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Abstract
Based on enhanced Vernier effect, a compact fiber sensor with ultrahigh sensitivity is proposed for simultaneous transverse load (TL) and temperature measurements. A single mode fiber (SMF) is spliced with a segment of hollow-core fiber (HCF) coated with polydimethylsiloxane (PDMS), some PDMS is injected into the HCF, forming a Vernier sensor with an air cavity adjacent to a PDMS cavity. It is shown that TL and temperature changes give rise to opposite and remarkable different variations in lengths of the two cavities, thereby enhancing Vernier effect and in favor of simultaneous measurements of TL and temperature. Moreover, the limited sensitivity magnification due to the length mismatch between the two cavities is compensated for by reconstructing the Vernier envelope with a broadened free spectrum range (FSR) from output signal. As a result, the highest TL sensitivity reported so far of −2637.47 nm/N and a good condition number of 69.056 for the sensitivity coefficient matrix have been achieved.
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1. Introduction
Fiber transverse load (TL) sensors are widely applied in bridge quality monitoring [1,2] and biomechanical research [3,4] due to their advantages such as small footprint, high sensitivity, and immune to electromagnetic interference. Compared with various fiber sensor structures such as fiber Bragg gratings, fiber multimode interferometers, and Sagnac interferometers [5], Fabry Perot (FP) microcavities formed inside or at the tip of fiber are very suitable for TL measurement due to their simple structure and low cost. When a transverse force is imposed on the cavity wall, the FP cavity should extend along the fiber axial in response to Poisson effect, leading the interference fringe to shift over the wavelength. The early reported fiber TL sensors were F-P microcavities with thick walls, which presented feeble Poisson effect and thus low sensitivity [6]. The subsequent researches focused on reducing the thickness of cavity walls [7–9], or using organic materials to increase the Poisson's ratio of cavities [10]. Overall, the TL sensitivity is usually within the range of only tens of nm/N. In addition, to accurately measure TL, the temperature crosstalk should be taken into account especially for FP cavities formed by organic materials.
Interferometric fiber sensors based on Vernier effect can further improve the sensitivity effectively, in which two cascaded or parallel interferometers with slightly detuned optical path differences (OPDs) are used. One of them serves as a sensing interferometer while the other as a reference interferometer. The two interference spectra overlap to form a high-frequency spectrum modulated by a Vernier envelope. When environmental parameters change, the Vernier envelope shifts much greater than the individual sensing spectrum, therefore significantly improving the measurement sensitivity [11–13]. In recent years, Vernier effect has been exploited in fiber sensors for various parameter measurements such as temperature [14], strain [15,16], refractive index [17], biological detection [18], and TL [19]. For Vernier-effect based fiber sensors, usually the sensing interferometer was exposed to changed environments, while the reference interferometer was kept as impervious as possible, making it only applicable for single parameter measurement. Recently, there were reports that use the slightly distinguishable sensitivities of two envelope dips to construct the sensitivity coefficient matrix, which would however introduce significant demodulation errors [20,21]. To address this issue, a study integrated a temperature sensitive fiber Bragg grating into a Vernier sensor to demodulate temperature crosstalk [22]; Another study designed a fiber sensor with two sets of Vernier envelopes, each of which was sensitive to one of two environmental parameters, respectively [23]. Although both types of fiber sensors have improved the matrix performance, they still show complexity in structures. Besides, these Vernier sensors have the problem of OPD mismatch between two interferometers that is caused by manufacturing defects, resulting in limited sensitivity magnification. Some existing methods have been proposed for sensitivity improvement, but they still presented limitations. For example, the use of femtosecond lasers is merely suitable for precisely engraving FP cavities on fibers [24]. Fiber sensors with an adjustable OPD in sensing/reference interferometer usually have complex structures [25], while harmonic Vernier-effect based fiber sensors exhibit finite points in envelope fitting [26]. Recently, we reported a scheme to introduce Vernier effect based on the output of a single-interferometer sensor, in which the reference spectrum with an adjustable free spectrum range (FSR) can be extracted from the output signal to serve the function of a reference interferometer. Such a scheme can magnify the sensitivity as required, but the sensors constituted by a single interferometer are not suitable for simultaneous measurements of two physical parameters [27].
In this paper, an ultrasensitive and compact fiber sensor based on enhanced Vernier effect is proposed for simultaneous measurement of TL and temperature. In the scheme, a single mode fiber (SMF) is spliced to a segment of hollow-core fiber (HCF) with its tip coated with polydimethylsiloxane (PDMS). A portion of PDMS can enter the HCF as a result of capillary phenomenon, forming a compact structure with an air cavity and a PDMS cavity adjacent to each other, which constitutes a Vernier effect-based sensor. When a TL is applied to the PDMS, Poisson effect causes the PDMS cavity to extend while the air cavity to compress along the fiber axis, so as to enhance Vernier effect. It is worth noting that the variation in environmental temperature can also generate enhanced Vernier effect, as the thermal expansion effect of PDMS dominates. However, responses of the two cavities to TL and temperature variations are significantly different, which facilitates the construction of sensitivity coefficient matrix with good performance. In addition, by shifting a portion of the spatial frequency in the output signal, the Vernier envelope with broadened FSR can be reconstructed, which has successfully compensated for the low sensitivity magnification in Vernier effect caused by cavity length mismatch.
2. Fabrication and principle
Figure 1(a)-(d) illustrate the fabrication process of the proposed Vernier sensor with an air cavity adjacent to a PDMS cavity. First, An SMF is spliced to a short segment of HCF with an inner diameter of 25 µm by a commercial fusion splicer (Furukawa FITEL S178C) as shown in Fig. 1(a). The discharge duration time and current are 800 ms and 10 bits, respectively. Then the HCF is cleaved at the position about 600 µm away from the fusion point with the help of a microscope, as shown in Fig. 1(b). Afterwards, the PDMS solution with a ratio of 10:1 between elastic material precursor and curing agent was dripped onto the end of HCF, as shown in Fig. 1(c). In order to obtain a symmetric sphere at the end of HCF, the structure is cured at room temperature. After a curing for 24 hours, a PDMS sphere is formed at the end of HCF owing to the combined effect of gravity and surface tension, with a portion of PDMS entering the HCF, hence forming a compact structure with an air cavity adjacent to a PDMS cavity, as shown in Fig. 1(d). The light emitted from a lead-in fiber is fed into the two adjacent cavities, and then is reflected from three interfaces, the ones between the SMF and air (M1), air and PDMS (M2), PDMS and air (M3), respectively. The total reflected intensity can be written as [28]:
Fig. 1. (a)-(d) Fabrication process of the proposed Vernier sensor with an air cavity adjacent to a PDMS cavity, (e) transverse load (TL) applied on the PDMS cavity.
When TL is applied to the PDMS as shown in Fig. 1(e), the PDMS cavity extends along the fiber axis, causing compression in the air cavity. As a result, the shifting direction of the interference fringe for the PDMS cavity goes into the reverse against that for the air cavity, leading to an enhanced shift of the Vernier envelope. As for the increase in temperature, both air cavity and PDMS cavity will experience thermal expansion. However, since the thermal expansion coefficient of PDMS is much greater than that of air, the expanded PDMS is bound to compress the air cavity, which also results in enhanced Vernier effect. According to Eqs. (4)–(6), magnification factors are determined by OPDs of both cavities. Since the response of each individual cavity to TL variation is significantly different from that to temperature variation, which would lead to significantly different response of envelope in terms of TL and temperature variations. This feature is particularly beneficial to constructing an effective matrix for simultaneous measurement of TL and temperature [30].
Two cavities with a slight difference in OPD are hard to fabricate, which compromises the sensitivity magnification based on Vernier effect according to Eqs. (5)–(6). In our scheme, it is proposed that the sensitivity can be improved by reconstructing a Vernier envelope with broadened FSR from the raw signal. This can be realized by shifting spatial frequency of the third term in Eq. (1) to approach that of the second term, and vice versa. To achieve it, a modulation function ${I_m}$ is introduced:
where ${L_m}$ is the modulation length, any value can be set as required. The third term in Eq. (1) is extracted and then modulated by Eq. (7), that is:The first term on the right side of Eq. (8) corresponds to a spatial-frequency shifted interference term of the PDMS cavity, which is then superimposed with the interference term of the air cavity in Eq. (1), namely:
Fig. 2. Schematic diagram of Vernier-effect reconstruction based on spatial-frequency shift for sensitivity improvement.
3. Experiment and discussion
Figure 3 shows the experimental setup of TL and temperature measurement using the Vernier sensor with an air cavity adjacent to a PDMS cavity. The light from a supercontinuum broadband optical source (SBOS, OYSL SC-5-FC), with wavelength range of 800 - 1700nm, is launched into the two adjacent cavities by a 3-dB coupler, and the output reflection spectrum is monitored by use of an optical spectrum analyzer (OSA, Yokogawa, AQ6370D). The microscope image of the two-cavity structure is shown in the inset. To characterize the TL response, the PDMS sphere is placed between two parallel glass slides and the TL is applied within the range of 0 to 49 mN.
Fig. 3. Experimental setup of TL and temperature measurement using the Vernier sensor with an air cavity adjacent to a PDMS cavity. (the inset is the microscope image of the sensor)
The reflection spectrum from two adjacent cavities undergoes a reconstruction process of Vernier effect, as illustrated in Fig. 4. Figure 4(a) shows a reflection spectrum from the two cavities, over a wavelength range of 1450 - 1650 nm. The FSRs near the wavelength of 1550 nm are 2.5 and 12.9 nm for the high-frequency interference spectrum and the envelope, respectively. The Fast Fourier Transform (FFT) operation is then applied to the spectrum in Fig. 4(a), and the result is shown in Fig. 4(f), where the spatial frequency is presented in terms of the OPD for more intuitive purposes. In Fig. 4(f), three peaks correspond to interferences from the PDMS cavity, air cavity, and cavity between M1 and M3, with OPDs of 180.331, 918.759, and 1100.5 µm, respectively, which is consistent with the result in Eq. (1). Due to the manufacturing imperfection, there is a significant difference in OPD between the air and PDMS cavities, resulting in a Vernier envelope with narrow FSR. To improve the sensitivity magnification of Vernier effect, the spatial frequency of the PDMS cavity in Fig. 4(f) is shifted towards that of the air cavity. The operation process is as follows: A band-pass finite impulse response filter with a Hanning window function is applied to the reflection spectrum in Fig. 4(a), so as to extract the interference spectrum corresponding to PDMS cavity as shown in Fig. 4(b), with its FFT result shown in Fig. 4(g). The interference spectrum in Fig. 4(b) is then shifted over its spatial frequency. The operation process of frequency shift has been discussed in detail in our previous works [25,28,29]. The spectrum and corresponding FFT result after spatial-frequency shift are shown in Figs. 4(c) and 4(h), respectively, with the OPD shifted from 180.331 to 880.331 µm. The interference spectrum of the air cavity is also extracted and normalized in the same way, as shown in Fig. 4(d), and the FFT result is shown in Fig. 4(i). The spectra in Figs. 4(c) and 4(d) are superimposed, as shown in Fig. 4(e), with the FFT result shown in Fig. 4(j). A reconstructed Vernier envelope appears with an FSR of 80.2 nm, which is significantly broadened compared with the value of 12.9 nm in Fig. 4(a).
Fig. 4. Reconstruction process of Vernier effect for the reflection spectrum. (a) raw reflection spectrum from the two adjacent cavities, (b) extracted and normalized interference spectrum from PDMS cavity, (c) spectrum after shifting the spatial frequency of (b), (d) extracted and normalized interference spectrum from air cavity, (e) superimposed spectrum of (c) and (d); (f)-(j) FFT results corresponding to (a)-(e), respectively.
Figure 5 shows the TL response of the sensor. With the increase of TL, the extension of PDMS cavity results in a red shift in its interference spectrum, as shown in Fig. 5(a), where the variation of a dip wavelength near 1550 nm versus the TL is shown in Fig. 5(d), demonstrating a sensitiviy of 242.466 nm/N. Due to the shortening of the air cavity, its interference spectrum undergoes a blue shift (Fig. 5(b)), resulting in a sensitivity of −20.525 nm/N around 1550 nm (Fig. 5(d)). The raw Vernier envelope can be directly fitted based on the reflection spectrum, as shown in Fig. 5(c), where a blue shift appears. The sensitivity is −253.364 nm/N, which is basically consistent with the theoretical value of −259.05 nm/N in Eq. (4). ${A_1} = 3.124$ and ${\textrm{A}_2} = 0.804$, which are calculated according to Eqs. (5)–(6), indicative of limited sensitivity magnification factors, which is caused by the OPD mismatch between the PDMS cavity and air cavity.
Fig. 5. TL responses of the sensor. Reflection spectra from (a) the PDMS cavity and (b) the air cavity, and (d) raw Vernier envelopes, under different TLs: (e) Dip wavelength versus TL corresponding to (a)-(c), respectively.
The raw Vernier effect is reconstructed according to the process illustrated in Fig. 4. Large ${L_m}$ values of 650 and 710 µm are selected respectively to ensure the shifted spatial frequency corresponding to PDMS cavity close enough to the spatial frequency corresponding to air cavity. Reconstructed Vernier envelopes under different TLs are shown in Figs. 6(b)–6(c), with broadened FSRs of 27.1 and 85.0 nm, and sensitivities of −807.38 and −2637.47 nm/N shown in Fig. 6(d), respectively. For Fig. 6(c), the theoretical sensitivity is worked out as −2426.286 nm/N based on $A_1^\mathrm{^{\prime}} = 33.238$ and $A_2^\mathrm{^{\prime}} = 32.238$. The difference mainly comes from the approximate 1550 nm selected in theoretical calculations based on Eqs. (10)–(12) [27]. The result in Fig. 6 sufficiently verifies that by reconstructing the Vernier envelope with a broadened FSR, the magnification factors of sensitivity can be effectively improved. The achieved sensitivity is the highest compared with those of TL fiber sensors reported in recent years, which is shown in Table 1.
Fig. 6. TL responses of reconstructed Vernier envelopes. Reconstructed Vernier envelopes with ${L_m}$ of (a) 0 µm, (b) 650 µm, and (c) 710 µm, under different TLs; (d) dip wavelength versus TL corresponding to (a)-(c), respectively.
Table 1. Representative transverse load (TL) sensors reported in recent years
The resolution of Vernier effect was also calculated. For the RI sensitivity of 2692.023 nm/N, the theoretical resolution of Vernier effect is $7.43 \times {10^{ - 6}}\; \textrm{N}$ when 0.02 nm wavelength resolution was selected in the OSA measurement [32]. In addition, the ultrahigh sensitivity results in limited TL measurement range, ranging from 0 to 0.033 N.
To tackle temperature crosstalk in TL measurements, the temperature response is monitored from 35.3 °C to 40.3 °C with a step of 1 °C, and maintained for 5 minutes at each step. Figures 7(a) and 7(b) show interference spectra of the PDMS and air cavities under different temperatures, respectively. In Fig. 7(a), as the temperature increases, thermal expansion effect causes the extension of PDMS cavity, resulting in a red shift in its interference spectrum, and the sensitivity is 1.330 nm/°C as shown in Fig. 7(d). In Fig. 7(b), the interference spectrum of the air cavity has a blue shift with a sensitivity of −0.355 nm/°C. The blue shift can be explained by the expanded PDMS cavity compressing the air cavity. The reconstructed Vernier envelopes by setting ${L_m}$ as 710 µm under different temperatures are shown in Fig. 7(c), and an enhanced Vernier effect also appears since the interference spectrum of the PDMS cavity shifts in an opposite direction to that of the air cavity. In addition, since the OPD of the air cavity is greater than that of the PDMS cavity, it can be inferred from Eq. (10) that the Vernier envelope has a blue shift. The sensitivity is −21.398 nm/°C, which is basically consistent with the theoretical value of −21.987 nm/°C according to Eqs. (10)–(12).
Fig. 7. Temperature responses of the sensor after the reconstruction of Vernier effect. Reflection spectra from (a) the PDMS cavity and (b) the air cavity, and (c) reconstructed Vernier envelopes (Lm = 710 µm), under different temperatures: (e) Dip wavelength versus temperature corresponding to (a)-(c), respectively.
In the simultaneous measurement of TL and temperature, the sensitivity coefficient matrix consists of TL and temperature sensitivities of the PMDS cavity, and those of the reconstructed Vernier envelope. In this way, the discrimination of TL and temperature can be achieved by solving the following matrix:
4. Conclusion
In summary, a novel compact fiber sensor with enhanced Vernier effect for simultaneous measurements of TL and temperature is proposed. In the scheme, An SMF is spliced with a segment of HCF coated with PDMS, forming a Vernier sensor with adjacent air cavity and PDMS cavity. TL and temperature changes result in opposite and significantly different variations in lengths of the two cavities, thereby enhancing Vernier effect, which is particularly beneficial to simultaneous measurements of TL and temperature. To compensate for the low sensitivity magnification in Vernier effect due to cavity length mismatch, the Vernier envelope with broadened FSRs is reconstructed, which is realized by shifting the spatial frequency of the PDMS cavity in the reflection spectrum to approach that of the air cavity. As a result, the TL sensitivity is improved from −253.364 nm/N to −2637.47 nm/N, which, to our best knowledge, is the highest in TL fiber sensors. The condition number is worked out as 69.056, indicative of good performance in simultaneous measurements. The sensor is simple in structure and has high sensitivities, Moreover, the proposed scheme of reconstructing Vernier effect can be extended as a universal signal processing method to other sensor structures and sensing fields.
Funding
National Natural Science Foundation of China (32071363); Natural Science Foundation of Guangdong Province (2022A1515011352, 2023A1515011196); Basic and Applied Basic Research Foundation of Guangdong Province (2022A1515110203).
Disclosures
The authors declare no conflict of interests.
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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