Hadamard-transform spectral acquisition with an acousto-optic tunable filter in a broadband stimulated Raman scattering microscope

: We present a novel configuration for high spectral resolution multiplexing acquisition based on the Hadamard transform in stimulated Raman scattering (SRS) microscopy. The broadband tunable output of a dual-beam femtosecond laser is filtered by a fast, narrowband, and multi-channel acousto-optic tunable filter (AOTF). By turning on and off different subsets of its 8 independent channels, the AOTF generates the spectral masks given by the Hadamard matrix. We demonstrate a seamless and automated operation in the Raman fingerprint and CH-stretch regions. In the presence of additive noise, the spectral measurements using the multiplexed method show the same signal-to-noise ratio of conventional single-wavenumber acquisitions performed with 4 times longer integration time.


Introduction
Coherent Raman scattering (CRS) microscopy uses the vibrational spectra of molecules as a source of contrast for label-free chemical imaging, and offers faster acquisition speed combined with intrinsic optical sectioning capability when compared to spontaneous Raman scattering microscopy [1].In particular, stimulated Raman scattering (SRS) microscopy [2] has recently established itself as a powerful technique for a wide range of applications in biology and medicine [3,4].Remarkably, among CRS methods, SRS provides vibrational spectra identical to Spontaneous Raman and the generation of a signal that is linearly dependent on the concentration of molecules, thus allowing a straightforward application of chemometric methods to obtain quantitative information [5].
Most of the used configurations for SRS microscopy probe one single Raman shift (wavenumber) at a time.However, it is possible to introduce multiplexed schemes to perform faster spectral acquisitions [6].One type of multiplexed approach entails measuring the SRS signal at several wavenumbers in parallel.This approach often requires the use of complex technical solutions, such as multi-channel detectors [7], dual-phase [8,9], dual-polarization [10], multi-frequency modulation schemes [11][12][13] and multi-channel lock-in amplifiers [14][15][16], that could be difficult to implement or not give the desired performances when using commercially available devices.Another approach to multiplexing in SRS microscopy exploits spectral reconstruction techniques -such as the Hadamard transform [17] -that increase the signal-to-noise ratio (SNR), thus speed-up the acquisitions.This is achieved through a reduction of the additive noise affecting the measurements [18].This approach is comparatively simpler and can be implemented using a single detector, a single lock-in amplifier and an Hadamard spectral mask encoder [19].The addition of such multiplexed capability to SRS microscopes reported in the literature require a change or addition of opto-electronic components to their optical setups.Also, these modifications typically work optimally only in a limited region of the vibrational spectrum.
Here, we present a novel configuration for acquiring the SRS signal using the Hadamard transform method.Our approach represents a straightforward implementation of such a modality allowed by our recently proposed SRS setup [20] that is characterized by broadband capability, high spectral resolution, and setup design simplicity.This configuration is based on the measurement of the stimulated Raman loss (SRL) signal with a single photodiode, and the use of a narrowband and multi-channel acousto-optic tunable filter (AOTF) for spectral shaping of the "pump" beam in an SRS microscope based on a dual-beam femtosecond laser.We generated the spectral masks needed for the Hadamard matrix method by controlling the transmission for each independent channel of the AOTF.This multiplexed acquisition modality allows performing fast SRS measurements from the fingerprint to the CH-stretch region, maintaining a consistently high spectral resolution without the need for realignment or replacement of optical components.Remarkably, the added option to perform SRS acquisitions with the Hadamard multiplexing method enables the use of broadband laser sources with a relatively low power spectral density for fast and high-resolution spectral acquisitions.

Methods
The here presented configuration for SRS acquisition with the Hadamard matrices method is based on the SRS microscope described in Laptenok et al. [20], and sketched in Fig. 1.In short, the laser source is a dual-beam femtosecond laser system (Chameleon Discovery, Coherent Inc., Santa Clara, CA) with a fixed wavelength output (1040 nm) used as the Stokes beam, and a tunable wavelength output used as the pump beam.The fixed wavelength output is amplitude modulated at 5 MHz and filtered down to a 1-nm bandwidth by using a transmission grating and a slit in a folded 4-f spectral shaper [20].The tunable output beam is spectrally filtered with an AOTF (Gooch & Housego, TF950-500-1-5-NT2) featuring a 7 cm −1 passband and driven by a programmable 8-channel digitally controlled frequency synthesizer.The two beams are then spatially and temporally overlapped and guided to an inverted microscope (Nikon Eclipse Ti-E).The laser beams are focused on the sample by a 1.27 NA microscope objective (Nikon CFI Plan Apo IR SR 60XWI), while a 1.15 NA microscope objective (Nikon CFI Apo LWD Lambda S 40XC WI) is used for signal collection.The laser power at the sample plane was adjusted according to the experiment's requirements, as it will be specified in the Results and discussion section.The relatively high excess relative intensity noise of our laser source is reduced with a balanced detection scheme [20], allowing to perform measurements close to shot-noise sensitivity.Under low pump laser power conditions, the main noise contribution is related to the detection electronics, mainly constituted by the dark current of the photodiodes and the pre-amplifier and lock-in amplifier input noise.
In an Hadamard-type detection scheme based on a single photodetector, and assuming a pure additive noise source, the matrix that gives the masks for the optimal acquisition is called the S-matrix [17,21].When a S-matrix of order n is used, only (n+1)/2 elements are non-zero in each row of the matrix, which means that only (n+1)/2 different spectral components (corresponding to different wavenumbers in spectroscopic measurements) are turned on simultaneously in each acquisition.As an example, in Fig. 2 we show, for the case of n = 7, a comparison of spectral scan methods exploiting a conventional raster (Fig. 2(a)) scanning technique and an S-matrix of order 7 (Fig. 2(b)).A single spectral measurement is completed after a sequence of n acquisitions, each with a different spectral mask pattern, has been performed and the spectrum is retrieved through the inverse Hadamard matrix.
To implement the Hadamard multiplexing approach, we need four different elements: an optical separator (which separates in n spectral components the probed spectrum), an encoding mask, a detection system, and a processor for the generated data.In our setup, the AOTF acts as  both the optical separator and the encoding mask, while the photodiode and the lock-in amplifier form the detection system, and a dedicated custom software performs the data processing.The entries of the Hadamard matrix, i.e. the spectral encoding masks, are obtained by turning on and off different subsets of AOTF channels, with each narrowband channel of the AOTF tuned to a different wavenumber available within the broad spectral bandwidth of the pump laser (about 150 cm −1 at Full-Width Half-Maximum -FWHM).The spectral patterns can be changed in about 40 µs, ultimately limited by the rise time of the AOTF.We note that, conversely to what done by Berto et al. [19], where a Digital Micromirror Device separated the pump spectrum after its interaction with the sample, in our approach the encoding mask on the pump beam is implemented before it reaches the sample.This reduces the optical power on the sample by removing spectral components that are not detected in each acquisition.After completing the sequence of acquisitions needed by the Hadamard method, the inverse Hadamard matrix is used to demultiplex and reconstruct the Raman spectrum of the sample (i.e., the individual contribution of each wavenumber to the overall signal).
In order to get an even sensitivity across the whole measured spectrum and maximize the efficiency of the Hadamard-type detection, it is useful to equalize the spectral density at the different wavenumbers of the excitation pump spectra, as suggested by Xu et al. [22].To this end, the transmission amplitude of the 8 channels of the AOTF can be independently controlled to equalize the laser spectral intensity across the selected spectral components.The equalization was carried out with a fully automated and quick procedure (about 500 ms), as explained in the following.We first performed a wavelength scan with a single AOTF channel at its maximum transmission amplitude across all the spectral components (wavenumbers) chosen for the SRS acquisition and lying within the pump laser spectral bandwidth (about 270 cm −1 , 1/e 2 width).The pump power detected by the photodiode was recorded for each filtered spectral component, allowing to map the spectral power density delivered by the pump laser.Then, the transmission amplitude was independently reduced for each AOTF channel, in order to have its optical power on the photodiode to match the power carried by the spectral component with the minimum power recorded in the previous step.In this way, we obtained the equalized pump laser spectrum reported in red in Fig. 3.The procedure has to be repeated only when the central laser wavelength of the pump beam or an optical element -like the microscope objective -is changed, to take into account possible wavelength-dependent variations.Even though a non-zero intensity is present between the selected wavelengths -due to the sidebands of the transmission band of the AOTF -this is still below 5% of the peak intensity.As it will be evident from the Result and Discussion section, this residual intensity did not affect in a significant way the retrieved SRS spectra.To avoid a cross-talk between the 8 independent channels of the AOTF, the minimum spectral distance between adjacent channels should be about three times the FWHM of the channel itself [23].For this reason, we set a minimum spectral separation of 20 cm −1 between the adjacent probed wavenumbers in each acquisition.In order to achieve a better final SRS spectral resolution, we devised a procedure in which the Hadamard acquisition was performed multiple times, applying each time a constant offset -given by the desired spectral sampling interval -to the spectral positions of all channels.This is illustrated in the simulated measurement displayed in Fig. 4: a SRS spectral acquisition was first performed using an Hadamard mask with a spectral step size equal to 20 cm −1 , giving the first reconstruction marked by the star points; then a second Hadamard-type spectral acquisition was performed using the same spectral step size but with all the wavenumbers shifted by a constant factor, obtaining the second reconstruction (cross markers); the procedure was then repeated until the spectrum was sampled as desired and all the reconstructions were combined together to get the final result.With this approach, it is possible to decrease the sampling interval just by performing more reconstructions, eventually using a sampling rate of 3 cm −1 , as required by the Nyquist principle to reach the spectral resolution allowed by the AOTF passband (7 cm −1 ).

Results and discussion
The SNR improvement given by the Hadamard spectral acquisition is related to the order of the matrix used as a mask and to the type of noise affecting the signal.In an ideal situation where the noise is purely additive, the improvement in the SNR of measurements using a n-order S matrix is given by [17]: The conditions for a purely additive noise are approximately verified when the main source of noise in the measurements is the input electronic noise of the detection chain, and other contributions, like the multiplicative laser intensity noise, are negligible.Conversely, in the presence of multiplicative noise sources the improvement given by the Hadamard reconstruction decreases, and other multiplexing masks may be preferable [21,24].In our setup, the highest order of the S-matrix that can be implemented with the 8 independent channels of the AOTF is 15, thus the maximum achievable improvement in the SNR is a factor of 2 (see Eq. ( 1)).We performed a set of SRS spectral measurements to test and validate the performance of our approach.We compared the SNR of the Hadamard-type acquisition to the one of a raster scan spectral acquisition using the same power as the one carried by each channel in the Hadamard scheme (Fig. 2(a)).In such a condition, and using the balanced detection scheme [20] to suppress the laser excess noise, the main source of noise is additive from the detection electronics, and the condition necessary for Eq.(1) to hold is satisfied [22].The SRS spectra shown in this section were obtained as an average of 20 different spectral acquisitions.The SNR was calculated for both acquisition methods as the ratio between the SRS signal at the specified wavenumber and the average of the standard deviation of the signal at the 7 adjacent wavenumbers.This approach was found to give consistent results across different measurements, with the number of chosen adjacent wavenumbers high enough to add statistical repeatability.
We first measured the SRS spectrum of olive oil in the CH-stretch region.We set the integration time to 1 ms per mask acquisition both for Hadamard and raster scan methods.The obtained SRS spectra are displayed in Fig. 5.The SNR was 20.2 and 11.8 respectively for Hadamard and raster scanning techniques, thus giving an improvement in the SNR by a factor of 1.7.We also measured the SRS signal of olive oil in the Raman fingerprint region (see Fig. 6) with both Hadamard-type and raster acquisitions performed using the same integration time and Stokes beam power.As one can see, a baseline signal due to the dark current of the detection system was present in both acquisition types (clearly visible between 1500-1600 cm −1 , where there is no Raman signal from the sample).However, the Hadamard reconstruction technique reduced this baseline from 6.7 ± 0.3 a.u. to 1.3 ± 0.3 a.u., as a result of the 8-times higher total laser power on the photodetector.After performing a baseline subtraction on the acquired spectra, we calculated the SNR at the two SRS peaks visible in Fig. 6, namely 1440 cm −1 and 1655 cm −1 .
We obtained an SNR of 10.0 and 8.8, respectively, using the raster scan modality, and an SNR of 14.4 and 12.6, respectively, with the Hadamard acquisition method.Therefore, the multiplexed approach gave an SNR improvement by a factor of 1.4 for both peaks.Remarkably, the predicted factor-of-2 improvement in the SNR (see Eq. ( 1)) provided by the Hadamard-type acquisition corresponds to the one obtained using a 4 times longer integration time with a conventional raster spectral acquisition.To test this, we performed a measurement in the fingerprint region of olive oil (see Fig. 7) using an integration time of 2.5 ms for the Hadamard-type acquisition, and two different acquisition times, namely 2.5 and 10 ms, for the raster acquisition.The obtained SNRs (referred to the 1440 cm −1 peak) are listed in Table 1.After the baseline subtraction, the SNR improved by a factor 1.9 -very close to the predicted value -in the Hadamard multiplexed acquisition with respect to the raster acquisition, when using the same 2.5 ms integration time.Moreover, the SNR obtained with the Hadamard acquisition at 2.5 ms was almost the same as the SNR for the raster acquisition at 10 ms, confirming the speed up capability of the multiplexed approach.An important application of SRS microscopy is the imaging and quantitative measurement of lipid droplets (LDs) in cancer cells [20,25].Hence, we also assessed the SNR improvement allowed by the Hadamard-type spectral acquisition in the SRS measurement of a LD found in a cancer cell (HepG2, hepatocellular carcinoma).We first identified a LD by performing an SRS image acquisition of the cell at 2860 cm −1 .We then acquired the SRS spectrum of the selected LD in the CH-stretch region with both the raster scan and the Hadamard spectral acquisition techniques, giving the spectra shown in Fig. 8.With reference to the SRS signal at 2860 cm −1 , the SNR of the spectra were 9.6 and 17.1 for raster and Hadamard-type acquisitions, respectively.The SNR improvement given by the multiplexed scan modality in this case was then 1.8.With our configuration, the SNR improvement in the SRS spectra obtained with the Hadamard technique was very close to but did not reach the theoretical value of 2. This can be mainly attributed to the fact that, when the AOTF was used in a multi-channel configuration for the Hadamard-type detection, i.e. with multiple acoustic waves at different frequencies simultaneously present into the device, the output power of each individual filtered channel presented additional noise as compared to the single-channel AOTF operation mode, due to residual cross-talk [23].

Conclusions
We demonstrated an Hadamard multiplexed approach for SRS microscopy based on a multichannel and narrowband AOTF.Our scheme improved the SNR of SRS spectra up to a factor of 1.9 with respect to a raster type acquisition, very close to the theoretical value of 2 obtainable in the presence of only additive noise.The multiplexed approach also reduced the baseline signal contribution due to the dark current in the detection system.Furthermore, we demonstrated that the Hadamard multiplexed approach allows to perform faster spectral measurements.In fact, the SNR obtained with an Hadamard-type acquisition was comparable with the one obtained with a 4-times longer integration time performed with a conventional single-channel raster acquisition modality.
The AOTF-based configuration proposed here showed a very high flexibility and applicability over a wide spectral range.In particular, it allowed using the Hadamard reconstruction algorithm in the fingerprint or in the CH-stretch regions without the need to change any optical device in the SRS microscope [20], thus giving access to fast and broadband acquisitions over the relevant Raman spectral regions.Even though the design of an ad-hoc wavelength selection scheme using a diffraction grating and a Digital Micromirror Device could potentially provide similar characteristics, the AOTF-based solution features a significantly less critical alignment and a straightforward intensity equalization of the selected wavelengths.Remarkably, in our implementation, the selection of the spectral components is performed before the interaction of the laser beam with the sample.Therefore, no unused optical power is sent to the specimens, in contrast to what happens with different implementations of the Hadamard transform method for SRS [19].This is an advantage with samples particularly sensitive to optical damage, such as live cells and microfibers [26].Moreover, a spectral selection made before the sample avoids the difficulties created by using a spectrometer in the detection path with highly scattering samples [19].On the other hand, the maximum SNR improvement factor of our configuration is limited by the number of channels available with the AOTF in use.
With the current implementation, the use of a pump laser with a spectral FWHM of about 15 nm would allow measuring a spectral range of 400 cm −1 -enough to cover the whole CH-stretch region -in a single acquisition without changing the central laser wavelength.Furthermore, the presented multiplexed approach can potentially be highly beneficial in SRS setups based on very broadband femtosecond laser sources (> 100 nm bandwidth).These laser sources would cover simultaneously a very broad vibrational spectral range (about 1500 cm −1 ), avoiding or minimizing any time-consuming laser tuning procedure in collecting SRS spectra.However, they present a relatively low spectral power density, which makes the additive input electronic noise the main noise source, hence the Hadamard multiplexed acquisition would provide a significant improvement in the SNR.This might be especially relevant in SRS measurements within the Raman fingerprint region, where the SRS signals are typically small.Instead, if the maximum power allowed by optical damage of the sample is a limiting factor, the improvement in SNR vanishes [17] and a conventional raster scanning modality might be preferable.
Finally, the flexible and simple Hadamard-transform modality presented here can be a valuable tool for broadband SRS imaging using compressive sensing techniques [19,27], where the channels of the AOTF are tuned to match a subset of vibrational frequencies of interest.This multiplexed modality can also be applied using a smaller matrix with n = 7 or 11, which would provide an SNR improvement of √ 2 or √ 3, respectively.These smaller matrix sizes would correspondingly allow for a 2-or 3-times faster integration time, which are smaller relative improvements but still remarkable.This could be particularly useful in some applications where a lower number of selected wavenumbers is sufficient for material recognition.Disclosures.The authors declare no conflicts of interest.

Fig. 1 .
Fig. 1.Schematic of the SRS microscope.The AOTF (acousto-optic tunable filter) in used to spectrally filter the femtosecond pump beam with eight independent narrowband channels.The inverse Hadamard matrix is used to reconstruct the signal from the acquired data.The balanced detection optics and electronics are not present in the figure for simplicity.AOM, acousto-optic modulator; PD, photodiode.

Fig. 2 .
Fig. 2. Comparison between a raster (a) and an Hadamard-type acquisition with a 7-order S-matrix (b).During a conventional raster spectral acquisition, only one channel of the AOTF is turned on and tuned in frequency to probe a single different wavenumber at each acquisition (A i ).In an 7-order S-matrix, 4 channels of the AOTF are turned on simultaneously in each acquisition.

Fig. 3 .
Fig. 3. Spectral shaping of the pump beam performed by the 8 independents channels of the AOTF.Black line: pump beam spectrum after the AOTF with the same transmission amplitude set to all channels.Red line: pump beam spectrum after the equalization used to perform the Hadamard multiplexed acquisitions.The spectral range shown here corresponds to a Raman shift from 2700 cm −1 to 3070 cm −1 , covering almost the whole CH-stretch region.

Fig. 4 .
Fig. 4. Numerical simulation showing the measurement of a test spectrum through multiple reconstructions to decrease the spectral sampling interval.

Fig. 5 .
Fig. 5. SRS spectrum of the CH stretch region of olive oil.The SNR was calculated at the wavenumber with the highest SRS signal (2860 cm −1 ).The range of adjacent wavenumbers used for noise calculation is highlighted by the dashed lines.SNR Hadamard = 20.2,SNR raster = 11.8.Stokes power 25 mW, pump power (8 channels on) 3 mW, and 1 ms integration time.

Fig. 8 .
Fig. 8. SRS spectrum of the CH-stretch region of a LD in a cancer cell.The SNR at 2860 cm −1 was 17.1 for Hadamard-type acquisition, and 9.6 for raster acquisition.A 40 mW Stokes beam power and a 1 ms integration time were used.