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Abstract
This article reports a novel concept of computational microwave photonics and distributed Vernier effect for sensitivity enhancement in a distributed optical fiber sensor based on an optical carrier microwave interferometry (OCMI) system. The sensor system includes a Fabry-Perot interferometer (FPI) array formed by cascaded fiber in-line reflectors. Using OCMI interrogation, information on each of the interferometers (i.e., sensing interferometers) can be obtained, from which an array of reference interferometers can be constructed accordingly. By superimposing the interferograms of each sensing interferometer and its corresponding reference interferometer, distributed Vernier effect can be generated, so that the measurement sensitivity of each of the sensing interferometers can be amplified individually. This technique is achieved entirely in software without any physical modification to the system and negates the need to carefully fabricate the reference interferometer to obtain the desired magnification factor, as is often the case for traditional Vernier effect-based optical fiber sensors. Importantly, the reference interferometers can be flexibly constructed such that the magnification factor for each sensing interferometer can be precisely and easily controlled. The operating principle is illustrated in detail, followed by a proof of concept. The experimental results match well with theoretical predictions.
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1. Introduction
Distributed optical fiber sensors (DOFSs) have attracted extensive research interest and have undergone tremendous growth and advancement in the past two decades [1,2]. The unique advantage of distributed sensing over a long distance provided by DOFSs makes them an excellent candidate in various applications, such as structural health monitoring [3], down-hole monitoring [4], pipeline monitoring [5], etc.
Distributed optical fiber sensing has been realized based on different techniques, such as fiber Bragg gratings [6], optical time-domain reflectometry [7], and optical frequency-domain reflectometry (OFDR) [8], where each of these techniques has its own unique feature. A detailed comparison of different DOFSs can be found in a recent review article [1]. Recently, with the advancement of microwave photonics, an interesting distributed sensing technique based on incoherent OFDR (I-OFDR) was demonstrated [9]. In an I-OFDR system, instead of using a tunable laser source as is the case for a conventional OFDR system, a broadband light source is intensity modulated by a microwave signal and then the intensity-modulated light is utilized to interrogate optical fiber sensors. Compared to traditional DOFSs, an I-OFDR system has some attractive advantages, such as a relieved requirement on the light source, high spatial resolution and long measurement range, and high signal-to-noise ratio [10]. Integrating the I-OFDR interrogation with interferometry, very recently, optical carrier-based microwave interferometry (OCMI) was proposed and demonstrated for spatially distributed optical fiber sensing [11]. A Fabry-Perot interferometer (FPI) array along an optical fiber was first fabricated using micromachining, and OCMI was utilized to interrogate the FPI array. Since the spatial position and the microwave interferogram of each of the FPIs in the array could be unambiguously determined, dark zone-free distributed measurement was achieved. The OCMI technique integrated strengths from two different areas, i.e., optics and microwave, and thereby provided several unique merits when it comes to sensing, including low dependence on the types of optical fibers, insensitivity to variations of optical polarizations, and relieved fabrication accuracy on sensors [12–16]. However, the limiting aspect of the OCMI system is the low measurement sensitivity. For example, a strain measurement sensitivity of only −2.26 kHz/µɛ was reported in [11], indicating a strain resolution of tens of µɛ, which is at least one order of magnitude lower than traditional optical fiber sensors. Different strategies were recently developed to increase the measurement sensitivity of OCMI, including a coherent-length-gated technique [17,18] and low-coherence interferometry [19]. However, these two approaches demanded additional requirements on the hardware of the system (e.g., the coherence length of the light source) and added more complexity to the system (i.e., additional hardware was required).
Vernier effect has been widely investigated as an effective approach to increasing the measurement sensitivity of optical fiber sensors [20–31]. Recent progress of Vernier effect-based optical sensors can be found in two recent review articles [20,32]. Inspired by the Vernier effect-based optical sensors, researchers recently demonstrated that Vernier effect could also be generated by two cascaded microwave-photonic interferometers and could be employed for measurement sensitivity amplification [33,34]. Thus, by combining Vernier effect and the OCMI interrogated FPI array, it is possible to implement the Vernier effect in a distributed optical fiber sensor, which will potentially lead to a high-sensitivity OCMI system with two orders of magnitude sensitivity amplification. As demonstrated in our recent work [35], the Vernier effect-amplified distributed sensor requires an additional reference interferometer in the system, compared to a conventional OCMI system. By superimposing the interferograms of the reference interferometer and each of the sensing interferometers in the FPI array, the measurement sensitivity of each sensing interferometer could be amplified, and thereby high-sensitivity distributed sensing was realized. However, adding one reference interferometer into the system increases the system complexity. Moreover, the length of the reference interferometer needs to be precisely controlled to obtain a desired sensitivity magnification factor for a given sensing interferometer. More importantly, for a given reference interferometer, it is challenging to achieve similar magnification factors for all the sensing interferometers in the FPI array because the lengths of these sensing FPIs might be different, as revealed in [35]. One solution to this could be to physically design a reference FPI array, similar to the sensing FPI array. In such a context, the previously demonstrated Vernier effect-amplified OCMI technique requires cautious hardware design to achieve satisfactory system performance and therefore is not readily applicable.
In this article, we propose a new concept of computational microwave photonics and virtual Vernier effect for sensitivity magnification in an OCMI system for single-point and spatially distributed sensing. The proposed technique negates the need for careful system design and the stringent requirement on the hardware, as is often the case for existing techniques. Compared to previously reported Vernier effect-based microwave-photonic single-point sensors [33,34], the proposed virtual Vernier effect-based sensor system is much simpler in structure due to the fact that only a single interferometer is employed. Meanwhile, a common challenge for conventional Vernier effect-based sensors regarding the maintenance of the reference interferometer is obviously overcome for the virtual Vernier effect-based sensor. In the case of distributed sensing, the computational and virtual Vernier effect-based technique is remarkably advantageous in flexibility and simplicity over the recently reported method [35], as it will be shown later.
The rest of the paper is organized as follows. In section II, the fundamental principle of the concept is presented in detail. In section III, the technique is first implemented on a single interferometer system, showing capability for sensitivity amplification and adjustable magnification factor. Then, sensitivity enhancement for a distributed sensor is experimentally verified based on the proposed technique and a conventional OCMI system without the addition of any hardware. Section IV concludes this work.
2. Methods
A schematic of a conventional OCMI-based distributed optical fiber sensing system is illustrated in Fig. 1(a) [35]. A broadband light source is utilized in the system. The intensity-modulated light is launched to the fiber under test (FUT) via an optical fiber coupler. The FUT includes cascaded in-fiber reflectors that form an FPI array. The reflected light signal is directed to a high-speed photodetector (PD) that converts the optical signal to an electrical signal, which is then sent into a microwave detector (e.g., a vector network analyzer, VNA). The complex frequency response of the FUT can then be obtained by sweeping the frequency of the microwave modulation signal and using synchronized detection at each frequency (Ω) and can be expressed as [35]
Fig. 1. High-sensitivity distributed sensing based on computational microwave photonics and Vernier effect. (a) Schematic of the microwave-photonic system for distributed optical fiber sensing. VNA, vector network analyzer; PD, photodetector. The FUT includes cascaded reflectors, i.e., R1, R2, … Ri, Ri+1, … RN, where N is the total number of the reflectors. (b) Illustration of the signal processing based on the proposed computational microwave photonics and distributed Vernier effect for high-sensitivity distributed sensing.
The following section discusses the concept of the proposed computational microwave photonics and distributed Vernier effect that is used for sensitivity enhancement in the distributed optical fiber sensing system shown in Fig. 1(a). From the calculated spatial domain signal of the FUT without external perturbations, the spatial location of each reflector can be unambiguously identified. The cascaded reflectors (N reflectors) form an FPI array with N-1 sensing interferometers. The OPD of each of the sensing interferometers can be obtained from the spatial domain signal. Also, the interferogram of each of the sensing interferometers [e.g., i-th sensing interferometer formed by i-th and (i+1)-th reflectors] can be reconstructed by: (1) applying a time gate function to the time-domain (spatial domain) signal of the FUT to isolate i-th and (i+1)-th reflectors, as illustrated by the dashed red line in Fig. 1(a), and (2) performing a Fourier transform to the gated time-domain signal. The reconstructed interferogram of i-th sensing interferometer can be expressed as
According to Eq. (4), a smaller OPD difference results in a larger magnification factor. However, the largest magnification factor that can be achieved is limited by the bandwidth of the microwave modulation signal [33]. The OPD of the artificial reference interferometer is determined for a desired sensitivity magnification factor based on Eq. (4). Subsequently, the magnitude spectrum (i.e., the interferogram) of i-th reference interferometer can be calculated by [33]
When there is an external perturbation exerted on the FUT, a new measurement from the system is acquired. Following the same procedures discussed above, the interferogram of each of the sensing interferometers can be unambiguously reconstructed. Conventionally, the spectral shift of the interference signal of each sensing interferometer is tracked, and spatially distributed sensing is realized by integrating the spectral shift information from all the sensing interferometers. Here, we introduce the technique of distributed Vernier effect for distributed sensitivity enhancement. Taking i-th sensing interferometer as an example, the interference signal Magi can be obtained based on Eq. (3). Meanwhile, the interference signal of i-th reference interferometer is extracted from the database. Superimposing the interferograms of i-th sensing and reference interferometers, i-th Vernier effect is generated (i.e., i-th Vernier effect generated), where a typical amplitude-modulation signal can be obtained, as illustrated in Fig. 2. The free spectral range (FSR) of the envelope signal is significantly larger than that of the sensing and reference interferometers and can be predicted by
where FSRsen and FSRref represent the FSR of the sensing and reference interferometers, respectively. Importantly, instead of tracking the shift of the interferogram of the sensing interferometer, the envelope signal in the superimposed spectrum is monitored, whose spectral shift is amplified by a factor of M according to Eq. (4). Repeating the process, N-1 Vernier effects can be obtained for the N-1 sensing interferometers included in the FUT, i.e., distributed Vernier effect generated. As a result, sensitivity-enhanced distributed sensing is achieved by the computational microwave photonics and the distributed Vernier effect technique.Fig. 2. Illustration of the i-th Vernier effect that is utilized to magnify the sensitivity of i-th sensing interferometer. The envelope signal is used for sensing.
3. Results and discussion
3.1 Demonstration of sensitivity enhancement for a single interferometer
To demonstrate the proposed concept of computational microwave photonics and Vernier effect for sensitivity-enhanced sensing, an OCMI system consisting of a single interferometer was first built, as shown in Fig. 3(a). All the experiments were performed at room temperature 22 ± 0.5 °C. The system is based on a simple direct-modulation system, including a direct-modulation laser source (HP 83402B), an VNA (P9375A), and a Michelson interferometer (MI) under test, similar to the setup employed in [35]. The length difference between the two branches of the MI (ΔL) was set to ∼1.65 m, which is significantly larger than the coherence length of the source (< 1 mm), to ensure that the system operates at an incoherent regime. The incoherent operation makes the system insensitive to changes in the polarization state of the probing light. Figure 3(b) gives the spatial domain signal of the MI obtained by performing an IFT to the recorded complex S21 in the VNA. The refractive index of the fiber (n0) was set to 1.468 in the calculation. Two individual peaks can be observed in the spatial domain signal, corresponding to the two fiber endface reflectors of the MI. The distance between the two peaks was found to be approximately 1.6395 m, corresponding to the length difference between the two fiber branches, which matched well with the designed value. Figure 3(c) gives the measured magnitude spectrum of the MI, i.e., the sensing interferometer, i.e., information for the sensing interferometer obtained. According to Fig. 1(b), the next step is to obtain the information on the artificial reference interferometer. Since the OPD of the sensing interferometer (i.e., OPDsen) is 4.8136 (i.e., 2 × 1.468 × 1.6395), we first set the OPD of the reference interferometer to 4.5802 (i.e., 2 × 1.468 × 1.56). According to Eq. (4), a sensitivity magnification factor of ∼20.6 could be expected. According to Eq. (5), a few constants (i.e., g, A1, and A2) need to be determined to calculate the magnitude spectrum of the artificial reference interferometer. The idea is to acquire a magnitude spectrum that is similar to the spectrum of the sensing interferometer in terms of amplitude and offset so that a distinct envelope signal with large fringe visibility can be obtained in the superimposed spectrum. These constants can be estimated by applying a nonlinear curve fit to the measured spectrum of the sensing interferometer. Figure 3(d) gives the calculated magnitude spectrum of the reference interferometer used in this experiment, where the frequency range is set to 1-6 GHz and the FSR is determined to be ∼65.5 MHz, i.e., artificial reference interferometer obtained. It is worth mentioning that small variations of the constants used to calculate the magnitude spectrum of the artificial interferometer have little influence on the performance of the virtual Vernier effect-based sensor.
Fig. 3. A direct-modulation-based microwave-photonic MI system. (a) Schematic of the system. (b) Spatial domain signal of the system. (c) Measured magnitude spectrum of the MI. (d) Magnitude spectrum of the artificial reference interferometer. The constants for the reference interferometer are: g = 0.16; A1 = 0.1521; A2 = 0.1764.
Next, an experiment was conducted to investigate the strain response of the MI shown in Fig. 3(a). Stress was applied to the long branch of the MI, which increased the length of the branch by 1000 µm in steps of 100 µm, corresponding to applied tensile strains ranging from 0-610 µɛ in steps of 61 µɛ provided the length difference between the two branches of the MI is 1.6395 m. The interferogram of the MI for each setting of the applied strains was measured and recorded. The superimposed spectrum of the artificial reference interferometer and the sensing interferometer at a pre-stress setting is plotted in Fig. 4(a). As expected, a typical amplitude-modulation signal was obtained, indicating that Vernier effect is generated, and the FSR of the envelope signal was found to be ∼1.280 GHz, which was close to the predicted value of 1.275 GHz based on Eq. (6). The envelope signal centered at ∼5.1 GHz, which would be tracked for sensing, is also indicated in Fig. 4(a). A four-degree polynomial model was then used to fit the sensing envelope. Figure 4(b) shows curve-fitted envelope signals for different settings of applied strains. The envelope signal shifted to the low-frequency region with increasing strains. The shift in dip frequency of the curve-fitted envelope signal as a function of the applied strain is plotted in Fig. 4(c). The shifts of dip frequency at ∼5 GHz of the interferogram of the sensing interferogram (i.e., without sensitivity amplification) are also included in Fig. 4(c) for comparison. As can be seen, the frequency shift of the envelope signal was substantially magnified due to the Vernier effect. Linear curve fits were applied to the two data sets. The sensitivities are determined to be −76.14 ± 0.73 kHz/µɛ and −3.615 ± 0.076 kHz/µɛ (spectral shift/strain, 95% confidence level) with correlation coefficients greater than 0.9995, revealing a magnification factor of ∼21.1, which matched well with the predicted value of 20.6. The root mean square errors (RMSEs) of the curve fits are 206 kHz and 23 kHz for the sensitivity amplified case and the case without amplification, respectively. The curve fit results reveal that the measurement error might also be magnified by a factor of 10, which, however, is smaller than the sensitivity magnification factor of 21.1. This experiment demonstrates that the measurement sensitivity of the MI can be drastically amplified using the concept of computational microwave photonics and the virtual Vernier effect.
Fig. 4. Computational microwave photonics for sensitivity enhancement with a magnification factor of ∼21.1. (a) Superimposed spectrum of the reference and sensing interferometers. The sensing envelope is also indicated. (b) Curve-fitted envelope signals for different settings of applied strains. (c) Shift of dip frequency of the envelope signal as a function of applied strain. The shift of dip frequency of the interferogram of the sensing interferometer (i.e., without sensitivity amplification) is also included for comparison.
The prominent advantage of the computational microwave photonics-based technique is that no additional hardware is needed to achieve sensitivity enhancement for the sensing interferometer. Moreover, the sensitivity magnification factor can be easily and flexibly varied in software simply by adjusting the OPD of the artificial reference interferometer. To demonstrate the flexibility, the OPD of the artificial reference interferometer was changed from 4.5802 (i.e., 2 × 1.468 × 1.56) to 4.7563 (i.e., 2 × 1.468 × 1.62), where a magnification factor of ∼84 could be expected. The same signal processing procedures were repeated. Figure 5(a) gives the superimposed spectrum when the pre-stress was applied to the MI. The FSR of the envelope increased to ∼5 GHz. The sensing envelope is also indicated in Fig. 5(a), which is obtained by curve fitting using a four-degree polynomial model. Figure 5(b) shows the sensing envelopes for different settings of applied strains. The dip frequency shift of the envelope signal as a function of the applied strain is plotted in Fig. 5(c), where the shifts of dip frequency at ∼5 GHz of the interferogram of the sensing interferogram are also plotted. A linear curve fit was applied to the dataset. The magnified strain sensitivity was determined to be −302.7 ± 2 kHz/µɛ with a correlation coefficient of 0.9999, indicating a magnification factor of ∼83.7 given the sensitivity without amplification to be −3.615 ± 0.076 kHz/µɛ, which again agreed with the predicted value of 84. The RMSE for the linear curve fit is found to be 563 kHz, indicating an amplification factor of 24 for the error. The error magnification factor is much smaller than the sensitivity magnification factor of 84, indicating that the measurement resolution of the sensor could be improved by the virtual Vernier effect-based technique. This experiment verifies that the sensitivity magnification factor of the computational microwave photonics-based (virtual Vernier effect-based) system can be flexibly tuned by simply changing the OPD of the artificial reference interferometer without making any modification to the system hardware. Meanwhile, the linearity of the system response after significant sensitivity amplification does not deteriorate.
Fig. 5. Computational microwave photonics for sensitivity enhancement with a magnification factor of ∼84. (a) Superimposed spectrum of the reference and sensing interferometers. The sensing envelope is also indicated. (b) Curve-fitted envelope signals for different settings of applied strain. (c) Shift of dip frequency of the envelope signal as a function of applied strain. The shift of dip frequency of the interferogram of the sensing interferometer (i.e., without sensitivity amplification) is also included for comparison.
Note that traditionally, a reference interferometer is physically required in an interferometer-based system to generate Vernier effect for sensitivity amplification. However, it would be rather challenging to precisely control the OPD of the reference interferometer to achieve a desired sensitivity magnification factor if the reference interferometer were physically implemented in the system. Instead, the proposed computational microwave photonics-based technique, i.e., virtual Vernier effect, is achieved entirely in software and negates the need to carefully design the system hardware (i.e., the OPD of the reference interferometer), which is especially advantageous when it comes to a distributed sensing system, as demonstrated in the next section. It is noted that the measurement error is also magnified by the virtual Vernier effect, as is often the case for the conventional “physical” Vernier effect-based systems. However, the error magnification factor is demonstrated a few times smaller than the sensitivity magnification factor in our case, which, unfortunately, is not discussed in most of the previous works. The origin of the error needs to be further investigated.
3.2 Demonstration of sensitivity enhancement for a distributed sensor
To demonstrate the effectiveness of the computational microwave photonics-based technique for sensitivity enhancement in distributed sensing, a spatially distributed optical fiber sensor is fabricated based on a direct-modulation OCMI system. As a proof of concept, four reflectors were cascaded along the FUT, as shown in Fig. 6(a). The four cascaded reflectors formed an FPI array consisting of three sensing FPIs. Each of the first three reflectors was fabricated by introducing an air gap between the lead-in fiber and the lead-out fiber (both supported in fiber ferrules) with the assistance of a ferrule mating sleeve, as shown in Fig. 6(c). The fourth reflector was the cleaved end facet of the FUT. Note that the system can be used to interrogate an FPI array with a much greater number of sensing FPIs by cascading ultra-weak reflectors, and detailed analysis regarding the multiplexing capacity of the OCMI system can be found in [35]. Figure 6(b) gives the spatial domain signal of the system shown in Fig. 6(a). The lengths of the three sensing FPIs (i.e., FPIS1, FPIS2, FPIS3 with lengths of L1, L2, and L3) were determined to be 2.076 m, 2.314 m, and 3.048 m.
Fig. 6. A distributed optical fiber sensor based on a direct-modulation microwave-photonic system. (a) Schematic of the system. (b) Spatial domain signal of the system. (c) Detailed view of the FPI array.
The responses of the system to multipoint perturbations were characterized to verify the capability for distributed sensing with substantially improved sensitivity. Stress was applied to FPIS1 and FPIS2, whereas FPIS3 was intact. The applied stress increased the length of the corresponding fiber section by 900 µm in steps of 100 µm. As a result, FPIS1 and FPIS2 experienced a total effective strain of ∼433.8 µɛ and ∼388.8 µɛ with a step-size of ∼48.2 µɛ and ∼43.2 µɛ, respectively. To employ the computational microwave photonics-based technique for signal processing, the information for sensing interferometers was first obtained. The lengths of FPIS1, FPIS2, and FPIS3 were 2.076 m, 2.314 m, and 3.048 m, respectively, from which the OPD of three sensing FPIs can be determined. To generate the distributed Vernier effect as mentioned above, three artificial reference interferometers, i.e., FPIR1, FPIR2, and FPIR3, were constructed. The lengths of the three reference interferometers were set to 2.055 m, 2.291 m, and 3.018 m, respectively. As a result, the sensitivity magnification factor for the three sensing interferometers (i.e., FPIS1, FPIS2, and FPIS3) could be expected to be ∼100 based on Vernier effect according to Eq. (4). Note that the feature of the computational microwave photonics and distributed Vernier effect-based technique is that an array of reference interferometers is generated based on the array of the sensing interferometers, where each of the sensing interferometers is paired with a reference interferometer to achieve a desired sensitivity magnification factor. This technique would have been challenging to be implemented based on the traditional approach, where an array of reference interferometers with precisely controlled lengths has to be physically constructed in the system. The computational microwave photonics-based technique is especially advantageous when it comes to an FPI sensing array with different individual lengths since the lengths of the reference FPIs can be easily adjusted in signal processing.
The responses of the system after Vernier effect amplification are given in Fig. 7. Figure 7(a) shows the evolution of the envelope signal of the superimposed spectra centered at ∼5 GHz obtained from FPIS1 and FPIR1 with increasing applied strains. The envelope signal shifted to the low-frequency region, which matched well with the previous results obtained from the single-interferometer system. The dip frequencies of the envelope signals as a function of applied strains are shown in Fig. 7(b). The slope of the linear curve-fitted model was found to be −387.2 kHz/µɛ at ∼5 GHz with linearity of 0.9997. The resonance frequency at ∼5 GHz of the interferogram of FPIS1 as a function of the applied strain (i.e., without sensitivity amplification) is also plotted in Fig. 7(b), where the sensitivity was determined to be −3.677 kHz/µɛ. Therefore, a sensitivity magnification factor of ∼105 was obtained for FPIS1 with the assistance of the 1st Vernier effect, which agreed with the predicted value of ∼100. Figure 7(c) and 7(d) give the results for FPIS2, where Fig. 7(c) shows the envelope signals of the superimposed spectra centered at ∼4.5 GHz obtained from FPIS2 and FPIR2 for different applied strains and Fig. 7(d) shows the corresponding dip frequencies as a function of applied strains. The shifts of the resonance frequencies of FPIS2 at ∼4.5 GHz for different settings of applied strains (i.e., without sensitivity amplification) are also plotted in Fig. 7(d) for comparison. Again, the envelope signal shifted to the low-frequency region with increasing strains. The measurement sensitivity of the envelope signal of the superimposed spectrum was determined to be −343.7 kHz/µɛ at ∼4.5 GHz with linearity of 0.9997, corresponding to a magnification factor of 103 generated by the 2nd Vernier effect, given the sensitivity without amplification to be −3.321 kHz/µɛ, which also matched well with the expected value of ∼100. It should be noted that in the experiment the interferogram of FPIS3 and the envelope signal of the superimposed spectrum obtained from FPIS3 and FPIR3 did not exhibit significant shifts due to the fact that FPIS3 was not disturbed in the experiment. Therefore, this experiment demonstrates that the computational microwave photonics and distributed Vernier effect can be used as a tool for sensitivity enhancement for a distributed sensor and, importantly without any hardware modification to the system.
Fig. 7. Computational microwave photonics for sensitivity enhancement in a distributed optical fiber sensor based on distributed Vernier effect. Envelope signals of the superimposed spectra generated by (a) the 1st Vernier effect and (c) the 2nd Vernier effect for different settings of applied strains. (b) The dip frequencies of the envelope signals shown in (a) as a function of applied strains. (d) The dip frequencies of the envelope signals shown in (c) as a function of applied strains. The measurement results without amplification are also included in (b) and (d) for comparison.
4. Conclusion
In summary, we have proposed and experimentally demonstrated a novel concept of virtual and distributed Vernier effect for sensitivity enhancement in OCMI-based point and distributed sensor systems (i.e., an MI and an FPI array). We have achieved two orders of magnitude magnification for strain measurement sensitivity of OCMI sensor systems, importantly, without any physical modification to the systems. The experimentally obtained sensitivity match well with the theoretically predicted ones. We have also demonstrated that the sensitivity magnification factor for sensing interferometers can be flexibly tuned by simply varying the parameters of the constructed reference interferometers.
Unlike traditional Vernier effect-based optical fiber sensors where a reference interferometer has to be physically fabricated and included in the sensor system, here, the Vernier effect is generated by using artificial reference interferometers, because doing the former would have added complexity to the system, especially for a distributed sensor with a large number of sensing interferometers. In addition to the OCMI system demonstrated in this work, we envision that the concept can be readily extended to other distributed sensing systems based on multiplexed interferometers. This work opens a new direction in distributed optical fiber sensing in which complexity in hardware to improve sensing performance (e.g., sensitivity and resolution) is shifted into software using simple and fast signal processing techniques.
Funding
Research Initiation Project of Zhejiang Laboratory (2022ME0PI01).
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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