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Abstract
Photoluminescence (PL) spectroscopy offers excellent methods for mapping the PL decay on the nanosecond time scale. However, capturing maps of emission dynamics on the microsecond timescale can be highly time-consuming. We present a new approach to fluorescence lifetime imaging (FLIM), which combines the concept of random temporal speckles excitation (RATS) with the concept of a single-pixel camera based on spatial speckles. The spatio-temporal speckle pattern makes it possible to map PL dynamics with unmatched simplicity. Moreover, the method can acquire all the data necessary to map PL decay on the microsecond timescale within minutes. We present proof-of-principle measurements for two samples and compare the reconstructed decays to the non-imaging measurements. Finally, we discuss the effect of the preprocessing routine and other factors on the reconstruction noise level. The presented method is suitable for lifetime imaging processes in several samples, including monitoring charge carrier dynamics in perovskites or monitoring solid-state luminophores with a long lifetime of PL.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fluorescence lifetime imaging (FLIM) is an essential spectroscopic method in various fields, including medicine, biology, and material science. Interest in FLIM and its broad applicability stimulate its development. Therefore, FLIM has many different implementations based on a variety of fundamental methods for measuring photoluminescence (PL) decay, which include gated photoluminescence counting [1], streak camera [2], time-domain analog recording technique [3], or frequency-domain analog recording technique [4]. However, the most commonly used method is time-correlated single-photon counting (TCSPC) [5,6].
TCSPC is a powerful method to trace PL decay with a lifetime in the order of nanoseconds. However, due to the principle of TCSPC operation, data acquisition can take several hours for samples with a PL lifetime on the microsecond timescale. Therefore, the reduction of the acquisition time in FLIM has become a topic discussed in the literature in its own right [7]. A possible way to reduce the acquisition time is to apply so-called compressed sensing, where the image can be reconstructed from a highly reduced dataset [8,9]. However, these works rely on TCSPC and, despite reducing the acquisition times, FLIM of the samples with a long-lived PL decay still represents an issue. It is also worth noting that standard FLIM methods usually require costly setups.
In this paper, we present an entirely new concept of FLIM. The concept is based on the use of speckle patterns, both in the spatial and temporal sense, to map the PL decay of a sample. We combine compressive imaging, namely the concept of a speckle-based single-pixel camera [10], with our recent work [11], where random temporal speckles (abbr. RATS) make it possible to trace PL dynamics. In the presented concept, we employ spatio-temporal speckles, which are generated by using two diffusers. The speckles can be generated with any coherent excitation source, i.e., without the need for a pulsed laser. At the same time, the detector is a standard single-pixel detector, e.g., a photomultiplier. The setup is, therefore, very simple, robust, and low-cost. Owing to the novel approach to PL decay acquisition, the method is highly suitable for mapping PL dynamics on the microsecond timescale, where the FLIM dataset can be acquired within minutes. We demonstrate this on proof-of-principle measurements by imaging PL decay of selected scenes (colour filters and Si nanocrystal layers) and we also discuss the effect of speckle properties on the resulting noise level.
The presented method can serve as a simple approach to characterizing the morphology of samples with prominent PL decay in the order of microseconds, which include halide perovskite samples, solid-state luminophores, or Si nanocrystals [12–14].
2. Principle of the method
2.1. Concept of RATS method
The cornerstone of the presented FLIM concept is the RATS method, which is described in detail in our previous work [11]. This novel method for the measurement of PL decay uses randomly fluctuating intensity IEXC to excite a sample. The PL signal IPL is then given as a convolution of IEXC and PL decay ID:
Therefore, ID can be extracted via the convolution theorem using the Fourier transform, where we apply the so-called Tikhonov regularization weighted with the factor ε [15]:
The random character of IEXC allows us to measure a broad range of frequencies. Thus, a single measurement of IEXC and IPL provides information sufficient for the complete ID reconstruction. Since the original method acquires PL decay for a single spot only, we will hereafter denote the method as 0D-RATS. The principle of the method is described in Fig. 1, based on simulated data. In order to get a randomly-fluctuating excitation signal, the demonstrated 0D-RATS method uses temporal speckles generated via a rotating diffuser. However, the presented approach can use any principle of random temporal signal generation, which means the RATS method can be understood in more general terms as the RAndom Temporal Signals method.
Fig. 1. Sequence showing the principle of ID evaluation using the 0D-RATS method. A) Simulated temporally fluctuating intensity IEXC (blue) and detected photoluminescence signal IPL (red) arising due to a monoexponential decay (lifetime τ = 50 µs). For clarity, a shorter time section is shown, than was used for reconstruction (0.1 s). B) Amplitudes of Fourier transform of IEXC (blue) and IPL (red). C) Reconstructed ID via convolution theorem, Eq. (2).
New approaches to generating a temporally random light signal are likely to be found. This could mean an improvement both in terms of excitation intensity and higher frequency of the excitation signal.
2.2. Concept of proposed 2D-RATS method
An efficient approach to converting the 0D-RATS method to the imaging mode is to use the single-pixel camera. The principle of a single-pixel camera can be seen in many review articles [16]. In a single-pixel camera experiment, the measured sample is illuminated by a set of masks (see Fig. 2), which, in our experiment, were speckle patterns. Each illuminating random mask excites PL in different parts of the sample. After illuminating the sample with a sufficient number of masks, it is possible to retrieve the spatial information by detecting the overall level of the emitted PL and by using dedicated algorithms, as we will describe below. However, the condition that must always be met is the linear dependence between the measured and the reconstructed data.
Fig. 2. Scheme of single-pixel camera image acquisition by using speckle patterns – see text for details.
In our FLIM approach, the illuminating masks are generated with a movable diffuser, which is placed behind the source of light with randomly fluctuating intensity in time, i.e., temporal speckles. Thus, we attain spatio-temporal speckles, which retain the same spatial pattern S(x,y), while the overall intensity is blinking rapidly as IEXC(t). In other words, the measured sample is illuminated with a blinking pattern P(x,y,t) = S(x,y)IEXC(t). To map the PL decay ID, i.e., to retrieve ID (x,y,t), it is necessary to detect IEXC (t) with a diode, IPL (t) with a photomultiplier, and the speckle pattern S(x,y) with an array 2D detector (e.g., CMOS camera).
Equation (1) can be rewritten for a 2D sample into a more general case, where n areas with different ID are measured. The total emitted IPL is the sum of the contributions from all sample spots:
For a given mask, we can evaluate from the measured data an average PL decay of the entire illuminated area IDA:
A different IDA will be detected for each mask, as illustrated in Fig. 3(A). The variation of the IDA value, i.e., PL decay, for a selected time and different masks will be denoted as d. See Fig. 3(B) for an example of a short subset of seven masks and four different times. We can vectorize each illumination mask into a single row of the so-called observing matrix A and we can also vectorize the map of the PL intensity into a vector m. In this case, we can express their relation as a simple matrix multiplication:
Fig. 3. (A) Examples of simulated ID curves, which differ due to the change of the illuminating mask. (B) Varying intensity for the seven different masks in selected time-points of simulated ID curves – see dashed lines in panel A. (C) Example of reconstructed PL maps. Selected pixels are marked with a colour corresponding to the time point. (D) A simulated example of reconstructed ID in four time points. Reconstruction at multiple points would copy the entire ID (solid black line).
Matrix A has a number of columns corresponding to the number of map pixels N, while the number of rows follows the number of used masks M, i.e., the number of measurements. The ratio between M and N determines the compression ratio k = M/N.
We aim at solving an underdetermined system, which can be accomplished by means of a compressed sensing algorithm where we employ a regularization. In this work, we used the algorithm TVAL3 [17,18], which is based on the minimization of total variation TV of reconstructed images and follows Eq. (6) [19].
Using Eq. (6), it is possible to reconstruct the PL map m(x,y) for each time point t [see Fig. 3(C)]. Knowing that we are reconstructing a PL image, we can constrain the solution to m∈R and m≥0. If we stack the individual m(x,y) behind each other, we create a 3D matrix m(x,y,t) that corresponds to the appropriate PL intensity ID (x,y,t) of the sample. Therefore, we can also extract PL decay for any selected spot of the sample [see Fig. 3(D)] and we can fit the obtained PL dynamics ID with a single- or multi-exponential decay to get the lifetime map.
3. Optical setup
The used optical setup is depicted in Fig. 4. We used a CW laser at wavelength 405 nm (IO matchbox laser diode, free-space) as a light source. The combination of a focusing lens A (f = 25.4 mm), a rotating diffuser (average grain size 3.87 µm) with a collimating lens B (f = 75 mm), and an aperture (diameter 1.5 mm) generated intensity randomly fluctuating in time IEXC (t).
The generation of a random mask (spatial speckles) is achieved with another focusing lens C (f = 25.4 mm). The beam is focused on a movable diffuser (average grain size 8.06 µm) and the diffused light is again collimated with lens D (f = 50 mm). The resulting mask pattern was blinking, according to IEXC (t).
The patterned beam is split twice with two N-BK7 glass wedges (5°), which reflect about 6% of the incident intensity. The first reflection is used to detect IEXC(t) with a Si amplified photodetector (Thorlabs PDA8A2, rise time 7 ns). The second reflected beam is used to acquire the mask pattern with a camera (CMOS, IDS UI-3240ML-M-GL). The transmitted pattern is used to illuminate the measured sample. The PL emitted from the excited sample, i.e., the IPL(t) signal, was detected with a type H10721-20 Hamamatsu photomultiplier (PMT) module (rise time 0.6 ns). The scattered excitation light was blocked by a cut-off filter at 500 nm (Thorlabs, FEL0500). The detected PL signal was amplified by a model SR445A SRS amplifier and read out by a TiePie Handyscope HS5-110XM USB oscilloscope.
The laser beam intensity entering the setup is 138.5 mW, while the full average intensity that illuminates the measured sample oscillates around 5.5 µW. The overall efficiency of the system is about 0.003%, which can be, however, improved approximately 10 times by optimizing the parameters of the optical elements. The size of the measured area was about 18 mm2 and is given by the size of the generated speckle masks. It is possible to scale the field of view by adjusting the collimating lens D.
The TCSPC setup which was employed for the reference measurements used a picosecond laser at 405 nm, 100 kHz repetition rate, and 0.2 nJ/pulse. The laser pulses excited a PL signal detected by a PMT. The decay data were acquired by a PicoHarp 300 module. The impulse response function (IRF) of the TCSPC setup was negligible (< 1 ns) in comparison with the lifetimes of the measured samples, and, therefore, it has not been taken into account.
4. Results and discussion
As a proof-of-principle experiment, we carried out imaging of a combination of an OG565 orange absorbing cut off filter and a Si wafer with a nanoporous surface prepared by electrochemical etching of the Si wafer in hydrofluoric acid and ethanol solution [14,20]. Both samples had been measured previously by the 0D-RATS method and the resulting PL decay shapes had been verified with a standard method, namely the streak camera, and can be found in a previously published article [11].
In order to compare the data with methods commonly used for FLIM, we verified the 0D-RATS method with a reference TCSPC method. The comparison depicted in Fig. 5 confirms the correctness of the RATS approach. The 0D-RATS data (symbols) were measured in the same configuration and with the excitation light parameters described in Section 3. For the sake of this comparison, the detected spectral region in both setups (RATS and TCSPC) was restricted by colour filters to 500–800 nm. To compare the decays from the zero time, the TCSPC data were convoluted with the IRF of the 0D-RATS method, i.e., Gauss function with a full width half maximum (FWHM) equal to 0.59 µs. This convolution caused the depicted TCSPC curves (blue curves in Fig. 5) to be very smooth, in spite of the significant noise level in the raw data.
Fig. 5. 0D-RATS method verification with TCSPC method. Excitation wavelength: 405 nm; energy 19 µW/pulse, 100 kHz repetition rate. Comparison of PL decays of OG 565 filter (A) and nanoporous Si wafer (B) acquired by 0D-RATS method (blue lines) and TCSPC data convoluted with impulse response function of RATS measurement (red marks). See text for details. For the sake of comparison, the data have been normalized.
For the benefit of the comparison of the two methods, it is worth noting that, due to the long PL lifetimes, it was necessary to use a low excitation repetition rate (100 kHz) in the TCSPC setup. This led to the TCSPC acquisition time of 20 minutes (used for data in Fig. 5). In contrast, the 0D-RATS method acquired the PL decay data within 2 seconds. This value is proportionate to the acquisition time of the methods commonly used for microsecond PL measurement, such as direct PMT decay acquisition. Nevertheless, as we showed in the previous section, the RATS method allows a simple and low-cost implementation of FLIM based on the use of a single-pixel camera.
4.1 Single-pixel camera PL map reconstruction
Our method is based on compressive imaging and requires iterative image reconstruction, which was described in Eq. (6). The crucial parameters (together with their set value) were: mu (29), beta (26). The reconstruction parameters were set according to the reconstruction of the testing experiments and simulations, and the same parameters are used for all the presented images.
4.2. Mask preprocessing
We captured the speckle mask on a CMOS chip and, prior to its use, we carried out a set of operations to convert the speckle image into a form suitable for our calculation.
The first part of preprocessing was cropping of the mask. Since the mask did not occupy the entire camera chip, the image was cropped so that the information value remains and at the same time we reduce the number of reconstructed pixels N.
The second part was the mask rescaling. A laser speckle pattern is a natural random pattern, where the dimensions of each speckle vary around a certain mean value. For this reason, it is unclear how the high-resolution camera image of laser speckles aM should be rescaled into the image aM’ used in the measurement matrix A while retaining the useful information. An example of such rescaling is presented in Fig. 6.
Fig. 6. Cropped original camera image of speckle patterns (aM, left-hand side) compared to the processed mask pattern (aM’, right-hand side) with a scaling factor h = 35 pixels, which corresponds with the mean speckle size of the aM pattern.
4.2.1 Mask rescaling effect
By using a set of simulations, we examined how the image reconstruction quality is affected by a varying mask scaling factor. The set of masks employed in the simulations, i.e., camera images of speckles, was acquired in the real measurements. The mean speckle size h for the examined set of masks is h = 35 pixels, which was calculated as the full width half maximum (FWHM) of the speckle pattern autocorrelation function [21]. The compression ratio k was set for the purpose of the simulations to 0.4, and the noise level of the PL intensity was set to the σ = 0.5%.
The reconstruction error of the PL maps was calculated as an l2 norm of the vectorized reconstructed image m and the original image U. To normalize the error for the image intensity, we calculate the relative error r:
Since the scaling factor changes the number of pixels of a mask, the number of reconstructed image pixels N changed accordingly. The straightforward evaluation of the reconstruction quality by using residues was not meaningful because a smaller number of pixels leads to a lower level of residues despite worse image quality since we are solving a highly underdetermined system.
The simulations based on two different PL maps in Figs. 7(A)–7(B) show that the relative error r does not have a strong systematic dependence on the scaling factor [see Fig. 7(C)]. It is only possible to observe a slightly decreasing trend of the error towards smaller scaling values.
Fig. 7. Effect of scaling factor h on relative error in image reconstruction of two different PL maps depicted in panel A (red line in C) and panel B (blue line in C). The black line in panel C denotes the scaling factor according to the mean speckle size.
However, maintaining a given compression ratio for a higher resolution implies increasing the number of scanned masks, thus increasing the total acquisition time. Therefore, as a reasonable compromise, we used the scaling factor h = 35 that corresponded to the average speckle size of the used patterns. The effect of this scaling is illustrated in Fig. 6, which was processed based on this value.
4.3. Proof-of-principle measurements
The first analyzed sample was an OG565 orange absorbing cut-off filter, which was divided with an opaque line into two regions with the same PL decay dynamics ID. Such a situation corresponds, for instance, to a mapping of a single PL marker in a sample. The illuminated spot was the size of ∼ 18 mm2, the number of masks M = 400. The mask resolution was rescaled according to the speckle size (h = 35 pixels), leading to the image resolution of 28 × 36 (N = 1008).
We tested image reconstruction for three different compression ratios k, where the number of pixels N remained the same and the number of used masks M was decreased accordingly. Namely, we employed the compression ratio k = 0.4 [see Fig. 8(A)], k = 0.2 [see Fig. 8(B)], and k = 0.05 [see Fig. 8(C)]. The corresponding data acquisition times were 47 min, 24 min, and 6 min, respectively. The results are summarized in Fig. 8 and divided into areas A, B, and C, correspondingly.
Fig. 8. Measurement of a masked OG565 filter: (A) compression ratio 0.4, (B) compression ratio 0.2, (C) compression ratio 0.05. Left panels: reconstruction of the PL map for two different times. Middle section: graphs “a” and “b” show the reconstructed ID from 2D-RATS in a randomly selected pixel (“a” pix [14,10], “b” pix [16,25]) and ID given via 0D-RATS; blue and violet stars denote the time of the PL maps on the left. Right section: map of the PL lifetimes for the points where the PL amplitude exceeded 10% of the maximum PL intensity.
The left part shows the reconstruction of the PL map for two different times. The middle part includes graphs “a” and “b”, which show the ID of a randomly selected pixel, which corresponds to the reconstructed area “a” or “b”. The graphs include two time points (blue and violet), which correspond with time points of the PL maps from the left part of the figure. The reconstructed ID data (lines) were compared to the 0D-RATS method (red circles). In all cases, the PL decays obtained by the 2D-RATS method are in perfect agreement with the data from the 0D-RATS method. Although the reconstructed PL maps for the compression ratio k = 0.05 are noisy compared to the higher compression ratios, the PL decays from 0D and 2D RATS methods are still in perfect agreement.
The FLIM spectrogram is shown on the right side of the image. Individual τ values were determined by the fitting algorithm. The reconstructed ID curves for each pixel were fitted with a bi-exponential function. Lifetime τ was then determined as the time when the intensity of the fitted bi-exponential decay decreased to 10% of the curve maximum. The impulse response function of the measurement was 0.47 µs.
The mean lifetimes for the sample measured with compression ratios 0.4, 0.2, and 0.05 are 1.31 µs, 1.29 µs, and 1.29 µs. The mentioned average lifetimes vary with standard deviations of 0.09 µs, 0.10 µs, and 0.13 µs. The statistical data do not include points that did not show a luminescence intensity lower than 10% of the sample maximum, as well as data from the sample edge, which were suffering from scattering signal and high noise level.
We observed that the lifetime precision, i.e., acquired standard deviations, are only marginally affected by the used compression ratio. This ratio has more effect on the quality of the lifetime maps.
In the second measurement, we acquired FLIM data of an artificially prepared sample with two different dynamics of PL decays ID. The first area was an OG565 colour filter, while the second area consisted of a Si wafer with a nanoporous surface.
Both the OG565 filter and the nanoporous Si had been previously tested with a standard method and the 0D-RATS method, and the results from both 0D-RATS methods (Fig. 9, red crosses) were compared in randomly chosen pixels of the 2D PL map (see Fig. 9, solid lines). The results are summarized in Fig. 9 which follows the same logic as Fig. 8 but the compression ratios are different.
Fig. 9. Measurement of nanoporous Si wafer. (A) compression ratio 0.9, (B) compression ratio 0.7, (C) compression ratio 0.5. Left panels: reconstruction of the PL map for two different times. Middle part: graphs “a” and “b” show the reconstructed ID from 2D-RATS in a randomly selected pixel (“a” pix [14,10], “b” pix [16,25]) and ID given via 0D-RATS; blue and violet stars denote the time of the PL maps on the left. Right part: map of the PL lifetimes for the points where the PL amplitude exceeded 10% of the maximum PL intensity.
The measured area was around 18 mm2; in total, 600 masks were scanned. Mask resolution was rescaled again according to the mean speckle size (35 pixels), leading to a resolution of the reconstructed PL map of 26 × 24 (N = 624). Due to the lower IPL amplitude of nanoporous Si, the reconstructed data suffer from a lower signal-to-noise ratio. For this reason, we present reconstructed data for compression ratios k = 0.9 [Fig. 7(B)], and k = 0.5 [Fig. 7(C)]. The corresponding data acquisition times were 63 min, 49 min, and 35 min, respectively. The PL maps in Fig. 9 (left-hand side) have been normalized so that each data point has the same amplitude. Therefore, we observe a flat PL image at the early times (0.6 µs), while for the later time (1.6 µs), the prominent PL intensity is emitted from the upper part, i.e., nanoporous Si with a long PL decay.
Analogously to the previous measurement, individual τ values were determined again by fitting the data with double-exponential decay for both areas (OG565 and nanoporous Si). Lifetime τ corresponds, analogously to the previous measurement, to the time where the intensity of fitted ID drops to 10% of the curve maximum. The impulse response function of measurement was 0.47 µs. For the nanoporous Si wafer, the mean lifetimes for the compression ratios of 0.9, 0.7, and 0.5 correspond to 21 µs, 21 µs, and 20 µs with a standard deviation of 3 µs, 3 µs, and 4 µs, respectively. For the OG565 filter, the mean lifetimes were 1.19 µs, 1.24 µs, and 1.28 µs, varying with a standard deviation of 0.09 µs, 0.16 µs, and 0.27 µs. The statistics included again only points that did not have a luminescence intensity greater than 10% of the sample maximum, as well as the edge points of the sample with the prevailing scattering signal. In the combined sample, we attained for all measurements a slightly lower lifetime of the OG565 filter area compared to the first sample. This arises due to the highly scattering Si wafer, which leads to a stronger leakage of the excitation signal compared to the first measurement. Subsequently, a larger amount of scattered excitation light reaches the detector and influences the results because it forms a response-function-limited peak, which it is not possible to completely separate from the PL decay.
4.4. Reconstruction error vs. intensity of PL decay
The intensity of PL is crucial for the resulting data reconstruction. This can be documented by the fact that the attained PL decay of the nanoporous Si suffers from a significantly higher noise level compared to the OG565 filter data. Analogously, we observed that the noise level of the PL decay increases with the delay after excitation, as the PL intensity decays and decreases. This effect was studied by using a relative error of reconstruction on the real dataset to capture the realistic behaviour of the experimental system, including the noise characteristics of the detectors. The relative error σ was determined as the average absolute deviation of the back reconstructed intensity signal dR=Am [see Eq. (6)] and the original signal d at a given time point relative to the average value d:
Figure 10(A) (top panel) shows representative reconstructed decays for the first measurement (two areas with the same PL decay (OG565)). The PL decay of the upper part of the measured sample is indicated by a red line and the lower part with a blue line. In the bottom panel of Fig. 10(A), the relative error of reconstruction is evaluated. The same logic is also applied in Fig. 10(B), which shows representative decays for the combined sample (nanoporous Si + OG565 filter). The red line shows the PL decay of the upper part of the sample (nanoporous Si) and the blue line shows the PL decay of the lower part of the sample (filter OG565). The bottom panel of Fig. 10(B) then shows the relative reconstruction error. The relative error comparison according to Eq. (8) depicted in Fig. 10 (bottom panels) was done for the same compression ratio k = 0.6 and identical image resolution 26 × 24. This ensures that the length of the vector d remains constant. For cases where the length of the vector d changes, it is more appropriate to observe the reconstruction error with Eq. (7) because a lower number of elements of d can cause the reconstruction algorithm TVAL3 to reach a better agreement between d and d0 while the reconstruction of the PL map can feature a lower quality.
Fig. 10. Relative reconstruction error evaluation with respect to the level of ID intensity. Upper panels: Two examples of PL decay curves (red and blue lines) extracted from the sample with two identical areas (filter OG565, panel A) and from the sample with two different areas (nanoporous Si + filter OG565, panel B). Bottom panels: reconstruction error σ is evaluated as a relative error via Eq. (8) in each reconstructed time point.
For both cases in Fig. 10, we observe that the relative error level steadily increases with the decreasing PL intensity (see the bottom panels). Thus, we can conclude that for a higher intensity of detected PL it would be possible to reconstruct decays with a lower relative error even for small compression ratios. However, the relative error still increases with the decreasing intensity of PL decay.
5. Conclusion
We present a new approach to FLIM, which is based on a combination of the random temporal speckles (RATS) method with the concept of a single-pixel camera. Spatio-temporal random speckle patterns make it possible to track both PL images and dynamics on the microsecond timescale. The speckle generation is based on rotating and movable diffusers, which reduces system requirements. The result is a low-cost FLIM setup of unrivalled simplicity. The strength of the new concept lies in the imaging of PL decay on the microsecond timescale because the lifetime acquisition time is reduced owing to the use of compressed sensing. At the same time, the method can be performed using a simple single-pixel detector.
When compared to other commonly-used options of FLIM, the sample point-by-point scanning of PL decay rapidly reaches extremely high acquisition times as the resolution of an image increases. For instance, a 60×60 pixel image measured at 2 s per decay requires a total acquisition time of two hours. The use of intensified CCD or TCSPC with a 2D array of single-photon avalanche diodes (SPAD) can provide fast FLIM even in the microsecond timescale. Nevertheless, the use of such an array detector dramatically increases the cost of the setup.
The acquisition time of 2D-RATS depends on several factors. The most prominent one is the PL map resolution and the related compression ratio. We have shown that it is reasonable to use scaling according to the mean speckle size. A lower resolution causes a loss in the image quality, while a higher resolution cannot provide more information, as the resolution is limited by the mean speckle size. The FLIM data reconstruction error also highly depends on the intensity of PL. Hence, we can achieve fast acquisition by using a higher PL intensity while decreasing the compression ratio. Under ideal conditions, i.e., highly emitting samples, we were able to reach an acquisition time of 6 minutes. For a standard sample, it was necessary to increase the compression ratio and the resulting acquisition time reached 35 minutes.
We would like to stress that the 2D-RATS method is a general concept, which uses spatio-temporal random patterns to carry out time-resolved imaging. It can be therefore generalized for the imaging of any temporal signal and has many possible ways of implementation. Since this article serves as a demonstration of the new method, further optimization of the optical setup can provide us with more efficient excitation use and PL collection. For instance, the use of a pair of diffusers causes the vast majority of the excitation light energy to be lost in the setup and the resulting low excitation intensity can be limiting. Nevertheless, this can be solved by modifying the approach to mask generation – for instance, by using a digital micro-mirror device (DMD) or a multimode fibre. An increase in the excitation intensity and the signal to noise ratio (SNR) allows a further reduction of the compression ratio, thus decreasing the number of measurements and saving additional data acquisition time.
In summary, the method is a low-cost and straightforward alternative to commonly-used methods, providing the possibility of speedy measurement of fast mapping of PL decays on the microsecond timescale.
Funding
Akademie Věd České Republiky (ERC-CZ/AV-B (RUSH, Reg. No. ERC100431901)); Ministerstvo Školství, Mládeže a Tělovýchovy (Reg. No. CZ.02.1.01/0.0/0.0/16_026/0008390); Technická Univerzita v Liberci (SGS-2020-3057); Grantová Agentura České Republiky (17-26284Y).
Acknowledgment
We gratefully acknowledge Lukáš Ondič (Institute of Physics, Czech Academy of Sciences) for providing us with samples of nanoporous Si.
Disclosures
The authors declare no conflicts of interest.
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