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Abstract
Impulsive stimulated Brillouin spectroscopy (ISBS) plays a critical role in investigating mechanical properties thanks to its fast measurement rate. However, traditional Fourier transform-based data processing cannot decipher measured data sensitively because of its incompetence in dealing with low signal-to-noise ratio (SNR) signals caused by a short exposure time and weak signals in a multi-peak spectrum. Here, we propose an adaptive noise-suppression Matrix Pencil method for heterodyne ISBS as an alternative spectral analysis technique, speeding up the measurement regardless of the low SNR and enhancing the sensitivity of multi-component viscoelastic identification. The algorithm maintains accuracy of 0.005% for methanol sound speed even when the SNR drops 33 dB and the exposure time is reduced to 0.4 ms. Moreover, it proves to extract a weak component that accounts for 6% from a polymer mixture, which is inaccessible for the traditional method. With its outstanding ability to sensitively decipher weak signals without spectral a priori information and regardless of low SNRs or concentrations, this method offers a fresh perspective for ISBS on fast viscoelasticity measurements and multi-component identifications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin spectroscopy is becoming an emerging tool in biomechanical sensing and imaging of cells [1–4], tissues [5–8], and organisms [9–11] because of its non-contact, label-free and sub-micrometric resolution. Large area or volume imaging [12], flow cytometry [13,14], in vivo imaging [15], and 3D bioprinting [16], have prompted a further push to speed up Brillouin spectroscopy to video-rate imaging. In addition, the need to identify small viscoelastic changes [17–19] and multi-component samples [1–3,11,13,20] calls for Brillouin spectrometers with high sensitivity and high spectral resolution. In this case, spontaneous Brillouin spectroscopy (SpBS) [4,5,12], stimulated Brillouin spectroscopy (SBS) [11,21], and impulsive stimulated Brillouin spectroscopy (ISBS) [13,22–28] have been attracting considerable interest recently.
Compared to the SpBS whose integration time is prolonged by weak scattering signals [23], and SBS which is slowed down by frequency scans [26], ISBS can get a strong broadband spectrum in a single pulse excitation, making fast measurement possible. Moreover, the accuracy of ISBS is not affected by the stability of a laser, and its spectral resolution is independent of the limited finesse of an external spectrometer or the linewidth of a laser [24]. ISBS was first focused on biomechanical imaging by researchers at Texas A&M University [23]. And then a group from TU Dresden enhanced the spatial resolution and applied ISBS to the measurement of hydrogels with different stiffness [25]. Recently, ISBS has been successfully applied in microfluidics, pushing it to a new insight [13].
The traditional data processing for ISBS is based on fast Fourier transform (FFT). To obtain frequency shifts and linewidths, the FFT spectrum is always fitted by the function of the Brillouin peak [27]. However, the key to speeding up ISBS is to reduce the number of averaged signals, resulting in low signal-to-noise ratio (SNR) signals [28], and the FFT-based methods are not satisfactory when applied to noise-contaminated signals [29]. Moreover, numerical limitations, such as difficulty in accurately finding peak between two frequency bins due to frequency discretization [30], broadening and sidebands due to inappropriate truncation time [31], and the picket fence and energy leakage due to inappropriate sampling rate [29,32,33], should also be concerned. Those noise and numerical problems introduce distortions to the FFT spectrum, affecting the accuracy of the spectral fitting. To accurately obtain spectral information, ISBS is usually with an exposure time of several seconds for a high-SNR spectrum. In addition, the performance of the spectral fitting relies on parameters such as the number and frequency range of Brillouin peaks, making it difficult to extract weak signals from strong components. To address the above shortcomings of spectral fitting, some novel data processing methods are proposed to deal with noise-contaminated or multi-component spectra in SpBS [34–36]. However, the frequency-domain signal of SpBS is acquired directly by the spectrometers, which is different from the time-domain signal of ISBS. For ISBS signals, there has not been a sensitive data processing method to accurately decipher weak signals for high-speed but low-SNR ISBS and multi-component viscoelastic identification.
In this paper, an adaptive noise-suppression Matrix Pencil (ANMP) method is proposed to replace the traditional FFT-based spectral fitting method for ISBS. Based on singular value decomposition (SVD), this time-domain spectral analysis method can adaptively estimate all Brillouin peaks without the need of a priori information. Several situations are processed computationally and experimentally, proving that the ANMP method maintains accuracy in sensitively deciphering weak Brillouin peaks regardless of low SNRs and small concentrations. For a methanol signal with an SNR of 1.85 dB and a total exposure time of 0.4 ms, the ANMP-combined ISBS can maintain an accuracy of 0.005% for sound speed. And the experiment of a mixture of two polymers demonstrates that the ANMP method can distinguish two peaks when one component only accounts for 6% at a frequency difference of 2.69 MHz, while the spectral fitting cannot extract this weak peak from another strong one. This sensitive ANMP method shows significant advantages over the traditional method in terms of noise suppression and sensitivity. And the speed and sensitivity of this ANMP-combined heterodyne ISBS have the potential to be further improved for fast viscoelasticity measurement and multi-component identification.
2. ANMP method for heterodyne ISBS
2.1 Principle of the heterodyne ISBS
In ISBS, a pair of pump pulses interferes on the sample, inducing density fluctuation due to the electrostriction and generating a pair of counter-propagating ultrasonic waves, as shown in Fig. 1(a). The thermal effect can be neglected due to the low optical density, as discussed later in the setup part. The probe laser is diffracted on this laser-induced grating with maximum efficiency at the Bragg angle, as shown in Fig. 1(b). This automatic angular matching is due to the well-designed transmission grating (TG) and 4f system [22]. The diffracted signal of the probe can be enhanced by heterodyne detection [37]. And the reference beam, attenuated by a neutral density (ND) filter, is automatically collinear with the diffracted probe beam because the probe beam and the reference beam are incident symmetrically at Bragg angles [22] and the first-order Bragg diffraction angle is equal to the incident angle, as shown in Fig. 1(c). The heterodyne ISBS signal of a multi-component sample is
Fig. 1. Principle of heterodyne ISBS. (a) Interference by a pair of pump pulses, which induces the oscillation of the acoustic standing wave. (b) The diffraction of the probe beam on the laser-induced grating. (c) The heterodyne detection of ISBS.
In this way, viscoelastic parameters, such as speed and attenuation coefficient of ultrasonic waves, can be obtained from Brillouin shifts and linewidths of the heterodyne ISBS spectrum. Details of principle and derivation can be found in Supplement 1.
2.2 ANMP method
As introduced in Section 2.1, the key to obtaining viscoelastic parameters is to analyze spectral information of heterodyne ISBS. Matrix Pencil (MP) method is commonly used to analyze frequency components of exponentially damped sinusoids in noise, which matches well with the heterodyne ISBS signal in Eq. (1). On one hand, compared with the commonly used FFT-based spectral fitting method, the MP method estimates the information directly in the time domain instead of fitting the spectrum, avoiding the numerical problems caused by FFT. And the introduction of the filtered matrix makes it more applicable to deal with noise-contaminated signals [29,33,38], offering the potential for fast ISBS. Moreover, the MP method can extract all the spectral information, including frequency, damping factor, amplitude and phase, in one step, avoiding computational complexity. On the other hand, the MP method shows better performance for signals with fewer frequency components and is, therefore, more applicable to Brillouin spectroscopy than, for example, Raman spectroscopy.
The noise-contaminated exponential signal can be estimated as a sum of M exponentially damped sinusoids [38], which can be expressed as
However, in traditional MP methods, ɛ needs to be artificially selected a priori for each ISBS signal, and improper selection may result in the loss of some weak signal components. If a too low ɛ is selected, some noise components will be introduced to the Brillouin spectrum. And if the ɛ is too high, the signal components will be at risk of being filtered out. Factors such as a short acquisition time, improper judgment of the time range of the noise, and a too strong frequency component can make the artificially selected noise threshold too large, resulting in some weak frequency components being drowned out by the noise or other strong frequency components.
In this case, an ANMP method is proposed to automatically calculate the normalization threshold ɛ by pre-filtering, which can sensitively decipher weak signals from strong noise or other frequency components. After setting an initial value of M0 as 2, the most dominant frequency component is estimated, including the dominant attenuation coefficient αM0. Meanwhile, a dominant signal s0(t) is reconstructed. The residual r0(t) between s0(t) and the original signal I(t) is calculated to filter the strong dominant component. The noise threshold ɛn is defined as the maximum amplitude of r0(t) after the dominant relaxation time τ0 (=1/αM0) because the main energy in this period is concentrated on noise disturbances. And after taking the envelope of I(t), the maximum amplitude of this envelope is considered as the signal threshold ɛs. In this way, ɛ is calculated as ɛn/ɛs and M is automatically selected.
After getting the parameter M, a filtered matrix V’ is constructed with M dominant right-singular vectors of V for noise filtering. The eigenvalues of the matrix pencil are equivalent to the eigenvalues of V2’H-λV1’H, where V1’ and V2’ are obtained by removing the last and first rows of V’, respectively. Thus, the problem of solving exp[(-αMi+j2πνi)kT] can be transformed into an eigenvalue problem of V2’H-λV1’H. Once αMi and νi are solved, Ai and ϕi can be calculated using the least-squares problem. In this way, all spectral information of multiple Brillouin peaks can be extracted from the time-domain heterodyne ISBS signal with the ANMP method.
In the sections below, the performance of the traditional FFT-based spectral fitting and the ANMP method is compared through simulations and experiments. For FFT-based spectral fitting, the first step is to transform the time-domain signal to the frequency domain by FFT. To enhance the accuracy, several zeros are padded to I(t) in the time domain to decrease the spectrum interval. In the second spectral fitting step, the number and the frequency range of the peaks are limited prior. The fitting is based on nonlinear least square, and the fitting function is based on Eq. (2) to obtain peak frequencies and attenuation coefficients. With the ANMP method and the FFT-based spectral fitting method, the sound speed is calculated from Brillouin shifts, and the attenuation coefficient is estimated directly (see Supplement 1 for details). All the data analysis is processed in Matlab using home-built scripts. The source codes of both the ANMP method and the FFT-based spectral fitting method have been uploaded to the supplemental material, as we show in Code 1 (Ref. [40]) and Code 2 (Ref. [41]), respectively.
3. Experimental setup
The experimental setup is illustrated in Fig. 2. The pump is a 532 nm, 10 ps solid-state pulse laser (Huaray Laser; PINE-532-15), which is vertically focused on the transmission grating (TG) with a period of 20.67 µm by a cylindrical lens with a focal length of 500 mm (Thorlabs; LJ1144RM-A). The use of the cylindrical lens improves the optical density of the pump while maintaining the number of fringes in the horizontal direction, thus enhancing the excitation of the acoustic wave. If not specifically stated, the pump laser is with 100 µJ per pulse at a 10 kHz repetition rate. The probe is a 780 nm, CW laser, which contains the seed laser and power amplification part. The seed is a semiconductor laser (Thorlabs; DBR780PN), and after passing through a tapered amplifier (New Focus; TA-7613), the maximum output power is about 350 mW. The probe is focused on the TG through a spherical lens with a focal length of 400 mm.
Fig. 2. Schematic of the ISBS setup. M1-M6: mirror, CL: cylindrical lens, L1 and L4: spherical lenses, DM: dichroic mirror, ND1 and ND2: neutral density filters, TG: transmission grating, L2 and L3: achromatic lenses, S: sample, F1 and F2: 780 nm bandpass filters, PD1 and PD2: photodetectors.
The pump and the probe are combined through a shortpass dichroic mirror (DM) (Thorlabs; DMSP650), incident on the TG in the same path, and then pass through the 4f system. Because the transmission rate of the DM is not 100% for 532 nm, a small part of the pump is reflected by the DM and detected by a photodetector PD1 (Thorlabs; PDA10A-EC) as a trigger for the oscilloscope. The 4f system consists of two achromatic lenses, L2 (Thorlabs; AC254-150-A) and L3 (Thorlabs; AC254-125-A), with focal lengths of 150 mm and 125 mm, respectively. On the one hand, the pump is divided into ±1 orders and interferes on the sample through the 4f system, reimagining a TG pattern with a fringe spacing of 8.61 µm on the sample and inducing an acoustic standing wave. On the other hand, the probe is divided into ±1 and 0 orders. In the 4f system, only ±1 orders are allowed to pass. One of them is attenuated in the Fourier plane by a neutral density filter, serving as a reference beam, and the other is diffracted at the Bragg angle on the sample. The first-order diffracted light is modulated by the acoustic wave excited by the pump. This diffracted light automatically overlaps with the reference beam because the diffraction angle in Bragg diffraction is equal to the incident angle and the two beams are symmetric, resulting in heterodyne interference.
The heterodyne interference light carrying acoustic information is focused on the photodetector PD2 (New Focus; 1601FS-AC) after passing through two 780 nm bandpass filters, F1 and F2, to remove any remaining 532 nm light. The signal from PD2 is filtered by a high-pass electrical filter (Mini Circuits; BHP-50+; 41-800 MHz) to remove the dc bias and low-frequency noise. After being amplified about 250 times by two cascaded amplifiers (Mini Circuits; ZFL-1000+), the signal is collected with an oscilloscope (Agilent Technologies; DSO9254A; 2.5 GHz bandwidth). Unless otherwise stated, the total pulse energy of the two pump beams on the sample is about 60 µJ at a 10 kHz repetition rate, with a vertical width of 232.5 µm and a horizontal width of 744 µm. And the total power of the probe and reference beams on the sample is about 80 mW with a width of 213.9 µm. The corresponding optical density of the pump is calculated to be 110.41 W/cm2 and that of the probe is 222.63 W/cm2. In this case, the thermal effect can be neglected and only the electrostriction needs to be considered when discussing the generation of acoustic waves [28]. All the measurements are taken at room temperature of 296.15 K.
4. ANMP for more sensitive low-SNR-signal analysis
4.1 Simulation of low-SNR signals
One of the advantages of the ANMP method is its robustness to noise, which is the key to improving the speed of ISBS. The main noise sources of ISBS are shot noise, dark current noise, thermoelectrical noise, and 1/f noise, all of which are white noise except for 1/f noise. Because the frequency range where the signal is located (∼100 MHz) is almost unaffected by 1/f noise, and the high-pass electrical filter suppresses the main energy of 1/f noise, the noise source affecting the SNR of ISBS is mainly white noise. To compare the noise feature of the ANMP method and the traditional spectral analysis, random Gaussian white noise is added to the ideal signal. To verify the robustness, signals with different SNRs from 1 dB to 35 dB are simulated with a sample size of 20 at each SNR. The theoretical sound speed and attenuation coefficient of the simulated sample are 1109.55 m/s and 19.97 dB/cm, respectively. The sampling rate is 1 GHz, and the spectrum interval is 488 kHz. For FFT-based spectral fitting, the spectrum interval is improved to 7.63 kHz after padding 100000 zeros to fitting the spectrum more accurately. The peak frequency range is limited to 0-258 MHz. We record the computation time at an SNR of 10 dB with a sample size of 20 as an example. The computation time required to process one spectrum for FFT-based spectral fitting is 1.221 ± 0.064 s, and for ANMP is 0.139 ± 0.002 s which meets the requirement of real-time processing.
The sound speed and attenuation coefficients extracted by the spectral fitting and the ANMP method are compared under different SNRs in the form of box plots, as shown in Fig. 3. Comparing the interquartile range (IQR), median, and mean values of the two methods, it can be seen that the ANMP method maintains the accuracy of extracted parameters from 1 dB to 35 dB, while the spectral fitting cannot fit the Brillouin peak stably until the SNR increases to 7 dB. And the ANMP results have much fewer outliers at low SNRs, which is more reliable in the experiments. Figure 3(b) also indicates that the ANMP method can more accurately obtain the attenuation coefficients at low SNRs where both methods can extract the Brillouin peak.
Fig. 3. (a) Sound speed and (b) attenuation coefficients extracted by the spectral fitting (top) and the ANMP method (bottom) under different SNRs in the form of box plots. 20 signals with different random noises are simulated at each SNR.
4.2 Fast and low optical damage ISBS measurement of methanol
The outstanding noise suppression of the ANMP method provides the possibility for fast ISBS. Considering that methanol is often chosen as a common sample to verify the ISBS performance [23,25,28], here we also choose methanol (≥99.5%, Analytical Reagent, Anhydrous) to verify the measurement speed. To start with, a high SNR (34.80 dB) ISBS signal with a long exposure time is measured as a standard for methanol, as shown in Fig. 4(a) (top). The standard spectrum is the FFT spectrum of this high SNR signal, as shown in the purple area in Fig. 4(b), from which the theoretical sound speed and attenuation coefficient of methanol are calculated, as listed in Table 1. On the sample, the total pulse energy of the pump is 60 µJ and the total power of the probe is 80 mW. The pump repetition rate is 10 kHz and the signals are averaged 65535 times by the oscilloscope, so a single point measurement takes up to 6.55 s.
Fig. 4. ISBS signals of methanol with a high SNR and a low SNR and corresponding Brillouin spectra. (a) Methanol signals with high SNR (top) and low SNR (bottom) and the reconstructed signal by the ANMP method. (b) FFT spectrum and extracted peaks of the low SNR signal and comparison with a standard FFT spectrum of the high SNR signal. The inset shows the details of the spectrum.
Table 1. Spectral Information and Viscoelastic Parameters of Methanola
The methanol signal with a low SNR of 1.85 dB is measured at a faster measurement and lower optical density. The repetition rate is increased to 20 kHz, and the signals are averaged only 8 times, reducing the exposure time to 0.40 ms. In addition, the total pulse energy of the two intersecting pump beams on the sample is reduced to 11.60 µJ and the corresponding optical density is 42.69 W/cm2. The SNR is calculated from the time-domain signal extracted by the ANMP method, and the noise is the standard deviation of the residual between the original signal and the extracted signal. In this case, the signal SNR is reduced to 1.85 dB which is in the range where the noise suppression performance of the two methods is significantly different, as discussed in the simulation part. As shown in Fig. 4(b), it is difficult to determine where the Brillouin peak is from the FFT spectrum (blue area) due to the low SNR. Despite limiting the central frequency parameter to 100 to 160 MHz, it is also impossible to extract the Brillouin peak from the noise by spectral fitting. The time-domain signal reconstructed by the ANMP method is shown in Fig. 4(a) (bottom), and the extracted Brillouin peak by the ANMP method is shown as the orange line in Fig. 4(b), which is in good agreement with the standard FFT spectrum obtained from the high SNR signal. The specific spectral information and calculated viscoelastic parameters are listed in Table 1. It can be seen from the table that for the low SNR ISBS signal from fast measurement, the FFT-based spectral fitting method can no longer accurately obtain the information of the Brillouin peak, while the relative error of sound speed obtained by the ANMP method is 0.005%. In a word, the ANMP method can accurately extract Brillouin spectral information from low SNR signals, allowing a shorter exposure time and lower laser power in heterodyne ISBS and offering the possibility of video imaging and other fast measurement applications.
5. ANMP for more sensitive multi-component identification
Compared to the FFT-based spectral fitting, the ANMP method shows better performance in sensitivity and is more applicable for a multi-peak spectrum because it can adaptively extract Brillouin peaks without the need of the number and frequency range of peaks. In this section, the sensitivity of the two methods is simulated with an ideal two-component sample. And a mixture of two polymers is measured to demonstrate that the ANMP method is more suitable for multi-component viscoelastic identification.
5.1 Simulation of sensitivity for a two-component sample
First, we compare the sensitivity of the two methods by simulating a two-component sample at different amplitude ratios. In Fig. 5, the theoretical viscoelastic parameters of two components are marked as dashed lines. The spectral difference between the two components are set to 2.69 MHz, and their attenuation coefficients are 36.22 dB/cm and 83.94 dB/cm. The amplitude percentage of component 1 varies from 0 to 100% with an interval of 2.5% when simulating the mixture signal, and the corresponding sound speed and attenuation coefficients estimated by the two methods are illustrated in Fig. 5(a) and Fig. 5(b), respectively. The ranges where the peaks can be distinguished are filled with colors. The ANMP method can distinguish two peaks when the amplitude percentage of component 1 is between 2.5% and 97.5%, while spectral fitting is only effective when the percentage is between 15% and 75%. It is found that when the amplitude difference between two peaks is too large for spectral fitting, the ANMP method can still extract viscoelastic parameters accurately. Taking component 1 as an example, the ANMP method could improve its detection sensitivity from 15% to 2.5% in the simulation, showing a strong ability to improve the sensitivity of heterodyne ISBS.
Fig. 5. The simulation of sensitivity for a two-component sample at different amplitude ratios. (a) The sound speed and (b) attenuation coefficients extracted by the spectral fitting (top) and the ANMP method (bottom) at different amplitude percentages of component 1. The black dashed lines represent the theoretical values. The light purple and orange areas mark the ranges where the spectral fitting and the ANMP method can distinguish the peaks, respectively.
5.2 Enhanced sensitivity for ISBS measurement of polymer mixtures
Polystyrene (PS) and polyvinyl chloride (PVC) are clinically common biomaterials. In this section, the ISBS spectra are measured at the interface between PS and PVC to test the ability of the ANMP method to extract Brillouin peaks from a multi-peak spectrum. The spectral linewidths of pure PS and PVC are 4.67 MHz and 10.92 MHz, respectively, and these two samples are at a frequency difference of 2.69 MHz. Figure 6 illustrates the results for mixtures with different percentages of PS in an optical volume. The percentages of PS are calculated based on the time-domain amplitudes of the two components extracted by the ANMP method. The PS and PVC peaks extracted by the FFT-based spectral fitting and the ANMP method from these mixtures are shown in Fig. 6(a) and Fig. 6(b), respectively, and the specific data are listed in Table 2.
Fig. 6. ISBS spectra of PS-PVC mixtures with different PS percentages and comparison with the standard FFT spectra of pure PS and pure PVC. (a) The PS and PVC peaks extracted from the mixture by FFT-based spectral fitting at different PS percentages, and (b) the corresponding extracted peaks by the ANMP method.
Table 2. Extracted Viscoelastic Parameters from ISBS Signals of PS-PVC Mixturesa
Compared with the standards measured from FFT spectra of pure PS and pure PVC, the ANMP method can accurately extract peaks when PS or PVC are in small content, while spectral fitting cannot even when the central frequency of the fitting function is set to 270 to 276 MHz. And in the case where both methods can distinguish two peaks, the ANMP method provides a more accurate estimate of the attenuation coefficient. When extracted from the mixture, the PS detection sensitivity is improved from 15% to 6% by the ANMP method. It is possible to increase the sensitivity to 2.5% as simulated without considering the limitation of sample preparation conditions. This experiment demonstrates that the ANMP method algorithmically enhances the sensitivity, offering the possibility of component identification and trace detection.
6. Conclusion and discussion
In conclusion, an alternative spectral analysis method, the ANMP method, is proposed to sensitively decipher weak signals in heterodyne ISBS regardless of a low SNR or a small concentration, speeding up the ISBS measurements and improving the sensitivity of multi-component identification. Compared to the traditional FFT-based spectral fitting, this ANMP method shows better accuracy for ISBS spectra with low SNR or multiple peaks, without the need for a priori information about Brillouin peaks. And compared to the traditional MP method, because the strong dominant frequency component is pre-filtered and the weak frequency components and noise are displayed, the ANMP method can automatically calculate a more accurate normalization threshold ɛ for weak signals without any parameter selection, algorithmically and adaptively enhancing the sensitivity of heterodyne ISBS.
Experimental results confirm that the ANMP method can sensitively extract Brillouin peak from the low SNR signal with an accuracy of 0.005% for methanol sound speed at an exposure time of 0.40 ms and an optical density of 42.69 W/cm2. Moreover, this method maintains the accuracy of <0.5% of sound speed when deciphering Brillouin peaks of a polymer mixture, even when the component is in small content, improving the PS detection sensitivity from 15% to 6%.
This ANMP method shed new light on the spectral analysis of ISBS. Combined with the ANMP method, heterodyne ISBS may add to the rapidly expanding field of fast viscoelasticity measurements such as flow cytometry and large-area imaging, and improve the performance of multi-component viscoelastic identification. In addition, the ANMP method may also be of assistance for other photoacoustic detections measuring time-domain oscillations of phonons, such as photoacoustic spectroscopy. Future research might be undertaken in optimizing the ANMP method with machine learning to automatically obtain more accurate M parameters with better noise suppression and adaptability.
The spatial resolution and measurement speed of this ANMP-combined heterodyne ISBS can be further improved by optimizing the setup. Based on our current setup, the spatial resolution is on the order of 100 µm. By increasing the focal length ratio of L2 to L3 in the 4f system and using larger numerical aperture lenses (for CL and L1) with shorter focal lengths before TG, the spatial resolution can be further improved and has the potential to reach the order of 10 µm [25]. In addition, the current exposure time for a spectrum is 0.4 ms, corresponding to a measurement speed of 2.5 kHz. In this case, the frame rate for an image of 500 pixels will be 5 fps. After optimizing the spatial resolution, the optical density of the pump will be increased, thus inducing a linear enhancement of the signal [42], which will be discussed more in future work. And the SNR is proportional to the root square of the average number of signals [28], so a $\sqrt {8} $-fold increase in pump optical density (∼120.75 W/cm2) can meet the ANMP requirement for SNR at a measurement speed up to 20 kHz for a single pixel. This measurement speed corresponds to a frame rate of 40 fps for a 500-pixel image, meeting the needs of video imaging [28]. With the ANMP method, heterodyne ISBS has the potential to map the viscoelasticity at video speed.
Funding
National Key Research and Development Program of China (2020YFB2010701).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. G. Scarcelli, W. J. Polacheck, H. T. Nia, K. Patel, A. J. Grodzinsky, R. D. Kamm, and S. H. Yun, “Noncontact three-dimensional mapping of intracellular hydromechanical properties by Brillouin microscopy,” Nat. Methods 12(12), 1132–1134 (2015). [CrossRef]
2. K. Elsayad, S. Werner, M. Gallemí, J. Kong, E. R. Sánchez Guajardo, L. Zhang, Y. Jaillais, T. Greb, and Y. Belkhadir, “Mapping the subcellular mechanical properties of live cells in tissues with fluorescence emission–Brillouin imaging,” Sci. Signaling 9(435), rs5 (2016). [CrossRef]
3. F. Pérez-Cota, R. J. Smith, H. M. Elsheikha, and M. Clark, “New insights into the mechanical properties of Acanthamoeba castellanii cysts as revealed by phonon microscopy,” Biomed. Opt. Express 10(5), 2399–2408 (2019). [CrossRef]
4. J. Zhang and G. Scarcelli, “Mapping mechanical properties of biological materials via an add-on Brillouin module to confocal microscopes,” Nat. Protoc. 16(2), 1 (2021). [CrossRef]
5. G. Scarcelli and S. H. Yun, “Confocal Brillouin microscopy for three-dimensional mechanical imaging,” Nat. Photonics 2(1), 39–43 (2008). [CrossRef]
6. M. Troyanova-Wood, C. Gobbell, Z. Meng, A. A. Gashev, and V. V. Yakovlev, “Optical assessment of changes in mechanical and chemical properties of adipose tissue in diet-induced obese rats,” J. Biophotonics 10(12), 1694–1702 (2017). [CrossRef]
7. S. Ryu, N. Martino, S. J. J. Kwok, L. Bernstein, and S.-H. Yun, “Label-free histological imaging of tissues using Brillouin light scattering contrast,” Biomed. Opt. Express 12(3), 1437–1448 (2021). [CrossRef]
8. H. Zhang, M. Roozbahani, A. L. Piccinini, F. Hafezi, G. Scarcelli, and J. B. Randleman, “Brillouin microscopic depth-dependent analysis of corneal crosslinking performed over or under the LASIK flap,” J. Cataract Refractive Surg. 46(11), 1543–1547 (2020). [CrossRef]
9. R. Raghunathan, J. Zhang, C. Wu, J. Rippy, M. Singh, K. Larin, and G. Scarcelli, “Evaluating biomechanical properties of murine embryos using Brillouin microscopy and optical coherence tomography,” J. Biomed. Opt. 22(08), 1 (2017). [CrossRef]
10. R. Schlüßler, S. Möllmert, S. Abuhattum, G. Cojoc, P. Müller, K. Kim, C. Möckel, C. Zimmermann, J. Czarske, and J. Guck, “Mechanical Mapping of Spinal Cord Growth and Repair in Living Zebrafish Larvae by Brillouin Imaging,” Biophys. J. 115(5), 911–923 (2018). [CrossRef]
11. I. Remer, R. Shaashoua, N. Shemesh, A. Ben-Zvi, and A. Bilenca, “High-sensitivity and high-specificity biomechanical imaging by stimulated Brillouin scattering microscopy,” Nat. Methods 17(9), 913–916 (2020). [CrossRef]
12. J. Zhang, A. Fiore, S.-H. Yun, H. Kim, and G. Scarcelli, “Line-scanning Brillouin microscopy for rapid non-invasive mechanical imaging,” Sci. Rep. 6(1), 35398 (2016). [CrossRef]
13. D. Doktor, S. O’Connor, J. Tronolone, A. Jain, and V. Yakovlev, “Impulsive stimulated Brillouin spectroscopy for non-invasive microfluidic-based viscoelastic measurements in vitro,” in SPIE BiOS (SPIE, 2021).
14. J. Zhang, X. A. Nou, H. Kim, and G. Scarcelli, “Brillouin flow cytometry for label-free mechanical phenotyping of the nucleus,” Lab Chip 17(4), 663–670 (2017). [CrossRef]
15. G. Scarcelli, P. Kim, and Seok H. Yun, “In Vivo Measurement of Age-Related Stiffening in the Crystalline Lens by Brillouin Optical Microscopy,” Biophys. J. 101(6), 1539–1545 (2011). [CrossRef]
16. M. A. Rad, H. Mahmodi, E. C. Filipe, T. R. Cox, I. Kabakova, and J. L. Tipper, “Micromechanical characterisation of 3D bioprinted neural cell models using Brillouin microspectroscopy,” Bioprinting 25, e00179 (2021). [CrossRef]
17. J. Xu, X. Ren, W. Gong, R. Dai, and D. Liu, “Measurement of the bulk viscosity of liquid by Brillouin scattering,” Appl. Opt. 42(33), 6704–6709 (2003). [CrossRef]
18. Z. Meng and V. V. Yakovlev, “Precise Determination of Brillouin Scattering Spectrum Using a Virtually Imaged Phase Array (VIPA) Spectrometer and Charge-Coupled Device (CCD) Camera,” Appl. Spectrosc. 70(8), 1356–1363 (2016). [CrossRef]
19. S. V. Adichtchev, Y. A. Karpegina, K. A. Okotrub, M. A. Surovtseva, V. A. Zykova, and N. V. Surovtsev, “Brillouin spectroscopy of biorelevant fluids in relation to viscosity and solute concentration,” Phys. Rev. E 99(6), 062410 (2019). [CrossRef]
20. F. K. Chun Yu Tammy Huang, Topojit Debnath, Bishwajit Debnath, Michael D Valentin, Ron Synowicki, Stefan Schoeche, Roger K Lake, and Alexander A Balandin, “Phononic and photonic properties of shape-engineered silicon nanoscale pillar arrays,” Nanotechnology 31(30), 30LT01 (2020). [CrossRef]
21. C. W. Ballmann, J. V. Thompson, A. J. Traverso, Z. Meng, M. O. Scully, and V. V. Yakovlev, “Stimulated Brillouin Scattering Microscopic Imaging,” Sci. Rep. 5, 18139 (2015). [CrossRef]
22. Z. Meng, G. I. Petrov, and V. V. Yakovlev, “Flow cytometry using Brillouin imaging and sensing via time-resolved optical (BISTRO) measurements,” Analyst 140(21), 7160–7164 (2015). [CrossRef]
23. C. W. Ballmann, Z. Meng, A. J. Traverso, M. O. Scully, and V. V. Yakovlev, “Impulsive Brillouin microscopy,” Optica 4(1), 124 (2017). [CrossRef]
24. C. W. Ballmann, Z. Meng, and V. V. Yakovlev, “Nonlinear Brillouin spectroscopy: what makes it a better tool for biological viscoelastic measurements,” Biomed. Opt. Express 10(4), 1750 (2019). [CrossRef]
25. B. Krug, N. Koukourakis, and J. W. Czarske, “Impulsive stimulated Brillouin microscopy for non-contact, fast mechanical investigations of hydrogels,” Opt. Express 27(19), 26910–26923 (2019). [CrossRef]
26. D. Doktor, Z. Coker, V. Cheburkanov, J. Lalonde, S. O’Connor, and V. Yakovlev, “Dynamic Brillouin microscopy imaging,” in SPIE BiOS (SPIE, 2020).
27. S. O’Connor, D. Doktor, M. Scully, and V. Yakovlev, “Impulsive stimulated Brillouin spectroscopy for assessing viscoelastic properties of biologically relevant aqueous solutions,” in SPIE BiOS (SPIE, 2021).
28. B. Krug, N. Koukourakis, J. Guck, and J. Czarske, “Nonlinear microscopy using impulsive stimulated Brillouin scattering for high-speed elastography,” Opt. Express 30(4), 4748–4758 (2022). [CrossRef]
29. K. Sheshyekani, G. Fallahi, M. Hamzeh, and M. Kheradmandi, “A General Noise-Resilient Technique Based on the Matrix Pencil Method for the Assessment of Harmonics and Interharmonics in Power Systems,” IEEE Trans. Power Delivery 32(5), 2179–2188 (2017). [CrossRef]
30. L. Bernard, S. Goondram, B. Bahrani, A. A. Pantelous, and R. Razzaghi, “Harmonic and Interharmonic Phasor Estimation Using Matrix Pencil Method for Phasor Measurement Units,” IEEE Sens. J. 21(2), 945–954 (2021). [CrossRef]
31. F. Sinjab, K. Hashimoto, X. Zhao, Y. Nagashima, and T. Ideguchi, “Enhanced spectral resolution for broadband coherent anti-Stokes Raman spectroscopy,” Opt. Lett. 45(6), 1515–1518 (2020). [CrossRef]
32. Q. Wang, X. Yan, and K. Qin, “Parameters estimation algorithm for the exponential signal by the interpolated all-phase DFT approach,” in 2014 11th International Computer Conference on Wavelet Actiev Media Technology and Information Processing (IEEE, 2014), pp. 37–41.
33. L. Wang and J. Suonan, “A Fast Algorithm to Estimate Phasor in Power Systems,” IEEE Trans. Power Delivery 32(3), 1147–1156 (2017). [CrossRef]
34. D. Fioretto, S. Caponi, and F. Palombo, “Brillouin-Raman mapping of natural fibers with spectral moment analysis,” Biomed. Opt. Express 10(3), 1469–1474 (2019). [CrossRef]
35. Y. Xiang, M. R. Foreman, and P. Török, “SNR enhancement in brillouin microspectroscopy using spectrum reconstruction,” Biomed. Opt. Express 11(2), 1020–1031 (2020). [CrossRef]
36. K. Elsayad, “Spectral Phasor Analysis for Brillouin Microspectroscopy,” Front. Phys. 7, 1 (2019). [CrossRef]
37. A. A. Maznev, K. A. Nelson, and J. A. Rogers, “Optical heterodyne detection of laser-induced gratings,” Opt. Lett. 23(16), 1319 (1998). [CrossRef]
38. T. K. Sarkar and O. Pereira, “Using the matrix pencil method to estimate the parameters of a sum of complex exponentials,” IEEE Antennas Propag. Mag. 37(1), 48–55 (1995). [CrossRef]
39. J. Song, J. Zhang, and H. Wen, “Accurate Dynamic Phasor Estimation by Matrix Pencil and Taylor Weighted Least Squares Method,” IEEE Trans. Instrum. Meas. 70, 1–11 (2021). [CrossRef]
40. J. Li, H. Zhang, M. Lu, H. Wei, and Y. Li, “Matlab Code for ANMP Method,” figshare (2022), https://doi.org/10.6084/m9.figshare.20311014.
41. J. Li, H. Zhang, M. Lu, H. Wei, and Y. Li, “Matlab Code for FFT-Based Spectral Fitting Method,” figshare (2022), https://doi.org/10.6084/m9.figshare.20337894.
42. R. J. D. Miller, R. Casalegno, K. A. Nelson, and M. D. Fayer, “Laser-induced ultrasonics: A daynamic holographic approach to the measurement of weak absorptions, optoelastic constants acoustic attenuation,” Chem. Phys. 72(3), 371–379 (1982). [CrossRef]
