We present a frequency-multiplexed multi-site two-photon imaging method utilizing amplitude modulation of femtosecond laser pulses in the MHz range to tag each excitation beam and the corresponding fluorescence signals with specific frequencies. The frequency tags are generated with an interferometric scheme employing acousto-optic deflectors (AODs) to achieve precise spatial overlap of femtosecond laser pulses with periodically varying phase shift. Creating matching excitation beam patterns in each interferometer arm using multiple AOD driving frequencies, and subsequently overlapping these matching patterns, results in multiple encoded excitation beams with unique beat frequencies available for scanning. As a proof-of-concept, we demonstrate multiplexed two-photon image acquisition using test samples, and compare the performance of this approach to conventional two-photon laser scanning microscopy.
© 2017 Optical Society of America
Two-photon laser scanning microscopy (TPLSM) has become a widely used tool for imaging neuronal structure and function in intact brain due to its ability to achieve imaging depths beyond 1 mm without significant loss of resolution . TPLSM with resonant galvanometer scanning provides data acquisition rates of about 10 Mpixels/s and allows for observation of fluorescently labeled neurons within limited regions-of-interest at 5–30 frames/s [2, 3]. Nevertheless, functional recordings from large ensembles of neurons labeled with Ca2+- or voltage-sensitive indicators remain challenging due to limitations in scanning speed and data acquisition rates. Only a few experimental techniques, including random-access scanning with acousto-optic deflectors AODs [4–6] and targeted path scanning with galvanometer mirrors , have been demonstrated to shorten the transition time between recording sites and thus to increase the overall speed of functional imaging. For example, AOD-based scanners allow hopping between user-selected recording sites in 2D or even 3D within 10–20 µs and achieve scan rates of 30–50 Kpixels/s [4, 6]. Driven by the need to improve data acquisition rates, multiplexed two-photon imaging techniques are emerging [8–10]. These methods enable simultaneous multi-site recordings with multiple excitation beams and a single detector. One approach, termed spatiotemporal multiplexing, utilizes multiple excitation pulse trains delayed in time relative to each other, separating the corresponding emission signals based on their arrival time to a detector [8, 10]. The useful number of data acquisition channels is ultimately limited by the laser pulse repetition rate and the fluorescence lifetime of the employed fluorophore, leaving room for only a few, e.g. 2-4, multiplexed channels with commonly used femtosecond-pulsed lasers. Another multiplexed detection scheme utilized a combination of a spatial light modulator (SLM) and a digital micromirror device (DMD) to create and assign a specific time-amplitude binary code to multiple excitation beams that enabled de-multiplexing of integrated emission signal into its individual components . Due to the need to measure on/off signal levels with sufficient accuracy, as well as limited SLM switching speed, the resulting pixel readout rates appear in the range of a several kHz.
Frequency-division multiplexing (FDM) is an attractive technique for optical imaging since it potentially allows for a large number of frequency-encoded channels within a wide detection frequency band and thus can provide a substantial increase in the rate of data recording. FDM, however, requires longer signal acquisition times to capture multiple periods of selected frequencies in order to resolve or de-multiplex individual frequency components. Several prior studies, see for example [11, 12], utilized mechanical beam chopping to achieve frequency-multiplexed imaging with frequencies in the kHz range. Therefore until recently it has been a challenge to reach the MHz pixel readout rates commonly used in TPLSM. A record-setting example of modulating transmission in the optical path of multiple beams demonstrated frequency-multiplexed multiphoton imaging using frequencies of 350-650 kHz .
Several prior studies demonstrated a different approach, making use of interference between co-aligned optical beams to create amplitude-modulated excitation from continuous wave laser sources [14, 15]. Based on this method, FDM has been recently employed by Diebold, et al.  to achieve frame rates of several kHz in single-photon imaging. In this proof-of-concept work we demonstrate the use of similar interferometric principles to enable frequency-multiplexed image acquisition in TPLSM and evaluate performance of this method.
Our approach utilizes interference of femtosecond laser pulses to create amplitude-modulated excitation beams. A customized Mach-Zehnder interferometric scheme (Fig. 1) with AODs positioned in each of its arms is used to achieve frequency-shifting and pulse overlap. A femtosecond pulse train generated by a mode-locked Ti:Sapphire laser (Chameleon Ultra II, Coherent) is passed through a non-polarizing beam splitter (NPBS) and two AODs (OAD-1121X, Isomet). When simultaneously driven by a set of n frequencies, these AODs create a fan of n diffracted beams, n = 2 in this work, with deflection angles proportional to the supplied frequencies. Matching beams are recombined at the interferometer output by another NPBS. AOD drive frequencies are generated by direct digital synthesis (AD9959, Analog Devices) and summed by a passive RF combiner before amplification. To compensate for spatial and temporal dispersion of femtosecond pulses by AODs and other optical elements, an additional AOD positioned at equal distance from each deflector is used . The intensity of femtosecond laser pulses is monitored with a fast photodetector (DET10A, Thorlabs) connected to an oscilloscope (WaveRunner 204MXi-A, LeCroy). A 1:1 optical relay was used to conjugate the AOD output to the input pupil of a water immersion objective lens (40 × Fluor/0.8 NA, Nikon) mounted on an upright microscope (Eclipse E600FN, Nikon). A motorized stage (MP-285, Sutter Instrument) was used for sample positioning and raster scanning. A standard epi-fluorescence detection scheme was employed to record emission signals. Samples were two-photon excited - at 820 nm wavelength. Emission within a 500-700 nm spectral window was detected by a hybrid avalanche photodetector (R11322U-40, Hamamatsu), connected to a pre-amplifier (C10778, Hamamatsu), and sampled with a waveform digitizer (first Compuscope 14100, GaGe, later ATS9350, AlazarTech). Recorded waveforms were analyzed with a numerical lock-in detection procedure to determine the weights of selected frequency components. Brightfield images were captured with a camera (Cascade 1K, Photometrics) mounted on the microscope. Custom MatLab routines were created to perform numerical modeling of detected emission signals with Poisson statistics and to analyze the influence of shot noise on frequency-multiplexed two-photon imaging.
3. Experimental results
Due to a constantly moving diffraction grating within the AOD material, the diffracted beams experience a time-dependent periodic phase shift in the direction of beam propagation which equals 2πΩ1t and 2πΩ2t, where Ω1 and Ω2 are the applied acoustic frequencies and t is the time. By adjusting the interferometer delay line (Fig. 1) while monitoring the pulse intensity, amplitude modulations with beat frequencies of ΔΩ = Ω1 - Ω2 can be seen when femtosecond pulses are overlapped in space. Figure 2 shows the initial femtosecond pulse train from a laser in a single interferometer channel, as well as an amplitude-modulated pulse train with a beat frequency of 4 MHz created by the pulse overlap at the interferometer output. Notably, neither spectral composition of a pulse nor its temporal width are relevant to the observed phenomenon: the effect remains after pulse stretching or compression with different optical elements and assemblies. The observed interferometric effect is also highly stable given the AOD-induced phase shift in the MHz range.
To enable frequency-multiplexed data acquisition it is necessary to create a unique beat frequency in each excitation beam. This is achieved by recombining the fan of beams coming from one AOD with the inverted or mirror-reflected fan of beams from the other AOD. In this arrangement, the beams corresponding to Ωc–f and Ωc + f frequencies are overlapped, where Ωc is the AOD central frequency and f is the arbitrary frequency offset. To demonstrate this effect, we acquired test images of 2 μm fluorescence beads deposited on a glass slide while simultaneously exciting the sample with two beams modulated at 8 MHz and 10 MHz, respectively. In the imaging plane, the foci of the excitation beams were offset by ~30 μm. An area of 25 × 50 μm was scanned mechanically at 0.5 μm steps, while recording 4,000 time samples per pixel. Frequency spectra of both excitation beams and the modulated two-photon emission signal from a microsphere are shown in Fig. 3.
Figure 4 shows images of fluorescent microspheres. The de-multiplexing procedure involves computing in-phase x and quadrature term y of a selected frequency and calculating its weight as . Here we used short waveforms comprised of 200 samples for image reconstruction, corresponding to 2 μs of measurement time per point. In order to avoid systematic errors when analyzing such short waveforms it is important to select a measurement interval containing an integer number of periods of a given frequency. The background in these images originates primarily from electronic white noise and photonic shot noise, the spectral densities of which remain approximately constant across the entire detection band. As a result, whenever a signal is present in a particular channel, contributions from its noise will be detected at every frequency. It is possible to evaluate average values of this cross-talk contamination for every pixel by computing weights of several arbitrary frequencies except those used for sample excitation, and the averaged cross-talk pixel values can be used to correct the images of interest.
4. Comparison with single-channel two-photon imaging
It is essential to compare the performance of frequency-multiplexed detection with non-multiplexed to assess whether the former approach offers tangible benefits in terms of scanning speed or detection sensitivity. While frequency-multiplexing allows for simultaneous data acquisition from multiple channels, it also requires longer sampling times to acquire a complete waveform. Further, we will consider only the influence of Poisson-distributed shot noise, which is the dominant source of noise in TPLSM, and leave other noise sources associated with specific experimental hardware out of the scope of this discussion.
The two-photon fluorescence signal intensity from a single excitation channel amplitude-modulated with temporal profile can be represented as follows:Eq. (1), the amplitude-modulated excitation is expected to generate 3/8th of the total emission as compared to conventional unmodulated excitation of the same peak power. Following similar derivation as described by Diebold, et al.  one may find that shot-noise limited signal-to-noise ratio (SNR) from one out of N frequency-multiplexed excitation channels equals:Eq. (1), the excitation intensity in each channel must be increased by a factor of , and the resulting expression for SNR becomes:Eqs. (2)-(4), we performed a series of numerical simulations to assess the SNR dependence of frequency-multiplexed and conventional data acquisition in the presence of shot noise, as a function of signal acquisition time, excitation/emission amplitude, and the number of channels. Simulated waveforms were synthesized using the expected values of the emission signal at any given time as defined by Eq. (1). Each time sample was randomly generated with Poisson statistics. These waveforms were analyzed with the same lock-in detection procedure to compute the weights, Ai, of arbitrary selected orthogonal frequencies within the detection frequency band. The use of orthogonal frequencies in the analysis ensured no cross-talk between different frequencies while not contaminating cross-talk caused by the shot noise components. Each averaged SNR value was computed from 2,500 waveforms. Figure 5 shows simulation results comparing SNR values in conventional and amplitude-modulated detection according to the C1 and C2 criteria, described earlier.
Note that SNR values corresponding to C1 and C2 cases appear on the same curve when plotted against the average emission signal. This confirms that the performance of both imaging techniques depends primarily on the number of emitted photons per channel and the signal acquisition time. Any increase in the data acquisition rate provided by multiplexed detection may potentially be compensated for by a corresponding reduction of signal integration time in conventional two-photon imaging. However, this is only valid if all channels contain signal at the same time. With the frequency-multiplexed approach, imaging sparsely labeled samples can be expected to result in significant gains in terms of scanning speed or noise reduction.
At present, imaging of biological specimen is hampered by the low scan speed of our current experimental hardware. Therefore, we recorded images from a tissue phantom containing a slide with embedded pollen grains sized ~20 μm, covered with a 250-μm-thick slice of brain tissue, using the same experimental setup. A single excitation beam with modulation frequency of 4 MHz and an unmodulated beam of equal power from one of the interferometer arms were used to record both frequency-encoded and conventional images (Fig. 6(a)). Instead of point-by-point stage positioning, scanning was performed by moving one of the stage axis back and forth at a speed of 0.5 mm/s while acquiring 1,000 time points at 250 MHz sampling rate every millisecond. A mismatch between different scan lines was corrected by post-processing of the images. The presented images were reconstructed from 250 time samples, corresponding to pixel dwell time of 1 μs. When we compared amplitude-modulated fluorescence signals to unmodulated two-photon emission at the same excitation power, the former exhibited higher average signals levels than predicted by Eq. (1). This was observed in several experiments when imaging stained pollen grains and fluorescein solutions. This behavior is likely caused by dynamic photobleaching effects that were observed previously in different fluorophores .
Figure 6(b) shows the waveforms corresponding to the brightest pixels in these images. We estimate the average emission intensity to be less than 1 photon per pulse in this experiment. The recorded images of objects with different brightness levels contained sufficient information to perform quantitative comparison of these methods. To compute the SNR values we selected three regions of interest (ROI), as shown in Fig. 6(a), from the areas that exhibited similar intensities. Each ROI contained 60 pixels. Since 1,000 time samples were recorded for each pixel, it was possible to compute SNR values from 4 images with pixel dwell times of 1, 2, 3, and 4 μs for each ROI. An average weight of a single photon count was computed from a low signal level waveform and further used to convert the measured values to corresponding photonic units. The resulting SNR dependences, plotted as a function of cumulative photon count, Fig. 6(c), appear the same for both imaging techniques. To evaluate the level of cross-talk, we performed a similar analysis using the selected ROIs and the modulation frequency of 10 MHz to compute the corresponding ROI averages and standard deviations. A comparison of these is presented at Fig. 6(d). We found even at low emission signal levels of ~0.4 photons per pulse good quality images could be acquired. We also note that averaging over a number of pixels within given area will result in significant SNR improvement. Averaging, however, will not remove shot noise-related background created by cross-talk with other active frequency channels. A better approach would be to combine individual waveforms from multiple pixels in the area into a single waveform, which is feasible when their relative phase is known, and thereby extend the measurement time by orders of magnitude. Then, the full power of a lock-in amplifier to filter out a single frequency component can be utilized.
We presented a new approach to create multiple amplitude-modulated excitation beams with frequencies in the MHz range using the interference of femtosecond pulses in a customized Mach-Zehnder interferometric scheme. Amplitude modulation is created by continuously varying the phase shift between the corresponding femtosecond wavepackets induced by the AODs. Proof-of-concept experiments demonstrated the feasibility of frequency-multiplexed data acquisition in two-photon imaging. The performance of this technique is ultimately limited by shot noise-induced cross-talk between channels, reducing its measurement accuracy. Our shot-noise limited SNR analysis predicts a similar performance of multiplexed detection and conventional single-channel scanning at equal data acquisition rates and the same amount of fluorescence photons per channel. In case of sparse sample labeling, the multiplexed detection can provide significant gain in terms of speed or SNR increase. In general, multiplexed imaging requires significant increase in the excitation power delivered to the sample, and this requirement may limit the imaging depth in live specimens. Input power is not an issue when imaging thin tissue slices, thus, frequency multiplexing may considerably enhance the performance of serial sectioning tomography systems . Finally, a frequency-multiplexed approach could be synergistically combined with temporal multiplexing to reduce cross-talk between different excitation channels to further push the performance limits of TPLSM.
We would like to thank our colleagues, Drs. Peter Ledochowitsch, Rui Liu, and Olga Gliko for discussion and experimental assistance during different stages of the project, and James Brockill for proofreading the manuscript. We wish to thank the founders of the Allen Institute for Brain Science, Paul G. Allen and Jody Allen, for their vision, encouragement and support.
References and links
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