Brillouin frequency shift measurement by zero-crossing point search in virtually synthesized spectra of Brillouin gain and loss

We demonstrate a method for fast and precise Brillouin frequency shift measurement based on searching for the zero-crossing point of a virtually composed spectrum of Brillouin gain and loss obtained by a dual-frequency probe beam. Simulations and experiments show that searching for the zero-crossing point of a virtually synthesized Brillouin gain spectrum can be easily done without a large error compared with peak search of the Brillouin gain spectrum in the conventional method.


D
][6] Among various types of Brillouin fiber optic sensing, which include time-, [7][8][9] frequency- 10) and correlation-domain 11,12) methods, Brillouin optical time-domain analysis (BOTDA) is an effective technique that can achieve both a high signal-to-noise ratio (SNR) and long-distance measurement.BOTDA uses stimulated Brillouin scattering (SBS) 13) induced in an optical fiber and monitors the frequency change of the BGS in the time domain. Conentional BOTDA systems measure the frequency change of the Brillouin frequency shift (BFS), i.e. the frequency difference between the BGS and the incident pump light, by directly measuring the BGS. 14,15)The BGS is measured by sweeping the probe light frequency around the gain peak and curve fitting the data of the probe light power, which is amplified by the SBS process as a function of swept frequency.
Efforts to reduce measurement time have been made in BOTDA research.One effective method is optical chirp chain (OCC) BOTDA, which uses frequency chirped probe light to reduce the time required for probe frequency sweeping. 16)nother method uses a multiple-frequency probe or pump to acquire BGS simultaneously. 17,18)A multiple-frequency probe and pump can also be used for controlling the BFS measurement sensitivity. 19)Another technique achieves short-time measurement by using the Brillouin gain ratio measured at both the upper and lower side slopes of two different BGS induced by two pump lights with different wavelengths. 20)Slope-assisted BOTDA (SA-BOTDA) is another effective technique for reducing the measurement time. 21)SA-BOTDA fixes the frequency of the probe light and measures the power of the probe light amplified through SBS.Because a one-to-one relationship must be satisfied between the amplified probe power and the BFS, SA-BOTDA needs to set the probe frequency on one side of the BGS.That generally limits the measurable BFS to less than around half the linewidth of the BGS.It has been suggested that multislope-assisted BOTDA can extend the linear slope region, where a dual-frequency probe and a singlefrequency pump are used. 22)Recently, we have successfully extended the measurable BFS by using the virtually synthesized Brillouin gain spectrum (VBGS) that is generated by multiple BGS 23) or by a simultaneously generated pair of BGS and the Brillouin loss spectrum (BLS), 24,25) where the synthesized VBGS has also a linear slope region.On the other hand, optical power fluctuation directly leads to measurement error in SA-BOTDA.
Regarding the error in BFS measurements, Lorentzian curve fitting (LCF) of the BGS is a reliable method in conventional BOTDA.Higher measurement accuracy in BFS estimation has been achieved by gain spectrum engineering based on superposition of the BGS and two BLS. 26)It is also reported that more accurate estimation of the BFS is possible using a crosscorrelation technique. 27)Other research shows that frequency accuracy is improved by narrowing the BGS. 28)Most techniques for BFS measurement do not interfere with methods for reducing BGS scan time.Therefore, it is even better if we can reduce the time for deriving the BFS from the measurement data.In this paper, we propose a fast, precise and simple BFS measurement technique for BOTDA based on zero-crossing point search (ZCPS) in a VBGS that comprises a BGS and BLS.Simulations and experimental results show that searching for the zero-crossing point of a VBGS can be achieved with smaller error than peak search of the BGS in the conventional method.
Figure 1 summarizes the generation of a VBGS based on simultaneous sweeping of BGS and BLS with dual-frequency probe light.In the proposed BOTDA system, the same light source is used for producing pump and probe light.The dualfrequency probe light is generated by slightly shifting the frequency of the laser light by Δν and applying intensity modulation in such a way that two sideband components are produced while suppressing the carrier component.This can be achieved by a lithium niobate (LN) Mach-Zehnder (MZ) intensity modulator (IM).By setting the operating point of modulation at the point where the optical output power is minimized, the carrier component is suppressed.The LN MZ IM typically has an extinction ratio of around 20 dB, which is sufficient to prevent the carrier component from inducing SBS.
By sweeping the modulation frequency n D , m the BGS and BLS are simultaneously swept by each frequency component of the probe light.The VBGS is obtained as a function of modulation frequency as follows: where n D B is the full width at half maximum of the BGS, n D BFS is the Brillouin frequency shift and g 0 is the peak gain of the spectrum.Because Compared with the conventional approach of nonlinear curve fitting for the BGS, the proposed method reduces computation time.
We conducted simulations to evaluate the accuracy of the proposed BFS measurement.Figure 2 shows the RMS error (RMSE) of the estimated BFS as a function of the SNR.Considering that each frequency component of the dualfrequency probe experiences the actual Brillouin gain or loss, we define the SNR of the VBGS by the ratio of the sum of the absolute values of the BGS and BLS peaks to the noise.Because the variation in n D changes the shape of the VBGS according to Eq. ( 1), the slope of the VBGS around the zerocrossing point also changes with n D .Therefore, the effect of the same amount of noise, and thus the BFS estimation error, can be different depending on n D , even if the SNR is the same.In the simulations, data with noise were generated and acquired with a step of 0.5 MHz for a frequency range that covers the entire VBGS.The BGS bandwidth, n D , B was also set to be randomly changed between 50 and 55 MHz.We also generated the BGS data under the same condition and evaluated the RMSE of the BFS that was derived from peak search of the BGS.We can see that the RMSE of the BFS is smaller in the method based on searching for the zerocrossing point of the VBGS than searching for the BGS peak for all the conditions considered, as long as the SNR is less than 50 dB.
Figure 3 shows the experimental setup of the proposed BOTDA with ZCPS of the VBGS.The light from a laser diode with a wavelength of 1550 nm is divided into pump and probe branches.In the pump branch, an IM is used to generate pulsed light with a period of 300 ns.The pulse width  ∆ ∆ 10.794, respectively.Both methods show the same results, while the time to obtain BFS from one spectrum is 0.22 ms for ZCPS whereas it is 63 ms for LCF.Considering that LCF is one of the most reliable BFS measurement methods, ZCPS is an effective method for shortening the measurement time.The CPU of the personal computer used for data processing was an AMD Ryzen 7 5800U with Radeon graphics.
Finally, we also evaluated the noise of the VBGS. Figure 5(a) shows an example of a VBGS normalized by the peak value of a single BGS.m The standard deviation of the right-hand or left-hand slope region for the VBGS is almost the same as that of the slope region for a single BGS or BLS.The central portion in the linear slope region of the VBGS is less noisy than the outside region of the spectrum.This phenomenon may be related to the fact that BGS and BLS are generated from the same pump light, and some noise is correlated and canceled by synthesizing the spectrum.Despite the need for further investigation, this feature is highly beneficial for the ZCPS method.
In summary, we have proposed a technique for accurately and quickly measuring the BFS by combining a BGS and a BLS to generate a VBGS and identifying the zero-crossing point.The measurement error and speed of the proposed method have been evaluated by simulations and experiments.The proposed technique can contribute to real-time distributed fiber optic sensing systems.On the other hand, since the proposed system uses dual-frequency probe light, a higher total optical power is required for the probe light compared with conventional BOTDA.The amplification by an erbium-  052003-3 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd doped fiber amplifier in our experiment may have increased the noise.However, the effect of the noise on the long-term stability of the measurement is expected to be suppressed due to the small fluctuations of the zero-crossing point and the point symmetry shape of the VBGS around the zero-crossing point.The next phase of this research will be to investigate the consistency with improvement in the spatial resolution, which is typically achieved by shaping pump pulses.Although some techniques may have little effect on the shape of the BGS in principle, 29,30) it is necessary to re-examine their effect on the BGS and the BLS for our BFS measurement methods.
zero if Dn = 0, m we can measure the BFS by finding the zero-crossing point of the VBGS instead of searching for the peak point of the BGS.The frequency of the zero-crossing point f zero of the VBGS is derived from a linear regression analysis within the range between the frequencies that give the maximum and minimum values, g max and g , min of the VBGS [Fig.1(b)].From the estimated value of the linear slope a VBGS and the intercept b VBGS in the mathematical expression of the linearly approximated VBGS in the vicinity of the zero-crossing point, we obtain
Figure 4(c) shows the temperature dependence of the BFS measured by the ZCPS and LCF methods, which are n = Figure 5(b) shows the standard deviation around the mean value after 50 measurements as a function of modulation frequency n .

Fig. 4 .
Fig. 4. BFS distribution measured by (a) zero-crossing point search (ZCPS) of the VBGS and (b) Lorentz curve fitting (LCF) of the BGS.(c) Temperature dependence of Brillouin frequency shift measured by ZCPS and LCF at 10 m from the end of the fiber under test.

Fig. 5 . 4 ©
Fig. 5. (a) VBGS at 5 m from the end of the fiber under test.(b) The standard deviation around the mean value after 50 measurements.