Fluorescence lifetime imaging with a single-photon SPAD array using long overlapping gates: an experimental and theoretical study

Abstract

Developing large arrays of single-photon avalanche diodes (SPADs) with on-chip time-correlated single-photon counting (TCSPC) capabilities continues to be a difficult task due to stringent silicon real estate constraints, high data rates and system complexity. As an alternative to TCSPC, time-gated architectures have been proposed, where the numbers of photons detected within different time gates are used as a replacement to the usual time-resolved luminescence decay. However, because of technological limitations, the minimum gate length implement is on the order of nanoseconds, longer than most fluorophore lifetimes of interest. However, recent FLIM measurements have shown that it is mainly the gate step and rise/fall time, rather than its length, which determine lifetime resolution. In addition, the large number of photons captured by longer gates results in higher SNR. In this paper, we study the effects of using long, overlapping gates on lifetime extraction by phasor analysis, using a recently developed 512×512 time-gated SPAD array. The experiments used Cy3B, Rhodamine 6G and Atto550 dyes as test samples. The gate window length was varied between 11.3 ns and 23 ns while the gate step was varied between 17.86 ps and 3 ns. We validated the results with a standard TCSPC setup and investigated the case of multi-exponential samples through simulations. Results indicate that lifetime extraction is not degraded by the use of longer gates, nor is the ability to resolve multi-exponential decays.

1. INTRODUCTION

Fluorescence lifetime imaging microscopy (FLIM) has become an important tool in the biological sciences because of its virtual insensitivity to fluorophore concentration and photo-bleaching.^1,2 In addition, using appropriate fluorophores, it can detect changes in environmental parameters such as pH or oxygenation levels, which makes it an attractive technique for functional imaging. However, FLIM has yet to achieve widespread use because of hardware cost and complexity, as well as the computational burden involved in extracting lifetime information. Conventional setups employ a beam-scanning confocal geometry using pulsed laser diodes as excitation sources, coupled with sophisticated time-correlated single-photon counting (TCSPC) electronics for data acquisition, and involve CPU-intensive curve fitting algorithms that work best with high signal-to-noise ratio data, and assume specific decay models open to some degree of interpretation. Alternative methods assuming single-exponential decays have been developed^3,4 to address these speed and complexity issues, but they are not necessarily appropriate for more complex situations.

The phasor-based FLIM method^5,6 introduced by Gratton and collaborators proposes to obviate most of these drawbacks, as (i) it uses only simple algebraic operations, (ii) can tackle multi-exponential decays while also (iii) providing a simple graphical representation of the detected lifetimes, (iv) all at high frame rates due to less strict hardware requirements. Phasor FLIM can be used with time gating⁷, which, while it is less photon-efficient, is more suitable for large format single SPAD chip solutions. However, SPAD array technological limitations set a lower bound on the minimum achievable gate length, on the order of several nanoseconds, which is larger than most fluorophore lifetimes of interest.

This work represents an investigation into the effects of using long overlapping gates to extracting the lifetimes of typical fluorescent samples. Uniform solutions of Cy3B, Rhodamine 6G and Atto 550, as well as simulated mixtures of dyes both with similar and different lifetimes were used. A large-format gated single-photon avalanche diode (SPAD) array, SwissSPAD2⁸, was used to perform FLIM measurements and phasor analysis was used to process the acquired and simulated data and extract the samples’ lifetimes and fluorophore concentration ratios.

2. MATERIALS AND METHODS

Three uniform solutions of Atto 550, Cy3B and Rhodamine 6G were prepared, with expected lifetimes of 3.6 ns, 2.8 ns and 4.08 ns respectively. The Atto 550 sample had a weaker intensity compared to the other two (Rhodamine 6G being the brightest) which allowed to study the long gate FLIM implementation over a relatively large range of sample intensities. Widefield illumination of the samples, sandwiched between coverslips, was performed with a 20 MHz, 532 nm pulsed laser (LDH-P-FA-530XL, PicoQuant, Germany) through a 60X high numerical aperture (NA = 1.45) oil immersion objective lens. Excitation and emission were separated with a 532 nm dichroic mirror and bandpass emission filter (center: 580 nm, width: 60 nm) installed in an Olympus IX71 inverted microscope. The lifetimes of all three samples were separately measured using a conventional TCSPC setup with similar specifications, and then used as a reference for the analyses.

FLIM was performed using the phasor method, where the discrete Fourier transform (DFT) of the acquired data is used to extract the sample lifetime. The method consists in performing the following computations:

$$\begin{gathered} g=\frac{1}{N_{\mathit{\text{count}}}}\sum _{i=1}^{N_{\mathit{\text{gates}}}}{N}_i\mathit{\text{cos}}\frac{2\pi {\tau }_i}{T} \\ s=\frac{1}{N_{\mathit{\text{count}}}}\sum _{i=1}^{N_{\mathit{\text{gates}}}}{N}_i\mathit{\text{sin}}\frac{2\pi {\tau }_i}{T} \\ {\tau }_{\varphi }=\frac{T}{2\pi }\frac{s}{g} \end{gathered}$$ (1)

where N_count is the total photon count in the pixel, N_gates the number of gate positions, N_i the photon count in pixel at gate i, τ_i the arrival time associated with gate i (for example the start of the gate), T the phasor harmonic period, usually taken as 1/f, where f is the laser frequency and τ_ϕ the phase lifetime.

All gated measurements were performed using SwissSPAD2. Table 1: SwissSPAD2 characteristics summarizes the main characteristics of the detector. The minimum gate step that can be implemented by the system is 17.86 ps (elementary step), while the smallest achievable gate width is 10.2 ns. Over the whole array, gates exhibit rise/fall times of around 500 ps and 700 ps respectively, with some gate length configurations presenting improved characteristics.

Table 1:

SwissSPAD2 characteristics⁸

Array format (chip)	512×512
Array format (system)	472×256
Pixel pitch	16.38 μm
Fill factor (native)	10.5%
Fill factor (microlenses)	46.9% (max. measured)
Chip size	9.5×9.6 mm2
Max. frame rate	97.7 kfps (1 bit)
Median DCR (@ VEX=6.5 V)	7.5 Hz/pxl 0.26 Hz/μm2
Max. PDP (@ VEX=6.5 V)	50% @520 nm

The data required for analyzing the effect of the gate length on lifetime extraction was collected by varying the actual gate length between 11.3 ns and 23 ns while the step was kept at 357.1 ps (20 elementary steps). To investigate the effect of gate step size, a single data set was acquired using a configuration with elementary gate step and a fixed length of 13.5 ns. The resulting 2,800 gates were then decimated and step sizes integer multiples of the minimum value were obtained.

The case of multi-exponential samples was analyzed with FLux, a simulation and analysis platform developed in-house, that was designed to generate frames of up to 3 fluorophores in any pattern on top of which hardware effects such as jitter and skew in the gate signal are added. Frames consisting of a mixture of two fluorophores at different concentration ratios were generated and then, using the phasor FLIM method^5,6, the observed concentration ratios were determined.

3. PERFORMANCE ANALYSIS

The effects of varying the gate length and the step size on extracting the previously described fluorophore samples’ lifetimes were evaluated by computing the relative error with respect to the TCSPC values, the standard deviation of lifetime across multiple pixels and the F-value⁹, a measure of additional lifetime dispersion that makes the results deviate from Poissonian characteristics:

$$F=\sqrt{N_{\mathit{\text{counts}}}}\frac{{\sigma }_{\tau }}{{\tau }_{\varphi }}$$ (2)

where N_counts is the total photon count, σ_τ is the phase lifetime standard deviation and τ_ϕ is the mean extracted phase lifetime.

3.1. FLIM performance for various gate lengths

Data from the Cy3B sample was collected using a fixed 357.1 ps gate step and 140 gate positions covering the 50 ns laser repetition period. The total number of removed hot pixels equaled 1% of the 350×250 pixel region that was selected for the analysis. The Rhodamine 6G sample measured under the same conditions was used as a reference for IRF compensation (phasor calibration^5,6). TCSPC measurements resulted in a calculated lifetime of 2.5 ns for the Cy3B sample.

Figure 1 shows the measurement results. The extracted lifetime accuracy (100% minus the relative error) does not vary significantly, remaining above 95% over the entire gate length range. The small change on the order of 10 ps of the standard deviation across the same range, when compared with the nanosecond sample lifetime, indicated that there is no influence of gate length on lifetime extraction. The F-value slightly degrades as the gates become longer, as expected from the small increase in lifetime standard deviation. It is worth mentioning that the ideal F-value of 1 may be unachievable through long gated FLIM due to inherent method characteristics, and further investigations are currently being carried out in this direction.

Figure 1.

From top left, clockwise: Average extracted sample lifetime; Accuracy of extracted lifetime varies with less than 5% over the entire range; F-value exhibits a small degradation linked to the changes in lifetime precision; Lifetime standard deviation across analyzed pixel region changes by less than 15 ps; All figures indicate that there is no significant influence of gate length on lifetime extraction.

3.2. FLIM performance for various gate steps

Data from the Rhodamine 6G and Atto 550 samples was collected using a fixed gate width of 13.5 ns for which various gate steps were emulated as described in the Materials & Methods section. The total number of removed hot pixels equaled 1% of the 472×256 pixel region that was selected for this analysis. The data was then further binned (4×4) resulting in a 118×64 format. The Cy3B sample measured under the same conditions was used as a reference for IRF compensation. TCSPC measurements resulted in a calculated lifetime of 3.9 ns for the Rhodamine 6G sample and 3.4 ns for the Atto 550 sample. The systematic discrepancy of 200 ps observed in the TCSPC measurements compared to literature values are probably due to imperfect IRF data (the laser used to perform TCSPC measurements exhibited a broadened temporal profile when operated at 20MHz, the repetition rate used for the measurements).

Figure 2 shows the measurement results for the two samples. The lifetime extraction accuracy remains relatively constant for both Rhodamine 6G and Atto 550, until the gate step becomes comparable to the sample lifetime, at which stage the measurements rapidly become inaccurate. The lifetime standard deviation exhibits a sample-dependent characteristic. For the high SNR Rhodamine 6G sample there is a lower bound after which further decreases in gate step provide no improvements in lifetime precision. This indicates that for high intensity samples the dominating noise source comes from the system (SPAD jitter, gate signal jitter etc.) and not from photon statistics (shot noise). The dimmer Atto 550 sample, on the other hand, exhibits a steady improvement in precision as the gate step decreases (and consequently the detected photon count increases) which indicates a dominating shot noise component.

Figure 2.

From top left, clockwise: Average extracted sample lifetime; Relative error of extracted lifetime remains small for all gate steps less than the sample lifetime; F-value of the high SNR Rhodamine 6G sample degrades as the step becomes smaller due to an increase in number of photons but no further improvement in lifetime precision. For the low SNR sample the method has constant efficiency; Lifetime standard deviation across analyzed pixel region reaches a lower bound for the high SNR sample, indicating the presence of a noise component that is not photon dependent (gate jitter, SPAD jitter).

The same conclusion can be drawn from the F-value plots where the Rhodamine 6G value degrades as the gate step is decreased due to the increase in the number of detected photons that bring no additional improvements in lifetime precision, thus lowering the overall efficiency. In the Atto 550 case, the increase in detected photons is counterbalanced by the decrease in lifetime spread, which results in a relatively constant F-value.

3.3. FLIM performance for multi-exponential samples

Simulated data was used to analyze the performance of long-gate FLIM in the case of multi-exponential samples. Two data sets, each based on a uniform mixture of two fluorophores with similar or significantly different lifetimes were generated, with their characteristics shown in Table 2. The concentration ratio between the two component fluorophores was varied between 1 to 9 and 9 to 1 and the phasor method was used to analyze the results. Figure 3 shows the phasor plot for a 4 to 6 mixture of two fluorophores with lifetimes of 2.5 ns and 14.7 ns (corresponding to the quantum dot sample used in ref.⁸). Due to the addition of a simulated background, the measured phasor points do not fall on the line between the two phasors corresponding to the lifetime components. However, the concentration ratios can still be recovered within ±5% of the actual value for all fluorophore combinations in both data sets, as shown in Figure 4. Results indicate that long-gate phasor FLIM can be used to analyze samples with bi-exponential decays, even when the two component lifetimes are close from one another and significantly shorter compared to the gate length, if the configuration parameters are chosen appropriately.

Table 2.

Simulated data sets

	Data set #1	Data set #2
Component lifetimes	2.5 ns & 3.6 ns	2.5 ns & 14.7 ns
Number of gates	800	150
Gate width	10.4 ns	20.7 ns
Gate step	34 ps	357 ps
Bit depth	10 bit	10 bit
Number of pixels	100	100
Laser PRF	20 MHz	20 MHz
Phasor frequency	40 MHz	20 MHz

Figure 3.

Phasor plot of simulated 4 to 6 ratio between two fluorophores with 2.5 ns and 14.7 ns lifetimes. The phasor projections (blue plus) onto the cord between the two component lifetimes (red plus) are used to recover the concentration ratio.

Figure 4.

Correspondence between extracted and actual concentration ratio of the two fluorophores for both data sets. The error bars show one standard deviation.

4. CONCLUSION

This paper reported on the performance of phasor-based time-gated FLIM using long overlapping gates and a large format CMOS SPAD array. Measurements were performed on uniform solutions of Cy3B, Rhodamine 6G and Atto550, all with shorter lifetimes than the gate lengths. Multiple step sizes starting from 17.86 ps and up to several nanoseconds were used, as well as gate lengths ranging from 11.3 ns to 23 ns. Simulations using a specially developed software explored cases where mixtures of dyes were imaged, in order to evaluate the method’s performance for multi-exponential samples.

Results indicate that implementing phasor-based FLIM with long overlapping gates allows accurate extraction of sample lifetime regardless of the gate length. Over the entire lifetime range, the method’s efficiency (F-value) was determined to be relatively insensitive to the gate length as well.

Varying the gate step resulted in minor changes in the accuracy of the extracted lifetime, as long as the gate step remained smaller than the sample lifetime. Above this threshold, results become inaccurate due to the high probability of a large number of gates not sampling the decay curve at all. The lifetime precision exhibited a sample dependent characteristic, which indicates that for high SNR samples the dominating error source comes from the system and not the photon statistics, meaning that after a certain point, decreasing the step size further will bring no reduction in the lifetime standard deviation. For low intensity samples, decreasing the gate step, which translates into the use of more gates and therefore more photons being captured, improves the overall precision.

Simulation results validated the use of long-gate phasor FLIM as a method for extracting fluorophore concentration ratios from a sample, even in the case where the fluorophores have similar lifetimes and background is present. The extracted concentration ratios were within ±5% of the actual value over the entire examined range for both data sets, indicating that with proper parameter configuration (phasor frequency, gate step) the long-gate phasor method is capable of resolving bi-exponential samples.

Additional long-gate FLIM performance analysis has been performed by Ulku et al.¹⁰ with focus on the achievable frame rate, lifetime resolving capabilities and lifetime dependency on intensity. Additional work will be carried out to investigate multi-exponential samples and theoretical limitations of the proposed phasor FLIM configuration.