Simultaneous stimulated Raman gain and loss detection (SRGAL)

: The ﬁdelity of stimulated Raman scattering (SRS) microscopy images is impaired by artifacts such as thermal lensing, cross-phase modulation and multi-photon absorption. These artifacts aﬀect diﬀerently the stimulated Raman loss (SRL) and stimulated Raman gain (SRG) channels making SRL and SRG image comparisons attractive to identify and correct SRS image artifacts. To provide answer to the question: "Can I trust my SRS images?", we designed a novel, but straightforward SRS scheme that enables the dectection of the s timulated R aman g ain a nd l oss (SRGAL) simultaneously at the same pixel level. As an advantage over the conventional SRS imaging scheme, SRGAL doubles the SRS signal by acquiring both SRL as well as SRG and allows for the identiﬁcation of SRS artifacts and their reduction via a balanced summation of the SRL and SRG images.


Introduction
Stimulated Raman scattering (SRS) is a powerful tool in biomedical research [1]. Virtual H&E staining of histopathological samples [2][3][4][5][6][7] as well as metabolic imaging using Raman tags [8,9] are just a few of the latest developments pushing coherent Raman imaging towards the application fields. As a key advantage over coherent anti-Stokes Raman scattering (CARS), SRS scales linearly with chemical concentration and is equal to the spontaneous Raman information as it probes the imaginary part of χ (3) [10]. This insensitivity of SRS to the real part of χ (3) has been acclaimed to provide background-free chemical imaging [11]. However, point scanning SRS is not entirely background free and various linear and non-linear effects such as, linear scattering (LS) and absorption (LA), thermal lensing (TL), multi-photon absorption (MPA) and cross-phase modulation (XPM) compromise the image fidelity [12] -see Fig. 1.TL and XPM change the refractive index for the probe beam within the focal volume leading to a variation of the collected probe light intensity while MPA reduce the number of detected probe signal photons. The optimization of parameters such as the excitation wavelength, the optical power or the increase of the collection numerical aperture (NA) as compared to the excitation (NA) can only reduce these artifacts but they can be prohibitive for low concentration chemical imaging. The evaluation of the impact of TL, MPA and XPM is not straightforward. The perfect way would be to remove the Raman active sample while keeping the artifacts, a situation often impossible to achieve experimentally. An alternative is to move the pump and Stokes focused laser beams away from the Raman active area to evaluate the SRS artifacts, assuming that they remain constant across the field of view. A safer way would be to evaluate both the stimulated Raman loss (SRL) and the stimulated Raman gain (SRG) as these two contributions should be equal in the absence of artifacts. Indeed the TL, MPA and XPM are likely to affect the SRL and SRG signals in the same way (positive or negative contribution) whereas the Raman effect affects the pump with loss and the Stokes with gain that are by essence opposite in sign. However, switching between SRL and SRG in a conventional SRS experiment is not easy as it requires the swap of the modulated source and color filter sets. Recently, an SRS measurement paradigm termed 'stimulated Raman gain and loss opposite detection' (SRGOLD) [12,13] was proposed to reduce the most striking SRS artifacts. Here, the fundamental (the beam pumping the OPO), signal and idler beams arising from a single optical parametric oscillator (OPO) are jointly focused onto the sample. The fundamental appears as the pump when combined with the idler and as the Stokes when combined with the signal addressing the same vibrational mode. In SRGOLD, the signal and idler beams are modulated at the same frequency but with a 180 • phase shift and the fundamental intensity is analyzed using a photo-diode and a lock-in amplifier. The energy transfers from the signal to the fundamental (SRG) and from the idler to the fundamental (SRL) are jointly detected within a single image. By adjusting the idler and signal power in a sample location where there is no Raman signal (i.e. background only), it is in principle possible to cancel the TL, MPA and XPM artifacts to provide background-free SRS imaging. However, SRGOLD has some limitations, (1) it requires 3 colors (fundamental, signal and idler) that brings alignment complexity, (2) the presence of all 3 colors at focus at the same time has to be avoided to prevent artifacts arising from a Four-wave-mixing (FWM) process and (3) large wavenumbers are inaccessible because the wavelength differences between idler, fundamental and signal are of such extent (for example 2850 cm −1 requires 796 nm signal, 1030 nm fundamental and 1458 nm idler) that chromatic aberrations alter dramatically the 3 beams overlap along the z direction. Moreover, artifacts arising from MPA and XPM have similar magnitude for SRL and SRG only if the pump and Stokes wavelengths are sufficiently close to each other, i.g. share the same absorption properties at the sample. We have found situations [13] where MPA magnitudes feature significant differences in SRL and SRG preventing the balance and artifact cancellation in SRGOLD. Thus, it is advantageous to have SRL and SRG images separately to evaluate and compare their respective artifact contributions.
Here, we design and implement a novel SRS scheme that we name SRGAL (stimulated Raman gain and loss). The SRGAL concept is to modulate the pump at radio frequency (RF) frequency f 1 and the Stokes at RF frequency f 2 while demodulating simultaneously the pump at f 2 to access SRL and the Stokes at f 1 to access SRG. SRGAL combines the advantages of using only 2 beams, i.e. the conventional SRS pump and Stokes beam, while the SRL and SRG images are collected simultaneously but within separate signal channels. Detecting the energy transfer from the pump to the Stokes and from the Stokes to the pump allows us to exploit the full signal strength inherent to the SRS process. As a result, the SRGAL scheme allows (1) faster imaging for a given signal-to-noise ratio (SNR) as the SRG and SRL channels can be added to double the SRS signal and (2) the semi-quantitative evaluation of the SRS artifacts by directly comparing the magnitude of the SRG and SRL channels at each pixel level. A fully quantitative artifact evaluation can be also achieved if a calibration is performed in a location where there is no active Raman molecules, assuming that the artifacts remain constant over the field of view. The additional complexity brought by SRGAL is manageable as it requires a second amplitude modulator placed into the previously not modulated beam path as well as a detector unit composed of a second photo-diode and lock-in amplifier. Finally, other work detecting SRL and SRG shall be acknowledged: Sirleto et al. [14] implemented a 3 beam approach, where SRL and SRG were acquired sequentially to extend the area of the accessible Raman shifts while Bremer and Dantus [15] detected SRL and SRG simultaneously arising from a single unmodulated broadband fs-laser for trace detection of explosives.

Experimental implementation
A scheme of the SRGAL implementation is shown in Fig. 2. Two ultra-steep long-pass filter (Semrock, LP02-1064RE-25), positioned one in transmission the other in reflection, are angletuned to separate a 1 nm (1ps FWHM pulse width) spectral narrow line at 1025 nm from the output of a 150 fs (pulse duration) 80 MHz (repetition rate) solid-state laser (Lightconversion, FLINT FL1-08) to serve as Stokes beam driving the SRS process. The remainder of the fs-laser centered around 1030 nm is frequency doubled (APE, HarmoniXX) to 515 nm and coupled into an optical parametric oscillator (OPO, APE Emerald). The SHG unit performs a bandwidth narrowing due to phase matching and generates a 1 ps pulse train that pumps the OPO which finally provides a tunable (from 680 nm to 980 nm) 1 ps, 80 MHz, pulse train that serves as pump to perform SRS. Following the noise measurement routine introduced by Audier et al. [16], it was confirmed that both the pump and Stokes laser are shot-noise limited above 1 MHz within the applied power detection ranges (∼15 mW per beam). The pump and Stokes beam The pump and Stokes beams are amplitude-modulated by electro-optical-modulators (EOM, APE, EOM 900) at the modulation frequencies f 1 = 17 MHz and f 2 = 10.8 MHz, respectively. Note that we discourage replacing EOMs by acousto-optic modulators (AOM) as considerable amounts of noise are added to the power spectral density of the modulated beam which is absent if the EOM is driven by an electronic resonant circuit filtering parasitic frequencies. Both beams are combined by a dichroic mirror (Semrock, FF930-SDi01) and coupled into a home-built laser scanning microscope. Using a 40x objective (Nikon, PLAN, NA = 1.15, immersion: water) the joint beams are focused onto the sample not exceeding 25 mW per color. Both beams are collected after the sample by a 60x objective (Nikon, Fluor, NA = 1, immersion: water), split by a dichroic mirror (Semrock, FF930-SDi01) and sent towards two photo-diodes (APE, PD) featuring similar quantum efficiencies (∼80%) for the pump (793-922 nm) and Stokes (1025 nm) wavelength. The signal outputs of the PDs are electrically filtered (Minicircuit, pump: BLP-15+ & SHP-20+, Stokes: BBP-10.7+) to damp the impact of the first and second harmonic of the modulation imprinted by the EOMs, and amplified (LNA, APE, +25dB 0.1-100 MHz) to bring the laser shot-noise level in the lock-in detection ranges. Two lock-in amplifiers (LIA, Zurich Instruments, HF2LI) with an integration time constant set to 20 µs are connected to the PDs to retrieve cross-talk-free SRGAL (SRL and SRG) images simultaneously. The LIAs SRGAL signal is digitized by 2 analog channels in "differential mode" of an NI USB-6363 data acquisition card which is controlled by a custom LabVIEW-based software [17].
To decrease the impact or TL and XPM artifacts, it is recommended, for pump-probe experiments, to employ a collection objective lens with an NA col that exceeds the one of the excitation (NA ex ). However, we implemented here the inverse case (NA col =1 and NA ex =1.15) to highlight artifacts for demonstration purposes. This situation has some advantages as objective lenses with an NA col > 1.15 and a working distance larger than the sample holder (> 1.5 mm) are expensive and utilize oil immersion. Further, spatially high-resolved SRS-images are frequently obtained in a NA ex ≥NA col configuration as the highest NA available is already applied for excitation to achieve the best spatial resolution.

Theory
The SRGAL double modulation scheme raises the question of which peaks dominate the power spectral density (PSD) of the pump and Stokes beam as well as what is the relative signal strength of SRGAL as compared to a standard SRS implementation. To answer these questions we derive below the SRGAL signal frequency content following [18]. If the direct current (DC) of the PD is blocked, its output voltage per laser pulse, averaged over the large number N of laser pulses, is given by: where R represents the load resistance, ∆t is the effective pulse width, η denotes the quantum efficiency of the detector, hν is the photon energy, q symbols the elementary charge, ∆I is the maximum intensity change due to the SRS process (SRG or SRL) while IRF(t) is the impulse response of the PD. The angular frequencies ω mp = 2πf 1 , ω mS = 2πf 2 and ω r correspond to the RF modulation frequencies of the pump and Stokes beam as well as the repetition rate of the laser, respectively. Neglecting the amplification, the lock-in returns a voltage: where ω L is the lock-in demodulation angular frequency. Dropping the constant terms and placing Eq. (1) into Eq. (2) yields: where the convolution theorem was used with ⊗ signifying the convolution operation. Performing the Fourier-transform (F ) of a comb of delta functions yields: Again, a delta-comb is received at multiples of ω r , i.e. 0, ±ω r , ±2ω r etc. which leads to the ω r -periodic repetition of the pattern provided by the cosine terms in Eq. (3) after convolution. The Fourier transform of the first term in Eq. (3) is provided by: We restrict our attention to modulation angular frequencies within ω mS <ω mp <ω r /2 and non-zero demodulation angular frequencies below half the laser repetition rate at 0<ω L <ω r /2. Placing the results of Eqs. (5) and (4) into Eq. (3) results: Thus, the PSD of both the pump and Stokes beam feature peaks at ω mS , ω mp , ω mp + ω mS and ω mp − ω mS . For the experiment, the demodulation frequency was set to ω L = ω mp for SRG and ω L = ω mS for SRL. A similar procedure with the same average optical power at the sample for the conventional single-beam modulated SRL leads to: As evident from the comparison of Eqs. (6) and (7), the SRL part has the same strength in single-beam modulated SRS as in SRGAL, but the latter provides another signal of equal strength at the frequency ω mp from which SRG can be extracted. Therefore, for a shot-noise limited system, SRGAL provides a 2-fold signal-to-noise (SNR -definition further down) increase or is twice faster as compared to standard SRS if the images are added up assuming that the photon noise for both channels is equal -see also the appendix. Furthermore, the mixing terms at ω mp − ω mS and ω mS + ω mp are also present in the power spectral density (PSD) of the Stokes and pump beam and can be readily extracted if necessary.

Experimental results
In the following we want to show and discuss some application examples highlighting the significance of SRGAL images. It should be noted that SRGAL does not allow for the direct quantification of the individual contribution of each artifact mechanism, i.e. TL, MPA and XPM, rather it provides the summation of these artifacts as observed in an SRL or SRG image. Further, without any prior external or internal calibration, i.e. performed on a known Raman active sample or at a sample location where there is no active Raman signal, SRGAL does not provide a full artifact quantification, rather it allows the direct comparison of the SRL and the SRG images, at the single pixel level, to reveal the artifact locations and their differential magnitude (SRL-SRG). Yet, additional information about the sample can help to exclude or identify artifact mechanism as for example MPA requires a suitable multi-photon chromophore whose presence or absence might be known depending on the sample. Finally, linear artifacts (absorption and scattering) typically reduce the signals of both channels (SRL and SRG) and can be removed by an in-line [19] or an auto-balanced detection [20]. Figure 3(a-f) displays SRGAL images (SRL: loss; SRG: gain) at the Raman resonance 2850 cm −1 (CH 2 -stretch) of various samples such as (a) polymer fibers (Grace Bio-Labs SecureSeal, GBL654008-100EA), (b) a 80 µ m thick section of a mouse spinal cord, (c) a 10 µm thick section of teased fibers from the common peroneal nerve of a mouse, (d) crypts of a 20 µ m thick section of the human colon as well as the top (e) and the mid layer (f) of a thick onion sample. The loss and gain images displayed are the raw SRL and SRG signals so their absolute magnitude are directly linked to the SRL and SRG amplification coming from the electronic components. We tried to balance these signals on a test oil sample (external calibration), however, this calibration is likely to drift with time due to laser beam alignments and should not be considered as absolute.
As the first observation, we find that the signal distribution in SRG and SRL appear similar for all samples as it would be expected considering artifact-free SRS. Thus, to highlight the difference between the SRL (green) and SRG (red) images, a composite image was added as well as the image of the ratio (SRL/SRG). The composite image was generated by using the red channel of an RGB image for SRG and the green channel for the SRL signal. To cancel the difference between the electronic signal amplifications in both SRG and SRL channels, the mean of the ratio (SRL/SRG) for the full image was set to 1. It results that the SRL/SRG images highlight the relative artifacts rather than their absolute ratio.
Investigating the results presented in Fig. 3, we find that the amount and strength of artifacts within SRGAL strongly depends on the sample under investigation. Since all the investigated samples show strong SRS signal at 2850 cm −1 and have a low amount of absorbing species the artifacts are likely to be attributed to residual XPM as observable for the polymer fibers in Fig. 3(a). Conversely, the SRL and SRG images in Fig. 3(b) of a spinal cord appear very uniform exhibiting no detectable artifacts (the smooth gradient in the SRL/SRG is attributed to illumination or collection non-homogeneity across the field of view). Interestingly, the SRL and SRG composite image reveal artifacts but also provides an alternative contrast mechanism outlining previously invisible features. As an example, the SRGAL composite image of the mouse nerve in Fig. 3(c) allows to highlight fibers in SRL while SRG reveals mostly localized structures that can be attributed to myelin ovoids [21] -in fact, the observed contrast within Fig. 3(c) relies to a vast extent on artifacts. In Fig. 3(d) arising from a human colon crypt, the composite image reveals localized artifacts, possibly coming from MPA of NADH rich leukocytes [22]. Figure 3(e) shows the surface layer of an onion skin featuring mostly uniform SRL and SRG images while the ratio SRL/SRG reveals artifacts at the cell wall junction. Underneath the onion's surface layer (Fig. 3(f)), the SRS signal is reduced within the cell body and uncovers the cell walls (cellulose) [23] featuring significant differences within the SRL and SRG channels.
The images of the ratio SRL/SRG in Fig. 3 may serve for a semi-quantification of the artifact in order to judge whether a SRS (SRG or SRL) image can be considered as sufficiently "artifact free" to secure a linear relationship between the SRS signal and the analyte concentration. As an example for a symmetric artifact, i.e. affecting equally SRL and SRG signals, the value of SRL/SRG = (1 − 0.5)/(1 + 0.5) = 1/3 would be obtained within the image of the ratio for e.g. XPM of 50 % strength relative to artifact-free SRS. Conversely the SRL/SRG ratio should be >1 in the case of MPA (MPA increases the loss and reduces the gain). However, note (1) that there is no generality in the example introduced above as Kerr lensing may have positive or negative contributions as a function of the pump and Stokes beam z overlap shifting the relative locations of the active volume of the SRS-and Kerr-effect and (2) the correct and quantitative interpretation of the SRL/SRG ratio would require a proper calibration that is difficult to achieve experimentally. As a consequence the SRL/SRG ratio images must not be over-interpreted. Finally, since both SRL and SRG signals depend linearly onto the pump and Stokes beam, the SRL/SRG ratio advantageously nullifies signal fluctuations due to small laser average power variations which are often visible as horizontal or vertical stripes within SRS images. This can be recognized in Fig. 3(e) where SRL and SRG images show horizontal lines that are absent in the SRL/SRG image.
Next, we move to SRGAL imaging in the 'fingerprint' and 'silent' vibrational frequency regions as important for applications since the SRS signal strength frequently drops significantly while the artifacts strength remains nearly constant as compared to the C-H lipid frequency range. As examples, we selected the surface of an oyster shell, the carotenoid distribution within carrot cells and deuterated baker's yeast (Saccharomyces cerevisiae) acquired at 1090 cm −1 (crystalline calcite CaCO 3 peak), 1560 cm −1 (near resonance) and 2150 cm −1 (C-D peak), respectively -see Fig. 4. In Fig. 4(a) of an oyster shell, some oval structures appear as strong artifacts. This artifact is likely XPM enhanced by the scattering nature [12] of a parasite populating the oyster's surface, but must not be interpreted as an elevated or diminished concentration of calcite (1090 cm −1 ) as confirmed by the SRL/SRG ratio image. Due to the strongly varying SRS signal strength, Fig. 4(b) of carrot carotenoid is plotted in log e -scale to show simultaneously areas with strong signal and, therefore, weak artifact contribution next to weak signals with a larger fraction of artifacts. Quite nicely these artifacts regions are highlighted in the SRL/SRG image. From Fig. 4(c) we observed that the cytoplasm of the deuterated yeast cells display larger artifact contributions in SRL. Note that empty areas outside the cells were set to zero in the SRL/SRG ratio image to diminish the noise contribution. The reason for the signal difference in the SRG and SRL channel could be a TL amplified MPA that is stronger for the pump (839 nm) than for the Stokes wavelength (1025 nm). Though this hypothesis may require further verification, Fig. 4(c) suggests that the SRG channel should be preferred if an image with a minimized quantity of artifacts is desired.
Last but not least, one of the key SRGAL advantage is to improve the SNR ratio by summation of the SRL and SRG images as predicted in the theory section above. Note that summing SRGAL images may also cancel symmetric artifacts as discussed in large detail for SRGOLD by Lombardini et al. [13]. The SNR improvement is demonstrated for the onion surface in Fig. 5 (derived from Fig. 3(d)). Here, the SNR was obtained for every line for a sliding 1D-window of 11 pixel within the delineated region of interests (ROI) (loss: dashed green ROI; gain: dashed red ROI). This rather short 1D-(not 2D-)window was applied to minimize artifacts arising from signal fluctuation due to the sample's structure and to remove the impact of strip pattern along the fast laser scan direction. As the definition of the SNR of a signal S we used SNR = <S> 2 /σ 2 (S), with σ(S) being the standard deviation. The SNR curves were averaged over 300 horizontal image lines (y direction) in the ROIs corresponding to the laser scanning direction. On Fig. 5, the SNR SRL (x) and SNR SRG (x) are displayed in green and red, respectively, while the SNR SRGAL (x) of the sum image SRL+SRG is drawn in black. Clearly, the SNR SRGAL , with SNR SRGAL = <S SRG + S SRL > 2 /[σ 2 (S SRG ) + σ 2 (S SRL )], is improved by a factor of 2 as compared to the average of the SNR SRL and SNR SRG meaning that the sum image may be acquired twice faster than a single SRL or SRG image. This two-fold improvement is further shown on Fig. 5 through the ratio 2 SNR SRGAL /(SNR SRL +SNR SRG ) that is constant along the scan direction and equal to 2. It shall be note that this comparison assumes a photon ration of 1:1 for pump:Stokes (p:S) while the best SNR in a standard SRS experiment is obtained at 2:1 (p:S) and 1:2 (p:S) for measuring separately SRL or SRG, respectively. Comparing SRGAL 1:1 (p:S) to standard SRS 1:2 (p:S or S:p) the SNR SRGAL /SNR SRS ratio still yields an improvement of 1.69 (27/16).

Conclusion
We have implemented and demonstrated a novel SRS experimental scheme termed SRGAL. SRGAL enables for the simultaneous detection of SRL and SRG by modulating both beams, i.e. pump and Stokes, at the RF frequencies f 1 and f 2 while performing a crosswise demodulation at f 2 and f 1 , respectively. As an add-on to a conventional 2-color SRS setup, SRGAL requires a second modulator and a photo-diode linked to a second lock-in amplifier.
Without internal or external calibration, SRGAL permits for a semi-quantitative evaluation (using the ratio SRL/SRG) of SRS artifacts such as TL, MPA or XPM. Information about the spatial distribution and strength of these artifact warrants for the correct interpretation of SRS images confirming the linear relationship of the SRS signal with the concentration of the molecular species under investigation. As a key advantage over conventional SRS, the SRGAL scheme increases the SNR of SRS by a factor of 2 by summation of the SRL and SRG channels. Alternatively, SRGAL enables to improve the image acquisition speed by a factor of 2 for the same SNR as in conventional SRS. Further, the balanced sum SRL+SRS cancels symmetric artifacts within SRS images. Compared to the SRGOLD scheme, SRGAL is simpler by requiring two colors only instead of three, needs less average power at the sample plane and permits to address vibration modes over the entire Raman spectral range without compromises such as a reduced power transmission after the objective lens for IR-wavelength or a drop of the spatial resolution. Furthermore, the SRL and SRG images are obtained separately enabling for an optimized image post-processing, e.g. by computing SRL+SRG, SRL-SRG or SRL/SRG.

Appendix
Here, it shall be shown why the sum (SRL+SRG) image in SRGAL can be acquired twice faster than a standard SRS (SRL or SRG) image for the same SNR. We assume that the numbers of photons N is equal for the pump and Stokes beam for standard SRS and SRGAL (N = N p = N S ) and that the signal integration time t is proportional to the number of photons N ∝ t arriving at the detector. The SNR SRS = SNR SRL = SNR SRG is given by: Where Var() is the variance. It was used that for a shot noise limited laser system the variance of the Poisson distributed photons equals to its expectation value. A similar analysis for SRGAL