Becker W. Advanced Time-Correlated Single Photon Counting Techniques

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184 5 Application of Modern TCSPC Techniques

pulses of the microscope (line clock and pixel clock) must be divided by two,

which can be easily accomplished by a single SN 74 HCT74 CMOS device.

5.10.3 Practical Tips

TCSPC-FCS with CW Excitation

The TCSPC-FCS technique can also be used in conjunction with a continuous

laser. Of course, in this case the measurement does not deliver a meaningful micro

time, and no lifetime data are obtained. Because the TCSPC module needs a syn-

chronisation pulse to finish the time measurement for a recorded photon, an artifi-

cial stop pulse must be provided. This can be the delayed detector pulse itself or a

signal from a pulse generator; see Fig. 5.116.

start

stop

Detector

Delay

Power

Splitter

Detector

start

stop

TCSPC

module

Pulse

Generator

10ns

= 2m cable

TCSPC

module

Fig. 5.116 Stop pulse generation for TCSPC-FCS with a continuous laser

Detectors for TCSPC-FCS

Compared to fluorescence decay measurements, the efficiency of FCS measure-

ments is relatively low. For a given number of photons, N, the SNR of a fluores-

cence decay measurement is proportional to N

1/2

, whereas the SNR of FCS is

proportional to N itself. This somewhat surprising behaviour results from by the

fact that two photons are needed to obtain one macrotime coincidence in the corre-

lation histogram. The strong dependence of the SNR on the number of detected

photons makes detection efficiency an important issue in FCS.

Most FCS setups therefore use single photon avalanche photodiodes [323, 424],

usually SPCM-AQR detectors from Perkin Elmer [408]. These detectors have a

quantum efficiency that reaches 80% at 800 nm. However, single photon APDs

often have a timing delay and transit time jitter dependent on wavelength and

count rate. The changes can be of the order of 1 ns. Recording a fluorescence

decay curve under this condition delivers questionable results.

Timing problems can be avoided by using PMTs with high-efficiency GaAsP

photocathodes, such as the Hamamatsu H742240 module [214]. The modules

have a stable and almost wavelength-independent transit time spread of about

300 ps duration (see Sect. 6.4.2 page 245). The quantum efficiency reaches 40% at

5.10 Fluorescence Correlation Spectroscopy 185

550 nm. Below 500 nm it is higher than for a single photon APD. Another benefit

of a PMT is the large cathode area. In two-photon FCS the light emitted at the

back of the sample can be collected by the condenser lens of the microscope and

directed to a second PMT. The poor optical quality of the condenser precludes

focusing on an APD, but is no problem for the PMT.

Another troublesome effect is light emission from single photon APD detectors

(Fig. 5.105, page 175) [299, 515]. Light emission has no effect on single-channel

FCS, but can cause a false cross-correlation component in fluorescence cross-

correlation experiments. The problem can be avoided by using carefully designed

beamsplitter optics (Fig. 5.106, page 175) or by using PMTs for detection

(Fig. 5.107, page 176).

All photon counting detectors show a more or less pronounced afterpulsing (see

Sect. 6.4, page 242). Afterpulsing causes a steep rise of the autocorrelation func-

tion towards short times in the range below one microsecond. Fortunately, most

diffusion phenomena happen at a longer time scale than the afterpulsing of fast

detectors. However, afterpulsing can interfere with conformational changes, inter-

system crossing, and rotational depolarisation.

The absolute amount of afterpulsing in PMTs increases with the gain. Reducing

the operating voltage of a PMT while increasing the preamplifier gain therefore

helps, but does not remove the problem entirely. Moreover, the height of the after-

pulsing peak in the autocorrelation function is proportional to the reciprocal count

rate. The reason is that the probability of detecting an afterpulse of a previously

detected photon is constant, whereas the probability of detecting another photon

increases with the count rate. The effect of the count rate on the afterpulsing peak

in the correlation function is shown in Fig. 5.117.

Fig. 5.117 Effect of the count rate on the height of the afterpulsing peak. H7422240 detec-

tor, count rate 10 kHz (left) and 100 kHz (right)

Afterpulsing can be almost entirely rejected from FCS results by cross-

correlation. The light is split into two equal beams that are detected by individual

detectors (see Fig. 5.100, page 171). Afterpulses in one detector are not correlated

with any counts in a second detector and therefore do not noticeably change the

cross-correlation function. Figure 5.118 shows autocorrelation and cross-

correlation curves recorded with two H742240 detectors at a Zeiss LSM 510

186 5 Application of Modern TCSPC Techniques

NLO laser scanning microscope. Curves a and b are the autocorrelation curves of

the individual detectors. Curves c and d are cross-correlation curves of the signals

of detector 1 against detector 2 and vice versa. The afterpulsing is almost entirely

removed in the cross-correlation.

Fig. 5.118 Rejection of detector afterpulsing by cross correlation. GFP solution, two

H742240 detectors, LSM 510 NLO microscope in beam-stop mode. Curves a and b: Auto-

correlation of the signals of the two detectors. Curves c and d: Cross-correlation detector 1

against detector 2 and vice versa

Background Signals

Background signals (e.g., detector background, leakage of daylight, or leakage of

excitation light) result in an apparent reduction of the correlation coefficient or even

in complete failure to record any FCS curve. Leakage from room lights has a strong

correlation at the line frequency. The problem can therefore easily be identified by

checking the autocorrelation function in the 100-ms range. Identification of leakage

from continuous light sources can be more difficult. The usual suspects are com-

puter screens and indicator LEDs of electronic devices. Microscopes often have

internal NIR LEDs to control filter wheels or sliders. Emission of these LEDs can

be a problem for detection around 820 nm. Other sources of background signals are

filter fluorescence, spurious laser emission at the detection wavelength and leakage

of excitation light. For pulsed excitation and TCSPC detection the source of the

background can often be identified by checking the fluorescence decay functions.

However, filter fluorescence can have extremely long lifetimes (see Fig. 7.13, page

275), and a pulsed laser may emit some continuous background.

Saturation and Photobleaching

The strong dependence of the SNR on the photon number makes it important to

record as many photons as possible. In principle, the count rate of an FCS experi-

ment can be increased by increasing the laser power. Theoretically, a single mole-

cule with a fluorescence lifetime of

can perform about 1/

absorption-emission

cycles per second. For a molecule with a quantum efficiency close to one,

5.11 Combinations of Correlation Techniques 187

= 5 ns, and a detection system of 5% efficiency the count rate would be 10

-1

This count rate is unrealistically high. Practically achieved count rates are between

a few 10

-1

and about 10

-1

. Higher excitation power yields higher count rates,

but increases the excited volume by saturation [101]. Moreover, photobleaching

within the diffusion time results in an apparent reduction of the correlation time

[49, 140, 539]. For comparable emission rates photobleaching is faster for two-

photon-excitation than for one-photon excitation [140].

Interference of the Laser Repetition Frequency with the Eecording

Clock

If FCS experiments are excited by a pulsed laser the laser pulse repetition fre-

quency can interfere with the recording clock of the correlator. The result is a

periodical variation of the number of laser pulses per macrotime period. The same

period shows up in the correlated intensity. Periodicity can appear on any time

scale, depending on the difference of the laser and macrotime clock frequencies or

their harmonics. The problem is most pronounced if both frequencies are almost

identical. Interestingly, the problem has never been mentioned for two-photon

FCS in conjunction with the commonly used correlators. The reason may be that

the progressive and overlapping binning used in these devices smoothes out a

possible periodicity. In modern TCSPC modules the problem is anticipated by

providing an optional clock path from the timing reference (Sync) input to the

macro time clock. The macro time clock is then synchronised with the laser pulse

repetition rate, which removes the problem entirely. Moreover, using the Sync

signal as a macro time clock is a simple way to synchronise several TCSPC chan-

nels of a multimodule system. However, using the Sync input as a clock source for

FCS requires that the Sync signal is free of glitches.

Dead Time and FCS Resolution

The minimal time at which correlation data can be obtained with a single TCSPC

module is the dead time. Currently fast TCSPC modules have dead times of 100 to

125 ns. A faster macro time clock yields more points on the auto- and cross-

correlation curves, but no correlation data below the dead time.

Correlation down to 100 ns is usually enough to resolve diffusion times and inter-

system crossing. Nevertheless, cross-correlation data at a shorter time-scale can be

obtained by using two TCSPC modules with synchronised macrotime clocks (see

Fig. 5.120). Synchronisation can be achieved by using the Sync signal, i.e. the laser

pulse repetition frequency, as a macro time clock for both modules. This synchroni-

sation works up to about 100 MHz, so that times down to 10 ns can be correlated.

5.11 Combinations of Correlation Techniques

The correlation techniques described above use different approaches for photon

correlation on the picosecond scale and FCS experiments. Although the same

188 5 Application of Modern TCSPC Techniques

TCSPC modules can be used for these experiments, antibunching and FCS data

are not obtained simultaneously. Several ways to combine the techniques are

shown below.

5.11.1 Combining Picosecond Correlation and FCS

At first glance combining a picosecond correlation experiment with FCS looks

simple. An antibunching experiment could be run in the FIFO mode, and the an-

tibunching and the FCS curves be obtained from the micro times and macro times,

respectively. Unfortunately this approach has a flaw. Most of the photons emitted

by the sample cause either a start without a stop, or a stop without a start;

however, the TCSPC module records only complete start-stop events. Therefore

the system records only a tiny fraction of the photons reaching the detectors. The

low efficiency makes the obtained time-tag data practically useless for FCS.

A useful way to record antibunching and FCS in one experiment is to use two

TCSPC channels of a multimodule system. Both channels are operated in the

FIFO mode. The photon pulses of the detectors are used as start and stop signals

of one TCSPC channel. The antibunching curve is obtained from the micro times.

Simultaneously, the detector signals are connected to a router. The router is con-

nected to the second TCSPC channel. This channel records the photon times of

both detector signals versus the laser reference signal, or, in case of a continuous

laser, versus an artificial reference signal. The FCS curves are calculated from the

macro times of this channel.

5.11.2 Correlation of Delayed Detector Signals

A single TCSPC module detecting via several detectors and a router is unable to

record several photons within the dead time of the signal processing electronics.

The signals of the detectors therefore cannot be correlated at a time scale shorter

than the dead time. The problem can be solved by routing of delayed detector

signals [538]. The principle is shown in Fig. 5.119.

CFD (start)

SYNC (stop)

Detector 1

Detector 2

Beam Splitter

FIFO Readout

Micro Time: Start-Stop Time

Macro Time: Time from start

of experiment

Pulsed Laser

Sample

Router

HRT-41

HRT-81

HRT-82

Timing

Routing

Detector

Channel

Detector Channel: 1 or 2Delay, > 150 ns

Fig. 5.119 Routing of delayed detector signals

5.11 Combinations of Correlation Techniques 189

Several detectors are connected via a router to the same TCSPC module. The

photon pulses from the second detector are delayed by more than the dead time of

the TCSPC module. More than two detectors can be used if their delay lines are

different by more than the module dead time. The stop pulses for the TCSPC mod-

ule come from the pulsed laser, or, if a CW laser is used, from an external clock

generator. Due to the different delay of the detector signals, photons detected

simultaneously do not arrive simultaneously at the router inputs. Therefore, pho-

tons detected in the same laser pulse period are recorded at different times and

stored in the FIFO data file with a macro time offset. The differences in the macro

times caused by the delay lines in front of the router are known and can easily be

corrected when the photons are correlated.

The setup was used to track the intensity fluctuations, the lifetime and the num-

ber of molecules in the laser focus simultaneously [538]. An application to single-

molecule FRET is described in [237].

5.11.3 Synchronisation of TCSPC Modules

As briefly mentioned above, a system of two synchronised TCSPC channels can

be used to obtain correlation data on a time scale shorter than the dead time. The

required system connections are shown in Fig. 5.120.

start

stop

Detector 1

Detector 2

Beam Splitter

FIFO Readout

Micro Time: Start-Stop Time

Macro Time: Time from start

of experiment

Experiment

Trigger

FIFO Readout

Micro Time: Start-Stop Time

Macro Time: Time from start

of experiment

(Pulsed

Clock Out

Clock In

Exp. Trg.

Sample

start

stop

Exp. Trg.

Laser

Laser)

Clock

Generator

(CW Laser)

Fig. 5.120 Correlation setup with two synchronised TCSPC modules

The start pulses for the TCSPC modules come from the detectors, the stop

pulses from the laser, or, if a CW laser is used, from an external clock source. To

make the detection times in both modules comparable, the internal macro time

clocks of the modules must be synchronised. This is achieved either by a clock

interconnection, i.e. by using the internal macro time clock of one module for

both, or by using the stop signals (i.e. the reference pulses from the laser) as macro

time clocks. Moreover, the recording must be started simultaneously in all mod-

ules by an external experiment trigger. The setup can be used to cross-correlate the

signals from both detectors down to the minimum macrotime period accepted by

the TCSPC modules, i.e. about 10 ns.

190 5 Application of Modern TCSPC Techniques

In principle, correlation at even shorter time-scales is possible by including the

micro times of both modules in the calculation of the correlation function. The

problem with this approach is that the micro time scales of the modules may be

slightly different, and the macro time transitions may be shifted due to different

transit times in the detectors, cables and TCSPC modules. Correcting all these

effects is extremely difficult, yet not impossible. Suitable calibration and correla-

tion algorithms were developed by S. Felekyan, R. Kühnemuth, V. Kudryavtsev,

C. Sandhagen, and C.A.M. Seidel, Universität Dortmund.

Figure 5.121 shows a correlation curve for an aqueous Rhodamine110 solu-

tion obtained in a setup of two channels of a Becker & Hickl SPC134. Two

H742240 PMT modules were used for detection. The solution was excited by a

CW Ar

laser at 496 nm. The acquisition time was 16 minutes.

Fig. 5.121 Correlation curve covering a continuous range from 10 ps to 100 ms obtained by

correlating two synchronised channels of an SPC134 system. Correlation of detector A vs.

detector B (grey) and detector B vs. detector A (black). Courtesy of S. Felekyan,

R. Kühnemuth, V. Kudryavtsev, C. Sandhagen, and C.A.M. Seidel, Universität Dortmund

At a time scale between 0.1 and 1 ms the curves are dominated by the diffusion

time. Intersystem crossing is apparent between 1 and 10 µs. Below 10 ns the

singlet lifetime causes the correlation curve to drop to one. A fit to a suitable

model delivers an average number of molecules in the focal volume of 3.5, a dif-

fusion time of 0.3 ms, an antibunching time of 3.5 ns, a triplet lifetime of 1.9 µs,

and a mean triplet population of 29%.

The synchronisation of the separate TCSPC channels can probably be simpli-

fied if a dual-channel TDC principle is used instead of the TAC-ADC technique.

TDC chips are commercially available with eight channels driven by a common

clock and a resolution of 120 ps [1, 2]; they are used in large numbers in experi-

ments of high energy physics. A correlator based on a chip like this would be able

to resolve correlation effects on a continuous time scale from the sub-ns to the ms

range.

5.12 The Photon Counting Histogram 191

5.12 The Photon Counting Histogram

The photon counting histogram (PCH) of an optical signal is obtained by re-

cording the photons within successive time intervals and building up the distribu-

tion of the frequency of the measured counts versus the count numbers. A charac-

terisation of the PHC was given in 1990 by Qian and Elson [420]. The technique

is also called fluorescence intensity distribution analysis, or FIDA. The principle

is explained in Fig. 5.122. For a light signal of constant intensity, the PCH is a

Poisson distribution. If the light fluctuates, e.g. by fluctuations of the number of

fluorescent molecules in the focus of a laser, the PCH is broader than the Poisson

distribution.

time

Number

photons

detected

Number of photons per

Number

containing

N photons

PCH

intervals

Fig. 5.122 Photon counting histogram. Left: Photons counted in successive sampling time

intervals. Right: Histogram of the number of time intervals containing N photons

The optical setup for PCH experiments is the same as for one-photon or two-

photon FCS. The sample is excited by a laser through a microscope objective lens.

The effective sample volume is confined to a few femtoliter by two-photon excita-

tion or by confocal detection. PCH recording requires a high-efficiency detector

and a multichannel scaler that records either the photon counts in successive time

bins or the time-tag data for the photons. The optimum sampling time interval

depends on the time-scale of the fluctuations and is usually in the 10 to 100 µs

range. Recording directly into fixed time bins yields relatively compact data sets.

Time-tag recording yields more flexibility and is usually preferred. Time-tag data

can be used to calculate PCHs in almost any sampling time interval, and to calcu-

late FCS curves and PCHs from the same data. A suitable device is described in

[156].

The PCH delivers the average number of molecules in the focus and their mo-

lecular brightness. Several molecules of different brightness can be distinguished

by fitting a model containing the relative brightness and the concentration ratio of

the molecules to the measured PCH. The theoretical background is described in

[91, 92, 256, 258, 373, 393, 394, 420].

The PCH/FIDA technique can be extended for two-dimensional histograms of

the intensity recorded by two detectors in different wavelength intervals or under

different polarisation. 2D-FIDA delivers a substantially improved resolution of

different fluorophores [257, 258]. Further improvement is achieved by using

192 5 Application of Modern TCSPC Techniques

pulsed excitation and using the fluorescence lifetime as an additional dimension of

the histogram. The techniques is termed „Fluorescence Intensity and Lifetime

Distribution Analysis“ or FILDA [258, 393]. Of course, accurate lifetimes cannot

be obtained from the small number of photons within the individual sampling time

intervals. However, useful lifetime information may be obtained from the photon

arrival times in the laser period averaged over the sampling time interval. The

average arrival time is directly related to the first moment of the decay function

and therefore to the fluorescence lifetime.

FIDA, 2D-FIDA and FILDA do not directly deliver information about the dif-

fusion times of the fluorescent species. Diffusion times are, however, obtained by

calculating the PCHs in different sampling time intervals and fitting the result by a

model that contains both the molecular brightness and the diffusion time [258].

In principle, FIDA, 2D-FIDA, and FILDA are possible by using any TCSPC

module that has the FIFO mode and the multidetector technique implemented. The

data recorded in the FIFO mode contain the individual arrival time of each photon

in the laser pulse sequence, the time from the start of the experiment, and the num-

ber of the detector that detected the photon. The PCHs can be built up from these

data for each detector and for virtually any sampling time interval. Figure 5.123

shows photon counting histograms of a 10

-9

molar GFP solution calculated from

the same FIFO data used for the FCS curve in Fig. 5.112, page 181. Figure 5.123,

left, compares a PCH of the GFP solution with the PCH of a light signal from an

LED, both calculated within a sampling time interval of 1 ms. Figure 5.123, right,

shows PCHs of the GFP solution calculated in sampling time intervals of 100 µs,

1 ms, and 10 ms.

Fig. 5.123 PCH obtained from the FIFO data used for FCS in Fig. 5.109, page 178. Count

rate 6,000 photons per second

Figure 5.124, shows distributions of the average photon arrival time for different

sampling time intervals. If the sampling time is reduced, the distribution of the

arrival time becomes wider. For very small sampling time intervals, most of the

time intervals contain either no photon or one photon. The distribution of the arri-

val time then converges with the fluorescence decay curve.

5.13 Time-Resolved Single Molecule Spectroscopy 193

Fig. 5.124 Distribution of the first moment, M1, of the photon arrival times, calculated

from TCSPC time-tag data. Sampling time interval 100 µs, 1 ms, and 10 ms. Count rate

3,000 photons per second

Figure 5.123 and Fig. 5.124 reveal a possible problem with applying the

PCH/FIDA technique to biological systems. On the one hand, the sampling time

interval should be shorter than the average diffusion time of the molecules through

the focal volume. On the other hand, more than one photon should be recorded per

sampling-time interval to obtain well-resolved histograms. The required count rate

is difficult to obtain from biological samples.

Although TCSPC is used successfully for BIFL experiments, little has been

published about applications for FIDA. The reason is probably that the dead time

of TCSPC is considered a drawback. However, a simple consideration shows that

the detectable burst rate is not substantially reduced by the dead time of the

TCSPC device. The commonly used detectors lose 50% of the photons at an input

rate of about 1610

-1

[408], fast TCSPC modules at 1010

-1

(see Fig. 5.94,

page 162). This means the dead time of the TCSPC module is only slightly longer

than the dead time of the detector. The use of TCSPC for PCH experiments

therefore does not result in a considerable increase of dead-time-related errors.

Moreover, BIFL applications have shown that the burst count rates are well within

the counting capability of TCSPC (see below).

5.13 Time-Resolved Single Molecule Spectroscopy

The techniques described under „Photon Correlation“ exploit the correlation be-

tween the photons emitted by single molecules and by a small number of mole-

cules. Picosecond photon correlation techniques investigate effects driven by the

absorption of a single photon of the excitation light. The effects investigated by

FCS are driven by Brownian motion, rotation, diffusion effects, intersystem cross-

ing, or conformational changes. Because of these random and essentially sample-

internal stimulation mechanisms, correlation techniques do not necessarily depend

on a pulsed laser.

A second way to obtain information about single molecules is time-resolved

spectroscopy with pulsed excitation at high repetition rate. The borderline between