Dead time and count rate saturation

The PTA, and to a lesser extent the MCP-PMT, saturate measurably at high count rates of several 100 kcps. For typical count rates of around 100 kcps only a few percent of counts are lost, which may however require calibration when absolute intensity measurements are performed. The causes and effects of dead time and corresponding count rate saturation of the detector and pulse processing electronics are discussed in detail below.

There are two idealised models for dead time behaviour: paralysable and non-

paralysable response [Knoll 1989]. hi the non-paralysable model any events that occur

during the dead time period are simply lost and have no effect at all on the response of the detector. In the paralysable case any events that occur during the dead time of a previous event are also lost, but act to extend the dead time period. Both models only differ signifi­ cantly when the count rates are high. For a discussion of the two models consider the following definitions:

Rtrue - true interaction rate (input) [sec'^J Rrec - recorded count rate (output) [sec'^J Tdead - dead time [sec]

Non-paralvsable model

The fraction of time at which the system is dead is Rj-ec tdead, and the rate at which events are lost is given by Rt^e Rrec 'Cdead- Therefore

R-true ” Rfec ~ Rtrue Rpec ^dead (7.1)

and hence

R* R _ = ‘true

1 + R r (7-2)

true dead

Par al VS able model

Since in the paralysable model dead periods are not always of the same length, it is necessary to take the distribution of intervals between random events into account. The probability P(t:) of an interval between successive events occurring that is longer than x can be shown ([Knoll 1989]) to be

P(T) = e'*^‘™^" (7.3)

Consequently, the rate of occurrence of such intervals is RtrueP(T), and hence

Rrec=RtrueG'^''"'""" (7.4)

Note the fact that in the paralysable model the recorded count rate actually decreases beyond a certain value of Rtrue.

The models described above, while adequate for this simple analysis, are only rough approximations. For instance, they do not take into account the fact that the laser light is pulsed and photons are only detected within a certain time interval (e.g. TPSF width), which is smaller than the laser repetition period. A more detailed analysis of the problem would probably require Monte Carlo simulations and experimental validation. The components which can contribute towards system dead time are the MCP-PMT detector, CFD and the PTA.

M CP-PM T

In the case of MCP-PMT detectors, Rtme corresponds to the number of photon events per second, i.e. the rate at which photoelectrons are produced (taking the finite quantum efficiency into account). The recorded count rate, Rrec, then equals the rate of recorded anode output pulses. Since photoelectrons produced during the dead time of a previous event still act to deplete charge carriers, the MCP-PMT detector can be treated as a

paralysable detector. However, it should be noted that this is an idealisation, and the true behaviour is likely to be somewhere between the two models.

In order to model the MCP-PMT an estimate of the dead time is required. The Hamamatsu documentation, however, does not specify a dead time value for its detectors, but quotes a 5% deviation from linearity for a 50 nA anode current. As shown in section 6.2.1.9 this corresponds to a recorded count rate of approximately Rrec = 3x10^ cps (counts per second) for this particular detector. Hence

R,„ = 0.95 (7.5)

which can be solved for the dead time to give

^dead = = 170 ns (7.6)

^true

This result is of course a very rough approximation, and should only be interpreted as an

equivalent, and not necessarily physical, dead time value^°.

CFD

The dead time of the CFDs corresponds to the Pulse-Pair Resolving Time, which is the minimum time required for two successive pulses to be resolved. Since it is only a negligible 5 ns it will be ignored in this analysis.

PTA

The PTAs, in contrast, exhibit a much longer dead time that depends on the Time Offset, the Event dead time, and End-of-Pass dead time (see section 6.2.2.6). Since MONSTIR is normally operated at the minimum Time Offset of 80 ns, and the Event dead time is only 50 ns, it is a reasonable approximation to equate the overall PTA dead time to the End-of-Pass dead time of ~1 fis (=maximum according to manufacturer’s specification). The PTA is basically a non-paralysable system because it simply ignores any incoming events (fast NIM pulses produced by the CFD) which occur during the dead time period.

Figure 7 -2 shows the MCP-PMT and PTA saturation estimates and actual measurements up to a count rate of 10^ cps. The estimated combined curve has been computed by multiplying the two probabilities. Measurements were performed by recording the CFD output count rates (= Rrec for the MCP-PMT curve, and Rtme for the PTA curve) with a separate counter

^ This value may appear very long in comparison with standard PMTs. Apart from it being only an approxima­ tion, this may also be the result of a much slower charge replacement in the microchannels as compared to that in a classical PMT dynode.

unit; the PTA count rates were simply recorded via its PC interface. The input count rate for the MCP-PMT (Rtme) was estimated from relative measurements of the MCP-PMT illumination laser power, and assuming linearity (i.e. Rrec=Rtme) for very low count rates (<40 kcps). Error bars for the measurements are not included for clarity. The error in the x- axis (Rtme) is estimated to be -1% , based on uncertainties in the power meter measurement and the linearity assumption described above. The error in the values has been calculated to be up to -3% for the lowest count rates (obtained from repetitive measure­ ments). While the estimated saturation curve for the MCP-PMT fits well with the actual measurements, the level of saturation appears to be overestimated in the PTA (and hence combined) curve for input count rates up to ;s300 cps. This is likely to be due to an overestimate in the dead time (1 |lis), because the specification for the PTA’s End-of-Pass dead time is ‘<1 |LIs’. Hence the curve represents the worst case scenario. The sharp drop in the PTA count rate at just under 300 kcps is due to an inherent limitation of the PTAs. Because the system is run in reverse start-stop mode and the laser repetition period (-1 2 ns) is short compared to the acquisition Time Span (-80 ns), the PTA registers (though ultimately rejects) multiple Stop pulses during this span and also during part of the End-of- Pass dead time, causing a buffer overflow^’. While this is currently limiting the maximum count rate to -300 kcps per channel, a laser system operating at a lower repetition rate will push this limit upwards, and has the additional benefit of increasing the effective acquisi­ tion window width (see section 6.2.2.Ô).

To put these numbers into perspective, consider the maximum count rate allowed by the single photon counting limit. For a laser operating at a repetition frequency of 80 MHz this is 800 kcps (1% of 80x10^ pulses per second), corresponding to a significant loss of about 50% (see Figure 7 -2 (c)). At 300 kcps (the PTA limit) the loss is -25% , while at a typical count rate of 100 kcps^^ it is only <10%. Finally, it should be mentioned that no dead time correction is required since MONSTIR is currently not used to record absolute

intensities, but time-resolved measurements only. Should absolute intensities, or the ratio of absolute intensities recorded at two wavelengths, be used in the future, calibration may be required.

One may interpret this as a special form of ‘paralysable’ behaviour.

Since the overall data acquisition time of the imaging system is limited by the detector channels with the lowest count rates (largest sour ce-detector optode spacing), high count rate channels are usually attenuated to detect only :SlOO kcps.

1,000,000 MCP-PMT 800,000 600,000 Q . rJ 400,000 200,000 0 200,000 400,000 600,000 800,000 1,000,000 (^) Rtrue [cps] 1,000,000 PTA 800,000 600,000 8- £ 400,000 200,000 0 200,000 400,000 600,000 800,000 1,000,000 Rtrue [cps] 1,000,000 MCP-PMT & PTA C om b in ed 800,000 ^ 600,000 £ 400,000 200,000 (C) 0 200,000 400,000 600,000 800,000 1,000,000 Rtrue [cps]

F igure 7-2 Saturation curves of the MCP-PMT (a), PTA (b), and the two combined (c). The dashed lines represent linearity (Rrec=Rtme)- The solid lines are the estimates, and the crosses represent the actual measurements.