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We report on a high-resolution static strain sensor developed with distributed feedback (DFB) fiber laser. A reference FBG resonator is used for temperature compensation. Locking another independent fiber laser to the resonator using the Pound-Drever-Hall technique results in a strain power spectral density better than Sε(f) = (4.6 × 10−21) ε2/Hz in the frequency range from 1 Hz to 1 kHz, corresponding to a minimum dynamic strain resolution of 67.8 pε/√Hz. This frequency stabilized fiber laser is proposed to interrogate the sensing DFB fiber laser by the beat frequency principle. As a reasonable DFB fiber laser setup is realized, a narrow beat frequency line-width of 3.23 kHz and a high beat frequency stability of 0.036 MHz in 15 minutes are obtained in the laboratory test, corresponding to a minimum static strain resolution of 270 pε. This is the first time that a sub-0.5 nε level for static strain measurement using DFB fiber laser is demonstrated.
© 2016 Optical Society of America
1. Introduction
Recently, high-resolution fiber Bragg grating (FBG) quasi-static strain sensor and static strain sensor have received considerable research interests in the field of optical fiber sensing and earthquake monitoring. For FBG quasi-static strain measurement, a frequency-locked laser and an absolute frequency referencing have been typically used to improve the strain measurement resolution. In 1999, Ady Arie used a stabilized laser source to measure low frequency strain with a sensitivity of 1.2 nε/√Hz at 1.5 Hz [1]. In 2008, Jong H. Chow et al used radio-frequency modulation interferometry and absolute frequency referencing for FBG quasi-static strain measurement, demonstrating a few tens of pε/√Hz sensitivity between 1 – 6 Hz [2]. In 2010, Timothy T.-Y. Lam et al present a quasi-static fiber optic strain sensing system capable of resolving signals below nanostrain from 20 mHz, using an H13C14N absorption line as a frequency reference to extract accurate low-frequency strain signals from the locked system [3]. In particular, G. Gagliardi et al report on strain measurements at the 0.1 pε/√Hz level from 100 mHz using a FBG resonator with a diode-laser source stabilized against a quartz-disciplined optical frequency comb [4]. Thanks to the capability of real-time, in situ, sensitive strain measurement with low cost, small size, fast response and immunity to electromagnetic interference, FBG may have a foreseeable application prospect in low-frequency seismic monitoring using above FBG quasi-static strain measurement technique [4–6]. However the above methods can’t be used for the field of static strain measurement, such as earth crust deformation observation.
High-resolution FBG static strain measurement is developed on the basis of quasi-static strain sensing. In order to achieve the static strain measurement, the environmental temperature and the ultra-low frequency noise of the system must be accurately compensated. A reference FBG is usually proposed to deal with this problem. Since 2010, Qingwen Liu et al used a narrow line-width tunable laser and two FBGs or FBG-FPs for static strain measurement, achieving an nε-resolution level [7–9]. In our previous works, we have proposed a π-FBG sensor head, cross-correlation method in wavelet domain and swept optical SSB-SC modulation technique for further improving static-strain measurement resolution [10–12]. But the static-strain resolution of these systems is around nε and one of the main limit factors on resolution is the line-width of FBG, FBG-FP, or π-FBG, although the line-width of FBG sensing system can be reduced by increasing the length of the resonator. For example, a π-FBG based fiber ring resonator is used [13]. The line-width of FBG sensing system is difficult to reach at 100 kHz and higher-resolution static-strain demodulation is limited.
Compared with traditional passive FBG sensing technique, active fiber laser has the advantage of ultra-narrow line-width [14, 15]. It can reach an ultra-high sensitivity for weak signals detection with high-resolution phase demodulation [15–18] and beat frequency demodulation technique [19, 20]. A dynamic (>2 kHz) and low-frequency (around 2 Hz) strain resolution better than pε have been achieved when using fiber laser as a sensor head [14, 15]. And we have done a lot of work about phase demodulation for DFB FL sensor [15]. However, the static strain measurement using fiber laser has not been reported up to now [21]. In this paper, we report on a high-resolution static strain sensor developed with DFB fiber laser (DFB FL). In our configuration, DFB FL consists of a length of Er3+-doped fiber with Bragg grating by introducing a π phase shift and is pumped with a 980 nm semiconductor laser. A reference FBG resonator is used for temperature compensation. Locking a commercial PZT-tunable fiber laser (NKT, line-width 100 Hz) to the resonator using Pound-Drever-Hall (PDH) technique. Then this frequency stabilized fiber laser is proposed to interrogate the sensing DFB fiber laser by beat frequency principle. As a reasonable DFB fiber laser setup is realized, a narrow beat frequency line-width of 3.2 kHz and a high beat frequency stability of 0.036 MHz in 15 minutes are obtained in the laboratory test, corresponding to a minimum static strain resolution of 270 pε. This is the first time that a sub-0.5 nε level for static strain measurement using DFB fiber laser is demonstrated.
2. Distributed feedback (DFB) fiber laser setup
DFB Fiber laser consists of a length of Er3+-doped or Yb3+/Er3+-codoped fiber with Bragg gratings. In order to operate in single mode, a short cavity with narrow-bandwidth FBG is required to effectively limit the spectrum therein allowing only a single dominant mode to be supported. In our configuration, a phase-shifted grating is formed into a length of Er3+ fiber, whose ends are spliced to a matching passive fiber for reducing splice loss. For a strong fiber grating with the reflection bandwidth of 0.2 nm, the effective length should be less than 4 mm for single mode operation, which requires the length between FBGs to be much shorter. The wavelength of DFB fiber laser is determined by the central wavelength in the reflective spectrum of phase-shifted grating, shown as
Where λB is the lasing wavelength, Λ is the period of grating, and neff is the effective index of fiber core. The period Λ and the effective reflective index neff are changed with the environmental conditions, such as strain, temperature, and acoustic wave.In the past 10 years, DFB fiber laser has attracted considerable research interests for wavelength demodulation, because it has the advantages of ultra-narrow line-width which will result in a low equivalent noise level. In our configuration, the picture of DFB fiber laser is shown in Fig. 1(c). The laser full-width half-maximum (FWHM) line-width was measured by using self-heterodyne method with a 25 km long delay fiber and a fiber coupled acousto-optic modulator (55 MHz). For the usual case of Lorentzian-shaped spectrum, the measured full-width at half-maximum (FWHM) line-width is about 3 kHz shown in Fig. 1(b) [15]. In order to get the beat frequency line-width and frequency stability between the proposed DFB fiber laser and the commercial PZT-tunable fiber laser (NKT, line-width 100 Hz), the test principle of beat frequency line-width and frequency stability of the DFB FL is found shown in Fig. 1(a). The active fiber Bragg grating is pumped with a 980 nm semiconductor laser by a wavelength division multiplex (WDM). The reflected light power from the DFB fiber laser is monitored by a spectrometer and beat with the NKT fiber laser around 1550 nm by a coupler and a high-speed photodiode. Then the oscilloscope can record the beat frequency line-width and frequency stability. Here, a NI FlexRIO boared (NI 7966R FPGA module and NI 5772 A/D board) and LabVIEW software are used to construct the oscilloscope. The sampling of NI 5772 is set to 50 MHz and the data length for line-width calculation is 0.01 s (correspond to 500000 sampling points). According to Nyquist Functions, the frequency resolution of the oscilloscope is 50 Hz.
Fig. 1 The DFB fiber laser step: (a) tests of beat frequency line-width and frequency stability, (b) the line-width of DFB fiber laser, (c) the picture of DFB fiber laser. WDM, wavelength division multiplex; CP, coupler; PD, photodiode.
The measured beat frequency line-width between DFB fiber laser and the NKT fiber laser is 3.23 kHz shown in Fig. 2 illustrating that the line-width of photocurrent is about the sum of those of two independent lasers. This beat signal can be used to record the frequency drift of the DFB fiber laser if the NKT fiber laser is stabilized. Considering that the sensitivity of the DFB fiber laser is about 0.78 με/pm, the strain resolution may reach better than 21 pε which is superior to the previous interrogation scheme based on traditional passive FBG, FBG-FP and π-FBG [7–12].
In fact, we can’t estimate the static wavelength/strain resolution only by the line-width of the beat frequency signal in the actual measurement, because the beat frequency signal is unstable. The beat frequency stability is seriously affected by the unstable pump power and the thermal environment [22]. In order to quantitatively evaluate the beat frequency stability and its relationship with the drift of pump power, we place two same-parameter DFB fiber lasers in the air and water environment respectively for simultaneous measurement. The two DFB fiber lasers are pumped by the same pump with a power stability of 1 mW @ 30 minute. In Figs. 3(a) and 3(b), the black lines are frequency drifts of the beat frequency signals when the DFB fiber laser is in the air and water respectively. Because the time is very short, we can suppose that the temperature effect on the frequency drifts of the beat frequency signals is very small. The frequency drifts of the two beats have the same trend and amplitude. As the same drift trend is so slow and the amplitude is about 10 MHz, we can easily judge that the big frequency drift is caused by the NKT fiber laser. Then we can get the frequency stability of the DFB fiber laser through signal processing (using multi-scale wavelet analysis method to eliminate the low-frequency oscillation frequency drift). The frequency stability of the DFB fiber laser is contained in the noise levels (red lines) respectively shown in Figs. 3(a) and 3(b). We can find that the frequency stability is about 1 MHz in one minute when the DFB fiber laser is in the air. But the frequency stability is better than 0.1 MHz when the DFB fiber laser is in the water. This suggests that water environment is helpful to improve the frequency stability of the DFB fiber laser because water is good for dissipation of the heat caused by the unstable pump. Shown in Fig. 3(c), we test the beat frequency using different pump power when the DFB fiber laser is in the air and water. The sensitivity of frequency drift against the pump power when the DFB fiber laser is in the air and water is about 1.90 MHz/mW and 0.13 MHz/mW.
Fig. 3 The beat frequency stability and its relationship with the drift of pump power: (a) and (b) the black lines are frequency drifts of the beat frequency signals when the DFB fiber laser is in the air and water respectively, the red lines are frequency noise level getting rid of the large and slow frequency fluctuation of NKT fiber laser, (c) the sensitivity of frequency drift against the pump power when the DFB fiber laser is in the air and water.
So a stable pump and a good thermal environment are the necessary conditions for high-resolution static wavelength/strain measurement using DFB fiber laser. It has a great guiding significance for the design of the follow interrogation system. Besides, the amplitude of the slow frequency drift and the fast frequency shake of the NKT fiber laser should also be limited. The system configuration and results are given in the next section.
3. Static strain interrogation based on a reference FBG resonator
The schematic principle and configuration of the DFB fiber laser static strain interrogation system is shown in Fig. 4. Here, a reference FBG resonator (π-phase-shifted-FBG) is used for temperature compensation. In order to maintain the same temperature sensitivity, the π-FBG is designed using the same parameters with the DFB fiber laser. At first, we lock the NKT fiber laser to the π-FBG using typical PDH technique. Then the wavelength of the NKT fiber laser is changed by the center wavelength of the π-FBG. Secondly, the DFB fiber laser is placed in the water and pumped by a high-stability 980 nm. The beat frequency signal between the locked NKT fiber laser and the DFB fiber laser is acquired by a high-speed analog to digital (A/D) board through a coupler and a high-speed photodiode. The polarization controllers are used to make the polarization state consistent between the two lasers before beating. So we can get the information of static strain when the locked NKT fiber laser beats with the sensing DFB fiber laser, because the perturbation of temperature and the frequency drift of the NKT fiber laser can be compensated accurately. In this manuscript, we select a pair of DFB FL and π-FBG whose wavelength difference is smaller than 1 pm (125 MHz). The bandwidth of the photodiode is 1 GHz. The sampling rate of the A/D board is set as 400 MS/s.
Fig. 4 The schematic principle and configuration of the DFB fiber laser static strain interrogation system. WDM, wavelength division multiplex; CP, coupler; CIR, circulator; PC, polarization controller; PD, photodiode; ISO, isolator; FG, function generator; PM, phase modulator; VA, voltage amplifier.
In order to make the system more practical, we generally use FBG Fabry-Perot cavity (FBG-FP) instead of the reference π-FBG. The free spectral range of the FBG-FP is design to be 2 pm (250 MHz). So the beat frequency between the DFB FL and the NKT locked on the reference FBG-FP is easily smaller than 250 MHz. Then the limiting condition of the bandwidth of the photodiode and the sampling rate of the A/D board is relaxed. Besides, Locking the NKT fiber laser to a passive FBG resonator which is packaged in a quiet environment, we can make the NKT fiber laser maintain high frequency stability. This is beneficial to improve the frequency stability (the measurement resolution of static strain) of the beat frequency signal when the locked NKT fiber laser is used to interrogate the sensing DFB FL.
In experiments, the sensing active DFB fiber laser and the reference passive π-FBG are packaged in a sealed box with water and the box is hanging on the spring to suppress the low-frequency vibration for reducing the influence of the external environment. A 10-cm thick stainless steel vacuum tank is used to suppress environmental noise interference and maintain a relatively constant temperature. We put the stainless steel vacuum tank in the 5 meter deep basement, where the environment is quiet and the temperature is relatively constant. The interrogation system is put in the monitoring laboratory. The sensors are connected to the interrogation system by a 100 m long armored optical cable. Now, the ultimate static strain resolution of the above system is mainly decided by two factors. One is the frequency stability of the NKT fiber laser which is locked on the reference π-FBG. In other words, it is the level of the strain power spectral density. Another is the frequency stability of the DFB fiber laser and the compensation precision of temperature and the frequency drift of the locked NKT fiber laser. To begin with, we learn the frequency stability of the locked NKT fiber laser (the level of the strain power spectral density). As the relative deviation of the Bragg wavelength (frequency) is related to the applied strain ε, the power spectral density of the applied strain is therefore give by [23]
where νB is the fiber Bragg resonance wavelength (frequency), ΔνB = KενB is the Bragg wavelength (frequency) deviation induced by the applied strain, K ≈0.78 is a constant related to the Poisson’s ratio and Pockels coefficients of the photo-elastic tensor of the fiber glass, SV(f) is the power spectral density of the error signal, D is the voltage to frequency conversion coefficient, and SΔV(f) = SV(f)/D2 is the power spectral density of the frequency fluctuations between the laser and the FBG resonance frequencies.Shown in Fig. 5, we get a result at a strain power spectral density better than Sε(f) = (4.6 × 10−21) ε2/Hz in the frequency range from 1 Hz to 1 kHz, corresponding to a minimum dynamic strain resolution of 67.8 pε/√Hz, which suggests that the ultimate static strain resolution is around 67.8 pε if environmental temperature and the frequency noise of the system are accurately controlled.
In order to accurately compensate temperature and the frequency drift of the locked NKT fiber laser, the speed of beat frequency interrogation should be faster than 1 Hz. In experiments, the interrogation speed is set to 10 Hz. Figure 6(a) reports the measured results of the static strain by beat with the locked laser to the sensing DFB fiber laser. A high beat frequency stability of 0.036 MHz (standard deviation) in 15 minutes is obtained corresponding to a minimum static strain resolution of 270 pε. In order to validate of strain detecting ability, a nano-strain signal is applied on the fiber laser sensor. The sen. DFB FL is fixed on a manual stage and a Piezo stage (PI, P-841). The adhesive bond length of the fiber including active region is accurate 10 cm. 1 nm displacement (correspond to 10 nε) by the Piezo stage is applied on the DFB FL. The result is shown in Fig. 6(b). Considering 1.21 pm/με (151.3 MHz/με) sensitivity, we can find that 1.513 MHz (correspond to 10-nε) square signal is recorded with high signal to noise ratio (> 20 dB), which implies that the proposed DFB FL static strain sensing system has the ability for nano-strain static signal measurement.
Fig. 6 The measured results of the static strain: (a) the sensing DFB fiber laser and the reference π-FBG are packaged in a sealed box, (b) a 10-nε square signal is applied on the sensing DFB fiber laser.
From Fig. 5 and Fig. 6, we can find that the ultimate static strain resolution is bigger than the strain power spectral density when the NKT fiber laser is locked to the reference π-FBG. This is because the amplitude of the frequency drift of the DFB fiber laser has a greater influence than the locked NKT fiber laser. A more stable pump and a more suitable cooling package for DFB fiber laser may help improve the demodulation resolution in the future work. In addition, the level of the pump power in Er3+-doped fiber lasers can be significantly decreased by using a high gain Yb3+/Er3+-codoped fiber laser due to the increased effective pump rate [24]. A lower frequency fluctuations caused by the instability of pump power can be reached and a higher beat frequency stability can be obtained when the Yb3+/Er3+-codoped fiber laser is used for strain sensing. This implied that a novel method for higher-resolution static strain measurement can be developed by use of ultra-narrow line-width fiber laser.
4. Conclusions
A high-resolution DFB fiber laser static strain sensor is proposed. A reasonable DFB fiber laser is introduced in detail. As the beat frequency signal has an advantage of ultra-narrow line-width and the reference laser is stabilized using PDH technique and a reference FBG resonator, a high beat frequency stability of 0.036 MHz in 15 minutes are obtained in the laboratory test, corresponding to a minimum static strain resolution of 270 pε. Higher demodulation resolution is also discussed in the future work. This is the first time that a sub-0.5 nε level for static strain measurement using DFB fiber laser is demonstrated, which suggest that the DFB fiber laser may have a good application prospect in static strain measurement such as earth crust deformation observation.
Acknowledgments
This work was supported in part by the 863 Program of China (2014AA093406), Youth Innovation Promotion Association CAS (2016106), and Key Instrument Developing Project of the Chinese Academy of Sciences (No. ZDYZ2012-1-08-03).
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