°°. Wherever the two functions intersect, find the integral of their product. In other words, compute a sliding, weighted-sum of function /(r). where the weighting function ispf-r). The resulting waveform (not shown here) is the convolution of functions f and g. If f(f) is a unit impulse, the result of this process is simply g(t), which is therefore called the impulse response. Formally: [X 5(r)g(t-r)dr = g(t) j—so /(() 1 2 3 4 5 6 wiki 2 3 4 5 6 1 2 3 4 5 6 -5 -4 -3 -2 -1 9(1 -t) a \ m (-4 (-3 (-2 (-1 i 2 3 4 5 6 ---_ T 1-4 (-3 (-2 1 t- -12 3 4 5 6 T 1 (-4 2 (-3 2 f-2 3 (- 1 1 5 (f*9)(t) = f(-t)*g(t) > (/*3)(r)d=f (/*P)(r)= £ f(t)g(r + t) -co | oo /(i)5(r + t)dt (6-fce) £= — oo! Relevant integral transformations Convolution Cross-correlation Autocorrelation f f n Different time scales and appropriate light detection techniques Gated cameras: • Time resolution from seconds to usually 2ns (new models down to 200 or even 50ps) • Almost impossible to synchronize to time-irregular emission events (random shot is the time consuming solution) • Sensitivity of the recording is given by the StNR of given device. Usually the noise increases linearly with number of accumulation cycles. Weak signals are not easy to record. Different time scales and appropriate light detection techniques PM Discriminator TPC PD Stop ^- Start 1 photons Laser-pulse Fluorescence photons U = U0(t-t0) Laser-pulse se rate Channel number ime-to-amplitude converter first time 1961 by Koechlin (Thesis, Uni Paris) Start-stop TCS PC: • Time resolution from hundreds of nanoseconds to lOps • Possible to synchronize to time-irregular emission events with the same high resolution in time • Sensitivity of the recording is given by the StNR of given synchronization arrangement. Poisson statistics is the limiting mechanism. • Limited for high-frequency repetition emission events. Limited by the speed of electronics of the counter dealing with high-frequency input. Different time scales and appropriate light detection techniques micro-discharge MAIN-Signal: • random single photons • spatially resolved • spectrally resolved SYNC-Signal: • represents shape of the full light pulse • giving a time reference START STOP n_n_rU Delay Reversed start-stop TCSPC: • Time resolution from hundreds of nanoseconds to lOps • Possible to synchronize to time-irregular emission events • Sensitivity of the recording is given by the StNR of given synchronization arrangement. Poisson statistics is the limiting mechanism. • No limitation for high-frequency repetition emission events. Input processing only for the "main" signal. Different time scales and appropriate light detection techniques Streak cameras: • Time resolution down to units of picoseconds (some new models down to hundreds of femtoseconds) • Sensitivity of the recording comparable to the TC-SPC Different time scales and appropriate light detection techniques M++e" Probe pulse at t = t-, Pump pulse att = 0 a Nj(t) At l^(ti) -► \ / Probe Pump pulse ^ Molecular " beam -U :'l Inn Pump-and-probe technique: • Time resolution down to femtoseconds using femtosecond laser pulses • Possible to synchronize due to the synchronous generation of the fluorescence by the pumping laser pulse. Light emission, fluorescence If an atom is excited (for instance by absorption of a photon, or by collisions with electrons) into a state with energy Et above that of the ground state, it can spontaneously relax back into a lower state with energy Ej by emitting a photon hv = Et — Ej. This spontaneous emission is called fluorescence. This lower state Ej may be still above the ground state E^. In this case it can further relax into the ground state by photon emission or by a collision-induced transition. After the mean lifetime (tt) = tt the initial population N( (t = 0) has decreased to N( (0) / e. Light emission, fluorescence A classical oscillating electric dipole (Hertzian dipole) with electric dipole moment p = qr = po sin cot emits the average power, integrated over all directions § against the dipole axis (Fig. 7.3a) [5.2] — 2 ~d^oo4 _ 1 P=rjS with P2 = oP2o- (?-U) 3 Attsqc5 2 In the quantum mechanical description, the average (p) of the electric dipole moment of an atomic electron in state (n, I, mi, ms) = / with stationary wave function ^ is given by the expectation value (p) = e (r) = e j ^rif/t dr . (7.12) The vector r is the radius vector of the electron from the origin at the atomic nucleus (Fig. 7.3b). a) b) Fig. 7.3. (a) Spatial radiation characteristics of a classical oscillating electric dipole. (b) The expectation value (Pk) = —e{rk) of the quantum mechanical dipole moment in level \k), determined by its wave function ^ Light emission, fluorescence For a transition E[ -> Ek the wave functions of both states have to be taken into account, because the transition probability depends on both wave functions ^ and Vot- We therefore define the expectation value of the so-called transition dipole moment Mik — (ptk) as the integral / Mih - e / f*rfh dr (7.13) where the two indices i — {ni,li,mirmSi) and k — (nk, h, mik, mSk) are abbreviations for the four quantum numbers of each state. Replacing the classical average p2 in (7.12) by the quantum mechanical expression 1 2 (see [7.1]), we obtain the average radiation power, emitted by an atom in level (i\ on the transition (i \ -> (k\ as -{\Mik\ + \Mki\f = 2\Mik\2 (7.14) (Pik) = ~- 4 coi \Mu (7.15) 3 4ttsoc3 which is equivalent to the classical expression (7.11) for the radiation power of the Hertzian dipole, if the average p2 is replaced by 2\Mik\2. Fluorescence Fig. 7.4. Mean radiation power {ptk) emitted by Nt excited atoms as fluorescence on the transition |/) —► \k) Nt atoms in level (i\ emit the average radiation power (P) = Ni(Ptk) on the transition (i\ —► (^| with frequency cd^. Using the Einstein coefficient for spontaneous emission, which gives the probability per second that one atom emits a photon on the transition (i\ —► (k\ the average power emitted by Nt atoms (Fig. 7.4) is (P) = NiAikhvik = NiAikfuotk . (7.16) The comparison of (7.15) with (7.16) yields the relation (7.17a) Radiative lifetime measurement After the mean lifetime (f,-) = t,- the initial population A^j (f = 0) has decreased to Nt (0) / e. Fig. 7.14. Experimental decay curve of the population 7V/ of an excited level with mean lifetime T/ Excitation A,=lA, G=n) (k = n) Effective lifetime and quenching Excitation Inelastic collisions ■o 0 nB vAB Fig. 7.16. Inverse effective lifetime 1 /reff as a function of the density tib of collision partners B (Stern-Volmer plot) dNi = -(Ai + Ri)Nidt Effective lifetime and quenching 14 - 12 - 10 - 'to 8 - o 6 - 4 - 2 - 0 - Pressure (Torr) Figure 6. Stern-Volmer plot of the NjC-B 2S+, v = 0) quenching rate in pure N2. The linear fit gives a slope of (2.5871 ± 0.027) x 107 Torr"1 s"1 and an intercept of (1.5228 ± 0.055) x 107 s_1. The inverse of the intercept, x = 65.67 ± 2.37 ns is in good agreement with the 62.33 ns radiative lifetime of [24]. 111 10- 9- 8- 7- 'to 6- 0 5- 4- 3- 2- 1 - 0- 1.0 1.5 2.0 Pressure (Torr) 3.0 Figure 7. Stern-Volmer plot of the N^(B 2E+, v = 0) quenching rate in N2 + 50%C>2. The linear fit gives a slope of (2.8236 ± 0.0128) x (1.5752 ±0.0178) x 10 Torr s and an intercept of 107 s-1. The inverse of the intercept, x = 63.48 ± 0.72 ns, is in good agreement with the 62.33 ns radiative lifetime of [24]. 2 iN2 ' 2 Dilecce et al. 2010 J.Phys.D TC-SPC technique MAIN-Signal: • random single photons • spatially resolved • spectrally resolved micro-discharge SYNC-Signal: • represents shape of the full light pulse • giving a time reference STOP n_n_nJ Delay relative ■ time information L single photon accumulation first counted photon triggering possible on stochastically appearing events in time as the time reference is set on the discharge itself »> cross-correlation spectroscopy time Convolution »> cross-correlation 1. Express each function in terms of a dummy variable r. 2. Reflect one of the functions: g(T)-*g( — 7"). 3. Add a time-offset, t, which allows g{t — r) to slide along the T-axis. 4. Start f at -°° and slide it all the way to +°°. Wherever the two functions intersect, find the integral of their product. In other words, compute a sliding, weighted-sum of function /(r). where the weighting function ispf-r). The resulting waveform (not shown here) is the convolution of functions f and g. If f(f) is a unit impulse, the result of this process is simply g(t), which is therefore called the impulse response. Formally: [X 5(r)g(t-r)dr = g(t) j—so /(() 1 2 3 4 5 6 wiki 2 3 4 5 6 1 2 3 4 5 6 -5 -4 -3 -2 -1 9(1 -t) a \ m (-4 (-3 (-2 (-1 i 2 3 4 5 6 ---_ T 1-4 (-3 (-2 1 t- -12 3 4 5 6 T 1 (-4 2 (-3 2 f-2 3 (- 1 1 5 (f*9)(t) = f(-t)*g(t) > (/*3)(r)d=f (/*P)(r)= £ f(t)g(r + t) -co | oo /(i)5(r + t)dt (6-fce) £= — oo! TC-SPC statistics basics 1 Pt(i)=—— e L Pi - 1 /! /-o Photoelectrons generated by impinged photons on the cathode with given quantum efficiency. The probability of emission of / photoelectrons in the /-th interval is given by the Poisson distribution. PoO') = e-w< Pl(i) = Wie~Wi P,>i(i) = 1 -PoiD-pid) = 1 — e ' w> — w,e"H"' The Taylor series of the exponential = J _11 + yt w> function is (l-Wj+w?/2+...), we take the first two. TCSPC statistics scheme NA number of counts in i-th interval FOCUSING ELECTRODE if ND«NE it follows that Nt = NA TC-SPC statistics basics 2 then P\(i) = w, After developing to Taylor series, as shown before: Pi > i (/) = m| « *j And it follows: After a large number of excitation pulses NE, the number of anode pulses NA in the /-th interval. Therefore the number of anode pulses NA is proportional to the intensity of the fluorescence at time ts. TCSPC statistics scheme NA number of counts in i-th interval FOCUSING ELECTRODE if ND«NE it follows that Nt = NA TC-SPC statistics basics 3 NA*Nh(w( + wf) = NEqzt. Relation of NA to number of Counts in the /-th channel A/, 1 i_1 l4l Hi Because the TAC detects only the first photon in given time interval for a given excitation cycle, NA is not the number of counts in the /-th channel A/;. The true relation is given left. number of detected anode pulses Consequently the count in channel / is a measure of the fluorescence intensity at time t;. if iVD«NE it follows that N, = NA TC-SPC statistics basics 4 Generally, ND is measured at the output of the TAC and ND/NE kept below a certain limit. If ND is not very much less than NE, data can be corrected using Equation 2.10 provided that wt« 1 (see Section 6.4). Collection at high ND/NE ratios need not lead to distorted curves if pile-up inspection is performed (see Section 5.2.5(b)). However, it is simpler and probably just as efficient, when data transfer and analysis are taken into account, to keep the ratio ND/Nh below a certain value. PILE-UP effect increasing count rate from 1 to 100% of excitation rate o 1 X 40 60 Time [ns] HI 100 120 Other issues to be aware of • Color effect (consequence of photoeffect) • Afterpulsing (consequence of PMT setup) • Ultra-short reflections • • • Sensitivity and precision • The effect of PMT noise is greatly reduced by the mode of TAC operation »> enhanced Signal-to-Noise ratio (up to lOOx noise reduction) • Noise due to the dark counts on PMT (cooling, background subtraction ...) • Noise due to the counting error, number of counts in each channel l(tj) follows a Poisson distribution with a standard deviation a, given by o=(\(t))1/2 • It follows that to have 5% precision in the number of A/, counts in /-th channel, where the the curve decayed to 1% of its maximum value, one has: 0.05=1/0, =l/(Nj)1/2 and Nj is 400, that means one has to measure 40000 counts in maximum • Signal-to-Noise ratio is given as well by the Poisson distribution and is equal to the standard deviation: ,— SNR = ^Ni • Dynamic range (ratio between the largest and smallest value of measured quantity): for ICCD typically 1000:1, streak 10000:1, for TCSPC usually 100000:1 and more Comparison Fundamental comparison of TCSPC, Gated ll-CCD and Streak TCSPC Gated ll-CCD Streak Recording method Records temporal traces, but only at a single wavelength at spectra, but only at a single wavelength at a time. The spectral axis must be scanned sequentially. Records full spectra, but only at a single time position at a time. The time axis must be sampled sequentially. Records full 2-dimensional time-resolved spectra simultaneously, without any scanning. Can exploit high rep-rate sources yes no yes Can exploit low rep-rate sources no yes yes Yields Poisson statistics yes no yes Typical lifetime ranges ps to ns ns to ms sub-ps to ms Hamamatsu News 2009 PMTand MCP structure DIRECTION OF LIGHT FACEPLATE FOCUSING ELECTRODE Micro Channel Plate (MCP) Cross Section SECONDARY ELECTRON LAST DYNODE STEM PIN ELECTORON MULTIPLIER (DYNODES) PHOTOCATHODE ANODE Gain of up to 108 PMT resolution, transit time Leading edge discrimination CFD pulse-height-induced timing jitter avoided Becker 2006 Advanced TCSPC techniques PMT resolution, transit time 1 ns/div 1 ns/div 1 ns/div Standard PMT Fast PMT (R5600, H5783) MCP-PMT Fig. 175: Single electron response (SER) of different photomultipliers Due to the random nature of the detector gain, the pulse amplitude varies from pulse to pulse. Becker 2006 Advanced TCSPC techniques PMT transit time spread 10' CO ILi > 10' ■ 1 1 1 •'1 : i\' i : 1/ A \ \ R2809UI Rl56411:1 / Ifim MCP PMT tProxim FWHM:2ai pe 2>rtt> MCP PMT (Prow in FWHM:421 ps | I «ty) I I >\ • ' ■ i : 1 • '1 : ' ill •' 1 \x MJ:W//m MCP PMT (Ho FWHM:100 ps > I o-ProxJmify) • * 11 ' '1 I i i i i i 1 if i il i ' 1 I \ \ 1 \ 1 \\ V \ \\ • ■ • • • • • « t \ • • • • 0 500 1000 TIME (psec) PMT transit Table 4.1. Transient Time Spreads of Conventional and MCP PMTsa Configuration Photomultiplier (upper freqeuncy) TTS (ns) Dynode Hamamatsu R928 Side-on (300 MHz)b 0.9 9 stage R1450 Side-on 0.76 10 stage R1394 Head-on 0.65 10 stage R7400 Compact PMT, 300 ps - TO-8 (900 MHz) H5023 Head-on (1 GHz) 0.16 10 stage RCA C31000M Head-on 0.49 12 stage 8852 Head-on 0.70 12 stage Philips XP2020Q Head-on 0.30 12 stage Hamamatsu R1294U Nonproximity MCP-PMT 0.14 2 MCP R1564U Proximity focused 0.06 2 MCP MCP-PMT, 6 micron (1.6-2 GHz) R2809U Proximity MCP-PMT, 0.03d 2 MCP 6 micron R3809U Proximity MCP-PMT 0.025d 2 MCP Compact size, 6 micron R2566 Proximity MCP-PMT with - 2 MCP a grid, 6 micron (5 GHz)c aRevised from [81]. bNumbers in parentheses are the approximate frequencies where the response is 10% of the low-frequency response. The H5023 has already been used to 1 GHz. cFrom [86]. dFrom [87]. Lakowicz 2006 Principles of fluorescence spectroscopy TC-SPC review light intensity > 0.01 to 0.1 photons per signal period -> Pile-Up Problem Reference pulses from light source threshold V CFD Preamplifier start Range Gain zero cross JL threshold JL Detector » CFD (7) zert stop TAC Offset zero cross Single-photon pulses @ = control elements ADC Address (time) Memory data +1 t Adder Relatively slow recording speed and long data acquisition times -> high repetition rates and low dead time (approx. 100 ns; i.e. 107 photons/s) Becker 2006 Advanced TCSPC techniques Use in plasma-physics and signal synchronization * Short discharges with high repetition: rf discharges, barrier discharges, Trichel pulsing corona, mw discharges, self-pulsing sparks • Synchronization via light pulse, current pulse, laser excitation or TTL of applied voltage waveform Kinetic scheme dependent example • Streamer discharges generated in atmospheric pressure air • Spectra is dominated by the second positive system of molecular nitrogen • Relatively weak bands of first negative system are present as well 50000 40000 >^ H—' c 30000 CD -)—' 0 > IS 20000 o 10000 300 320 340 360 380 400 420 440 wavelength (nm) Kinetic scheme dependent example • Streamer discharges generated in atmospheric pressure air • Spectra is dominated by the second positive system of molecular nitrogen • Relatively weak bands of first negative system are present as well e + N^X1^)^ —► N+(B2£+V=0 + 2e, AE = 18.7 eV; e + N^X^+^o —► N2(C3nu)^=0 + e, AE = 11.0 eV; N^(B2S+)w/=0 N+(X2^+)^=o + hi/, A = 391.5 nm, r0B = 64.0 ns N2(C3nu)^=o N2(B3n^)w//=0 + hi/, A = 337.1 nm, r0c = 36.6 ns N£(B2£+)w/=o + N2/02 products, reBff = 0.045 ns N2(C3nu)^=0 + N2/02 products, re^ = 0.640 ns Kinetic scheme dependent example • Streamer discharges generated in atmospheric pressure air -—- kB{E/N)riK2ne(x,t)--ö— -—- kc{E/N)nN2ne(x,t)--^— ^ Teff dJB(r,t) JB(r,t) dt rB rB dJc(r.t) , JcM)^ = ^ns/sps(£/A0 at reff Trichel pulse corona Breakdown in negative corona Trichel pulse 100 microns "c5 a Ph -a ö z 0.0 electric field FNS at 391.5 nm SPS at 337.1 nm 16.5 16.6 16.7 16.8 16.9 17.0 17.1 17.2 17.3 time [ns] FIG. 3. Experimentally obtained FNS and SPS signals of positive streamer in its early stage together with determined electric field development for Trichel pulse in negative corona discharge.41 Delays of the FNS and SPS signals maxima to the electric field maximum are denoted. The uncertainty of the obtained delay values is not worse than ±20 ps. Setup for corona and calibration Townsend discharge monochromator -uc ■DC —J corona main signal PMT#1 adjustable -mirror current measurement discharge -4- optical fibre synchronizing signal -10 accumulations CFD I cfd I_ r 7V_ ADC TAC TC-SPC module MEM photon counts 1 t pulse 1 intensity 1 development ^ Kt) t(ns) PM" #2 AT coaxial delay cable Figure 1: Experimental setup for the E/N determination in TP discharge. DC: direct current power supply; PMT: photomultiplier; CFD: constant fraction discriminator; TAC: time-to-amplitude converter; ADC: analog-to-digital converter. Calibration • Streamer discharges generated in atmospheric pressure air Trichel pulse electric field i ■' ■ ■ ■ ■ 'I ■......' I.....................i 180 185 190 195 200 205 time [ns] Limits for TCSPC on streamers FIG. 4. Experimentally obtained SPS signal of positive streamer propagating towards dielectric cathode in barrier discharge arrangement42 with depicted coordinates for the estimation of the delay dilatation (a). The dilatation of the delay Sdelay as well as the increase of the emitted intensity of the SPS signal from the streamer head is shown in part (b). Quantum mechanics based example He I 492.19 nm 3x10s i- 491.8 492.0 492.2 492.4 492.6 Wavelength (nm) FIG. 2. Typical tt polarized spectra of the He I 492.1 nm line and its forbidden counterpart. Discharge conditions: (a) 200 mbar and £/gap=490 V; (b) 800 mbar and U&p=610 V. Obradovic 2008 APL Quantum mechanics based example 0 05 I_i_i_i_i_i_i_i__i........l —.....L._i_ ..... i_i_i__i_ i _,_ 0 2 4 6 8 10 12 14 16 18 20 Electric Field (kV/cm) FIG. 2. The polynomial best fits of the calculated wavelength separation AXap of 77 components of the 402.6 nm line and its forbidden line: wupper = 0^ralower=0 transition (dashed line), «?Upper~l^miower~l transition (dotted line) and average between m — 0 and m—l displacements, Eq. (3) (solid line). For the 492.1 nm and 447.1 lines only average values [solid lines, Eqs. (1) and (2), respectively] are given. The results (scattered graphs) of the experimental testing of Eqs. (l)-(3), obtained by measuring AA.AF for all three He I lines vs electric field strength determined from the tt shape of Hp profile in helium-hydrogen mixture, are also given. Kuraica 1997 APL RF discharge in helium at latm Navrátil 2015 TCSPC results Quantum mechanics based example t-1-1-1-1-1-1-1-r Time (ns) Figure 5. Time-development of electric field strength at the driven electrode obtained from the fit of forbidden and field-free component. Solid and the dotted line denote the applied RF voltage development and the development of intensity integrated over the spectral profile, respectively. Navrátil 2015 TCSPC results Summary • The principles and technical realization of the TCSPC technique were introduced • The measured fluorescence from the atomic/molecular transitions was followed back to its origin • Selected examples of quantitative high-resolution spectroscopy were presented