Open Access
Add to BibSonomy
Abstract
A method to reconstruct the spatial distribution of Brillouin gain spectrum from its Radon transform is proposed, which is a type of optical computed tomography. To verify the concept, an experiment was performed on distributed Brillouin fiber sensing, which succeeded in detecting a 55-cm strain section along a 10-m fiber. The experimental system to obtain the Radon transform of the Brillouin gain spectrum is based on a Brillouin optical correlation-domain analysis with a linear frequency-modulated continuous-wave laser. Combining distributed fiber sensing with computed tomography, this method can realize a high signal-to-noise ratio Brillouin sensing.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Computed tomography (CT) has been used as a non-invasive tomographic method in a wide range of applications from medical diagnosis to astronomy [1–6]. In X-ray CT, a narrow beam is injected into the human body at various angles and the transmittance is measured. We can reconstruct a two-dimensional profile of the absorption rate from the transmittance of the beams in the same plane. This reconstruction is based on the mathematical fact, proven by Radon in 1917 [1,7], that a two-dimensional function with compact support can be reconstructed from its line integrals over an arbitrary straight line. That is, the Radon transform (RT), which is such a point-to-line transformation, has an inverse. In recent years, high-performance reconstruction methods using the inverse RT have been developed [8–10].
In this study, we apply CT to distributed fiber sensing [11,12] for the first time, to the best of our knowledge. Our method is based on the Brillouin optical correlation domain analysis (BOCDA) [13–20], which is a distributed sensing method of temperature and strain from the Brillouin gain spectrum (BGS) with high spatial resolution [16,21,22] and random accessibility [14,23]. The output spectrum of the BOCDA is represented by a two-dimensional (position and frequency) convolution of the BGS of the fiber and the beat spectrum of the light [13,14]. The BGS at each fiber position is a Lorentzian function of frequency, and its peak frequency shifts almost linearly owing to strain and temperature changes along the fiber. The beat spectrum represents the spatial distribution of the frequency difference between pump and probe beam counter-propagating in the fiber with each other. In all the correlation-domain methods proposed so far, the beat spectrum is shaped into a point or delta-like function as much as possible and scanned in the position-frequency space. Thus, the correlation-domain method has a unique property of random access, which is the ability to measure an arbitrary point directly [14,23]. However, this property also poses the challenge that all contributions from places other than the measurement point, referred to as the correlation peak, become noise. Thereafter, techniques such as temporal gating are required to realize the measurement along a long fiber with a high spatial resolution at the expense of brightness [15,20,24–26]. Another solution is applying two-dimensional deconvolution, but the deconvolution based on the delta-like function is vulnerable to noise. In addition, scanning the correlation-peak position is sometimes problematic [27].
In the proposed method, the beat spectrum is shaped into a straight line to obtain the RT of the BGS distribution. We refer to the proposed method as the RT-BOCDA. We conducted a proof-of-concept experiment of the RT-BOCDA, which succeeded in detecting a 55-cm strain section along a 10-m fiber. The reconstructed BGS is in good agreement with the theoretical prediction. As the optical power everywhere along the “line” is utilized for the signal, a higher performance can be achieved at the cost of random accessibility. The reconstructed BGS is approximately Lorentzian, which has no optical background spectrum seen in the conventional BOCDA [14]. The RT-BOCDA is the first example of a correlation-domain method with a beat spectrum that is not a delta-like function. It does not require correlation peak scanning but instead requires the inverse transformation of all measured data collectively after the measurements are completed. This concept presents the possibility of novel sensing using the correlation-domain technique with various beat spectra [27].
2. Principle
As mentioned above, the output spectrum of a correlation-domain method is determined through the BGS distribution and the beat spectrum. In Section 2.1, we illustrate a typical BGS distribution and its RT. In Section 2.2, we describe the method for forming the straight-line beat spectrum required for the RT-BOCDA. In Section 2.3, we show that the output of the RT-BOCDA is represented by the RT of the BGS distribution.
2.1 BGS distribution and its Radon transform
Figure 1 illustrates the RT of a typical BGS distribution. We assume a situation where the frequency shift of the BGS due to strain occurs in a relatively short section. The intrinsic BGS, the measurand of Brillouin fiber sensing, is a Lorentzian function as follows:
where $g_{B0}$ is a gain coefficient, $\Gamma$ is a linewidth of the BGS, and $\Omega _B(z)$ is a Brillouin frequency shift (BFS) proportional to the strain. For simplicity, we ignore position dependencies other than the BFS, although our method can measure these dependencies as well.
Fig. 1. (a) Schematic of the RT of a typical BGS distribution. (b) Typical BGS distribution, $g_B^N(x,y)$, and (c) its RT calculated in Matlab, $\mathcal {R} g^N_B(p,\theta )$ at $N=600$. Here, $\theta$ represents a direction of the projection as shown in Fig. 1(a), along which the line integral is performed. $p$ represents the amount of the straight line shifted in the direction of its normal. In principle, the RT, $\mathcal {R}$, has the inverse, $\mathcal {R}^{-1}$.
Let us describe schematically the RT of a BGS distribution in Fig. 1(a). For simplicity, we limit the discussion to $(N+1)\times (N+1)$ square matrix images of the BGS distribution within the range of $-L/2\leq z\leq L/2$ and $-\Omega /2\leq \omega \leq \Omega /2$, where $N$ is a sufficiently large natural number, $L$ is the fiber length, and $\Omega$ is the range of the optical frequency, as shown in Fig. 1. If the measured area ($L,\ \Omega$) is wider than the area where the gain exists, we can make a square image by padding 0 to an image of any size. To treat each side of the image equally, we introduce dimensionless variables $(x,y)$ representing the number of pixels, not limited to integers:
We define the RT as the line integral on a straight line at a distance $p$ shifted from the center of the original image with an angle $\theta$ as follows:
2.2 Straight-line beat spectrum at each angle
Figure 2 illustrates how our RT-BOCDA system creates the straight-line beat spectrum using a frequency-swept laser [28–30], whose frequency changes $\sigma$ during time $\tau$. We introduce the electric field of the pump $E_1$ and probe $E_2$ as follows:
Further, $\omega _0$ is the center frequency of the light source, $\Delta \omega$ is the probe frequency shift, and $\sigma$ is an FM amplitude. We also use a rectangular function, $\textrm {rect}(t)=\begin {cases}1\ (|t|\leq 0.5)\\ 0\ (|t|>0.5)\end {cases}.$ We assume them to be single pulses with the duration $\tau$ for simplicity of calculation. Their beat signal $B$ is defined as follows,
We use a triangular function $\textrm {tri}(x)=\textrm {max}(1-|x|,0)$, which originates from the convolution of the rectangular function. It should be noted that the square of the sinc function is approximated by the delta function. As in the preceding section, we rewrite $S_b(z,\omega )$ as $S_b^N(x,y)$:
Fig. 2. Creation of the straight-line beat spectrum $S_b(z,\omega )$ in the RT-BOCDA system. (a) System configuration using the linearly frequency-swept laser, which makes the chirp pulses. FUT: fiber under test. (b) Calculated beat spectra at each angle $\theta$, which can be controlled by the chirp rate, $\sigma /\tau$ (we change $\sigma$ with a fixed $\tau$). Although not drawn in the figure, each straight line can be translated in the frequency axis direction according to the probe frequency shift, $\Delta \omega$.
From the argument of the delta function, we obtain the following equation of the straight line:
The angle $\theta$ of the line, which was schematically illustrated in Fig. 1(a), can be defined in radians as follows,
The examples of the straight-line beat spectrum created using the frequency-swept laser are shown in Fig. 2(b).
2.3 Output spectrum of RT-BOCDA and reconstruction of BGS
The output spectrum of the RT-BOCDA with probe frequency shift $\Delta \omega$ and FM amplitude $\sigma$ is an overlap integral of the BGS distribution and the beat power spectrum, which is expressed as
We rewrite $P(\Delta \omega, \sigma )$ as $P^N(p_\theta, \theta )$:
Thus the variable conversion from $(\Delta \omega,\ \sigma )$ to ($p_\theta, \theta$) is realized using Eqs. (12) and (18).
From Eqs. (17) and (19), it can be seen that the RT-BOCDA output is expressed through the RT of the BGS distribution multiplied by the square of the triangular function. Since the signal intensity decreases at the end of the pulses, it is more practical to set the sensing fiber length shorter than the pulse length. However, the triangular function may not affect the deduction of a BFS at each fiber position. Additionally, it can be compensated for following the inverse RT. For example, in a uniform fiber, this compensation can be made by utilizing the fact that the integration of the BGS with respect to the frequency at each position is the same or a theoretical value such as Eq. (19).
Further, to translate a straight line by the same distance at each angle $\theta$, it is necessary to perform a frequency shift ($\Delta \omega$) of the value divided by $\sin \theta$, as shown in Eq. (18). The output spectrum also needs to be divided by $\sin \theta$ as shown in Eq. (17). This is a consequence of translating the straight line at each angle only by changing the probe frequency shift $\Delta \omega$ in the $y$-axis direction. Similarly, it is possible to realize it only in the $x$-axis (position) direction or to use both the $x$- and $y$-axis direction. When the translation range ($\Omega _\theta$, see Eq. (21)) of the straight line is changed for each angle with the same width of the straight line, it is necessary to correct the integrated value. The advantage of using only the $y$-axis direction is that it is not necessary to move the correlation peak position, thereby avoiding the need for delay fibers [14,27].
3. Experiment
The experimental system of RT-BOCDA is illustrated in Fig. 3. The delayed fiber was removed from the standard BOCDA system, and the intensity modulator (IM1) was added after the laser. The frequency of the laser (Eblana Photonics, EP1550-DM-B) was modulated with a triangular wave through the injection current. We extracted the linearly frequency-modulated pulse using the intensity modulator, IM1. The pulse duration was selected to correspond to the measurement fiber length ($L=10$ m). The frequency of the probe light was downshifted by $\Delta \omega$ using the single side-band modulator (SSBM), and the detuning $\Delta \omega$ was scanned linearly by changing the voltage applied to the VCO. The Brillouin gain of the probe was measured by using lock-in detection synchronized to the chopping frequency introduced to the pump by IM2. The entire fiber system is composed of polarization-maintaining fibers.
Fig. 3. Experimental setup of RT-BOCDA. LD: laser diode, IM: intensity modulator, FM: frequency modulation, EDFA: erbium-doped fiber amplifier, SSBM: single side-band modulator.
The detailed protocol of the RT-BOCDA is described in Fig. 4. First, we determine the length and the frequency range of the BGS image. We are trying to reconstruct the image in the area of ($L,\Omega$) and the pixel numbers $N$, as depicted in Fig. 4(I). The measurement length should be the shorter one among the sensing fiber length and pulse width. In the experiment, however, we assume that they are the same, $L=c\tau /n$. The pulse width $\tau$ should be long enough compared to $1/\Gamma$ for avoiding spectrum broadening. In our experiment, it does not fully meet the requirement because of the short length of the sensing fiber $L$. However, we can use the short pulses to some extent if there is no effect of the transient response [31]. Thereafter, we determine the angle range to measure. In our experiment, the angle range was limited to $30^\circ \leq \theta \leq 150^\circ$ due to the frequency range of our VCO (> 8 GHz) driving the SSBM, which can be significantly improved using other oscillators. From Figs. 4(II) and (III), the FM amplitude $\sigma _\theta$ and the probe frequency scan range $\Omega _\theta$ at each angle $\theta$ are determined, respectively, as follows:
The number of the pixels in the measured spectrum (1001 pixels in the following experiment) should be the same at each angle. The factor $\sqrt 2$ in Eq. (21) indicates the reduction of an inverse RT in its size. As illustrated in Fig. 4(III), this reduction can be understood by considering a square image inscribed in the blue circle through which all straight lines pass. By repeating the processes shown in Figs. 4(II) and 4(III), with changing the angle $\theta$, we can obtain the sinogram as shown in Fig. 4(IV). As depicted in Fig. 4(V), the spectrum measured at the angle $\theta$ is divided by $\sin \theta$. Finally, the original BGS image is reconstructed by performing an inverse RT, as depicted in Fig. 4(VI). We use a built-in function iradon in Matlab with a Ram-lak filter for the inverse RT.
The experimental results are shown in Fig. 5. Figure 5(a) shows the $1001\times 121$ image of the sinogram measured from an angle of $30^\circ$ to $150^\circ$ in the increment of $1^\circ$. The pixel on the ordinate corresponds to the distance $p$ in the direction normal to the straight line of the beat spectrum. The image range to be measured was set to $\Omega =1.575$ GHz, $L=10.3$ m. Thereafter, the FM amplitude and probe frequency scan range was determined using Eqs. (20) and (21). The tensile strain was applied to the 55-cm section near the center of the measurement fiber. The inverse RT image of Fig. 5(a) is shown in Fig. 5(b). This reconstructed $705\times 705$ image is in good agreement with the calculated results shown in Fig. 4. Figure 5(c) and 5(d) present the line profiles of Fig. 5(b) in the frequency and position axis direction (represented by the four arrows in Fig. 5(b)), respectively. The BGS of the strained position (blue curve) and the unstrained position (red dashed curve) are presented in Fig. 5(c). The reconstructed spectrum is approximately Lorentzian, which has no optical background spectrum seen in the conventional BOCDA [14]. We can see the frequency shift at the strained position in the blue curve, but the residual peak can also be seen at the zero frequency shift. The reason for this residual peak may be the nonzero linewidth of the laser (0.8 MHz in the datasheet) and its broadening effect owing to the shortened pulse. In Fig. 5(d), the spatial distributions at the frequency deviations of zero (yellow dashed curve) and 135 MHz (green curve) are presented. We estimated the actual BFS as 135.87$\pm$0.42 MHz from the measured spectrum at the angle of $90^\circ$ in Fig. 5(a), and it agrees well with the reconstructed image. The green curve indicates the successful detection of the 55-cm strained section, and its sum along with the yellow curve represents the square of the triangle function in Eq. (19), as predicted.
Fig. 5. Experimental results. (a) Measured sinogram and (b) reconstructed BGS distribution by applying the inverse RT to (a). (c) and (d) The line profiles of (b) at the positions represented by four arrows in (b).
4. Discussion and conclusion
We proposed a method to reconstruct the spatial distribution of a BGS from its RT, which is a type of optical CT. The line integrals of the BGS image were measured using the correlation-domain technique with a linearly frequency-swept laser at various FM amplitudes. To verify the concept, we conducted an experiment of distributed fiber sensing and succeeded in detecting a 55-cm strain section along a 10-m fiber. By applying the inverse RT to the measured sinogram, we obtained the intrinsic BGS distribution. Owing to the equivalence of the formulas [32], our method could be applied to the reflectometry using spontaneous Brillouin scattering as well [33]. We also expect our scheme can be applied to other optical sensing of spectrum data, such as FMCW ranging [29,30,34] and imaging [35–37]. The RT-BOCDA can realize a high signal-to-noise ratio (SNR) sensing at the cost of random accessibility and expand the possibilities of implementation of the correlation-domain technique for various beat spectra. Newly developed reconstruction methods such as compressed sensing will greatly improve its performance [8–10].
We summarize the features of the proposed RT-BOCDA compared to the conventional BOCDA as follows. (i) In principle, the output is an intrinsic BGS distribution and does not contain background optical noise. (ii) It is not required to scan the correlation peak position. (iii) Because the Brillouin interaction other than at the correlation peak position also contributes to the signal, there is no wastage of optical power. (iv) There is no random accessibility. (v) An inverse transform is required for the measurement signal.
We have not obtained a theoretical formula for the performance of RT-BOCDA, such as spatial resolution. Nonetheless, better spatial resolution can be achieved using a light source with a higher chirp rate $\sigma /\tau$ and narrower line width. The effectiveness of the RT-BOCDA can be demonstrated when measuring higher resolving points (ratio of the spatial resolution to the measurement range). The SNR of the correlation-domain method decreases in inverse proportion to this ratio, but the proposed method does not. Image resolution will determine the performance limits of this method, which is related to the controllability of the straight-line beat spectrum. An external cavity laser diode with a wider tunable range seems to be a suitable light source. By increasing the measurement length $L$ and pulse width $\tau$, the width of the straight line of the beat spectrum becomes narrower, and higher resolution sensing can be achieved. When the measurable range becomes longer than the coherence length of the light source, the spectrum width of the light source determines the width of the beat spectrum. Another performance limiting factor is the non-linearity of the frequency sweep [28,38].
Funding
Japan Society for the Promotion of Science (JP19K14999).
Acknowledgement
Youhei Okawa's present affiliation is Japan Aerospace Exploration Agency.
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.
References
1. S. R. Dean, The Radon Transform and Some of Its Applications (Dover, 2007).
2. T. Ilovitsh, A. Ilovitsh, J. Sheridan, and Z. Zalevsky, “Optical realization of the radon transform,” Opt. Express 22(26), 32301–32307 (2014). [CrossRef]
3. S. Dongfeng, H. Jian, M. Wenwen, Y. Kaixin, S. Baoqing, W. Yingjian, Y. Kee, X. Chenbo, L. Dong, and Z. Wenyue, “Radon single-pixel imaging with projective sampling,” Opt. Express 27(10), 14594–14609 (2019). [CrossRef]
4. B. Ferguson, S. Wang, D. Gray, D. Abbot, and X.-C. Zhang, “T-ray computed tomography,” Opt. Lett. 27(15), 1312–1314 (2002). [CrossRef]
5. S. D. Rawson, J. Maksimcuka, P. J. Withers, and S. H. Cartmell, “X-ray computed tomography in life sciences,” BMC Biol. 18(1), 21 (2020). [CrossRef]
6. J. H. Thomson, J. E. B. Ponsonby, and A. C. B. Lovell, “Two-dimensional aperture synthesis in lunar radar astronomy,” Proc. R. Soc. Lond. A 303(1475), 477–491 (1968). [CrossRef]
7. J. Radon, “Über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten,” Ber. Sächs. Akad. Wiss 69, 262–278 (1917).
8. K. Choi, J. Wang, L. Zhu, T.-S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order methoda),” Med. Phys. 37(9), 5113–5125 (2010). [CrossRef]
9. M. J. Willemink, P. A. de Jong, T. Leiner, L. M. de Heer, R. A. J. Nievelstein, R. P. J. Budde, and A. M. R. Schilham, “Iterative reconstruction techniques for computed tomography part 1: Technical principles,” Eur. Radiol. 23(6), 1623–1631 (2013). [CrossRef]
10. T. Würfl, M. Hoffmann, V. Christlein, K. Breininger, Y. Huang, M. Unberath, and A. K. Maier, “Deep learning computed tomography: Learning projection-domain weights from image domain in limited angle problems,” IEEE Trans. Med. Imaging 37(6), 1454–1463 (2018). [CrossRef]
11. A. H. Hartog, An Introduction to Distributed Optical Fibre Sensors (CRC, 2017).
12. P. Lu, N. Lalam, M. Badar, B. Liu, B. T. Chorpening, M. P. Buric, and P. R. Ohodnicki, “Distributed optical fiber sensing: Review and perspective,” Appl. Phys. Rev. 6(4), 041302 (2019). [CrossRef]
13. K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique–proposal, experiment and simulation–,” IEICE Trans. on Electron. E83-C, 405–412 (2000).
14. K. Hotate, “Brillouin optical correlation-domain technologies based on synthesis of optical coherence function as fiber optic nerve systems for structural health monitoring,” Appl. Sci. 9(1), 187 (2019). [CrossRef]
15. A. Denisov, M. A. Soto, and L. Thévenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light: Sci. Appl. 5(5), e16074 (2016). [CrossRef]
16. R. Cohen, Y. London, Y. Antman, and A. Zadok, “Brillouin optical correlation domain analysis with 4 millimeter resolution based on amplified spontaneous emission,” Opt. Express 22(10), 12070–12078 (2014). [CrossRef]
17. J. Zhang, M. Zhang, M. Zhang, Y. Liu, C. Feng, Y. Wang, and Y. Wang, “Chaotic Brillouin optical correlation-domain analysis,” Opt. Lett. 43(8), 1722–1725 (2018). [CrossRef]
18. A. Zarifi, B. Stiller, M. Merklein, Y. Liu, B. Morrison, A. Casas-Bedoya, G. Ren, T. G. Nguyen, K. Vu, D.-Y. Choi, A. Mitchell, S. J. Madden, and B. J. Eggleton, “Brillouin spectroscopy of a hybrid silicon-chalcogenide waveguide with geometrical variations,” Opt. Lett. 43(15), 3493–3496 (2018). [CrossRef]
19. Y. Okawa, R. K. Yamashita, M. Kishi, and K. Hotate, “Analysis of Brillouin dynamic grating localized by intensity-modulated correlation-domain technique for distributed fiber sensing,” Opt. Express 28(5), 6981–6994 (2020). [CrossRef]
20. Y. Okawa, R. K. Yamashita, M. Kishi, and K. Hotate, “Distributed measurement of Brillouin dynamic grating spectrum localized by an intensity-modulated correlation-domain technique,” Opt. Express 28(14), 21310–21317 (2020). [CrossRef]
21. K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Lett. 31(17), 2526–2528 (2006). [CrossRef]
22. D. Ba, Y. Li, J. Yan, X. Zhang, and Y. Dong, “Phase-coded Brillouin optical correlation domain analysis with 2-mm resolution based on phase-shift keying,” Opt. Express 27(25), 36197–36205 (2019). [CrossRef]
23. A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thevenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012). [CrossRef]
24. K. Hotate, H. Arai, and K. Y. Song, “Range-enlargement of simplified Brillouin optical correlation domain analysis based on a temporal gating scheme,” SICE J. Control. Meas. Syst. Integration 1(4), 271–274 (2008). [CrossRef]
25. Y. Mizuno, Z. He, and K. Hotate, “Measurement range enlargement in Brillouin optical correlation-domain reflectometry based on temporal gating scheme,” Opt. Express 17(11), 9040–9046 (2009). [CrossRef]
26. R. Shimizu, M. Kishi, and K. Hotate, “Enlargement of measurement function in Brillouin optical correlation domain reflectometry with combining four performance improvement schemes,” in 25th International Conference on Optical Fiber Sensors, vol. 10323Y. Chung, W. Jin, B. Lee, J. Canning, K. Nakamura, and L. Yuan, eds., International Society for Optics and Photonics (SPIE, 2017), pp. 1391–1394.
27. Y. Okawa and K. Hotate, “Distributed measurement of the Brillouin dynamic grating spectrum using the correlation-domain method with a fixed correlation peak position,” OSA Continuum 4(3), 990–999 (2021). [CrossRef]
28. X. Zhang, J. Pouls, and M. C. Wu, “Laser frequency sweep linearization by iterative learning pre-distortion for FMCW LiDAR,” Opt. Express 27(7), 9965–9974 (2019). [CrossRef]
29. X. Lou, Y. Feng, C. Chen, and Y. Dong, “Multi-point spectroscopic gas sensing based on coherent FMCW interferometry,” Opt. Express 28(6), 9014–9026 (2020). [CrossRef]
30. Z. Li, Z. Zang, Y. Han, L. Wu, and H. Y. Fu, “Solid-state FMCW LiDAR with two-dimensional spectral scanning using a virtually imaged phased array,” Opt. Express 29(11), 16547–16562 (2021). [CrossRef]
31. E. Preter, D. Ba, Y. London, O. Shlomi, Y. Antman, and A. Zadok, “High-resolution brillouin optical correlation domain analysis with no spectral scanning,” Opt. Express 24(24), 27253–27267 (2016). [CrossRef]
32. Y. Okawa and K. Hotate, “Brillouin optical correlation-domain reflectometry theory using stochastic representation of spontaneous brillouin scattering light,” J. Opt. Soc. Am. B 37(7), 2157–2162 (2020). [CrossRef]
33. Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express 16(16), 12148–12153 (2008). [CrossRef]
34. J. Riemensberger, A. Lukashchuk, M. Karpov, W. Weng, E. Lucas, J. Liu, and T. J. Kippenberg, “Massively parallel coherent laser ranging using a soliton microcomb,” Nature 581(7807), 164–170 (2020). [CrossRef]
35. R. Prevedel, A. Diz-Muñoz, G. Ruocco, and G. Antonacci, “Brillouin microscopy: an emerging tool for mechanobiology,” Nat. Methods 16(10), 969–977 (2019). [CrossRef]
36. S. H. Kassani, M. Villiger, N. Uribe-Patarroyo, C. Jun, R. Khazaeinezhad, N. Lippok, and B. E. Bouma, “Extended bandwidth wavelength swept laser source for high resolution optical frequency domain imaging,” Opt. Express 25(7), 8255–8266 (2017). [CrossRef]
37. J. P. Kolb, T. Pfeiffer, M. Eibl, H. Hakert, and R. Huber, “High-resolution retinal swept source optical coherence tomography with an ultra-wideband Fourier-domain mode-locked laser at MHz A-scan rates,” Biomed. Opt. Express 9(1), 120–130 (2018). [CrossRef]
38. P. A. Roos, R. R. Reibel, T. Berg, B. Kaylor, Z. W. Barber, and W. R. Babbitt, “Ultrabroadband optical chirp linearization for precision metrology applications,” Opt. Lett. 34(23), 3692–3694 (2009). [CrossRef]
