Becker W. Advanced Time-Correlated Single Photon Counting Techniques

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7.7 Setting the TCSPC System Parameters 325

Reference pulse Photon pulses from Detector

Laser

Fluorescence

Detector transit time

Time

Time interval to be recorded

from laser

Delayed

reference

Delay to be inserted in reference channel

Time

TAC stopPrevious

reference pulse,

pulse

delayed

Fig. 7.67 Reversed start-stop requires a delay in the reference channel to stop the TAC with

the correct laser pulse

The detector transit time is about 1 ns for an MCP, 5 to 6 ns for a TO8 PMT

or a photosensor module, and 20 to 30 ns for side-window and linear-focused

PMTs (see Sect. 6.2.3 page 224). A good reference delay to start with is 15 ns or

3 m cable for an MCP PMT and 25 ns or 5 m cable for TO

8 PMTs.

The delay in the reference path is particularly important in experiments with

pulse pickers or kHz lasers. With insufficient delay in the reference path it can

happen that a time interval completely outside the signal is recorded. Because the

signal does not wrap around a short signal period, finding the correct reference

delay can be difficult. An example is shown in Fig. 7.68.

Fig. 7.68 Recording of a low-repetition rate signal with different delay in the reference

path. Left: The delay in the reference channel is smaller than the delay in the detection

channel. A time interval before the fluorescence pulse is recorded. Right: Recorded signals

for a reference delay increased by 5, 10 and 15 ns

If long time intervals at low repetition rate are to be recorded, the delay re-

quired for the reference channel becomes correspondingly long. Unless the re-

quired delay is longer than 150 ns, a cable is the best way to delay the signal. A

high-quality cable should be used to reduce noise pickup and temperature drift in

the cable transit time, see Fig. 7.49, page 310. If an electronic delay generator is

326 7 Practice of TCSPC Experiments

used, it should be taken into account that it does not have the same timing accu-

racy as a system with a constant fraction discriminator in its trigger input. If the

reference pulses are not really stable, some timing drift and loss of resolution are

unavoidable.

7.7.4 Choosing the TAC Parameters

The TAC parameters determine the time scale and the part of the signal that is

recorded. The available parameters may differ for different TCSPC devices. Espe-

cially devices based on direct time-to-digital conversion (TDC) or sine-wave con-

version may differ considerably from devices using the TAC/ADC principle and

reversed start-stop, which will be considered below.

The time measurement block of a TCSPC device working in the reversed start-

stop mode is shown in Fig. 7.69.

ADC

TAC

start

stop

Range

Gain

Offset

AMP

detector

reference

Offset

ADC

Input

Range

TAC Range

Recorded

Interval

TAC

Time

Voltage

Gain

Core

Characteristic

Fig. 7.69 TAC control parameters in the time measurement block of TCSPC.

The TAC core generates a linear-voltage ramp that is started with the detector

pulse and stopped with the next reference pulse. The parameter „TAC Range“

governs the selection of the TAC slope. An amplifier then amplifies a selectable

voltage interval of the ramp into the input voltage range of the ADC. Conse-

quently, the offset of the amplifier acts as a delay and the gain of the amplifier as a

magnifier.

The effect of the TAC settings on the recorded data is shown in Fig. 7.70 and

Fig. 7.71. For the interpretation of the curves it is important to remember that the

device uses reversed start-stop, and that the corresponding reversal of the time

axis is corrected by reversed readout of the memory. Therefore late photons ap-

pear right, early photons appear left in the curve. However, late photons deliver

low TAC voltages, and early photons deliver high TAC voltages. Consequently,

photons with low TAC voltages appear right, photons with high TAC voltages

appear left. Figure 7.70 shows the effect of different TAC range and TAC gain,

Fig. 7.71 the effect of the TAC offset.

7.7 Setting the TCSPC System Parameters 327

Fig. 7.70 Effect of different TAC range (left) and TAC gain (right)

Fig. 7.71 Effect of different TAC Offset in a reversed start-stop system. Left: Increased

offset shifts the curve right, i.e. shifts the recorded time interval to an earlier part of the

signal. Right: For very small and very large offsets the beginning and the end of the TAC

characteristic come into view. A: Offset 0, B: Offset 50% of maximum TAC core voltage

Increased offset shifts the curve right, i.e. shifts the recorded time interval to an

earlier part of the signal. For very small and very large offsets the beginning and

the end of the TAC characteristic come into view and may cause peaks in the

recorded photon distribution (Fig. 7.71, right). These peaks are frequently the

subject of misunderstanding and discussion. They result from the nonlinear por-

tions of the TAC characteristic at the extreme ends and can easily be avoided by

using a proper signal delay and TAC offset.

At high pulse repetition rates the recording-time interval of the TAC can be

longer than the pulse period. Of course, there are no photons with TAC times

longer than one stop period. Consequently, the recorded photon distribution drops

sharply down to zero left of the TAC time corresponding to the stop pulse period.

An example is shown in Fig. 7.72.

328 7 Practice of TCSPC Experiments

Fig. 7.72 Without a reference frequency divider, photons with TAC times longer than one

pulse period do not exist. The photon distribution drops sharply down to zero left of the

TAC time (A) corresponding to the stop pulse period. The missing photons (B) are re-

corded at the end of the previous stop period

The resulting signal shape is a frequent source of confusion. Sometimes the

step at time A is even mistaken for the rise of a fluorescence signal. Of course, the

recorded curve is absolutely correct. The photons left of the cutoff point, A, are

not lost. They were recorded shortly before the previous reference pulse and ap-

pear where they should be, i.e. in the late part of the period, B, at the right end of

the photon distribution. The curve can be centred in the recorded time interval by

adjusting the signal delay in the detector or reference channel.

As in any electronic circuitry, there is some unavoidable electronic noise in the

TAC. To get the best time resolution, the TAC should be operated in the shortest

TAC range possible. The TAC core then delivers maximum voltage and the gain

of the TAC amplifier can be kept low, which results in a correspondingly low

noise at the output.

An extremely unfavourable TAC operation mode is occasionally used for re-

versed start-stop measurements with pulse pickers (Fig. 7.73, left). The laser pulse

period used is a few hundred ns, and the TAC is operated over a correspondingly

large range of the TAC core. The photons are detected only in the first few nano-

seconds of the signal period. Due to the reversed start-stop principle the TAC core

voltage varies in a small interval located far in the upper part of the TAC charac-

teristic. An extremely large offset and a high TAC amplifier gain are used to mag-

nify this interval into a reasonably short recording time span. This mode of opera-

tion has several disadvantages; electronic noise is unnecessarily amplified, a

possible pulse-to-pulse jitter appears in the photon times, and the dead time ex-

tends into the next signal period. This makes it impossible to record a new photon

in a period after a previously detected photon (see also Sect. 7.9.2, page 338).

7.7 Setting the TCSPC System Parameters 329

TAC Range

measured photon times

TAC Offset

recorded

interval

TAC Rng.

recorded

interval

measured

photon

times

delayed

reference

pulse

Stop

with

Stop

with

laser

pulse

Fig. 7.73 Recording a short signal within a long laser pulse period. Left: The stop pulse is

the next laser pulse. The measured photon times are large but vary only within a short

interval. A large TAC range and a large TAC offset have to be used. Right: The stop pulse

is the delayed laser pulse. The measured photon times are short and vary over the full TAC

range. A small TAC range and TAC offset can be used

A far better solution is to use a delay cable in the reference channel, which

shifts the photons to smaller TAC times (Fig. 7.73, right). Consequently, a smaller

TAC range and a smaller TAC gain can be used. The result is lower noise in the

TAC output signal and a correspondingly better time resolution. Moreover, the

dead time is shorter because a smaller TAC range is used. The dead time may

even be entirely hidden within the late part of the signal period that does not con-

tain any signal photons (see Sect. 7.9.2, page 338).

An example of the two modes of TAC operation is shown in Fig. 7.74. The

signal had a sharp peak followed by a slower exponential decay. The signal pe-

riod was 400 ns. The signal shape shown left was recorded by stopping TAC with

the next laser pulse. The TAC range was 500 ns, and a TAC gain of 10 in combi-

nation with a large offset was used to record the last 50 ns of the signal period.

Fig. 7.74 Recording of a signal within a 400 ns pulse period in the reversed start stop mode.

: Stop with the next laser pulse. TAC range = 500 ns, TAC gain = 10. Right: Stop with

the delayed laser pulse. TAC range = 50 ns, TAC gain = 1. The FWHM of the peak is

reduced from 216 ps to 87 ps

330 7 Practice of TCSPC Experiments

An additional zoom factor of 5 was used in the display of the data. The initial peak

of the signal is recorded with an FWHM of 216 ps.

The signal shape shown right was recorded with 10 m delay cable in the stop

signal path. A TAC range of 50 ns, a TAC gain of 1, and display zoom factor of 5

were used. The FWHM of the initial peak of the signal is reduced to 87 ns.

Further improvement is achieved by using a higher TAC gain. Figure 7.75

shows a recording with TAC range = 50 ns and TAC gain = 5. By properly adjust-

ing the TAC offset, the 10 ns interval of the signal is stretched over the full length

of the ADC characteristic. This not only delivers more time channels and a shorter

time channel width but also reduces the recorded FWHM of the signal peak to

72.4 ns.

Fig. 7.75 Recording of the same signal as in Fig. 7.74, but with a TAC gain of 10. The time

interval of the signal is stretched over the full ADC range, resulting in an increase of the

available number of time channels and a recorded width of the peak of 72.4 ns

7.8 Differential Nonlinearity

The differential nonlinearity (DNL) is the nonuniformity of the time channel

width in a TCSPC system. Because the number of photons collected in the chan-

nels is proportional to the channel width, any nonuniformity appears as a modula-

tion in the recorded photon distributions. DNL is the most important source of

systematic errors in TCSPC measurements.

Often the TAC and the ADC are considered the main source of differential

nonlinearity. This is clearly not correct for advanced TCSPC modules based on a

TAC/ADC principle using the error cancellation technique described under

Sect. “Fast ADC with Error Correction“, page 52. The DNL contribution of the

TAC and the ADC in these modules is so small that the most important source of

DNL is crosstalk between the start and stop pulses. The signals can couple be-

tween the detector and the reference channel outside the TCSPC module, or inside

the module between the two CFDs. There may also be spurious pickup of other

start- or stop-related signals: routing signals, switching signals from pulse pickers,

or signals from the driver of a pulsed laser diode. Any signal that is synchronous

with the recorded light signal is a potential source of increased DNL.

7.8 Differential Nonlinearity 331

There are two different ways a synchronous spurious signal can distort the re-

corded waveforms in a TCSPC measurement. The first one is by directly influenc-

ing the timing. Depending on the shape and phase of the spurious signal, the CFD

may trigger a bit earlier or later, resulting in a change of the apparent time-channel

width. The second source of distortion is an apparent modulation of the CFD

threshold. Because of the amplitude jitter of the detector pulses, more or fewer

photons may be detected depending on the voltage of the spurious signal at the

moment when the of the photon pulse arrives.

In practice it is almost impossible to distinguish between these two effects. The

most efficient way to avoid DNL problems is good detector shielding. The cables

of the detector signal and the reference signal should be kept well separated. The

detector should be operated at the highest possible gain. Sufficient preamplifier

gain should be used so that the CFD threshold in the plateau of the counting char-

acteristic is no smaller than 50 mV; this avoids detecting an unnecessarily high

number of low-amplitude pulses, which are more likely to be influenced by syn-

chronous noise.

A second strategy is, of course, to avoid the generation of synchronous noise in

the system. Typical sources of coherent noise are cavity dumpers, pulse pickers,

and picosecond diode lasers. For the shielding of these devices the same rules

should be applied as for detector shielding.

The DNL of a TCSPC measurement can be improved by running a reference

measurement with a continuous light signal and by dividing the measured wave-

forms by the reference recording. Unfortunately, dividing the two signals adds the

noise of the reference measurement to the result. The reference curve should

therefore be recorded with as high a number of photons as possible. In many cases

it is possible almost entirely to avoid introducing noise into the result by smooth-

ing the reference curve. The period of the DNL-induced ripple is usually longer

than the time-channel width. A symmetrical smoothing algorithm then does not

noticeably change the ripple on the reference curve but efficiently removes the

noise.

Figure 7.76 shows an example of improving a poor DNL by using a reference

measurement. Figure 7.76, left, shows the raw data of the recorded fluorescence

decay and the reference recording. Figure 7.76, right, shows the smoothed refer-

ence curve, and the decay curve divided by the smoothed reference.

It should be noted that a reference measurement efficiently removes DNL-

induced ripple but does not remove distortion caused by reflections in the optical

system (see Fig. 7.27, page 287).

332 7 Practice of TCSPC Experiments

Fig. 7.76 Improving poor DNL by using a reference measurement of continuous light. Left:

Recorded fluorescence decay function and reference curve. Right: Smoothed reference

curve, and decay curve divided by smoothed reference curve

7.9 Counting Loss in TCSPC Systems

There are several reasons why a TCSPC system may lose photons. The most obvi-

ous one is that the detector delivers an output pulse for only a fraction of the pho-

tons that reach its active area. Moreover, not all of the detected photons deliver a

useful output pulse with an amplitude above the CFD threshold.

Loss of photons inside the TCSPC module results from the facts that a single

TCSPC channel can record only one photon per signal period, and that the module

is blind during the dead time, i.e. the time during which a detected photon is proc-

essed. The detection and consequent loss of a second photon in one signal period

is usually called „pile-up“ effect. The term „counting loss“ covers both pile-up-

related and dead-time-related loss.

7.9.1 Classic Pile-Up Effect

The classic pile-up effect is shown in Fig. 7.77. A single TCSPC channel is unable

to record a second photon in a single signal period. Consequently, the second

photon is lost. (Actually the term „pile-up“ is not quite correct. It comes from

nuclear particle detection and means the detection of several particles within the

luminescence lifetime of a scintillator.)

Detection and loss of a second photon is more likely to occur in the later part of

the signal, therefore the recorded waveform is distorted. Pile-up distortion be-

comes noticeable if the count rate exceeds a few percent of the pulse repetition

rate.

7.9 Counting Loss in TCSPC Systems 333

counts counts

Fluorescence Decay Continuous Light

intensity

increases

intensity

increases

channel channel

Fig. 7.77 Effect of classic pile-up on the recorded waveforms. a: correct curves. b,c: curves

distorted by pile-up

Classic pile-up is the principal source of signal distortion in experiments with

lasers or flashlamps working at a repetition rate in the kHz range. If the experi-

ment is run at too high a count rate, extreme pile-up effects can impair the results

so severely that any attempt at correction is useless. If the detector actually sees

hundreds or thousands of photons per laser pulse, pile-up can even mimic signals

shorter than the detector transit time spread. However, classic pile-up should not

be confused with multiphoton detection. Multiphoton detection can happen if the

discriminator threshold in the detection channel is set above the single-photon

pulse amplitude. In this case, events are recorded only if several photons are de-

tected within the single-electron-response width of the detector (see Fig. 7.62,

page 320).

The pile-up distortion of the signal shape is predictable if the detector count

rate and the signal repetition rate are known [103, 104, 105, 238, 389, 549]. Sup-

pose the number of counts in a time channel,

i, is N

and the total number of exci-

tation cycles is

E. A photon in channel i cannot be detected if a photon in a previ-

ous channel,

j < i, is detected. The effective number of excitation cycles for

channel

i is then



NEE (7.9)

The probability of a count in channel

i in one excitation cycle is



(7.10)

The relation can be used for a first-order correction of the pile-up distortion. For

exceeding 10% the influence of the pile-up on

becomes noticeable, and a detec-

tion probability of

5.0

iii

PPS  (7.11)

should be used for correction [103, 389].

334 7 Practice of TCSPC Experiments

The influence of the (uncorrected) pile-up on a single-exponential lifetime can

be estimated as shown below. The probability,

, that a photon appears at a time

corresponding to channel

j in one signal period is

ePP

'

(7.12)

with

t = time-channel width,

= fluorescence decay time, P

= probability of a

count in the first channel of the fluorescence decay. The sum of the probabilities,

, for all time channels is the probability, P, of detecting a photon in one signal

period

PP =

'

(7.13)

Please note that

P can become greater than one and must therefore be considered

the average number of photons per signal period rather than a probability.

P can

be written as

'



(7.14)

The probability that a photon is detected (but not necessarily recorded) at a time

corresponding to channel j is therefore





tjt

eePP

''

 (7.15)

A photon in channel

j is recorded only if no photon was detected at any time cor-

responding to all channels before

j. The probability that no photon was detected in

these channels is obtained as follows. The average number of photons detected in

the time channels before

j is



¦¦



''



tit

itoj

eePPP

(7.16)

The sum can be written as

'



'



(7.17)

Therefore

)1(

toj

ePP

'



 (7.18)

The probability that the number of photons in the channels 0 to

j1 is zero is ob-

tained from the Poisson distribution of

0toj



and is



toj

nocount

eeP

'







(7.19)