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Abstract
An FBG sensor interrogated by an optical carrier microwave interferometry (OCMI)-based three-arm Mach-Zehnder interferometer (MZI) is proposed and experimentally demonstrated. In our sensing scheme, the interferogram generated by interfering the three-arm-MZI middle arm with the sensing arm and the reference arm respectively is superimposed to produce a Vernier effect to increase the sensitivity of the system. The simultaneous interrogation of the sensing fiber Bragg grating (FBG) and the reference FBG by the OCMI-based three-arm-MZI provides an ideal solution to the cross-sensitivity problems (e.g. temperature vs. strain) associated with conventional sensors that produce the Vernier effect by cascading optical elements. Experimental results show that when applied to strain sensing, the OCMI-three-arm-MZI based FBG sensor is 17.5 times more sensitive compared to the two-arm interferometer based FBG sensor. And the temperature sensitivity is reduced from 371.858 KHz/°C to 1.455 KHz/°C. The prominent advantages of the sensor, including high resolution, high sensitivity, and low cross-sensitivity, make it a great potential for high-precision health monitoring in extreme environments.
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1. Introduction
Optical fiber sensors have attracted much attention due to their small size, light weight, resistance to electromagnetic interference, chemical resistance, and high-temperature survivability [1,2]. Among the various types of optical fiber sensors, FBGs are widely used for structural health monitoring (SHM) because of their simple structure, inherent sensing element, inherent self-reference, and easy multiplexing capability [3]. In order to monitor the health of structures such as buildings, pipelines, and aircraft, FBG sensors should ideally have the combined characteristics of high sensitivity and high resolution. The operation of the FBG sensor is based on the principle of detecting wavelength shifts in resonant wavelengths caused by the action of an external stimulus [4]. The resolution and speed of FBG sensors that are demodulated by scanning the central wavelength of the reflectance spectrum are limited by the measurement equipment [5].
In recent years, many microwave photonics (MWP) interrogation methods have been proposed and demonstrated for FBG sensing [6–9]. As a result of combining the advantages of both optics and microwaves, MWP-based FBG sensing systems have improved both speed and resolution [10]. Among the many MWP-based interrogation methods, one of the concepts called OCMI has gained attention due to its characteristics in terms of its sensing applications [11]. These characteristics include structural simplicity, insensitivity to variation in the polarization of the probing light, signal-to-noise ratio, and streak visibility [12]. These advantages also make OCMI-based interferometers ideal for interrogating FBG sensors.
The Vernier effect has been demonstrated to be one of the most effective methods of improving the measurement sensitivity of fiber optic sensors [13,14]. The construction of the Vernier effect in an OCMI system normally requires the cascading of two optical fiber interferometers (OFIs) with slightly different optical path differences (OPDs) [13]. The interrogation principle based on the Vernier effect is by tracking the envelope of the amplitude-modulated spectrum resulting from the superposition of the spectra of the two cascaded OFIs [15]. Due to the Vernier effect, the shift produced by the envelope in the output spectrum of two cascaded OFIs is greater than the spectral shift of a single OFI when subjected to the same external stimulus [16,17]. Note that as optical fiber sensors are sensitive to multiple parameters, an OCMI system based on cascading two OFIs to produce a Vernier effect does not avoid OPD caused by interfering parameters. Therefore an OCMI based on cascading two OFIs to produce a Vernier effect increases the sensitivity of the system while amplifying errors caused by interfering parameters. This greatly limits the application scenarios for such FBG sensors.
In this paper, an FBG sensor interrogated by OCMI-based three-arm-MZI is proposed to solve the cross-sensitivity problem when applying the Vernier effect to improve measurement sensitivity in OCMI systems and is applied to strain sensing for experimental validation. The Vernier effect is created by superimposing the interferograms produced by interfering the middle arm of three-arm-MZI with the sensing arm and the reference arm respectively. The sensitivity of the system to strain can be significantly improved by tracking the frequency shift of the dip frequency of the envelope signal of the superimposed spectrum. The OPD caused by temperature is compensated by simultaneous interrogation of the sensing FBG and the reference FBG through OCMI-three-arm-MZI, thus achieving insensitivity to temperature. To the best of our knowledge, this is the first demonstration of an FBG sensor interrogated by OCMI-three-arm-MZI. This effectively solves the problem of cross-sensitivity for the OCMI sensing systems based on the Vernier effect.
2. Principle
A conceptual diagram of the proposed system is shown in Fig. 1. The light from a light source is reflected by a sensing head consisting of two cascaded FBGs with resonance wavelengths of λFBG1 and λFBG2 respectively. The reflected light is intensity-modulated by the microwave signal from the vector network analyzer (VNA) in the modulator and then fed into the three-arm-MZI consisting of a wavelength division multiplexer (WDM) and an optical coupler (OC). WDM1 and OC1 split the light into three paths based on wavelength. Each of the three optical paths passes through three CFBGs with different pigtail fiber lengths. The three CFBGs act as dispersion elements in the three-arm-MZI, converting the wavelength shift into a change of OPD. The three pigtail fiber with different lengths are intended to make the initial optical paths of the three arms of the three-arm-MZI different, and in this way make the initial FSRs of the reference MZI and the sensing MZI slightly different, thereby generating a Vernier effect. These three optical paths are combined by OC2 and WDM2 and the total optical signal is then routed to a photodetector for photoconversion. The electrical signal is finally sent to the VNA. The signal S21 measured by the VNA can be expressed as
where f is the frequency; t is the time term; Φeff denotes the phase of the microwave signal; Aeff is the magnitude of the microwave signal and can be described asThe optical signals in the three arms of the three-arm-MZI interfere with each other and the resulting interferograms are superimposed on each other, thus creating the Vernier effect in the frequency response of the system. The free spectral range (FSRen) of the envelope signal can be given by
When strain sensing is performed under the disturbance of temperature, the resonance wavelengths of the reference FBG (FBG1) and sensing FBG (FBG2) are shifted, and dispersion is introduced by the CFBG on the three arms of three-arm-MZI, which translate the wavelength shifts of FBG1 and FBG2 caused by temperature and strain into different time delays of the optical signals on each of the three arms, ultimately leading to FSR changes. Equations (4) and (5) give the time delay caused by temperature (°C) and strain (με) respectively.
Comparing Eqs. (6) and (8) it can be seen that when the temperature is changed by 60°C and the difference between λFBG1 and λFBG2 is 5 nm, the OPD generated is only about the OPD generated by applying 1.85με. It can therefore be assumed that the change in FSR is determined by the strain only and its value can be deduced as
According to Eq. (7), the shift of the dip frequency of the envelope signal caused by the strain can be expressed as
Under the same strain, thanks to the Vernier effect, compared with the interferogram produced by the MZI consisting of the intermediate arm and the sensing arm, the frequency shift of the envelope is amplified by
3. Experiment
To further verify the feasibility of the proposed sensing scheme, experiments are carried out based on the setup shown in Fig. 2. The broadband optical source (BOS, OPEAK, LSM-ASE-C) covers the spectral range 1530-1560 nm and has an output power of 15 dBm. The two cascaded FBGs both have a bandwidth of 0.2 nm and resonance wavelengths of 1560 nm (FBG1) and 1555 nm (FBG2) respectively. The coherence lengths of the light reflected by the two FBGs are ∼0.0121 m and 0.012 m respectively. The Mach-Zehnder modulator (MZM, Photline, MX-LN-20) has a bandwidth of 20 G and a half-wave voltage of 5.5 V. The lengths of the reference, middle, and sensing arms of the three-arm-MZI consisting of WDM and OC are set to 3 m, 10.405 m, and 17.397 m respectively. The difference in length between the three arms is much greater than the coherence length of the reflected light and much less than the coherence length of the microwaves (∼1500 m), so interference only occurs between the microwaves. The three CFBGs embedded on three-arm-MZI have the same bandwidth, dispersion value, and chirp rate with values of 20 nm, 4.69 ps/nm, and 7.1 nm/cm. The bandwidth of the PD (Finisar, XPDV2120RA) is 20 G. The measurement range of the VNA (Anristu, MS2024A) is 0 to 20 G.
Firstly, the system shown in Fig. 2 is applied to strain sensing as a means of demonstrating the system's ability of enhanced sensitivity. Figure 3 shows the interferogram in the frequency domain of the OCMI-MZI consisting of a reference arm and a middle arm (OCMI-MZI 1), the OCMI-MZI consisting of a sensing arm and a middle arm (OCMI-MZI 2), and the OCMI-three-arm-MZI respectively. The FSRs for OCMI-MZI 1, OCMI-MZI 2, and OCMI-three-arm-MZI are 27.94 MHz, 29.59 MHz, and 502 MHz, respectively, which are consistent with the theoretical values 27.9401 MHz, 29.5904 MHz, and 501.05 MHz obtained from Eq. (3). It is worth noting that the Vernier effect is essentially the superposition of two interferograms, and when the power of the light signal fluctuates, the visibility of the corresponding interferogram changes as well, which ultimately affects the envelope signal extracted from the Vernier effect. By using a spectrum flatter and power-stable high-performance light source, and by repeatedly extracting and fitting the envelope to the Vernier effect, the errors introduced in the extraction of the envelope can be greatly reduced.
Fig. 3. The interferogram in the frequency domain of the (a) OCMI-MZI 1, (b) the OCMI-MZI 2, and (c) the OCMI-three-arm-MZI (Grey line: upper envelope of the interferogram).
As shown in the illustration in Fig. 1, strain is applied to the sensing FBG by gluing it to a pair of micrometric translation stages with a resolution of 0.02 mm. Figure 4(a) and Fig. 4(b) show the constructed interferograms of OCMI-MZI 2 and the envelope signals of the superimposed spectra of OCMI-three-arm-MZI for different strain settings at ∼7 GHz, respectively. The envelope signal is obtained by curve fitting using the Trigonometric cosine model. It can be seen that as the strain increases, the dip frequency in the interferogram and envelope signal shifts towards the low-frequency region. This is due to the negative sensitivity factor caused by the longer optical path of the sensing arm than the remaining two arms, as predicted by Eq. (9). The shift in dip frequency as a function of strain for both cases is plotted in Fig. 4(c) and Fig. 4(d). The sensitivity amplification factor is determined to be ∼17.5, which closely matches Eq. (10). The maximum frequency deviations of the five repeated measurements for both cases are 1.089 KHz and 22.21 KHz respectively, corresponding to a maximum strain error of the repeatability are 0.492 με and 0.573 με respectively. The strain error of the repeatability does not increase significantly as the sensitivity is amplified.
Fig. 4. Sensitivity-enhanced Strain sensing. (a) Constructed interferograms of OCMI-MZI2 centered at ∼6.57 GHz for different settings of strain. (b) Curve-fitted envelope signals of the superimposed spectra of OCMI-three-arm-MZI centered at ∼7 GHz for different settings of strain. (c) The shift in dip frequency of the interferograms is shown in panel (a) as a function of strain. (d) The shift in dip frequency of the envelope signals is shown in panel(b) as a function of strain.
Next, an experiment is conducted to verify that the proposed sensing scheme is insensitive to temperature. The sensing test platform is shown in Fig. 5. The sensing FBG and reference FBG are placed on a hot plate and each end of the sensing FBG is glued to a pair of micrometric translation stages, thus enabling strain to be applied to the sensing FBG in the presence of temperature disturbances. In each strain, the temperature varies from 25°C to 85°C with steps of 10°C. Figure 6(a) depicts the dip frequency shift of the envelope signal as a function of strain at different temperatures. At 0 με, the maximum frequency shift caused by a 60°C change in temperature has a value of 87.3 KHz. The standard deviation has been calculated to be only ±31.57 KHz, corresponding to a maximum strain error of ±0.82 με. The measured temperature sensitivity of the proposed system with temperature compensation and the theoretical temperature sensitivity of the proposed system without temperature compensation (the sensing FBG is placed on a hot plate and the reference FBG is placed at room temperature) at the 0 με are given in Fig. 6(b), with values of 1.455 KHz/℃ and 371.858 KHz/℃ respectively. It can be seen that the proposed sensing scheme significantly reduces the temperature sensitivity when applied to strain sensing.
Fig. 6. (a) Relationship between strain and shift in dip frequency of the envelope signal at different temperatures (inset: Zoom-in view). (b) The comparison between frequency shift as a function of temperature variation for the proposed sensing scheme with and without temperature compensation.
Finally, the stability of the OCMI-three-arm-MZI is evaluated and its resolution is discussed. We set the proposed sensing scheme to run at 0 με (25℃) for 100 min. The dip frequency in the envelope signal is recorded every ten minutes. The results are shown in Fig. 7, where the maximum frequency variation is as low as 8.121 KHz, corresponding to 0.209 με. Ideally, the resolution of the proposed sensing scheme is limited only by the VNA resolution (∼1 Hz), the value of which can be calculated as 2.58 × 10−5 με. It can be seen that the measured noise floor will be much higher than the theoretical resolution due to the noise of the RF device and the instability of the constructed interferometer. Integration of the sensors or the use of packaged modules can improve system stability.
It is worth noting that unlike demodulating FBG sensors in the optical domain, OCMI-based FBG sensors are more complex and expensive. However, OCMI-based FBG sensors benefit from the large frequency gap between the optical wave and microwave [13], and an interrogation method based on RF signal intensity variations [5], therefore allowing for high resolution and faster interrogation speed in the frequency domain. To reduce system complexity and application cost, the VNA in the experiment can be replaced with an RF signal generator and RF dynamometer [18]. Thus, the proposed sensing scheme does not significantly increase the cost and complexity while increasing the sensitivity.
To demonstrate the performance of this work more clearly, a comparison of the sensing performance of our scheme with other recently reported schemes is shown in Table 1. The proposed sensing scheme offers significant improvements in sensitivity and resolution and features low cross-sensitivity when applied to strain sensing compared with other work.
Table 1. Comparison between this work and the others
4. Conclusion
In conclusion, a sensitivity-enhanced FBG sensor that can resist cross-sensitivity is proposed through OCMI-based three-arm-MZI generation of the Vernier effect and applied to strain sensing for experimental validation. The Vernier effect is produced by superimposing the interferogram generated by interfering with the three-arm-MZI middle arm with the sensing arm and the reference arm respectively. By tracking the frequency shift of the envelope signal of the superimposed spectrum, the sensitivity of the system can be improved. Compared to the two-arm-MZI, the sensitivity of the three-arm-MZI has been amplified by a factor of 17.5, from -2.209 ± 1.089 KHz/με to -38.695 ± 22.21 KHz/με. When the system is applied with strain sensing, compensation for temperature disturbances is achieved by simultaneous interrogation of the sensing FBG and reference FBG by three-arm-MZI, which effectively amends the cross-sensitivity of temperature and strain. The proposed sensing scheme is characterized by high sensitivity, low cross-sensitivity, and ease of implementation, and can therefore be applied in a variety of complex environments. It can be expected that the proposed sensing scheme has good potential for practical applications in structural health monitoring.
Funding
National Natural Science Foundation of China (61975082, 62205149).
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant 61975082 and 62205149.
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.
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