Quantitative measurements of material mechanics with spontaneous Brillouin scattering spectroscopy has gained much interest in recent years [1–4]. To produce the spontaneous Brillouin spectrum, a single laser beam at an angular frequency ${\omega }_1$ illuminates the sample. Light is then elastically and inelastically scattered from nonpropagating and propagating density fluctuations, respectively, to yield a spectrum that includes a single Rayleigh peak at ${\omega }_1$ and two Brillouin peaks with linewidth of ${\mathrm{\Gamma }}_B$ at the acoustic Stokes and anti-Stokes resonances of the material. These Brillouin resonance frequencies are shifted from ${\omega }_1$ by the so-called Brillouin shift, ${\mathrm{\Omega }}_B$, given for ${\mathrm{\Omega }}_B\ll {\omega }_1$ by [5]

Recently, extensions of VIPA spectrometers for spontaneous Brillouin scattering spectroscopy of scattering samples have been devised. One extension, proposed by Scarcelli and Yun, made use of multiple VIPA etalons cascaded in a cross-axis configuration to significantly suppress elastic scattering background [10], allowing in vivo imaging of the human eye [1]. Nevertheless, the throughput of multistage VIPA spectrometers decreases and their complexity increases with the number of VIPA stages. Another extension, reported by Meng et al., employed a heated iodine cell prior to the VIPA spectrometer to substantially filter out elastic scattering background [11], enabling probing of the mechanical properties of different tissue types [3]. However, application of molecular absorption cells as narrowband notch filters in spontaneous Brillouin spectroscopy setups requires the use of highly frequency stabilized lasers and algorithms that compensate for the distortion of measured Brillouin lines by the multiple absorption bands of the cell. Recently, Antonacci et al. have shown an interferometric method for significantly suppressing strong specular elastic reflections from planar interfaces in VIPA-based Brillouin spectroscopy [12]; yet, the question of how well this method performs in scattering samples remains to be investigated.

In this Letter, we show the utility of a different approach, based on stimulated Brillouin scattering (SBS) (de)amplification at 780 nm, for eliminating the elastic scattering background in transmission-mode Brillouin spectroscopy in thick and thin scattering tissue phantoms. To the best of our knowledge, although Brillouin spectroscopy using SBS (de)amplification was established a few decades ago, it was not applied to scattering, tissue-like, samples [13–18]. Given the emerging importance of Brillouin spectroscopy in tissue [3,4], it is critical to study the effectiveness of SBS spectroscopy in tissue phantoms, particularly within the biological spectral window where light attenuation is governed by scattering rather than absorption. In SBS (de)amplification, the acoustic phonons are driven by interaction of the medium with two laser beams at angular frequencies ${\omega }_1$ (pump frequency) and ${\omega }_2$ (probe frequency) that intersect at an angle $\theta$ in the sample. When the frequency difference, $\mathrm{\Omega }={\omega }_1-{\omega }_2$, matches a particular Brillouin shift of the material $\pm {\mathrm{\Omega }}_B$, amplification (${\omega }_1>{\omega }_2$) or deamplification (${\omega }_1<{\omega }_2$) of the probe signal at ${\omega }_2$ occurs via stimulated Brillouin gain or loss (SBG/SBL) processes, respectively, [5,13]. Otherwise, when $\mathrm{\Omega }$ does not match any acoustic resonance, no (de)amplification takes place. Consequently, unlike spontaneous Brillouin scattering, SBS (de)amplification does not exhibit elastic scattering background, thus, inherently providing excellent contrast, even in the presence of strong elastic scattering. Assuming a quasi-backscattering SBS process in scattering media ($\theta \approx 180°$) and that changes in the pump power are governed by attenuation (due to scattering), SBG/SBL, defined as the steady-state small-signal stimulated fractional change in the probe power at ${\omega }_2$, $G=\mathrm{\Delta }{P}_2/P_2^L$, is given by [19].

The SBS spectrometer arrangement is shown in Fig. 1(a). Unlike SBS spectroscopy systems that made use of solid-state and dye lasers as the pump light [14–17], our setup employed two continuous-wave (CW) diode lasers as the pump and probe beams. Concretely, an amplified CW distributed feedback (DFB) laser and a second CW DFB laser (Toptica), both vertically polarized, thermally stabilized, and coupled into a polarization-maintaining single-mode fiber, were used as the pump and probe beams, respectively. Laser mode hop-free tuning ranges $>50\mathrm{GHz}$ and $<4\mathrm{MHz}$ laser linewidths were selected to offer wide spectral range and high spectral resolution. Note that the use of CW lasers avoids nonlinear sample photodamage induced by the high peak power of pulsed lasers. The pump and probe beams were focused into the sample, housed in a glass chamber, and were brought to coincide within the cuvette in a quasi-backscattering configuration for reducing stray pump light. Unless stated otherwise, pump and probe average powers of 270 and 15 mW were used on the sample, respectively. It is noteworthy that similar average power levels were employed in optical tweezers and showed no damage of living cells for $<2\min$ exposure times [20]. Unlike SBS spectroscopy systems reported in [17,18], we implemented a double-modulation lock-in detection scheme at radio frequencies (MHz range where diode lasers have low intensity noise) to measure the small SBG/SBL signals (${10}^{-6}<G<{10}^{-5}$) with adequate signal-to-noise ratio (SNR). Explicitly, the intensity of the pump and probe beams was sinusoidally modulated at $f_{m1}=4\mathrm{MHz}$ and $f_{m2}=5.1\mathrm{MHz}$, respectively, by acousto-optic modulators (Gooch & Housego, AA Opto-Electronic) and the resulting power modulation of the probe beam, conveying the SBG/SBL power signals, was detected at the difference frequency $f_{m2}-f_{m1}=1.1\mathrm{MHz}$ with a large-area photodiode (Thorlabs) and a high-frequency lock-in amplifier (Stanford Research Systems) set to a specific time constant of ${\tau }_{\mathrm{LIA}}=10$, 100 ms, as depicted in Fig. 1(b).

 

Fig. 1. Transmission-mode SBS spectroscopy at 780 nm. (a) Experimental setup. $C_1/C_2$, fiber collimators; $L_1/L_2$, focusing lenses; AOM, acousto-optic modulator; $L_3-L_4/L_5-L_6$, relay lenses; MO, microscope objective; PD, large-area photodiode; FS, fiber splitter; FPD, fast photodetector; LIA, lock-in amplifier; FC, frequency counter, OSC, oscilloscope. (b) Spectrum diagram at PD output. RIN, relative intensity noise; dark red pump modulation power at $f_{m1}$; light red probe modulation power at $f_{m2}$; blue-red gradient, SBG/SBL modulation power at $f_{m2}-f_{m1}$, which comprises the SBG/SBL signals in this Letter; red-blue gradient, SBG/SBL modulation power at $f_{m2}+f_{m1}$.

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To obtain stimulated spectra, we recorded SBG/SBL power signals as a function of the frequency detuning between the pump and probe lasers, $\mathrm{\Omega }$, with an oscilloscope (Tektronix). $\mathrm{\Omega }$ was altered by scanning the frequency of the probe laser across the pump-laser frequency at a constant rate ($d{\omega }_2/2\pi dt=2$, $0.2\mathrm{GHz}/\mathrm{s}$) via linear ramp small modulation of the probe laser current. The frequency difference, $\mathrm{\Omega }$, was measured continuously by detecting the beat frequency between beams peeled from the main beams of the pump and probe lasers with a fast photodetector (New-Focus) followed by a frequency counter at a resolution of 10 MHz (Phase Matrix), as seen in Fig. 1(a). We first verified that the SBS spectrometer robustly produces spectra of nonscattering liquids. Figure 2(a) shows representative SBS spectra of methanol and dimethyl sulfoxide (DMSO). Dotted curves are the measured spectra, and solid curves are nonlinear least-squares fits of a pair of Lorentzians to the data. For these measurements, ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$ and $d{\omega }_2/2\pi dt=0.2\mathrm{GHz}/\mathrm{s}$. In addition, the pump and probe beams, crossed at $\theta \approx 179°$, were focused to $\sim 100\mathrm{\mu m}$ diameter spots into a 10 mm thick glass chamber by 200 mm lenses, resulting in an estimated $\eta \sim 28\%$.

 

Fig. 2. Transmission SBS spectra of (a) nonscattering liquids and (b) water and scattering Intralipid solutions. The cuvette photos show increased light attenuation with increasing Intralipid concentration in the solution (red, 0%; lightest gray, 0.019%; black, 0.103%). Note that a pump power of 95 mW was used on the methanol samples.

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From Fig. 2(a), we see that the Stokes-SBG and anti-Stokes-SBL peaks are evident in the spectra of methanol and DMSO while, unlike in spontaneous Brillouin spectra, the Rayleigh peak is eliminated. In addition, we observe that the fitted Lorentzian line shapes agree well with the measured spectra. Note that our SBS spectra of nonscattering liquids show comparable peak gain to that in [17], but that our SBS spectra were acquired at a 10–20 fold higher rate and without balanced detection. Using multiple fits to repeatedly measured stimulated spectra, estimates for the Brillouin shifts and linewidths of methanol (${\widehat{\mathrm{\Omega }}}_B/2\pi =3.799\pm 0.006\mathrm{GHz}$ and ${\widehat{\mathrm{\Gamma }}}_B/2\pi =187\pm 7\mathrm{MHz}$) and DMSO (${\widehat{\mathrm{\Omega }}}_B/2\pi =5.655\pm 0.016\mathrm{GHz}$ and ${\widehat{\mathrm{\Gamma }}}_B/2\pi =547\pm 23\mathrm{MHz}$) were obtained. These estimates are comparable to published Brillouin data [5,11,13].

Next, to show the effectiveness of our SBS spectrometer in scattering tissue phantoms at 780 nm with no elastic scattering background, we acquired stimulated spectra of Intralipid solutions at concentrations of 0.019%, 0.052%, and 0.103% in a 10 mm thick glass chamber. These concentration values correspond to media, where ballistic/quasi-ballistic light propagates with a number of mean-free paths of $N_s=0.47$, 1.33, and 2.61, respectively, evaluated by Beer–Lambert’s law [21]. Experimental conditions were the same as for DMSO in Fig. 2(a). The solid curves in Fig. 2(b) depict representative stimulated spectra from these solutions where the curve’s gray tone darkens with Intralipid concentration. For clarity, only fits to the measured spectra are shown. In addition, for comparison, we present the measured (blue dots) and fitted (red solid line) stimulated spectrum of water. The stimulated spectra of the Intralipid phantoms in Fig. 2(b) show excellent contrast and are similar to that of water in terms of Brillouin shifts and linewidths (${\widehat{\mathrm{\Omega }}}_B/2\pi =5.087-5.102\pm 0.009-0.038\mathrm{GHz}$ and ${\widehat{\mathrm{\Gamma }}}_B/2\pi =290-296\pm 17-46\mathrm{MHz}$). Small stimulated Rayleigh peaks were infrequently observed in the Intralipid stimulated spectra, probably due to the nonzero absorption of Intralipid at 780 nm. Finally, Fig. 2(b) shows a reduction in the SBG/SBL peaks (and, hence, in SNR) with increasing scattering.

To quantify the dependence of the SBG signal’s SNR and precision of the Brillouin shift estimates on the degree of scattering and acquisition time, we measured the SNR of SBG power spectra of 0-0.119% Intralipid solutions in a 10 mm thick glass chamber under the same focusing and power conditions of Fig. 2(b). Spectra were acquired around their Stokes resonance over a 2 GHz bandwidth at ${\tau }_{\mathrm{LIA}}=10$, 100 ms and $d{\omega }_2/2\pi dt=2$, $0.2\mathrm{GHz}/\mathrm{s}$, respectively, resulting in a total acquisition time per spectrum of 1, 10 s, respectively. Note that heating by absorption of water can be neglected here as it was estimated to be $<0.35\mathrm{K}$ [22]. The SNR was evaluated as the ratio of the SBG peak power (at the Intralipid’s Brillouin shift) to the standard deviation of the noise skirt in the spectrum over a bandwidth of 1 GHz [17]. Figure 3(a) displays the mean (circles) and standard deviation (error bars) of the SNR estimated from 10 repeatedly measured spectra as a function of $N_s={\mu }_{t}L$ and corresponding Intralipid concentration for ${\tau }_{\mathrm{LIA}}=10\mathrm{ms}$ (blue) and ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$ (red). For comparison, Fig. 3(a) also shows fits (solid lines) of the experimental SNR to the theoretical SNR given by

 

Fig. 3. Measurements of (a) SBG signal’s SNR and (b) precision of the Brillouin shift estimates in scattering Intralipid solutions in a $L=10$-mm-thick glass chamber at ${\tau }_{\mathrm{LIA}}=10\mathrm{ms}$ (blue) and ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$ (red).

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The three terms in the denominator represent photodetector and lock-in amplifier electrical noise, shot noise, and RIN, respectively. Here, $N_E$ is the power spectral density of the photodetector and lock-in amplifier electrical noise, $B\propto {\tau }_{\mathrm{LIA}}^{-1}$ is the effective detection bandwidth, $q$ is the electron charge, $\mathfrak{R}$ is the photodetector responsivity, $\mathrm{RIN}$ is the power spectral density of the probe laser RIN at $f_{m2}-f_{m1}$, and $\mathrm{\Delta }{P}_2^{\mathrm{peak}}=G({\mathrm{\Omega }}_B)P_2^L$ is the SBG peak power [Eq. (2)]. Note that Eq. (3) becomes Eq. (4) in [17] for ${\mu }_t=0$, $N_E=0$ and negligible stray pump light. Fit parameters for Fig. 3(a) were $G=4.23\times {10}^{-6}$, $\mathfrak{R}=0.55\mathrm{A}/\mathrm{W}$, $P_1^0=270\mathrm{mW}$, $P_2^L=15\mathrm{mW}$, $A=\pi ·{50}^2{\mathrm{\mu m}}^2$, $N_E=0.014{\mathrm{nA}}^2/\mathrm{Hz}$, $B=0.692\mathrm{Hz}$ at ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$, $B=6.92\mathrm{Hz}$ at ${\tau }_{\mathrm{LIA}}=10\mathrm{ms}$, $q=1.6\times {10}^{-19}\mathrm{C}$, and $\mathrm{RIN}=-137.9\mathrm{dB}/\mathrm{Hz}$. Overall, we see from Fig. 3(a) that there is good agreement between the experimental and theoretical SNRs with a difference of $\sim 10\mathrm{dB}$ in the SNR measured with ${\tau }_{\mathrm{LIA}}=10$, 100 ms, as predicted by Eq. (3). We can also observe that the dominant noise source depends on the value of $N_s={\mu }_{t}L$. In the current spectrometer, the RIN dominated for $N_s<1.5$ whereas, for $N_s>2.5$, the electrical noise became dominant, and the SNR degraded at a higher rate with increasing $N_s$ (than that for $N_s<1.5$), as indicated by the RIN and electrical noise limited SNR curves (gray dashed lines) in Fig. 3(a). Note that the SNR could be improved to be RIN limited for $N_s>1$ by amplifying the SBG signal with a low-noise, 20 dB gain amplifier prior to lock-in demodulation. Figure 3(b) shows the accuracy, $\delta {\widehat{\mathrm{\Omega }}}_B$, in terms of standard deviation, in determining the Brillouin shifts from the SBG power spectra (circles) against $N_s$ of the Intralipid phantoms at ${\tau }_{\mathrm{LIA}}=10\mathrm{ms}$ (blue) and ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$ (red). Dashed lines are drawn to guide the eye for the $\delta {\widehat{\mathrm{\Omega }}}_B$ measurements. We see that the precision for the Brillouin shift estimates decreased with increasing $N_s$ for both time constants (due to the lower SNR in the more scattering samples) and was lower for ${\tau }_{\mathrm{LIA}}=10\mathrm{ms}$ than for ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$ (due to decrease in SNR measured with a smaller time constant). Note that a lower precision for ${\widehat{\mathrm{\Omega }}}_B$ yields a larger value of $\delta {\widehat{\mathrm{\Omega }}}_B$ in Fig. 3(b). While the above results demonstrate the ability of the prototype spectrometer to effectively measure SBS spectra of Intralipid tissue phantoms of ${\mu }_t<\sim 3{\mathrm{cm}}^{-1}$ (as ${\mu }_t=N_s/L$ with $N_s<\sim 3$ and $L=10\mathrm{mm}$), biological tissues have attenuation coefficients, ${\mu }_t$, larger by one order of magnitude or more [23]. To validate our SBS spectrometer for stimulated spectra measurements, we repeated the measurements of Fig. 3 for ${\mu }_t=0–60{\mathrm{cm}}^{-1}$ and $L=500\mathrm{\mu m}$, so that $N_s$ was still $\le 3$. Figures 4(a) and 4(b) show, respectively, experimental SNR (circles are mean values and error bars are standard deviations) and Brillouin shift estimation accuracy, $\delta {\widehat{\mathrm{\Omega }}}_B$, of the SBG signal against $N_s$ and Intralipid concentration alongside fits (solid lines) to the theoretical SNR [Eq. (3)] for ${\tau }_{\mathrm{LIA}}=10\mathrm{ms}$ (blue) and ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$ (red). Note that Intralipid concentrations are $\sim 20$ fold higher for $L=500\mathrm{\mu m}$ than for $L=10\mathrm{mm}$. Fit parameters were the same as in Fig. 3(a), with the exception of $G=4.86\times {10}^{-6}$, $A=\pi ·8^2{\mathrm{\mu m}}^2$, $N_E=0.027{\mathrm{nA}}^2/\mathrm{Hz}$, and $\mathrm{RIN}=-136.5\mathrm{dB}/\mathrm{Hz}$. In addition, for these measurements, the pump and probe beams, crossed at $\theta \approx 176°$, were focused to $\sim 16\mathrm{\mu m}$ diameter spots into the 500 μm thick glass chamber by using 30 mm lenses. Note that heating by absorption of water can be neglected here as it was evaluated to be $<0.53\mathrm{K}$ [22]. The SNR and $\delta {\widehat{\mathrm{\Omega }}}_B$ measured for the thin tissue phantoms showed a similar behavior to that observed for the thick phantoms, as evidenced by comparing Fig. 3 with Fig. 4. This similarity can be explained by noting that SBG/SBL [Eq. (2)] depends on the product of the medium’s length, $L$ (as ${\mu }_t^{-1}=L/N_s$), and the pump intensity, $P_1^0/A$, with $L$ and $P_1^0/A$ scaling quadratically and inversely quadratically with the focused pump waist, respectively, removing the dependence of SNR [Eq. (3)] on the beam focusing numerical aperture.

 

Fig. 4. Measurements of (a) SBG signal’s SNR and (b) precision of the Brillouin shift estimates in scattering Intralipid solutions in a $L=500\text{\hspace{0.17em}-\hspace{0.17em}}\mathrm{\mu m}$-thick glass chamber at ${\tau }_{\mathrm{LIA}}=10\mathrm{ms}$ (blue) and ${\tau }_{\mathrm{LIA}}=100\mathrm{ms}$ (red).

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In conclusion, we have demonstrated the usefulness of transmission-mode SBS spectroscopy based on diode lasers for background-free Brillouin spectroscopy in thick ($L=10\mathrm{mm}$, ${\mu }_t<\sim 3{\mathrm{cm}}^{-1}$) and thin ($L=500\mathrm{\mu m}$, ${\mu }_t\le 60{\mathrm{cm}}^{-1}$) tissue phantoms of $N_s<\sim 3$ at 780 nm. The measurement precision and number of scattering events for photons in the phantoms can be further increased by using balanced detectors (to achieve shot-noise limited detection with $>\sim 14\mathrm{dB}$ improvement in SNR for $N_s\le 3$) and a true backscattering geometry (to maximize the crossing efficiency of the pump and probe beams in the sample and obtain a $\sim 11\mathrm{dB}$ improvement in SNR). In future work, we intend to use the SBS spectrometer for Brillouin imaging in submillimeter-thick scattering (rather than nonscattering [18]) samples.