1. Introduction

Time-correlated single photon counting (TCSPC) is a standard measurement method of the time-resolved spectroscopy for fluorescence lifetime [1–3], Foster resonance energy transfer [4,5], diffuse optical tomography [6], and fluorescence correlation [7]. A TCSPC system is intended to count single-photon detection events for extraction of accurate timing information. But the classic TCSPC instrument counts the photoelctronic pulses with no sense of the actual number of photons in the pulse [8]. The photon statistics of the single-photon property is only regulated by the intensity of the light. The average probability of photon detection in a measurement cycle should be a few percent or lower to ensure the single-photon property. Increasing the count rate over 5% brings a considerable chance of multiple photons detected in a pulse (multi-photon pulse). It results in undesirable timing errors known as the photon pile-up effect [1]. In time-resolved counting of TCSPC, the produced temporal histogram of photon detection times can be distorted if the signal intensity is too high. Thus, the effective maximum count rate must be much lower than the nominal maximum of the TCSPC instrument.

To alleviate the photon pile-up limitation of effective counting speeds, several methods have been devised for TCSPC. A simple but costly solution is to parallelize the detection channels. The photon collection speed can be increased by using many TCSPC channels which reduces the per-channel intensities [9,10] or by minimizing the dead time of TCSPC [11]. An economic approach is devised by physically modeling and compensating the impact of the multi-photon pulse counts [12]. Meanwhile, it was recently demonstrated that a TCSPC instrument can be implemented by the state-of-the-art digital technology replacing the old analog signal processing techniques [13]. So-called digital TCSPC shares the same operation principle as that of the conventional TCSPC instrument based on analog electronics. By utilizing a high-speed analog-to-digital convertor (ADC), the core components of TCSPC, i.e., the constant fraction discriminator (CFD) and the time amplitude convertor (TAC) are all implemented in software algorithms. A valuable advantage of the digital TCSPC over the classic scheme is found in that it can digitally filter out multi-photon pulses by analyzing the pulse characteristics. This allows the digital TCSPC to exhibit higher effective maximum count rates. However, the enhancement was not so impressive in the earlier demonstration described in Ref. [13], even though very rigorous discrimination methods were applied in their digital processing. The maximum of the single-photon count rate was only 4% of the measurement rate, while the Poisson photon statistics suggests it could reach more than 30% in the theoretical limit. This was partially involved with the random fluctuation of the photoelectronic signal gain found in the photo-multiplier tube (PMT). For single photons detected individually, the pulse heights deviate so largely that the height-based discrimination of single-photon pulses becomes less effective.

The digital TCSPC scheme can be greatly improved by better selection of the high-gain photodetector for reduced gain fluctuations. If it better resolved the number of photons in a pulse by the pulse height, the digital TCSPC could reliably filter the multi-photon pulse counts out. A hybrid photodetector (HPD) can be a very suitable photodetector for this reason. It gives a combined signal gain of vacuum tube-based electronic acceleration and diode-based avalanche effect [14]. Because of its single-stage electronic bombardment, the HPD does not have stochastic electron multiplications but produces a nearly constant gain. It is well suited for the digital TCSPC as the multi-photon pulses can be discriminated by the pulse heights.

In this study, we demonstrate that the single-photon count rate of the digital TCSPC can be enhanced by simply utilizing an HPD in a fluorescence lifetime measurement system. In our experiment, we found that the count rate can be increased up to 29% of the measurement rate without significant degradation of measurement accuracy. This counting speed nearly reached the theoretical limit. It was an order of magnitude higher than what can be achieved by a classic single-channel TCSPC system. Such a high measurement speed can be very useful in quantification of fast dynamics or in fluorescence lifetime imaging (FLIM).

2. Hybrid photodetector

Let us start with explaining the characteristic difference of the HPD from ordinary PMTs for better understanding of the present study. Figure 1 shows the schematic probability distribution of ordinary PMT’s pulse heights (a), and that of an HPD (b), respectively. In the inset diagrams, the schematic structures of the PMT and the HPD are illustrated.

 

Fig. 1. Effect of gain fluctuation on photon collection. Pulse height distribution of electron amplification of PMT (a) and HPD (b). The schematic structure of PMT with multiple dynodes (inset of (a)), and that of HPD with two steps, which consist of electron bombardment using high-voltage electron acceleration and avalanche amplification using AD (inset of (b)).

Download Full Size | PDF

In the PMT, the initial photoelectron produced at the photocathode is emitted and accelerated across the voltage difference between the electrodes called dynodes. Multiplication of electrons is made in multiple stages. In each stage, the accelerated electrons are bombarded onto the metallic dynodes resulting in re-emission of electrons for the next stage. Each stage gives a relatively low gain, typically lower than 10 depending on the voltage difference. Because of the random nature of the electron multiplication, the final number of photoelectrons widely spreads in probability so that the pulse height defined by the peak pulse voltage randomly fluctuates for single-photon pulses. In the case of two photons captured by the photocathode at the same time, the number of final photoelectrons is doubled but more widely fluctuates because the probability distribution function is given by convolution of two probability distributions of individually detected photons.

On the other hand, the HPD has two-stage multiplication: electron bombardment based on high-voltage electron acceleration and avalanche amplification based on a solid-state diode. The first stage gives a high gain above 1000 from its very large voltage difference of thousands of volts. By the Polya probability distribution [15], the relative variance in the number of generated photoelectrons is inversely proportional to the voltage difference. As a consequence, the relative gain variance of the HPD is much lower than that of the PMT. But the gain obtained by the single-stage bombardment is not high enough compared to multi-stage bombardment. In the second stage of the HPD, the avalanche diode (AD) under a high reverse bias provides avalanche multiplication through which the number of electrons in the conduction band continuously increases by a high electric field in the semiconductor. Still, the total signal gain of the HPD is limited typically below ${10^6}$, and may demand a secondary high-gain electric amplifier following the HPD.

For either a PMT or an HPD, the multiplied photoelectrons form an electric pulse at the output with a pulse duration of a few nanoseconds. In an average sense, a pulse height is proportional to the number of detected photons, but with a considerable random deviation. In Fig. 1, the solid blue lines indicate the probability distributions of the pulse heights in the case of single photons detected, while the solid orange lines indicate those of double-photon cases. The height-based discrimination of single-photon pulses is hindered by randomness of the heights that brings overlapped areas of the two curves. A decision threshold must be set at the pulse height where single-photon pulses are selectively obtained with minimal chances of multi-photon pulses included in the group of low-height pulses. For the PMT, the optimal threshold is too low in terms of counting efficiency because of the large gain variations. In contrast, using the HPD allows a higher decision threshold so that a dominant portion of single-photon pulses are saved to be counted.

3. Digital TCSPC

The digital TCSPC is a digitally instrumented TCSPC utilizing a high-speed ADC [13]. The light under measurement is generated by pulsed excitation. Its photoelectronic pulse is produced by a high-gain photodetector and digitized into a digital signal form for further digital processing. The pulse time is extracted for each count of a single photon. The accumulated data are constructed in a histogram of the pulse times. For the fluorescence lifetime measurement, curve fitting of the histogram determines the lifetime of the decay curve. In the digital TCSPC, pulse discrimination can be added in counting for minimization of the photon pile-up effect.

We constructed our digital TCSPC system using a pulsed light source and a high-speed ADC digitizer. Figure 2 shows the schematic of our digital TCSPC system (a), an exemplary electric pulse digitized (b), and a temporal histogram obtained from our fluorescence lifetime measurement (c). In our system, we used a gain-switched pulse laser (PicoQuant, LDH-P-C-473) operating at a pulse repetition rate of 10 MHz. Thus, the TCSPC measurement rate was 10 MHz in the TCSPC operation. The laser pulse was incident on a fluorescent sample (1 μM Coumarin-6 in methanol) contained in a cuvette. The produced fluorescence light centered at 534 nm was collected by a lens. It passed through a long-pass filter of a cutoff wavelength of 505 nm. In our experiment, we used two different types of photodetectors for comparison: one was an ordinary PMT (Hamamatsu, H10721-20-01), and the other one was an HPD (Hamamatsu, R10467U-40). The electric pulse signal from the detector was electrically filtered for anti-aliasing filtering (Minicircuit, SLP-250) and electrically amplified (Minicircuit, ZPUL-30). The final signal was converted by a high-speed digitizer (GaGe, EON-Express) operating at a sampling rate of 1.25 GSa/s and a depth of 12 bits. The acquired signal of the digital form was processed in the processing computer. In our system, the digitizer was synchronized with the pulsed laser so that the sampling rate was an exact integral multiple of the pulse rate.

 

Fig. 2. Schematic of digital TCSPC setup (a), definition of pulse parameters from digitized signal and interpolated signal (b), and build of TCSPC with ${t_0}$ and exponential fitting (c).

Download Full Size | PDF

The acquired pulse signal was digitally processed for pulse time extraction and single-photon discrimination. The temporal shape of the pulse acquired by our digitizer is shown in Fig. 2(b). In our digital TCSPC system, a pulse was characterized by three parameters: pulse height of V_max, pulse width of Δt, and pulse time of t₀. For precise determination of the pulse parameters, the signal was interpolated for 100 times denser data points for the central part of the pulse. The pulse height of V_max was first determined at the peak amplitude. The pulse edges were found at the level of V_max/2. The time of the first edge was found for t₀, which is the very pulse time. The full temporal width of the two edges was to found for Δt. For a pulse, its single-photon property could be examined by the height and the width. Excessive heights are very likely to be produced by more than two photons detected simultaneously. Two photons detected sequentially could produce a lower height but with a larger width. Thus, it was necessary to take both height and width into account for successful pulse discrimination of single-photon counts. More details on the pulse discrimination will be given in the following section.

After repeating a number of measurement cycles, lifetime determination was performed with histogram of the pulse times (t₀) by the curve-fit to an exponential decay function. Figure 2(c) shows the temporal histogram of ${t_0}$ in log scale. The black dots are experimental data obtained from Coumarin-6 fluorescence. The red solid line shows the exponential curve fit. This measurement was performed at a low intensity and did not demand pulse discrimination. The curve fit gave a lifetime of 2.45 ns.

4. Experimental results

In this section, the operation characteristics of our TCSPC in various fluorescence intensities is described. It is related to the maximum single-photon count rate under the optimal height-based discrimination. In this report, the photon rate of detected fluorescence photons or the light intensity is measured by the average number of photons per period, denoted by N. It is calculated by

In our experiment, impact of the photon pile-up effect on the measured lifetimes were clearly observed in the cases of high intensities. Figure 3 shows the fluorescence lifetimes, experimentally obtained with the PMT (a), and with the HPD (b), depending on the average number of photons, N. In case of no pulse discrimination (red diamonds), the measured lifetimes undesirably decreased as N increased. In the low-intensity conditions where the multi-photon pulses were negligible, the fluorescence lifetime of Coumarin-6 was found to be 2.45 ns regardless of the photodetector type (yellow dotted lines). It well agreed with the reported value [16]. However, in the high-intensity conditions with considerable chances of the photon pile-ups, the lifetime measurement was severely flawed when N>0.1. The probability that two or more photons are detected in a measurement period gradually increases as N increases. Since ${t_0}$ is the temporal point of the first photon signal in a period, subsequent photons are not included in the ${t_0}$ histogram. Therefore, as the probability that two or more photons are emitted increases, the fluorescence lifetime tends to decrease (red diamonds) [1].

 

Fig. 3. Measured fluorescence lifetimes of the Coumarin 6 using the PMT (a) or HPD (b) with ${V_{max}}$ thresholding (blue squares) or without ${V_{max}}$ thresholding (red diamonds), lifetimes measured in 5% photon count rate (yellow dotted lines), and measured ${V_{max}}$ distributions (inset figures) with threshold (black dotted line).

Download Full Size | PDF

The impact of the pile-up effect can be neutralized by careful discrimination of the pulses for excluding the multi-photon pulses in counting. Single-photon pulses could be selectively collected by the pulse height and the pulse width. Width-based discrimination was made by simply excluding the pulses of widths larger than 110% of the reference width. The reference width was determined by a separate measurement of single-photon pulses. Height-based discrimination was applied differently to the measurements of the two different detectors. In the measurements with the PMT, the threshold of heights was set to be 76.3 mV, lower than the average height of single-photon pulses for surely excluding multi-photon pulses. In the measurements with the HPD, it was set to be 29.9 mV, which was slightly higher than the average height of single-photon pulses. The pulses of higher heights were discarded in counting. Blue squares of Fig. 3 show the fluorescence lifetimes obtained with the PMT (a), and with the HPD (b). The inset diagrams show the height histograms of all the pulses and the discriminated pulses for the two cases of N=0.61. The decision threshold for the height was depicted by the dashed vertical line for each histogram. As observed in blue squares of Fig. 3, the pulse discrimination was so effective that the measured lifetime remained nearly constant. This suggests that our digital TCSPC can successfully operate regardless of multi-photon pulses.

The advantage of using an HPD in the digital TCSPC is found in its higher single-photon count rate. By the pulse discrimination, the digital TCSPC could successfully count single-photon responses with both of the two different types of photodetectors. However, it was achieved by discarding a dominant portion of pulses with the PMT. In the measurements with the HPD, the pulse discrimination did not significantly sacrifice the count rate because of the higher decision threshold. Figure 4 shows the discriminated single-photon count rates of the digital TCSPC measurements with the PMT and the HPD. The dashed line depicts the theoretical single-photon rate given by the Poisson distribution. The single-photon rate increases linearly for N<<1. But it reaches the peak and eventually decreases for N>1.0. The maximum single-photon rate is 0.37. In our measurements with the HPD, the single-photon count rate follows the same trend but approximately 20% lower than the theoretical limit. It is peaked at 0.29, which suggests 79% of the single-photon counts were successfully saved. In contrast, our measurements with the PMT exhibited much lower the count rate below 0.09. At N=1, this suggests more than 75% of the single-photon counts were wasted due to the limited discrimination capabilities. For our measurement rate of 10 MHz, the effective maximum count rate obtained with the HPD is 2.9 Mcps which is three-fold improvement compared to what is achieved with the PMT.

 

Fig. 4. Pile-up-free photon count rate by the average number of photons for the HPD (square dots) and PMT (diamond dots). Dotted line: ideal single photon rates based on Poisson distribution.

Download Full Size | PDF

It is simple to determine the HPD's optimal height threshold because there is a critical threshold in which multi-photon is completely eliminated. On the other hand, in case of PMT, it is difficult to determine the optimal height threshold since there is no critical threshold. As the PMT's threshold is lowered, the accuracy of fluorescence lifetime measurement becomes better, but the photon count rate decreases. In this study, the PMT's height threshold was set when the measured lifetime is within the shot noise range of the theoretical fluorescence lifetime. We should note that this condition does not give a general solution to determine the optimal threshold of height of pulses obtained with the PMT. More detailed research is required to find a generally optimized threshold in this case. Such research is beyond the scope of this paper, but it needs to be discussed in future work.

5. Conclusion

In this work, we achieved high pile-up-free count rates of digital TCSPC by applying the HPD without compromising accuracy. Since the digital TCSPC can discriminate a single photon pulse from multi-photon pulse by amplitude threshold, it is possible to measure the fluorescence lifetime accurately regardless of the average mean photon number. Furthermore, lower gain fluctuation property of HPD make it easier to separate single photon pulses from multiple photon pulses, which make the difference of pile-up-free photon counts between PMT and HPD. When the ideal maximum of single photon count rate is 0.37, the maximum count rate of the PMT and HPD are approximately 0.09 and 0.29, respectively. It means HPD can measure more than three times of the photon counts than PMT. Therefore, digital TCSPC with HPD can help to measure fluorescence lifetime in environments with significant background noise. We expect that these technological improvements will help various measurements that are difficult to increase signal-to-noise ratios.