In many time-domain single-photon measurements, wide dynamic range (more than 5 orders of magnitude) is required in short acquisition time (few seconds). We report on the results of a novel technique based on a time-gated Single-Photon Avalanche Diode (SPAD) able to increase the dynamic range of optical investigations. The optical signal is acquired only in well-defined time intervals. Very fast 200-ps gate-ON transition is used to avoid the undesired strong signal, which can saturate the detector, hide the fainter useful signal and reduce the dynamic range. In experimental measurements, we obtained a dynamic range approaching 8 decades in few minutes of acquisition.
©2011 Optical Society of America
In many optical applications, the Dynamic Range (DR) plays an important role in the extraction of information of the physical processes under investigation. Since DR is essentially the ratio between maximum and minimum detectable signal intensities, the DR upper limit is normally given by the saturation level of detection electronics, while the lower limit is usually set by background noise, e.g. at the level where Signal-to-Noise Ratio (SNR) approaches unity.
A field where DR is crucial is in fluorescence lifetime imaging and spectroscopy. The capability to separate and quantify distinct fluorophores – or the same fluorophore in different environments or conformations – on the basis of the decay constant largely depends on the available DR. This aspect is very important when total acquisition time is an issue as for Fluorescence Lifetime Imaging Microscopy (FLIM) , where lifetime reconstruction needs to be performed for a large number of points. An important application of FLIM is exploited in the study of protein–protein interactions via Förster Resonance Energy Transfer  where distances among molecules in the order of few nanometers can be measured based on changes in lifetime [1,3]. The use of time-resolved detection systems, and in particular of Time-Correlated Single-Photon Counting (TCSPC), can be particularly useful since they provide high lifetime resolution and separation of multi-exponential decays. Yet, the maximum count rate is limited by both TCSPC electronics and single-photon counting statistics requirements.
Time-resolved Near-InfraRed (NIR) spectroscopy , performed in reflectance geometry at small or null sourcedetector separation [5,6], is another application demanding a high DR (i.e. more than 5 orders of magnitude in measurements lasting a few seconds). When such technique is exploited for functional brain imaging [7,8], the localized brain activation is quantified thanks to the hemodynamic response to a specific exercise, which implies a change in the concentration of both oxygenated and deoxygenated haemoglobin [9,10], hence a change in optical parameters due to the different absorption spectra of the two chromophores . Usually, a short (few picoseconds or less) near-infrared laser pulse is injected in a region of the head and back-scattered photons are collected by means of an optical fiber. It has been demonstrated that the mean penetration depth of photons detected at a given delay after the injection of the light pulse into the medium is independent of the source-detector separation, but it increases with the photon arrival delay . Moreover, the number of photons detected at any time increases if the source-detector separation decreases. In order to increase the investigation depth and the SNR, the source-detector separation can be decreased so as to increase not just the number of collected photons at any time, but also image contrast and spatial resolution [5,6]. However, too many “early photons” (i.e. photons scattered by surface regions such as skin, skull, and cerebrospinal fluid) usually prevent the use of very small source-detector separations (few millimetres), since their number overcomes by many orders of magnitude the count of “late photons” (i.e. photons back scattered by the deeper regions under investigation). Indeed, due to the very low level of the optical signal scattered from the inner regions of the head, a single-photon detector is quite advantageous. Additionally, the DR has to be wide in order to properly measure the few late photons compared to the large number of early photons.
Another field that could benefit for a large DR is molecular optical imaging of small animals, based on imaging of genetic expression in whole animals exploiting the specific binding of fluorescence labels . The extraction of early photons – that have travelled a shorter path through the tissue – could lead to better spatial resolution of reconstructed fluorescence distribution . Here the situation is just the opposite of the previous case, since few early photons must be extracted out of a larger optical signal. Still, this can be accomplished using a high DR detection system.
Unfortunately, in Time-Correlated Single-Photon Counting (TCSPC) the maximum counting rate is limited by both the saturation of the detection electronics and the so-called “pile-up” distortion effect , arising when more than one photon reach the detector during the same measurement time slot. The reason being that only the first photon can be detected because of the dead-time of either the single-photon detector or the related electronics, which prevents to acquire a late photon when an early photon has been detected in the same time slot. Therefore, the optical power injected into the medium must be reduced of various orders of magnitude in order to avoid such saturation, thus strongly reducing the number of detectable photons , and increasing the measurement time required to achieve a desired DR.
A possible way to increase the DR of TCSPC systems is the use of a fast-gated single-photon detector with a sub-nanosecond transition of the detector from the OFF to the ON state. We have already given a first proof-of-principle of this approach applied to the functional imaging of the brain using a small source-detector separation , achieving a DR of 6 decades by means of a Single-Photon Avalanche Diode (SPAD) . Further, the dedicated electronics for fast-gating of the SPAD has been developed so to yield a sharp (200-ps rise and fall times) and flat time-gate (amplitude oscillations are limited to few per cents) . In the present paper we propose the time-gated SPAD approach as a general purpose technique to overcome DR limitations of TCSPC. To this aim, first the basic principles of the technique are presented, experimentally demonstrating a record DR approaching 8 decades with a few minutes measurements time, due to the sub-nanosecond rise-time of a short-tail SPAD. Then, an in-depth characterization of the system is performed in the 600-1100 nm wavelength range with two kinds of SPADs that have different temporal response. Such analysis will demonstrate that the dynamic range can be extended even further by improving the experimental setup and exploiting SPADs with very short diffusion tail.
Finally, an example of an application of the proposed approach to recover a weak temporal component is shown and compared to results achievable using the standard TCSPC technique. Numerical simulations will help to quantify the improvement of the novel approach in the extraction of the information.
2. SPAD detector
In order to avoid the detection of unwanted photons, either preceding or following the useful signal, the photodetector has to be kept OFF in well-defined time intervals. Then, it has to be turned ON, in a very short time (few hundreds of picoseconds), in order to reconstruct the signal with low distortion.
Some photocathode-based detectors (e.g. microchannel plate photomultiplier tubes, MCP PMTs, intensified charge coupled devices, ICCDs, and streak cameras) can be operated in fast-gated mode (with sub-nanosecond transition time), but their performances are severely limited by the fact that early photons always hit the photocathode, thus increasing the background noise and even damaging it. Thin Single-Photon Avalanche Diodes (SPADs)  do not degrade when illuminated by high-power light pulses during the OFF phase.
A SPAD is a microelectronic detector based on a p-n junction, reverse-biased above the breakdown voltage, in order to exploit the fast avalanche build-up ignited by the absorption of a single photon. The rising edge of the avalanche current marks with high precision (tens of picoseconds) the photon arrival time. An external circuit must be used to sense the avalanche ignition, to quench the detector by lowering the reverse voltage close to (or even below) the breakdown level, and finally to reset the SPAD above the breakdown. Compared to other photodetectors, the key advantage of SPADs is the capability to be gated ON and OFF very quickly (in less than 1 ns), by rising and lowering the bias voltage with respect to breakdown (which is normally of some tens of volt), and the insensitivity to large amount of photons arriving during the OFF-state, when the SPAD is biased below breakdown and the impact ionization cannot self-sustain.
Planar silicon SPADs offer high quantum efficiency in the visible spectrum and in the first part of the NIR range (about 60% at 550 nm, 20% at 800 nm and still 4% at 950 nm), thus allowing detection of very faint optical signals on a wide spectral range . The Dark Count Rate (DCR) is quite low, being of few thousands of counts per second (cps) at room temperature for a detector with 100 µm active area diameter. Timing performance can easily reach 35 ps resolution in free-running . Finally, the active area of SPAD detectors is small compared to PMTs (about 1600 times lower when comparing a 200 µm diameter SPAD with a small PMT of 8 mm). Therefore, the collection efficiency can be much lower when the optical signal arises from a large area and wide emitting angle. Notwithstanding the small area of SPADs, the benefits of the gated technique make their use in wide-dynamic range optical applications most advantageous.
The optimal operation of a SPAD in fast-gate mode is not straightforward. When gate transitions are faster than 1 ns, there are strong spurious spikes on the avalanche signal during the opening and closing of the gate because of the feed-through due to the SPAD junction capacitance . Additionally, switching transitions of 200 ps and large SPAD capacitance (few pF) give spurious spikes much higher than the avalanche pulse, thus preventing photon detection by means of standard SPAD circuits . In literature, different solutions have been proposed to solve this problem in time-resolved applications using SPADs [19–23]. Our solution is to operate the SPAD by a custom passive-quenching circuit with active reset , and to generate an auxiliary (dummy) signal that reproduces only the spurious peaks. By means of differential sensing between the SPAD signal and the dummy signal, we are able to detect the avalanche pulse and to avoid any common-mode disturbance, such as the spurious voltage spikes .
Compared to PMTs, SPADs are more affected by afterpulsing: carriers are trapped during the avalanche and are not completely released during the OFF time . Therefore, afterpulsing probability is typically stronger than in PMTs, thus increasing the noise background, in particular at gate frequency higher than 20 MHz (i.e. OFF time intervals shorter than 50 ns).
Finally, the last issue of using SPADs is represented by the diffusion tail of the temporal response. The SPAD impulse response function to a laser pulse is essentially composed by two contributions, since photons can be absorbed either in the depletion layer of the active junction or in the deep neutral region, which mainly extends below the active junction, as shown in Fig. 1 (left) [16,25]. A photon absorbed in the high-field depleted region produces a fast detector ignition, since the photo-generated electron-hole pair is quickly accelerated by the electric field, with a timing jitter essentially due to the statistical fluctuation of the avalanche build-up. Instead, a photon absorbed in the neutral regions produces an electron and a hole that slowly and randomly diffuse. Only if the electron (in n++-p+ junctions) does not recombine and eventually reaches the depleted region, it gets accelerated and triggers an avalanche, but with a significant delay. Figure 1 (right) clearly shows the two contributions in the SPAD time response: a fast peaked response (whose Full-Width at Half Maximum, FWHM, is typically few tens of picoseconds) and a slow tail (with a time constant typically greater than 100 ps) due to diffusing carriers.
When the SPAD is OFF, carriers photo-generated in the high field region (which is biased slightly below breakdown during the OFF phase) are separated and accelerated, thus leaving the depletion layer in few tens of picoseconds without triggering any avalanches, neither during the OFF state nor during the following ON state. Instead, carriers photo-generated in the neutral regions have longer lifetime and it is possible that one of them does not recombine before the rising edge of the gate pulse, thus entering the depleted region during the following ON time-slot and igniting a delayed avalanche. Therefore, in applications where a fast-gated device must detect only late photons, the diffusion tail is the main limitation for the full suppression of early photons. In fact, because of the large amount of early photons, the number of avalanche ignitions due to photons absorbed in the neutral region during OFF state is not negligible. In particular, the faster the diffusion tail, the higher the rejection of early-photons reaching the detector during the OFF state preceding the detection window. In this paper, the effect of the diffusion tail in the SPAD response is investigated for two different detector structures with different diffusion lifetimes.
3. Measurements in gated-mode
The dynamic range of the instrumentation is given by the ratio between the peak of the acquired curve (limited by the injection/stimulus optical power) and the noise floor after background subtraction (usually limited by the Poisson statistics in photon counting). In Ref , we proposed a solution to measure an optical waveform over a very wide DR. Essentially, we acquired different slices with different power intensities and then we reconstructed the whole waveform by combining slices acquired at different delays, after amplitude normalization according to the different power intensities. Figure 2 (left) shows how the waveform to be acquired (red curve) is divided in many slices (i.e. Gate1, Gate2, etc.) at different delays. By turning ON the detector during the first gate (Gate1), the first part of the curve is acquired with a certain optical power (Fig. 2, center). Then, by increasing the gate delay, a second part of the curve is acquired (Gate2), where the optical signal is weaker and, therefore, the optical power can be increased (Fig. 2, center). By repeating such procedure many times, many slices are acquired at progressively higher optical powers. Finally, the slices are normalized on the basis of the optical power and are combined together in order to reconstruct the whole waveform (Fig. 2, right). As shown, by increasing the signal level (i.e. the optical power) at longer delays, the characterization of the curve tail was improved, thus achieving a very high DR because the noise (also represented in Fig. 2) is not the same along the curve. Indeed, the signal-to-noise ratio in each slice, before normalization, is always the same, and it is that of a standard TCSPC measurement. But in the slices that acquire the tail, the signal has been greatly amplified because the gated detector is not overwhelmed by the many photons of the peak. However, after power normalization and waveform reconstruction, the noise level at the beginning of the reconstructed curve is higher than that at the end of the curve (see Fig. 2, right). It is worth noting that a high power laser and high dynamic range optical attenuators are not enough to attain a wide dynamic range on a time-scale of few nanoseconds if a non-gated detector (able to properly suppress the initial strong pulse) is used.
4. Instrumentation for fast-gated measurements
The fast gated-mode approach for extending the dynamic range has been implemented for test and exploitation for time-resolved spectroscopy. Figure 3 shows the experimental setup we used. A supercontinuum fiber laser (SC450, Fianium Ltd., UK) delivers white-light picosecond pulses at a repetition rate of 40 MHz. An Acousto-Optic Tunable Filter (Neos Technologies, FL, USA) is used to select a wavelength between 600 nm and 1000 nm, with a spectral resolution of about 5 nm. Light is injected and collected from the sample under investigation by means of two 1 mm core fibers. A small amount of the source beam is split-off and sent to a photodiode for continuous monitoring so as to compensate slow laser power fluctuations occurring during data acquisition. A stack of 3 metallic variable circular attenuators (the whole maximum attenuation is 120 dB) is used right before the injecting fiber in order to keep the total count rate within single-photon counting statistics to avoid pile-up distortion. The calibration of the attenuators is used in post-processing for normalizing all acquisitions to the same equivalent input energy.
A synchronism signal is derived directly from the master oscillator of the supercontinuum laser source and is fed both to the TCSPC board (Becker&Hickl, Germany) and to the ultra-fast pulse generator of the fast-gated SPAD system for driving the SPAD by turning-ON the detector in less than 200 ps with an adjustable time delay with respect to the laser pulse. The temporal position of the gate window can be shifted at steps of a few tens of picoseconds due to an external passive delayer, while the gate width is adjustable from less than 1 ns up to 10 ns in 10 ps steps. The time-gated curves are acquired by means of the TCSPC board.
We used two SPADs (both developed at Politecnico di Milano ) from two different production runs. Even if they are both planar devices, the two SPADs have been designed with different cross sections, namely depletion layer thickness and dopant diffusions are not the same. As a consequence, the timing responses to a pulsed laser have diffusion tails with different decay time constants . In detail, the first detector (SPAD1) has a breakdown voltage of 22 V, a decay time constant of 85 ps and an active area diameter of 100 µm, while the second one (SPAD2) has a breakdown voltage of 36 V, a decay time constant of 240 ps and an active area diameter of 200 µm. In our measurements, we compared the two SPADs in order to evaluate the influence of the diffusion tail, because the latter affects the Instrument Response Function (IRF) and the capability of the system to reject early photons.
5. Results and discussion
In order to assess the dynamic range of the developed system, we measured the IRF at 900 nm by directly coupling the injecting fiber with the collecting one. We acquired different “slices” by fast-gating the detector at different time delays from the laser peak. Starting with the laser pulse peak in the middle of the gate interval, we delayed the gate window at steps of about 37 ps for a total of 201 acquisitions (see Fig. 4 , left). For each delay, we acquired photons for 5 s, therefore the total acquisition time was about 17 minutes. When the pulse peak was inside the gate window, we attenuated the laser power by means of the variable attenuator to avoid distortions during TCSPC measurements (we kept the count-rate well below 1 Mcps, corresponding to 0.025 photons per signal period). When the gate signal was sufficiently delayed, only the pulse tail was inside the gate window and was measured. Since the longer the gate delay, the fainter the IRF, we progressively increased the laser power while increasing the delay, in order to progressively improve the SNR. By combining many slices acquired at the different delays, we reconstructed the whole IRF after normalization for the different attenuation used at each delay step (see Fig. 4, right). The time constant of the SPAD1 response tail is short (85 ps), thus allowing to reconstruct the curve with a narrow response and a wide dynamic range (note that the noise level before the main peak is in accordance with what expected from the description of the principle of Fig. 2).
Figure 5 shows the IRFs at different wavelengths for the SPAD1 as acquired, with no post-processing. The time constant of the SPAD1 response tail is almost the same at all wavelengths between 600 and 1000 nm. Therefore, the rejection of early photons is the same over the whole range. However, in this setup the DR is mainly limited by the background level after the IRF tail. Such baseline is possibly due to faint fluorescence phenomena occurring inside the optical fibers. Indeed, the background becomes lower as the wavelength increases from 600 nm to 900 nm, probably due to different excitation of the fluorophores, while it increases above 900 nm because of the laser background around 1064 nm (because of the pumping diodes of the super-continuum source). This proves that our setup has a sufficiently wide dynamic range that the very faint fluorescence of the fibers and the laser pumping background can be measured even though they are 107 times fainter than the stimulus laser pulse. Furthermore, such measurements point out that the dynamic range is limited by some components of the present experimental implementation, not by the technique itself. Experimentally, the dynamic range could be increased either by a more powerful laser or by a wider range optical attenuator, but the fluorescence of the optical fibers and the background of the laser are limiting the bottom end of the dynamic range.
Figure 6 shows an IRF measured at 700 nm with the SPAD2 (solid line) compared to that of SPAD1 (dotted line). The longer time constant of the response tail (240 ps, i.e. about 3 times longer than that of SPAD1, due to the different designs ) causes a worsening of the temporal performances of the device since the maximum DR is reached only after 5 ns. This limitation counteracts the improvement in the collection efficiency due to the wider active area (200 µm vs. 100 µm) that would reduce the measurement time. Generally speaking, the diffusion tail of the SPAD sets a limit on the fastest decay that can be measured with the proposed fast-gated technique: the faster the decay of the signal to be measured, the shorter has to be the time constant of the diffusion tail. For example, an optical waveform with a decay time constant of 150 ps could not be measured by means of the SPAD2 because its diffusion tail would be too slow that it would hide the signal.
In photon migration measurements at null source-detector distance there are fast-decaying phenomena that are very difficult to be measured. Indeed, the widening of the curve due to the absorption of photons can be seen only many orders of magnitude below the main peak , with an overall time-scale of few ns, thus the SPAD2 response tail can hide small changes in the absorption coefficient of the diffusive media. Therefore, depending on the application, a proper trade-off between detector response tail and photon collection efficiency must be chosen in order to employ either SPAD1 or SPAD2.
Fast-gated vs. standard TCSPC
In Fig. 7 , we compare IRFs acquired with different techniques. The dotted line is the IRF of SPAD2 acquired by means of the gated technique. The solid lines represent the IRFs of the same SPAD2 acquired with different measurement times by means of a standard TCSPC scheme (the non-gated technique), i.e. with the laser pulse peak always inside the acquisition window. In order to fairly compare the two techniques, a proper background subtraction must be applied to the non-gated curves for exploiting the increase in SNR at longer acquisition times. Nevertheless, a non-gated technique would require an excessive measurement time in order to reach the same wide DR of the fast-gated one.
For a better comparison of gated and non-gated techniques, with no artifacts, we performed numerical simulations. Figure 8 shows some numerical simulations of IRF curves with different integration times for a non-gated single-photon detector with a DCR of about 15 kcps (counts per second), as measured by a TCSPC instrumentation with 3 ps channel width (the same conditions of the measurements previously shown). Figure 8 left reports simulations without background subtraction, while Fig. 8 right shows the same simulations with background subtraction, thus highlighting the DR improvement due to longer acquisition time (the DR increases with the square root of measurement time).
Example of application: Time-resolved diffuse optical spectroscopy
Besides measuring the IRF of the fast-gated setup, we proved the capabilities of the system in a specific application, i.e. the time-resolved diffuse optical spectroscopy. A diffusive mediumis illuminated from a point source (e.g. an optical fiber) and diffused photons are collected at a given distance from the source (e.g. by means of another optical fiber).
In Fig. 9 two diffuse reflectance photon distributions are acquired at a small source-detector separation of 2 mm by means of SPAD1  from homogeneous liquid phantoms with a reduced scattering coefficient of 0.5 mm−1, and different absorption coefficients of 0.01 and 0.005 mm−1. As can be seen, the discrimination between the two curves acquired from the phantoms and that of the IRF is possible only three decades below the main peak. Therefore, the 7 orders of magnitude DR of our setup guarantee a good fitting of the curves with the theoretical model and a good accuracy in the estimation of absorption coefficients [26,27]. It is worth noting that the differences between the two phantoms can be appreciated by the combination of: i) the gated technique; ii) a detector with short diffusion tail (SPAD2 cannot detect such differences since its temporal response at a delay of 2 ns from the main peak is more than two orders of magnitude higher than that of SPAD1, see Fig. 6).
Comparing the present technique with the well-known standard technique, it is worth noting that the reconstructed IRF of Fig. 9 consists of a total amount of about 5·1011 equivalent photon counts, but the number of photons collected after 2 ns from the main peak is only 6.4·106. Therefore, at such long delays a standard non-gated technique would have collected about one photon every 105 photons of the whole curve, i.e. one photon every 2·106 laser pulses (since the counting rate must be more than 20 times lower than the laser pulse rate in standard TCSPC technique in order to avoid pile-up distortion). Hence, with a pulse repetition frequency of 40 MHz in this experiment, only about 20 photons/s can be detected after 2 ns from the main peak with a non-gated technique.
In addition to the measured curves, a simulated IRF of a non-gated instrument, with and without background subtraction, acquired with two different integration times (105 s (left) and 108 s (right)) is shown in Fig. 9. It is worth noting that 105 s (i.e. about 28 hours) are necessary to achieve a DR of about 6 orders of magnitude. Such a wide DR is hardly sufficient to discriminate changes in the absorption coefficient when performing photon migration measurements at small source-detector separation, since the background noise is still overlapping with the last part of the curves, thus hiding the widening of different pulses. Such a long measurement time prevents the possibility to perform spectroscopy measurements with the approach of null source-detector separation when using a non-gated detection system. A wider DR would be preferable, such as the 7.5 orders of magnitude, achievable in 108 s (Fig. 9, right). In this case, background fluctuations are well below the signal, thus ensuring a good SNR, but the remarkable measurement duration (more than 3 years) is of course unreasonable.
In order to further reduce the measurement time of the gated technique (that is about 17 minutes for the measurements reported in this paper), when the information is expected around a given delay in the reflectance curve, it is possible to acquire only one slice of the curve at such a delay, thus avoiding the whole curve reconstruction and adjusting the laser power accordingly. For instance, a measurement time of 1 s could be sufficient to detect possible changes in the reflectance curve at a given delay, thus further reducing the measurement time of 108 times shorter than required by a standard instrumentation.
We presented a novel instrumentation based on fast time-gated Single-Photon Avalanche Diode (SPAD) aimed at avoiding the limiting trade-off between measurement time and dynamic range in TCSPC measurements. The fast-gating approach (200 ps rise/fall times of the gate signal) allows a precise selection of photons to be detected at a given arrival time.
After a description of the fast-gated technique, we discussed instrument response functions of two experimental implementations, highlighting the important role of the detector response tail in the assessment of the dynamic range. Moreover, in this paper we investigated the main limitation of the experimental implementation of the proposed technique, pointing out that the continuous laser background and the fluorescence of the optical fiber are the main limits). We also compared standard and fast-gated TCPSC measurements by means of numerical simulations in order to evaluate the improvement in terms of acquisition time. Finally, in time-resolved reflectance optical spectroscopy we obtained a 108 dynamic range in a measurement time 105 times shorter than traditional TCSPC techniques.
The fast-gated SPAD can be successfully exploited in many different applications where a large amount of photons leading or following the useful signal to detect must be avoided, such as time-resolved near-infrared spectroscopy at small or null source-detector separation, fluorescence lifetime imaging and spectroscopy, molecular optical imaging of small animals.
The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7 2007-2013) under grant agreement n°. HEALTH-F5-2008-201076. The authors wish to acknowledge Prof. Sergio Cova, Prof. Massimo Ghioni and Dr. Ivan Rech for the development of silicon SPADs.
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