1. Introduction

Two-photon microscopy (TPM) is among the favored tools for fluorescence imaging in thick tissues [1]. It is minimally invasive and yet offers high spatiotemporal resolution even in the presence of scattering. However, its penetration depth is limited usually as a result of loss of contrast (defined here as the ratio between in-focus signal and out-of-focus background, or SBR). For example, the maximum depth penetration in mouse brain tissue is generally $\sim 0.6$ mm [2] (though it has been pushed to about 1 mm using low repetition-rate lasers and longer excitation wavelength [3–5]). After this point, the exponentially decaying in-focus signal drops below the out-of-focus background, much of which can arise from near the sample surface [6, 7]. Clearly, it is beneficial to be able to reject out-of-focus fluorescent background when using TPM for deep tissue imaging.

We have previously demonstrated a simple out-of-focus background rejection technique for nonlinear microscopy, called differential aberration imaging (DAI) [8, 9], where background is removed from fluorescence images simply by subtracting an aberrated image from an unaberrated one. For example, in [9], an unaberrated image was produced with a Gaussian focus whereas an aberrated image was produced with a donut-shaped focus. Similar approaches, with various names, have been developed for confocal microscopy [10–12] and also applied to nonlinear microscopy [11, 13, 14]. In essence, when imaging deep in thick tissue with nonlinear excitation, the fluorescence from an unaberrated focus contains both in-focus signal and out-of-focus background. An aberration applied to the focus suppresses the signal while leaving the background relatively unchanged. A subtraction of the aberrated from unaberrated image thus preserves only the in-focus signal, thereby improving the resultant signal contrast. In our previous implementation, a deformable mirror was used to toggle between unaberrated and aberrated focuses, with images taken alternately. This strategy, though flexible, requires the use of an active optical element and reduces the imaging speed by a factor of two. Alternative approaches also made use of active optical elements, as well as a lock-in amplifier.

We describe here a simple technique to perform DAI that uses only a passive optical element and acquires unaberrated and aberrated images near-instantaneously. Our technique makes use of temporal multiplexing, where the excitation laser pulses are split into interleaved trains, and the fluorescent signals from each pulse train are demultiplexed upon readout [15]. To date, temporal multiplexing in nonlinear microscopy has been applied only to multi-region imaging, where signal demultiplexing has been performed either in hardware using high-speed custom gating electronics [16–18] or with FPGA after acquisition using an ultra-high speed digitizer [19]. In all such multi-region applications, the aberration state of the beam focus has been keep fixed, namely unaberrated.

Here, we use temporal multiplexing to near-instantaneously toggle between unaberrated and aberrated states of the beam focus. Our technique is based on a simple approach for signal demultiplexing based on synchronous sampling, and requires no custom gating nor ultra-high speed digitization, meaning it can be operated with a standard two-photon microscope setup (80 MHz excitation laser with standard detection electronics). Because DAI is performed near-instantaneously, our microscope speed is not hampered in any way. We demonstrate the resulting contrast improvement by imaging fluorescently labeled mouse brain tissue at video-rate (30 Hz).

 

Fig. 1 (a) Optical setup. f₁ = -50 mm, f₂ = 200 mm, f₃ = 500 mm, f₄ = 125 mm, f₅ = 100 mm, f₆ = 300 mm, f₇ = 250 mm. (b) Demultiplexing scheme.

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2. System design

Our system schematic is shown in Fig. 1(a), and is based on a standard TPM configuration where a laser beam with 80 MHz pulse rate (Spectra-Physics Tsunami operating at 897 nm) is scanned by a pair of galvanometric scan mirrors (Cambridge Technologies CRS8K/6215H), expanded by a 4f system (f₅ and f₆) and focused by an objective (Obj, Olympus 40×/0.8W UMPlanFLN) into the sample. The average power after the objective is 140 mW, which is used for all of our following experiments. The resulting fluorescence is epi-collected by the same objective, directed by a dichromatic mirror (DM, Chroma 695dcxru) and a lens f₇ onto a hybrid photodetector (HPD, Hamamatsu R11322U-40-01). The signal from HPD is amplified by a high speed transimpedance amplifier (Femto HCA-400M-5K-C), and sent for subsequent demultiplexing. Additionally, a lowpass filter with 90 MHz cutoff (LPF, Mini-Circuits BLP-90+) is inserted after the amplifier, the point of which is described below.

To perform DAI, we use temporal multiplexing for simultaneous acquisition of both unaberrated and aberrated images. The difference between our microscope and a standard two-photon microscope is that we separate the excitation beam into two illumination paths of differing optical path length, such that the pulse train through one path is time-delayed by 6.25 ns (half the laser pulse period, 1.875 m longer in free space) relative to the pulse train through the other. These paths are split and recombined before entering the microscope using two polarizing beam splitters (PBSs), resulting in an interleaved 160 MHz pulse train from the two separate arms. The longer arm produces a conventional unaberrated, or Gaussian, focus at the sample. The shorter arm produces an aberrated focus. This is achieved by inserting a spiral phase plate (SPP, RPC Photonics VPP-2) that is imaged onto the scan mirrors using the additional 4f relay system (f₃ and f₄), thus creating a donut-shaped focus at the sample. A half-wave plate inserted in front of the first PBS is adjusted to ensure both arms transmit equal power.

Our demultiplexing scheme is shown in Fig. 1(b). We use a two-channel digitizer (National Instruments NI-5732) whose sampling frequency is 80 MHz. While at first glance it may seem problematic to use a 90 MHz lowpass filter and 80 MHz electronic sampler to parse out a 160 MHz fluorescence signal, however these constitute the crux of our technique. The key idea is to exploit the two-channel capacity of our digitizer and to synchronize the electronic sampling of each channel. Specifically, after amplification and filtering, we split (Mini-Circuits ZFRSC-2050+) the fluorescence signal into both channels, such that the second channel is delayed relative to the first by 6.25 ns by using a longer BNC cable (approximately 1.25 m longer assuming $2\times {10}^8$ m/s electric signal propagation speed). Next, we synchronize the electronic sampling clock to the laser pulse clock (the latter is monitored by an internal photodiode obtained from the laser itself), with the sampling clock phase adjusted using a time delay box (Stanford Research DB64). The adjustment is made so that channel 1 samples at the peaks of the signals obtained from the Gaussian pulses, while channel 2 samples at the peaks of the signals obtained from the donut pulses. In this manner, we are able to demultiplex fluorescent signals by sampling only at the peak signals of either the Gaussian or donut pulses. The purpose of the lowpass filter is to increase the number of detected photons per sampling event, so as to improve SNR, as will be detailed below.

All microscope hardware and image acquisition are controlled by the freely available version of ScanImage, which is capable of dual channel acquisition with sampling clock synchronized to external laser clock [20]. Imaging was performed at video-rate (30 Hz) with 8 MHz pixel rates.

3. Inter-channel crosstalk

While simple to implement, temporally multiplexed DAI presents a small drawback related to inter-channel crosstalk. Two mechanisms can contribute to crosstalk. First, because the time delay between the acquisition of unaberrated and aberrated images is short here (6.25 ns), there is the possibility that fluorescence arising from a single laser pulse becomes spread from one channel to the next owing to the finite lifetime of the fluorescent indicators (typically a few nanoseconds). Second, because of the finite response time of the detection electronics, as principally defined by the LPF, signal voltage from one channel can leak into the next.

We note that the overall inter-channel crosstalk in DAI does not produce image artifacts as it does in previous multi-region implementations of temporal multiplexing. This is because both beams in our system image the same sample region. As a result, the crosstalk becomes cancelled upon DAI subtraction (assuming equal temporal spacing between the two channels, and hence equal crosstalk between channels), and the net effect is simply a reduction in the DAI signal by a fixed scaling factor. On the other hand, inter-channel crosstalk does have repercussions on SNR. In particular, optical crosstalk reduces the SNR of the DAI signal, and the addition of electrically-induced crosstalk, if not managed properly, only degrades this further.

 

Fig. 2 (a-d) Images from both channels when imaging a fixed GCaMP6-labeled mouse brain with the Gaussian beam (a,b) or the donut beam (c,d). For visualization, both (a,d) are normalized to their respective maxima. The upper right part of (b) is normalized to 1/8 the maximum of (a), and (c) to 1/4 the maximum of (d). Lower left parts of (b,c) are normalized to the maxima of (a,d) respectively. (e) Probability density function (PDF) of the measured crosstalk with and without the 90 MHz LPF. (f) Time-resolved fluorescence signals from both channels (red, blue curve) and system instrumentation response (purple curve), vertical gray dashed lines represent sampling events. (g) Same as (f) but without the LPF. Scale bars in (a-d) are 50 μm. Color bars in (a-d) represent intensity.

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3.1. Crosstalk characterization

To begin, we performed crosstalk measurements on a fixed mouse brain labeled with GCaMP6. Figure 2 shows the images from both channels when imaging with either the Gaussian beam (Fig. 2(a,b)) or the donut beam(Fig. 2(c,d)). All images were averaged over 30 frames. It is apparent that signals from the Gaussian beam mostly concentrate on channel 1 with only a small amount leaking to channel 2, and vice versa for the donut beam.

We can quantify the amount of crosstalk as the image-averaged intensity ratio obtained at the same pixel for both channels. The probability density distributions of these crosstalks are shown in Fig. 2(e). On average, the crosstalk is about $8.1\pm 2.2\%$ (mean ± standard deviation) from channel 1 to channel 2 when measured with only the Gaussian beam, and $8.8\pm 3.3\%$ from channel 2 to channel 1 when measured with only the donut beam (green and purple areas in Fig. 2(e)). For comparison, we performed similar experiments with the LPF removed, in which case the system bandwidth increased to about 350 MHz. The measured crosstalks are $17.2\pm 2.1\%$ from channel 1 to channel 2 and $19.4\pm 3.1\%$ from channel 2 to channel 1 (red and yellow areas in Fig. 2(e)). In both cases, the slightly imbalanced crosstalk between both channels is likely due to a small discrepancy between the time delay of channel 2 and half the laser pulse period, caused by the drifting of laser frequency and/or mismatch of physically imparted optical/electronic signal delay.

Interestingly, the addition of the LPF in our detection electronics has the effect of reducing inter-channel crosstalk. To better characterize this, we measured the system’s single photon response both with and without the LPF, using a fast oscilloscope (Tektronix DPO4104B, 1 GHz bandwidth, 5 GS/s), as shown in the purple traces in Fig. 2(f,g). The traces were averaged over about 50k individual acquisitions. Without the LPF, the impulse response is quite narrow, with a main peak of only about 1.9 ns full width at half maximum (FWHM). With the LPF, the main peak FWHM increases to about 6.1 ns, which is comparable to our 6.25 ns channel spacing. For a single-pole LPF, such a broad impulse response would lead to significantly worsened crosstalk. However, due to the multi-pole nature of our LPF, the impulse response becomes negative at 6.25 ns after the peak, effectively cancelling part of the decayed fluorescence signals, leading to a smaller measured crosstalk.

To further illustrate this, we measured the time resolved fluorescence signals with and without the LPF using the same tissue sample (blue and red curve in Fig. 2(f,g)). Measurements were made with only the Gaussian beam, averaged over about 350k individual acquisitions, and triggered using the laser clock signal. Ideally, we would like to minimize the crosstalk arising from channel 2 when sampling at the peak of channel 1. When the LPF is present (Fig. 2(f)), the peak of channel 1 signal actually aligns with the valley of channel 2 signal because of the LFP impulse response. The valley-to-peak ratio, which is our measured crosstalk, is about 9.8% (2 circled points in Fig. 2(f)). When the LFP is absent, the measured fluorescence trace is closer to an exponential decay, as expected. But when sampling at the peak of channel 1, the crosstalk becomes worse, at about 18.9%.

 

Fig. 3 (a,b) Averaged unaberrated and aberrated images of a fluorescent bead sample with the 90 MHz LPF system. (c) DAI image taken with no-LPF system. (d) DAI image taken with 90 MHz LPF system. (e) DAI image with 50 MHz LPF system where unaberrated and aberrated images were taken separately. Inserts in (c-e) represent the SNR image over the red dashed square in (c-e). (f) Pixel SNR comparison of 90 MHz system (red dots) and no-LPF system (blue dots) versus the 50 MHz system. Only pixels with average intensity greater 14 are compared, as masked by the top left insert. (g) SNR profiles along the yellow dashed lines in the inserted SNR images of (c-e). (h,i) Time resolved fluorescence signals with the 90 MHz and no-LPF system, respectively. Scale bars in (a-e) are 50 μm. Color bars in (a-e) for the large images represent intensity (arbitrary unit). Color bars in (c-e) next to the small inserts represent SNR. All intensity and SNR images are normalized to maximum.

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3.2. Signal-to-noise ratio

While the presence of the LPF has the effect of decreasing our measured crosstalk, we emphasize that this decrease in crosstalk does not, in itself, lead to increased SNR. This is because the maximum SNR is governed by the optical crosstalk only, which is caused by finite fluorescent lifetime and remains unaffected by the LPF. On the other hand, the LPF does play a critical role here, which is to enhance the collection efficiency of each sampling event by temporally stretching the signal from a single photon. Because sampling occurs only once per laser pulse, it is important that each sampling event “sees” as many of the fluorescence photons associated with this pulse as possible. If the system bandwidth so high that photons are missed between sampling events, then the corresponding reduction in photon collection efficiency leads to a reduction in SNR. On the other hand, if the system bandwidth is so low that the crosstalk becomes significant, then the DAI signal decreases due to subtraction while the electronic and digitization noises remain the same, also leading to a reduction in SNR. In other words, there is an optimal LPF bandwidth that maximizes SNR, which is roughly given by the laser repetition rate. In our case, we chose a LPF of bandwidth 90 MHz.

Using a fluorescent bead sample (Phosphorex Inc., Fluorophorex polystyrene microspheres, 1 μm and 5 μm in diameter embedded in clear PDMS), we compared the SNR of three different DAI systems: 1) temporally multiplexed DAI system as described in Fig. 1, where crosstalk and the missing of photons are minimized with the use of the 90 MHz LPF; 2) same as 1) but with the LPF removed, thus leading to a greater chance of missing photons; 3) conventional DAI system without temporal multiplexing where the unaberrated and aberrated images are taken separately, here using a 50 MHz LPF (Mini-Circuits BLP-50+). The last system is analogous to our previous DAI implementation, which features no crosstalk and maximum photon collection efficiency. In all cases, we took 100 unaberrated and aberrated images each, and calculated 100 DAI images. For each pixel, the SNR was calculated as the mean divided by standard deviation across the image stack. In the rare instances that pixel values after averaging were negative, these were set to zero.

The averaged DAI images for three systems are shown in Fig. 3(c-e), with the lower right corners showing the corresponding SNR images over the red squared regions. Of the three systems, as expected, the 50 MHz system produces the highest SNR owing to its absence of crosstalk and missing photons, the 90 MHz system produces a somewhat reduced SNR, and the 400 MHz system produces the worst SNR. For a detailed comparison, Fig. 3(f) shows a scatter-plot of the pixel SNR of the no-LPF and 90 MHz systems versus the 50 MHz system, for all pixels of intensity greater than 14 (mask at top left of Fig. 3(f)). The average SNR ratio was computed as the average over all pixel SNR ratios between 90 MHz/no-LPF and the 50 MHz system among pixels considered above. On average, the 90 MHz system produces a SNR only 94.6% smaller than the 50 MHz system, suggesting that our temporally multiplexed DAI system does not significantly grade image SNR. On the other hand, the no-LPF system produces a SNR 78.3% smaller than the 50 MHz system, confirming the effectiveness of the LPF in improving SNR.

We note that the above reductions in SNR are dependent on the fluorescence lifetime of the sample. As a reference, we measured the time resolved fluorescent signals on the fluorescent beads sample for the no-LPF and 90 MHz systems (Fig. 3(h,i)). The measured crosstalk is about 6.8% for the 90 MHz system and 14.1% for the no-LPF system, indicating that the beads exhibited somewhat shorter fluorescence lifetimes than the brain tissues used above.

 

Fig. 4 (a-d) Unaberrated (i.e. standard) two-photon images at depths 125 μm, 250 μm, 375 μm and 500 μm. (e-d) Corresponding DAI images at the same depths as in (a-d). (i) Intensity profiles along the red dashed lines in (a,e). (j) Intensity profiles along the red dashed lines in (d,h). The intermediate aberrated images corresponding to the orange traces in (i,j) are not shown. (k) Average contrast enhancement when using DAI as compared to standard two-photon imaging for depths ranging from 100 μm to 500 μm. All images are normalized to their maxima. Scale bars in (a-h) are 10 μm. A.U., arbitrary unit.

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4. Contrast enhancement

To experimentally characterize the contrast enhancement provided by DAI, we imaged fluorescent beads embedded in a scattering fluorescent medium. The medium was prepared by mixing 0.4 g of agarose powder (Sigma A5093-100G), 0.8 ml of 1 μm suspended polystyrene microspheres (Polysciences Inc. Cat# 07310-15) as scatterers, and 0.02 g of fluorescein sodium salt as uniform fluorescent background, with 20 ml of distilled water, which was then heated to 75 °C on a hot plate, poured onto a microscope slide, mixed with 1 μm fluorescent beads (Phosphorex Inc., Fluorophorex polystyrene microspheres), and allowed to solidify at room temperature. Imaging was performed at 30 Hz with Gaussian and donut beams interleaved. A median filter of 2×2 pixels was applied to both unaberrated and aberrated images to reduce HPD noise, and a constant bias that came from our detection electronics (measured in advance) was subtracted from all images.

In order to compare image contrasts at different depths, we acquired a z stack over the depth range $100-500$ μm by axially translating the sample in 1 μm increments. Because of the limit of our laser power, images below 300 μm were averaged over 30 frames to improve SNR. Figure 4(a-d) shows the unaberrated (i.e. standard two-photon) images at depths 125 μm, 250 μm, 375 μm and 500 μm, along with the intensity profiles across a fluorescent bead at two different depths shown in Fig. 4(i,j). As expected, the contrast degrades as the imaging depth increases and the fluorescence background progressively overwhelms the in-focus signal. However, with DAI, an improved image contrast is restored because of the suppression of out-of-focus background, as can been seen in Fig. 4(e-h) as well as the red traces in Fig. 4(i,j).

We then quantified the image contrast enhancement as a function of depth. We define contrast for each fluorescent bead as $\left({\mu }_s-{\mu }_b\right)/{\mu }_b$, where μ_s is the average intensity over the region of a fluorescent bead, and μ_b is the average intensity over the region of 50-pixel radius surrounding that bead. The estimated contrast enhancement at each depth is then defined as the average contrast ratio between the DAI and unaberrated images for all fluorescent beads at that particular depth, with results plotted in Fig. 4(k). The benefit of DAI for deep tissue imaging is apparent, as the signal contrast is found to increase $\sim 20\times$ compared to standard two-photon when imaging at the depth of 500 μm.

 

Fig. 5 (a,b) Unaberrated and aberrated images acquired simultaneously at 30 Hz. (c) DAI image obtained by subtracting (a) from (b). (d) Image (b) after spatial lowpass Gaussian filtering. (e) DAI image obtained by subtracting (a) from (d). (f,g) Intensity profiles along the yellow dashed lines in (a,b,c) and (a,d,e). (h,i,j) Expanded views over the square areas in (a,c,e) respectively. All images are normalized to their maxima. Scale bars are 50 μm. A.U., arbitrary unit.

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5. Instantaneous two-photon differential aberration imaging

Finally, we performed real-time two-photon DAI imaging of a fluorescent mouse brain tissue with our system. Both Gaussian and donut beams were interleaved, and the unaberrated and aberrated images were acquired simultaneously at video-rate (30 Hz). The imaging depth is about 150 μm. The results are shown in Fig. 5(a,b). A median filter of 2 × 2 pixels was used to reduce HPD noise. As expected, the background is much more prominent in the aberrated image than in the unaberrated one. The resulting DAI image (Fig. 5(c)) is computed by subtracting Fig. 5(a) from Fig. 5(b). After subtraction, all negative pixel values were set to zero. Manifestly, the contrast of the DAI image is improved, as exemplified by the line profiles shown in Fig. 5(f).

A disadvantage of DAI, and image subtraction approaches in general, is that while background becomes subtracted from the image, the noise from the background becomes added, leading to an increase in SBR at the cost of a somewhat decreased SNR. This difficulty can be partially corrected with the use of a priori information. In particular, the aberrated image in nonlinear microscopy, because it arises primarily from sample structure that is out of focus, is comprised primarily from low spatial frequency components. We can thus apply a spatial lowpass filter to the aberrated image before subtraction [21]. Such filtering decreases the noise in the aberrated image (because noise is uniformly distributed over all spatial frequencies), while not substantially affecting the structure of the aberrated image (which is confined to lower frequencies). The addition of noise in the final DAI image is thus mitigated. As an example, we filtered Fig. 5(b) with a lowpass Gaussian filter with standard deviation of 1 pixel (0.66 μm), resulting in Fig. 5(d). The resultant DAI image (Fig. 5(e)) was obtained by subtracting Fig. 5(a) from Fig. 5(d). The corresponding line profiles are shown in Fig. 5(g). As can be observed in these profiles, the noise in the aberrated trace (orange) is reduced by spatial filtering, leading to a cleaner DAI trace (red). We note that the implementation of more sophisticated image subtraction approaches based on local intensity weighting can also be considered [22].

6. Discussion

The aim of this work is to describe an implementation DAI that is near-instantaneous (using temporal multiplexing), and simple to implement (using synchronized sampling). However, both advantages of near-instantaneity and simplicity incurred some drawbacks in our implementation. These drawbacks can, of course, be mitigated with improved implementations.

For example, our two-photon microscope made use of a 80 MHz laser, which, upon temporal multiplexing, forced us to use a delay between unaberrated and aberrated imaging of only 6.25 ns. While this delay is longer than the fluorescence lifetimes of most indicators, it is nevertheless not long enough to avoid a small amount of optical crosstalk, which leads to an inevitable slight decrease in SNR relative to DAI systems where the unaberrated and aberrated images are acquired separately. However, we envision that our DAI technique will be most useful when applied to deep tissue imaging, where loss of image contrast plays a dominant role in undermining depth penetration. For deep tissue imaging applications, lower repetition-rate lasers are advantageous since they lead to increased depth penetration [3, 4]. Such low repetition-rate lasers would also enable the possibility of temporal multiplexing with increased channel separation, thus eliminating optical crosstalk and recovering full SNR.

Moreover, due to the limit of 80 MHz maximum sampling rate of the digitizer, a two channel sampling strategy with a power splitter was used to demultiplex fluorescent signals, which incurs a 3 dB signal loss. Although this does not translate to a loss in detected photons, it lowers the SNR somewhat due to the electronic and digitization noises. However, this can be easily compensated with the use of a higher gain amplifier. Better still, a 160 MHz digitizer would circumvent the 3 dB loss through single channel acquisition, with temporal demultiplexing performed post-detection using a FPGA or software. The key to this strategy remains a proper synchronization and adjustment of the sampling phase to be at the peaks of filtered fluorescent signals. Other temporal demultiplexing strategies could also be considered here, but they would continue to require synchronization with the laser clock [16–19]. They would also involve the addition of more sophisticated electronics than proposed in our simple setup, which can be implemented with standard two-photon microscopes using cost-effective, off-the-shelf components with minimal modifications of the detection electronics.

In summary, we have demonstrated a new strategy for performing differential aberration imaging using temporal multiplexing. The proposed system uses only passive optical elements and overcomes the drawbacks of acquisition speed and cost in our original implementations. Moreover, it remains simple and robust, enabling high speed two-photon imaging with enhanced contrast.