Single-shot time-gated fluorescence lifetime imaging using three-frame images

Qualitative and quantitative measurements of complex flows demand for fast single-shot fluorescence lifetime imaging (FLI) technology with high precision. A method, single-shot time-gated fluorescence lifetime imaging using three-frame images (TFI-TGFLI), is presented. To our knowledge, it is the first work to combine a threegate rapid lifetime determination (RLD) scheme and a four-channel framing camera to achieve this goal. Different from previously proposed two-gate RLD schemes, TFITGFLI can provide a wider lifetime range 0.6 ~ 13ns with reasonable precision. The performances of the proposed approach have been examined by both Monte-Carlo simulations and toluene seeded gas mixing jet diagnosis experiments. The measured average lifetimes of the whole excited areas agree well with the results obtained by the streak camera, and they are 7.6ns (N2 = 7L/min; O2 < 0.1L/min) and 2.6ns (N2 = 19L/min; O2 = 1L/min) with the standard deviations of 1.7ns and 0.8ns among the lifetime image pixels, respectively. The concentration distributions of the quenchers and fluorescent species were further analyzed, and they are consistent with the experimental settings.


Introduction
Planar laser-induced fluorescence (PLIF) sensing technologies are widely used in many scientific fields, such as airflow, combustion, and plasma diagnostics [1] due to its ability to measure the concentration, temperature, pressure and velocity [2,3].
Compared to other diagnostic techniques such as coherent anti-Stokes Raman scattering (CARS) or tunable diode laser absorption spectroscopy (TDLAS), the advantage of PLIF is the ability to perform two-dimensional (2D) sliced wide-field imaging by shaping the excitation light into a light sheet [4].Although the fluorescence signals carry the information about the concentrations of the probed species, it is challenging to conduct qualitative and quantitative measurementsmultiple parameters need to be confirmed in order to either relatively compare or precisely obtain the species concentrations [5].It is a challenging task to accurately assess the fluorescence quantum yield that is affected by collisions, simulated emissions, predissociations, and photoionizations.It is difficult to assess the impact of the collisional quenching in collisional processes, since the quenching depends on temperature, pressure, and quenchers, making PLIF only suitable for flow visualization.For example, OH-PLIF, CH2O-PLIF, and CH-PLIF are used respectively to observe the reaction, preheating and heat releasing zones in a combustion field [6].Accurately assessing the collisional quenching rate is the main key to achieving qualitative and quantitative measurements.
The collisional quenching rate can be directly determined by measuring the fluorescence lifetime.The fluorescence lifetime measurement techniques can be divided into time-domain and frequency-domain methods [7].In time-domain methods [8], such as time-correlated single-photon counting (TCSPC) [9 ~ 11] and time-gated FLI [12 ~ 14], the fluorescence intensity decay is measured with pulsed laser excitations.
In frequency-domain methods [15,16], the sample is illuminated with a modulated light source.In addition, streak cameras can also be used to obtain time-resolved fluorescence intensity curves [17].Unfortunately, these conventional FLI methods fail to observe instantaneous phenomena in a complex flow in 2D.
For non-repetitive dynamic events in complex flows and combustions, we expect to obtain the fluorescence lifetime images with a single excitation to freeze the instantaneous structures.Conventional time-gated FLI measures the fluorescence delay functions by gating the image intensifier of an ICCD camera with different delays.It usually needs to acquire more than one time-gated shot.Single-shot lifetime measurements can be achieved by replacing the single ICCD camera with two or more ICCD cameras to take time-resolved images simultaneously.Omrane et al. measured phosphorescence images with a high-speed framing camera containing eight independent ICCD image detectors, their system can obtain lifetimes in the order of milliseconds using an exponential fitting procedure [18].However, this method is not suitable for measuring lifetimes around nanoseconds in a single shot.Ehn.et al.
presented a single-shot FLI method with PLIF, using a dual ICCD detection setup with different gating characteristics for the two cameras, and they successfully demonstrated real-time acquisition of formaldehyde in a premixed, laminar methane/oxygen flame.
The most traditional approach for lifetime estimations is to acquire a multipoint decay curve and analyze it with least-square methods.This approach, however, requires considerable acquisition and computational time and is therefore unsuitable for singleshot time-gated FLI.The rapid lifetime determination (RLD) method was previously proposed to allow analyzing the decay data in real-time.For single-exponential decays, the lifetimes can be easily evaluated.RLD is suitable for single-shot time-gated FLI, if two ICCD cameras are used.RLD has a variety of gating schemes [14,20], such as the standard RLD (SRLD) using two gates of the same width or other more optimized RLD (ORLD) approaches.We can select a proper gating scheme to achieve a certain lifetime measurement range.In 2012, Ehn et al. achieved single-shot FLI of a toluene seeded gas mixture jet [21] using the same experimental setup as their earlier work [19], and they presented an evaluation algorithm, DIME (Dual Imaging and Modeling Evaluation), based on an ORLD scheme to evaluate image data.They estimated the lifetimes around 800ps with a standard deviation around 120ps (from 100 repeated measurements).Later they reported the fluorescence lifetime of toluene as a function of the oxygen concentration in toluene/nitrogen/oxygen mixtures.The results agreed with the Stern-Volmer model, showing the potential for detecting the oxygen concentration through fluorescence lifetime measurements.Monte-Carlo simulations were performed to evaluate the sensitivity of DIME for oxygen detection.The results indicated a high measurement sensitivity in the range 0.5 ~ 6mol/m 3 [22], showing that DIME has potential for quantitative diagnosis of complex flows.However, traditional RLD methods have a drawback: they are unable to offer robust estimations if the samples to be tested have a wide range of lifetimes.In order to solve this problem, Ehn et al. also proposed an approach that the measurement precision is virtually insensitive to the lifetime with ramped gain functions for the two ICCD cameras.However, this solution requires extra modifications on the driving front-ends to generate the ramped gain function, which might be challenging to achieve.
We described an approach named 'single-shot time-gated fluorescence lifetime imaging using three-frame images (TFI-TGFLI)' to provide high-speed, high-precision and wide dynamic range (0.6 ~ 13ns) FLI.In this paper, we will firstly demonstrate the relationships between the fluorescence lifetimes and the quencher concentrations and the relationships between the pre-exponential factors and the fluorophore concentrations using the simple two-state fluorescence emission model.The TFI-TGFLI experimental setup will then be described.Secondly, we will introduce the lifetime (and pre-exponential factor) determination algorithm for TFI-TGFLI and will show the Monte-Carlo simulation results.Finally, the experimental results will be presented with the image data processed and analyzed to obtain the fluorescence lifetime images and the normalized fluorophore concentration images in two tolueneseeded gas mixing jets: 1) N2 = 7L/min, O2 < 0.1L/min (denoted as N2:O2 > 7:0.1 hereafter for simplicity), and 2) N2 = 19L/min, O2 = 1L/min (denoted as N2:O2 = 19:1 hereafter).The results will also be compared with those obtained from a streak camera.

Theory and experimental setup
Figure 1 shows a two-state system model of a fluorescent molecule [23].The quantum states |1> and |2> are the ground state and the first excited state, respectively.n1 and n2 are the concentrations at the states |1> and |2>.B12，B21，Q21 and A21 are the stimulated absorption, stimulated radiation, collisional quenching (non-radiation) and spontaneous emission probabilities, respectively.Iν is the intensity of the laser pulse in absorption lines.The rate equation at the state |2> can be expressed as After the excitation, i.e.Iν = 0, , where n2 AE is the concentration at the state |2> after the excitation.Because the fluorescent signal is the spontaneous emission from the state |2>, the time resolved signal Nf can be derived as where, Ω is the solid angle for detection and V is the exited volume.ηc is the quantum efficiency of the collection optical system including a UV lens and a filter.Due to A21 << Q21, τ ≈ 1/Q21.
Under the weak excitation limit (linear LIF), n2 << n1, Eq. ( 1) can be transformed to , where n1 0 is the concentration of the total toluene molecules at the states |1> before the laser excitation.Substituting Eq. ( 3), the pre-exponential factor A can be written as Therefore, n1 0 can be quantified by measuring A, which can be directly calculated from with the lifetime τ being measured and A21, B12, and Iν already known.S is the integrated fluorescent intensity over the exposure time.We can conclude that measuring τ and A plays an important role in quantifying the concentrations of the quenchers and the fluorophores.The streak camera has a slit with 2mm width and 20mm length in parallel to the gas jet (+x).And the measuring time window and scanning step are 40ns and 200ps, respectively.We used a UV lens (f = 60mm, F/1.7) to gather the signal to the streak camera.Additionally, the distance between the jet tube and the slit of the streak camera is ~0.3m.The directions of the laser propagation and the gas jet are in +z axis and +x axis, respectively.

The lifetime algorithm of TFI-TGFLI
This section describes the proposed three-gate rapid lifetime determination scheme, implemented on a newly developed four-channel framing camera to achieve single-shot FLI.We will compare its performance with an ORLD scheme [20].
The configuration of the three-gate RLD scheme is shown in Fig. 3 proposed algorithm are indeed insensitive to the IRF for single-exponential analysis.In fact, gating approaches are in general less sensitive (compared with traditional TCSPC approaches) to the imperfections of the IRF for single-exponential analysis.The impact of the IRF in our instruments contributed to errors only around 3% (for τ = 0.6ns) and is therefore negligible in our discussions for simplicity.If the FWHM of the IRF is larger, we can time-shift the gate signal a bit away from the decay peak.This would sacrifice the photon efficiency a little bit, but for single-exponential analysis it is a wellknown approach to reduce the bias [14,24].The orange, green, and purple areas represent three time-gates; their start times t i start and end times t i end (i = 1, 2, and 3) are listed in Table 1.TG represents 'time-gate'.The time-gate parameters used in this article are Δt = 3ns, Y1 = 0, P1 = 50/3, Y2 = 1, P2 = 50/3.Two gating schemes can be formed with the three time-gates listed in Table 2. Gating Scheme 1 consists of TGs 1 and 2; Gating Scheme 2 consists of TGs 2 and 3.The ranges in the parentheses represent the widths of the time-gates.The signal in TG i is ,( 1, 2,3) k is the photoelectric conversion factor for the three channels, k ~ ηPCGMCPηpCηCCD, where ηPC is the quantum efficiency of the photocathode, GMCP is the gain factor of the microchannel plate, ηp is the quantum efficiency of the fluorescent screen, C is the coupling efficiency of the coupled optical system, and ηCCD is the quantum efficiency of the CCD, pi is the percentage of the total signal.Dj is the ratio of the signal Nj+1 to Nj, (j=1,2).For TFI-TGFLI, the coefficients k for the ICCD cameras in the framing camera are similar, therefore the effects caused by the differences in the gain functions (timedependent gain) can be neglected.To achieve single-shot acquisition based on three-gate RLD, a four-channel framing camera can be used to split a signal into four channels equally to obtain three images in Channels 1, 2, and 3 with TGs 1, 2, and 3 respectively.The signal collected in each channel would decrease to Ntot/4, i.e. pi = 25% (i = 1, 2, and 3); Ntot is the total number of the photons detected by the framing camera.In this work, we present singleshot and wide dynamic-range FLI using three images (i = 1, 2 and 3), but we would also be able to fully use four images (i = 1, 2, 3 and 4) to improve the photon efficiency and to perform bi-exponential analysis in the future.

Gating
From D1 and D2, the lifetimes can be calculated rapidly and efficiently by using the Newton-Raphson method.We define 0 The Newton iteration formula can be written as where τj,0 is initial value of the iteration, with j = 1, 2 representing Gating Schemes 1 and 2. Applying Eq. ( 7) to all pixels, and two lifetime images, τ1 and τ2, can be obtained.
Hence, two A images (A1 and A2) can also be obtained by Eq. ( 5).
To simplify the discussions, the technical details regarding the detectors were not considered.There are three types of noise in the signal obtained by the framing camera: shot noise, dark current noise and readout noise.Among them, shot noise is the dominating factor to determine the signal-to-noise ratio (SNR).Therefore, we only consider the influence of the shot noise on the precision of the lifetime estimations.To quantify the performance of a lifetime determination scheme, we use the figure of merit introduced by Draaijer et al. [25] for the lifetime estimations.The definition is στ is the standard deviation of τ, and hence στ/τ is the relative standard deviation.And, the figure of merit FA can also be defined for A, where σA is the standard deviation of A and σA/A is the relative standard deviation.Under a fixed Fi, (i = τ, A), increasing Ntot will improve the SNR of τ and A images.If Ntot is fixed, an FTI method with a larger Fi, (i = τ, A) has worse precision (larger relative standard deviation).the mole fraction of oxygen could vary between 1.64 and 8.36 mol/m 3 , the lifetime can vary between 0.7 and 3.0ns.It would be very useful for a FLI instrument to be able to resolve lifetimes in this range.TFI-TGFLI optimizes in the ranges, τ < 2.7ns for Fτ and τ < 1.3ns for FA, whereas ORLD optimizes in a longer range.ORLD can be adjusted to provide better sensitivity in a certain narrow range [20], whereas TFI-TGFLI can provide a more robust analysis if the lifetime varies significantly within the field of view.
The above simulation results show that we can simply take either τ1 or τ2 (similarly A1 or A2) images according to the following equations, ,, ,, With Eqs.(10) and (11), we can obtain τ and A images with Fi (i = τ, A) < 6 for 0.6 < < 13ns and with high precision for 0.6 < < 2.7ns.
Although Channel 4 was not used in this work, it can be employed to enhance the photon efficiency in the future.If we set the time-gate of Channel 4 the same with that of Channel 1 and merge the two images (Channels 1 & 4), the precision of Gating Scheme 1 would be further improved.The Fτ and FA curves (dash blue lines) for the enhanced Gating Scheme 1 is shown in Figs.4(a) and 4(b).The other advantage of using multi-framing cameras is that we can expand our applications for bi-exponential analysis in the future.
The fluorescence lifetimes of a complex flow may vary significantly according to the temperature, pressure, or quencher concentration gradients.The proposed TFI-TGFLI can achieve single-shot acquisition, provide a wide dynamic range and improve the precision significantly in the short lifetime range, promising wider applications.

Analysis of the experimental results
The toluene seeded flows are consisted of N2 and O2 with different mixing ratios.
Two cases are demonstrated here; Case 1: N2:O2 > 7:0.1 (N2 = 7L/min; O2 < 0.1L/min. The minimum significant digit that the flow meter can provide is 0.1L/min, therefore any rate lower than this value would indicate 0.0L/min.Thus, we tuned the meter of the O2 supply for Case 1 to 0.0L/min, but the actual flow rate should be < 0.1L/min) and Case 2: N2:O2 = 19:1 (N2 = 19L/min; O2 = 1L/min).From the fluorescence lifetimes we obtained in the experiments described below, we could conclude that the N2:O2 ratio for Case 1 could be up to 120:1 whereas the measured lifetime  = 2.6ns for Case 2 is in a good agreement with the literature compared with the results reported in [22,26].
The purpose of the experiments designed for this work is to evaluate the performances of the proposed lifetime determination methods, and the experiments indeed confirm that the measurements obtained from the proposed camera are in good agreement with those obtained by the streak camera.τ and A images can be calculated from the three intensity images shown in Fig. 5 using the lifetime determination algorithm mentioned in Section 3. In order to visualize the distributions of the toluene molecules, the intensity profile of the pulsed laser Iν should be confirmed.We assume that the intensity of the laser approximately stays the same along the propagation (+z) axis through the target flow and has a Gaussian distribution perpendicular to the propagation direction (+x), i.e.

  
, where I0 is the peak intensity, x0 is the position of the peak value, and xν is the full width at half maximum (FWHM).Then the relative concentration distributions n1 0 can be obtained from Eq. ( 4).respectively.For Case 1 (blue), τimage = 7.6ns and the standard deviation for all the pixels in the lifetime image is στ image = 1.7ns.For Case 2 (red), τimage = 2.6ns and στ image = 0.8ns.
As the gain of the ICCDs used in Case 1 is bigger than that used in Case 2, the largest intensity in Case 1 is larger than that in Case 2. The scatter plot for Case 1 contains 123 saturated pixels (peaked at 2 14 -1), and they are contributed by the saturated 14-bit A/D converter.The statistical results are, however, not influenced.We can tune the gain in the future to avoid saturated pixels.

Fig. 1 .
Fig. 1.Different transitions that are included in the two-state model.

Fig. 2 .
Fig. 2. Schematic illustration of the experimental setup.The laser beam is expanded through a beam expander (BE) and focused to a laser sheet by a cylindrical lens (CL) in the target area above the jet tubes (JT).A triggering pulse is sent to the digital delay generator DG645 to trigger both the streak camera and the framing camera to record filtered signals.The multi-channel framing camera contains an image splitter and four ICCDs.3.The lifetime algorithm of TFI-TGFLI , the black solid line is the normalized fluorescence intensity curve with a 10ps excitation pulse (red line).Since the fluorescence lifetime is usually a few nanoseconds, much greater than the pulsed laser duration 10ps, the fluorescent signals can be simplified as a single exponential decay model, i.e. of the IRFs are minor, and we can neglect the IRFs in our experiments.To examine this, we have conducted Monte-Carlo simulations.The results show that the lifetime estimations with our

Fig. 3 .
Fig. 3. Graphical illustration of the three time-gates used to estimate lifetimes.

Figs. 6
Figs. 6(a) and 6(b) show the lifetime and the normalized n1 0 images for Case 1 (N2:O2 > 7:0.1), whereas Figs.6(c) and 6(d) show the lifetime and n1 0 images for Case 2 (N2:O2 = 19:1).Fig. 6(e) shows the sectional view of the gas jet.The red dotted box indicates the gas jet section illuminated by the laser sheet.The two lifetime images in Figs.6(a) and 6(c) are uniform, implying that the distributions of the quencher (O2 and N2) concentrations are uniform.The two normalized n1 0 images shown in Figs.6(b) and